The Comprehensive LaTeX Symbol List

4 Science and technology symbols 67Table 197: gensymb Symbols Defined to Work in Both Math and Text Mode . . . . . . . . . . . . . 67Table 198: wasysym Electrical and Physical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Table 199: ifsym Pulse Diagram Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Table 200: ar Aspect Ratio Symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Table 201: textcomp Text-mode Science and Engineering Symbols . . . . . . . . . . . . . . . . . . . 67Table 202: wasysym Astronomical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 203: marvosym Astronomical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 204: mathabx Astronomical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 205: wasysym APL Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 206: wasysym APL Modifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 207: marvosym Computer Hardware Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Table 208: keystroke Computer Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Table 209: ascii Control Characters (CP437) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Table 210: marvosym Communication Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Table 211: marvosym Engineering Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Table 212: wasysym Biological Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Table 213: marvosym Biological Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Table 214: marvosym Safety-related Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Table 215: feyn Feynman Diagram Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 Dingbats 71Table 216: bbding Arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 217: pifont Arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 218: universal Arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 219: marvosym Scissors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 220: bbding Scissors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 221: pifont Scissors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 222: dingbat Pencils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 223: bbding Pencils and Nibs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 224: pifont Pencils and Nibs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 225: dingbat Fists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 226: bbding Fists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 227: pifont Fists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 228: bbding Crosses and Plusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 229: pifont Crosses and Plusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 230: bbding Xs and Check Marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 231: pifont Xs and Check Marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 232: wasysym Xs and Check Marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 233: universal Xs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 234: pifont Circled Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 235: wasysym Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 236: bbding Stars, Flowers, and Similar Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 237: pifont Stars, Flowers, and Similar Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 238: wasysym Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 239: MnSymbol Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 240: ifsym Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Table 241: bbding Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Table 242: pifont Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Table 243: universa Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 244: universal Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 245: igo Go Stones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 246: manfnt Dangerous Bend Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 247: skull Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 248: Non-Mathematical mathabx Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 249: marvosym Information Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 250: Miscellaneous dingbat Dingbats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Table 251: Miscellaneous bbding Dingbats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775

1 IntroductionWelcome to the Comprehensive L A TEX Symbol List! This document strives to be your primary source of L A TEXsymbol information: font samples, L A TEX commands, packages, usage details, caveats—everything needed toput thousands of different symbols at your disposal. All of the fonts covered herein meet the following criteria:1. They are freely available from the Comprehensive TEX Archive Network (http://www.ctan.org).2. All of their symbols have L A TEX 2ε bindings. That is, a user should be able to access a symbol by name,not just by \char〈number〉.These are not particularly limiting criteria; the Comprehensive L A TEX Symbol List contains samples of 4947symbols—quite a large number. Some of these symbols are guaranteed to be available in every L A TEX 2ε system;others require fonts and packages that may not accompany a given distribution and that therefore need tobe installed. See http://www.tex.ac.uk/cgi-bin/texfaq2html?label=instpackages+wherefiles for helpwith installing new fonts and packages.1.1 Document UsageEach section of this document contains a number of font tables. Each table shows a set of symbols, with thecorresponding L A TEX command to the right of each symbol. A table’s caption indicates what package needs tobe loaded in order to access that table’s symbols. For example, the symbols in Table 35, “textcomp Old-StyleNumerals”, are made available by putting “\usepackage{textcomp}” in your document’s preamble. “AMS”means to use the AMS packages, viz. amssymb and/or amsmath. Notes below a table provide additionalinformation about some or all the symbols in that table.One note that appears a few times in this document, particularly in Section 2, indicates that certainsymbols do not exist in the OT1 font encoding (Donald Knuth’s original, 7-bit font encoding, which is thedefault font encoding for L A TEX) and that you should use fontenc to select a different encoding, such as T1(a common 8-bit font encoding). That means that you should put “\usepackage[〈encoding〉]{fontenc}” inyour document’s preamble, where 〈encoding〉 is, e.g., T1 or LY1. To limit the change in font encoding to thecurrent group, use “\fontencoding{〈encoding〉}\selectfont”.Section 7 contains some additional information about the symbols in this document. It shows which symbolnames are not unique across packages, gives examples of how to create new symbols out of existing symbols,explains how symbols are spaced in math mode, presents a L A TEX ASCII and Latin 1 tables, and providessome information about this document itself. The Comprehensive L A TEX Symbol List ends with an index ofall the symbols in the document and various additional useful terms.1.2 Frequently Requested SymbolsThere are a number of symbols that are requested over and over again on comp.text.tex. If you’re lookingfor such a symbol the following list will help you find it quickly., as in “Spaces are significant.” . . . . . . . . 8í, ì, ī, î, etc. (versus í, ì, ī, and î) . . . . . . . . 13¢ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17©, ®, and . . . . . . . . . . . . . . . . . . . . . . 18‰ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27∴ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30≔ and . . . . . . . . . . . . . . . . . . . . . . . . . 31 and . . . . . . . . . . . . . . . . . . . . . . . . . 37. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62°, as in “180°” or “15℃” . . . . . . . . . . . . . . 64L, F, etc. . . . . . . . . . . . . . . . . . . . . . . . . 65N, Z, R, etc. . . . . . . . . . . . . . . . . . . . . . . 65∫− . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92´ā, `ê, etc. (i.e., several accents per character) 94, and | (instead of ¡, ¿, and —) . . . . . . 100ˆ and ˜ (or ∼) . . . . . . . . . . . . . . . . . . . . . 1017

2 Body-text symbolsThis section lists symbols that are intended for use in running text, such as punctuation marks, accents,ligatures, and currency symbols.Table 1: L A TEX 2ε Escapable “Special” Characters$ \$ % \% \_ ∗ } \} & \& # \# { \{∗ The underscore package redefines “_” to produce an underscore in text mode (i.e., itmakes it unnecessary to escape the underscore character).Table 2: Predefined L A TEX 2ε Text-mode Commandsˆ \textasciicircum < \textless˜ \textasciitildeaª \textordfeminine∗ \textasteriskcenteredoº \textordmasculine\ \textbackslash \textparagraph ∗| \textbar · \textperiodcentered{ \textbraceleft ∗ ¿ \textquestiondown} \textbraceright ∗ “ \textquotedblleft• \textbullet ” \textquotedblrightc○ © \textcopyright ∗ ‘ \textquoteleft† \textdagger ∗ ’ \textquoteright‡ \textdaggerdbl ∗ r○ ® \textregistered$ \textdollar ∗ § \textsection ∗. . . \textellipsis ∗ £ \textsterling ∗— \textemdash TM \texttrademark– \textendash \textunderscore ∗¡ \textexclamdown \textvisiblespace> \textgreaterWhere two symbols are present, the left one is the “faked” symbol that L A TEX 2εprovides by default, and the right one is the “true” symbol that textcomp makesavailable.∗ It’s generally preferable to use the corresponding symbol from Table 3 because thesymbols in that table work properly in both text mode and math mode.Table 3: L A TEX 2ε Commands Defined to Work in Both Math and Text Mode$ \$ \_ ‡ \ddag { \{ \P c○ © \copyright . . . \dots } \}§ \S † \dag £ \poundsWhere two symbols are present, the left one is the “faked” symbol that L A TEX 2εprovides by default, and the right one is the “true” symbol that textcomp makesavailable.Table 4: AMS Commands Defined to Work in Both Math and Text Modě \checkmark R \circledR ✠ \maltese8

Table 5: Non-ASCII Letters (Excluding Accented Letters)å \aa Ð \DH ∗ ̷L \L ø \o ß \ssÅ \AA ð \dh ∗ ̷l \l Ø \O SS \SSÆ \AE Ð \DJ ∗ Ŋ \NG ∗ Œ \OE Þ \TH ∗æ \ae đ \dj ∗ ŋ \ng ∗ œ \oe þ \th ∗∗ Not available in the OT1 font encoding.alternate font encoding, such as T1.Use the fontenc package to select anTable 6: Letters Used to Typeset African LanguagesÐ \B{D} ° \m{c} ¤ \m{f} ¨ \m{k} » \M{t} – \m{Z}ž \B{d} \m{D} „ \m{F} \m{N} › \M{T}  \T{E}‡ \B{H} ð \M{d} † \m{G} ­ \m{n} º \m{t} â \T{e}§ \B{h} Ð \M{D} ¦ \m{g} ª \m{o} š \m{T} Å \T{O}· \B{t} ¡ \m{d} À \m{I} Š \m{O} ® \m{u} ∗ å \T{o}— \B{T} ‚ \m{E} à \m{i} ‘ \m{P} Ž \m{U} ∗\m{b} ¢ \m{e} ‰ \m{J} ± \m{p} \m{Y}€ \m{B} ƒ \M{E} © \m{j} ¬ \m{s} ¯ \m{y}\m{C} £ \M{e} ˆ \m{K} Œ \m{S} \m{z}These characters all need the T4 font encoding, which is provided by the fc package.∗ \m{v} and \m{V} are synonyms for \m{u} and \m{U}.Table 7: Letters Used to Typeset VietnameseƠ \OHORN ơ \ohorn Ư \UHORN ư \uhornThese characters all need the T5 font encoding, which is provided by the vntexpackage.Table 8: Punctuation Marks Not Found in OT1« \guillemotleft ‹ \guilsinglleft „ \quotedblbase " \textquotedbl» \guillemotright › \guilsinglright ‚ \quotesinglbaseTo get these symbols, use the fontenc package to select an alternate font encoding,such as T1.Table 9: pifont Decorative Punctuation Marks❛ \ding{123} ❝ \ding{125} ❡ \ding{161} ❣ \ding{163}❜ \ding{124} ❞ \ding{126} ❢ \ding{162}9

Table 10: tipa Phonetic SymbolsÈ \textbabygamma P \textglotstop ï \textrtailnb \textbarb ; \texthalflength ó \textrtailrc \textbarc ż \texthardsign ù \textrtailsd \textbard # \texthooktop ú \textrtailté \textbardotlessj á \texthtb ü \textrtailzg \textbarg ê \texthtbardotlessj $ \textrthookÜ \textbarglotstop Á \texthtc À \textsca1 \textbari â \texthtd à \textscbł \textbarl ä \texthtg ď \textsce8 \textbaro H \texthth å \textscgÝ \textbarrevglotstop Ê \texththeng Ë \textsch0 \textbaru Î \texthtk @ \textschwaì \textbeltl Ò \texthtp I \textsciB \textbeta Ó \texthtq ĺ \textscjò \textbullseye č \texthtrtaild Ï \textscl\textceltpal É \texthtscg ð \textscnX \textchi Ö \texthtt Œ \textscoeligÅ \textcloseepsilon ß \texthvlig ś \textscomegaÑ \textcloseomega Û \textinvglotstop ö \textscrÆ \textcloserevepsilon K \textinvscr A \textscriptaÞ \textcommatailz Ì \textiota g \textscriptg^ \textcorner ń \textlambda V \textscriptvă \textcrb : \textlengthmark Ú \textscuą \textcrd ş \textlhookt Y \textscyg \textcrg ę \textlhtlongi ­ \textsecstressè \textcrh ű \textlhtlongy ž \textsoftsignÛ \textcrinvglotstop Ô \textlonglegr  \textstretchcň \textcrlambda ¡ \textlptr tC \texttctclig2 \textcrtwo M \textltailm Ù \textteshligC \textctc ñ \textltailn T \textthetać \textctd ë \textltilde þ \textthornćý \textctdctzlig Ð \textlyoghlig £ \texttoneletterstemš \textctesh Í \textObardotlessj ţ \texttsligJ \textctj ŋ \textOlyoghlig 5 \textturnaő \textctn ř \textomega ŕ \textturnceligť \textctt _ \textopencorner 4 \textturnhťC \textcttctclig O \textopeno ľ \textturnkÿ \textctyogh % \textpalhook Õ \textturnlonglegrý \textctz F \textphi W \textturnmdý \textdctzlig | \textpipe î \textturnmrlegS \textdoublebaresh " \textprimstress ô \textturnr} \textdoublebarpipe ij \textraiseglotstop õ \textturnrrtail=/ \textdoublebarslash ğ \textraisevibyi 6 \textturnscripta{ \textdoublepipe 7 \textramshorns Ø \textturntŞ \textdoublevertline \ \textrevapostrophe 2 \textturnvŤ \textdownstep 9 \textreve û \textturnwà \textdyoghlig 3 \textrevepsilon L \textturnydz \textdzlig Q \textrevglotstop U \textupsilonE \textepsilon ź \textrevyogh Ţ \textupstepS \textesh Ç \textrhookrevepsilon Š \textvertline(continued on next page)10

(continued from previous page)R \textfishhookr Ä \textrhookschwa ğ \textvibyiě \textg ~ \textrhoticity ů \textvibyyG \textgamma ¿ \textrptr ß \textwynnŮ \textglobfall ã \textrtaild Z \textyoghŰ \textglobrise í \textrtailltipa defines shortcut characters for many of the above. It also defines a command\tone for denoting tone letters (pitches). See the tipa documentation for moreinformation.Table 11: tipx Phonetic Symbols" \textaolig 3 \texthtbardotlessjvar ´ \textrthooklongB \textbenttailyogh ; \textinvomega q \textscaolig. \textbktailgamma p \textinvsca r \textscdeltaD \textctinvglotstop ! \textinvscripta s \textscf2 \textctjvar I \textlfishhookrlig t \textsck% \textctstretchc # \textlhookfour w \textscm& \textctstretchcvar < \textlhookp x \textscp@ \textctturnt 1 \textlhti y \textscq) \textdblig > \textlooptoprevesh ˝ \textspleftarrowH \textdoublebarpipevar 6 \textnrleg $ \textstretchcvarG \textdoublepipevar 9 \textObullseye ˙ \textsubdoublearrowˇ \textdownfullarrow ˆ \textpalhooklong ¯ \textsubrightarrow7 \textfemale ˜ \textpalhookvar P \textthornvari5 \textfrbarn F \textpipevar Q \textthornvarii’ \textfrhookd = \textqplig R \textthornvariii( \textfrhookdvar ¨ \textrectangle S \textthornvariv? \textfrhookt ˚ \textretractingvar E \textturnglotstop- \textfrtailgamma v \textrevscl u \textturnsckT \textglotstopvari z \textrevscr { \textturnscuU \textglotstopvarii ␣ \textrhooka C \textturnthreeV \textglotstopvariii * \textrhooke A \textturntwo, \textgrgamma + \textrhookepsilon 8 \textuncrfemale0 \textheng : \textrhookopeno ˘ \textupfullarrow4 \texthmlig / \textrtailhthTable 13: wsuipa Phonetic Symbols! \babygamma 8 \eng 4 \labdentalnas \schwa¦ \barb \er / \latfric * \sci \bard M \esh 6 \legm : \scn' \bari \eth E \legr J \scr. \barl D \flapr 1 \lz ¡ \scripta(continued on next page)11

(continued from previous page)< \baro b \glotstop ¢ \nialpha \scriptgA \barp ¨ \hookb © \nibeta Y \scriptv+ \barsci \hookd [ \nichi W \scuX \barscu \hookg \niepsilon ] \scyT \baru $ \hookh \nigamma § \slashb; \clickb % \hookheng ) \niiota \slashc \clickc \hookrevepsilon 2 \nilambda \slashdR \clickt " \hv > \niomega U \slashu? \closedniomega \inva C \niphi \taild \closedrevepsilon , \invf O \nisigma H \tailinvr¥ \crossb d \invglotstop S \nitheta 0 \taill \crossd & \invh V \niupsilon 9 \tailn# \crossh I \invlegr 7 \nj F \tailr3 \crossnilambda 5 \invm @ \oo L \tails \curlyc G \invr = \openo P \tailtN \curlyesh K \invscr \reve _ \tailza \curlyyogh £ \invscripta f \reveject Q \tesh^ \curlyz ¤ \invv \revepsilon B \thorn( \dlbari Z \invw c \revglotstop - \tildel \dz \ \invy \scd ` \yoghe \ejective \ipagamma \scgTable 14: wasysym Phonetic Symbols̷D \DH ð \dh \openoÞ \Thorn \inve þ \thornTable 15: phonetic Phonetic Symbolsj \barj f \flap ī \ibar A \rotvara i \vari¡ \barlambda ? \glottal c \openo w \rotw ¨ \varomegaM \emgma B \hausaB ¯h \planck y \roty C \varopenon \engma b \hausab U \pwedge e \schwa \vod v˚N \enya D \hausad ¢ \revD p \thorn h \voicedh" \epsi T \hausaD \riota u \ubar x \yoghs \esh k \hausak m \rotm u \udescd \eth K \hausaK \rotOmega a \varaF \fj D \hookd r \rotr G \varg12

Table 16: t4phonet Phonetic Symbolsž \textcrd ¡ \texthtd | \textpipe§ \textcrh ¨ \texthtk ð \textrtaild¢ \textepsilon ± \texthtp » \textrtailt¬ \textesh º \texthtt ¡ \textschwa\textfjlig à \textiota ¬ \textscriptv\texthtb © \textltailn œ \textteshlig° \texthtc ª \textopeno \textyoghThe idea behind the t4phonet package’s phonetic symbols is to provide an interfaceto some of the characters in the T4 font encoding (Table 6 on page 9) but usingthe same names as the tipa characters presented in Table 10 on page 10.Table 17: semtrans Transliteration Symbols↪ \Alif ↩ \AynTable 18: Text-mode AccentsÄä \"{A}\"{a} Àà \‘{A}\‘{a} Ạạ \d{A}\d{a} Åå \r{A}\r{a}Áá \’{A}\’{a} A¿a ¿ \|{A}\|{a}‡ AŸa Ÿ \G{A}\G{a}‡ Aa \t{A}\t{a}Ȧȧ \.{A}\.{a} Ãã \~{A}\~{a} Ảả \h{A}\h{a} § Ăă \u{A}\u{a}Āā \={A}\={a} Āā \b{A}\b{a} ˝A˝a \H{A}\H{a} A¼a ¼ \U{A}\U{a}‡Ââ \^{A}\^{a} A¸ ¸a \c{A}\c{a} Ąą \k{A}\k{a} † Ǎǎ \v{A}\v{a}Aa \newtie{A}\newtie{a} ∗ A○ a○ \textcircled{A}\textcircled{a}∗ Requires the textcomp package.† Not available in the OT1 font encoding. Use the fontenc package to select analternate font encoding, such as T1.‡ Requires the T4 font encoding, provided by the fc package.§ Requires the T5 font encoding, provided by the vntex package.Also note the existence of \i and \j, which produce dotless versions of “i” and “j”(viz., “ı” and “j”). These are useful when the accent is supposed to replace thedot. For example, “na\"{\i}ve” produces a correct “naïve”, while “na\"{i}ve”would yield the rather odd-looking “naïve”. (“na\"{i}ve” does work in encodingsother than OT1, however.)Table 19: tipa Text-mode Accents´Ā´ā´Ǎ´ˇa\textacutemacron{A}\textacutemacron{a}\textacutewedge{A}\textacutewedge{a}13(continued on next page)

(continued from previous page)A ffi a ffi \textadvancing{A}\textadvancing{a}

(continued from previous page)A a \textsyllabic{A}\textsyllabic{a}" " ˜Ȧ˜ȧ \texttildedot{A}\texttildedot{a}> A > a \texttoptiebar{A}\texttoptiebar{a}IJAIJa\textvbaraccent{A}\textvbaraccent{a}tipa defines shortcut sequences for many of the above. See the tipa documentationfor more information.Table 20: extraipa Text-mode Accents”A” ” a” \bibridge{A}\bibridge{a} – AŔ» – »˚a˚\partvoiceless{A}\partvoiceless{a}Ãã Ŕ \crtilde{A}\crtilde{a} Āā \sliding{A}\sliding{a}. à ã .. \dottedtilde{A}\dottedtilde{a} Ȧȧ \spreadlips{A}\spreadlips{a}Ãã \doubletilde{A}\doubletilde{a} \subcorner{A}\subcorner{a}A^ a^Aˇa» » \finpartvoice{A}\finpartvoice{a}\subdoublebar{A}\subdoublebar{a}ˇĀ¯ā¯A »˚a»˚ \finpartvoiceless{A}\finpartvoiceless{a} A "" a \subdoublevert{A}\subdoublevert{a}""A–ˇa \inipartvoice{A}\inipartvoice{a} A a \sublptr{A}\sublptr{a}¡ ¡A–˚a \inipartvoiceless{A}\inipartvoiceless{a} A a \subrptr{A}\subrptr{a}”–˚ ¿ ¿A ” a \overbridge{A}\overbridge{a} AŢaŢ\whistle{A}\whistle{a}A–ˇa »– ˇ»\partvoice{A}\partvoice{a}Table 21: wsuipa Text-mode AccentsAg agA a\dental{A}\dental{a}\underarch{A}\underarch{a}Table 22: phonetic Text-mode AccentsA {a {\hill{A}\hill{a} ©A©a \rc{A}\rc{a} Ãã \ut{A}\ut{a}A \od{A}\od{a} Aa \syl{A}\syl{a}˚å {A a { \ohill{A}\ohill{a} Ạ.ạ. \td{A}\td{a}The phonetic package provides a few additional macros for linguistic accents.\acbar and \acarc compose characters with multiple accents; for example,\acbar{\’}{a} produces “´ā” and \acarc{\"}{e} produces “¨ē”. \labvel joinstwo characters with an arc: \labvel{mn} → “ mn”. ⌢ \upbar is intended to gobetween characters as in “x\upbar{}y’’ → “x y”. Lastly, \uplett behaves like\textsuperscript but uses a smaller font. Contrast “p\uplett{h}’’ → “p h ”with “p\textsuperscript{h}’’ → “p h ”.15

Table 23: metre Text-mode AccentsÁá \acutus{A}\acutus{a}Ăă \breve{A}\breve{a}Ãã \circumflexus{A}\circumflexus{a}Ää \diaeresis{A}\diaeresis{a}Àà \gravis{A}\gravis{a}Āā \macron{A}\macron{a}Table 24: t4phonet Text-mode AccentsŸAŸa¿A¿a¼A¼a\textdoublegrave{A}\textdoublegrave{a}\textvbaraccent{A}\textvbaraccent{a}\textdoublevbaraccent{A}\textdoublevbaraccent{a}The idea behind the t4phonet package’s text-mode accents is to provide an interfaceto some of the accents in the T4 font encoding (accents marked with “‡” in Table 18on page 13) but using the same names as the tipa accents presented in Table 19 onpage 13.Table 25: arcs Text-mode Accents⌢A a⌢ \overarc{A}\overarc{a} ⌣A ⌣a \underarc{A}\underarc{a}The accents shown above scale only to a few characters wide. An optional macroargument alters the effective width of the accented characters. See the arcs documentationfor more information.Table 26: semtrans AccentsÄä \D{A}\D{a} Ăă \U{A}\U{a}a A\T{A}\T{a} ∗\T is not actually an accent but a command that rotates its argument 180° usingthe graphicx package’s \rotatebox command.Table 27: wsuipa Diacriticss \ain v \leftp x \overring h \stress } \underwedgek \corner n \leftt ~ \polishhook j \syllabic t \uppu \downp q \length w \rightp r \underdots l \uptm \downt { \midtilde o \rightt y \underringp \halflength z \open i \secstress | \undertildeThe wsuipa package defines all of the above as ordinary characters, not as accents.However, it does provide \diatop and \diaunder commands, which are used tocompose diacritics with other characters. For example, \diatop[\overring|a]produces “xa”, and \diaunder[\underdots|a] produces “ra”. See the wsuipa documentationfor more information.16

Table 28: textcomp Diacritics˝ \textacutedbl ˇ \textasciicaron ¯ \textasciimacron´ \textasciiacute ¨ \textasciidieresis ̏ \textgravedbl˘ \textasciibreve ` \textasciigraveThe textcomp package defines all of the above as ordinary characters, not as accents.Table 29: textcomp Currency Symbols฿ \textbaht $ \textdollar ∗ \textguarani ₩ \textwon¢ \textcent $ \textdollaroldstyle ₤ \textlira ¥ \textyen¢ \textcentoldstyle ₫ \textdong ₦ \textnaira₡ \textcolonmonetary € \texteuro ₱ \textpeso¤ \textcurrency ƒ \textflorin £ \textsterling ∗∗ It’s generally preferable to use the corresponding symbol from Table 3 on page 8because the symbols in that table work properly in both text mode and math mode.Table 30: marvosym Currency Symbols¢ \Denarius e \EUR D \EURdig e \EURtm £ \Pfund \Ecommerce d \EURcr c \EURhv ¦ \EyesDollar ¡ \ShillingThe different euro signs are meant to be visually compatible with different fonts—Courier (\EURcr), Helvetica (\EURhv), Times Roman (\EURtm), and the marvosymdigits listed in Table 182 (\EURdig). The mathdesign package redefines \texteuroto be visually compatible with one of three additional fonts: Utopia (€), Charter(€), or Garamond (€).Table 31: wasysym Currency Symbols¢ \cent ¤ \currencyTable 32: eurosym Euro SignsAC \geneuro BC \geneuronarrow C \geneurowide e \officialeuro\euro is automatically mapped to one of the above—by default, \officialeuro—based on a eurosym package option. See the eurosym documentation for moreinformation. The \geneuro. . . characters are generated from the current bodyfont’s “C” character and therefore may not appear exactly as shown.17

Table 36: Miscellaneous textcomp Symbols∗ \textasteriskcenteredaª \textordfeminine‖ \textbardbloº \textordmasculine○ \textbigcircle \textparagraph ∗␢ \textblank · \textperiodcentered¦ \textbrokenbar ‱ \textpertenthousand• \textbullet ‰ \textperthousand† \textdagger ∗ \textpilcrow‡ \textdaggerdbl ∗ ' \textquotesingle \textdblhyphen ‚ \textquotestraightbase \textdblhyphenchar „ \textquotestraightdblbase⁒ \textdiscount \textrecipe℮ \textestimated ※ \textreferencemark‽ \textinterrobang § \textsection ∗ \textinterrobangdown — \textthreequartersemdash♪ \textmusicalnote \texttildelow№ \textnumero \texttwelveudash◦ \textopenbulletWhere two symbols are present, the left one is the “faked” symbol that L A TEX 2εprovides by default, and the right one is the “true” symbol that textcomp makesavailable.∗ It’s generally preferable to use the corresponding symbol from Table 3 on page 8because the symbols in that table work properly in both text mode and math mode.Table 37: Miscellaneous wasysym Text-mode Symbols\permil19

3 Mathematical symbolsMost, but not all, of the symbols in this section are math-mode only. That is, they yield a “Missing $inserted” error message if not used within $. . .$, \[. . .\], or another math-mode environment. Operatorsmarked as “variable-sized” are taller in displayed formulas, shorter in in-text formulas, and possibly shorterstill when used in various levels of superscripts or subscripts.Alphanumeric symbols (e.g., “L ” and “”) are usually produced using one of the math alphabets inTable 196 rather than with an explicit symbol command. Look there first if you need a symbol for a transform,number set, or some other alphanumeric.Although there have been many requests on comp.text.tex for a contradiction symbol, the ensuing discussioninvariably reveals innumerable ways to represent contradiction in a proof, including “©” (\blitza),“⇒⇐” (\Rightarrow\Leftarrow), “⊥” (\bot), “↮” (\nleftrightarrow), and “※” (\textreferencemark).Because of the lack of notational consensus, it is probably better to spell out “Contradiction!” than to use asymbol for this purpose. Similarly, discussions on comp.text.tex have revealed that there are a variety ofways to indicate the mathematical notion of “is defined as”. Common candidates include “” (\triangleq),“≡” (\equiv), “≔” (\coloneqq), and “ def=” (\stackrel{\text{\tiny def}}{=}). See also the example of\equalsfill on page 95. Depending upon the context, disjoint union may be represented as “ ∐ ” (\coprod),“⊔” (\sqcup), “ ·∪” (\dotcup), “⊕” (\oplus), or any of a number of other symbols. 1 Finally, the averagevalue of a variable x is written by some people as “x” (\overline{x}), by some people as “〈x〉” (\langle x\rangle), and by some people as “⌀x” or “∅x” (\diameter x or \varnothing x). The moral of the story isthat you should be careful always to explain your notation to avoid confusing your readers.Table 38: Math-Mode Versions of Text Symbols$ \mathdollar \mathparagraph £ \mathsterling. . . \mathellipsis § \mathsection \mathunderscoreIt’s generally preferable to use the corresponding symbol from Table 3 on page 8because the symbols in that table work properly in both text mode and math mode.Table 39: cmll Unary Operators! \oc ∗ ˆ \shneg ? \wn ∗˜ \shift ´ \shpos∗ \oc and \wn differ from “!” and “?” in terms of their math-mode spacing: $A=!B$produces “A =!B”, for example, while $A=\oc B$ produces “A = !B”.Table 40: Binary Operators∐ \amalg ∪ \cup ⊕ \oplus × \times∗ \ast † \dagger ⊘ \oslash ⊳ \triangleleft○ \bigcirc ‡ \ddagger ⊗ \otimes ⊲ \triangleright▽ \bigtriangledown ⋄ \diamond ± \pm \unlhd ∗△ \bigtriangleup ÷ \div ⊲ \rhd ∗ \unrhd ∗• \bullet ⊳ \lhd ∗ \ \setminus ⊎ \uplus∩ \cap ∓ \mp ⊓ \sqcap ∨ \vee· \cdot ⊙ \odot ⊔ \sqcup ∧ \wedge◦ \circ ⊖ \ominus ⋆ \star ≀ \wr∗ Not predefined in L A TEX 2ε. Use one of the packages latexsym, amsfonts, amssymb,txfonts, pxfonts, or wasysym.1 Bob Tennent listed these and other disjoint-union symbol possibilities in a November 2007 post to comp.text.tex.20

Table 45: mathabx Binary Operators¦ \ast N \curlywedge [ \sqcap¦ \Asterisk £ \divdot \ \sqcupX \barwedge \divideontimes ^ \sqdoublecap \bigstar ¡ \dotdiv _ \sqdoublecup \bigvarstar \dotplus ¥ \square \blackdiamond ¢ \dottimes ] \squplusX \cap Z \doublebarwedge ¤ \udot¨ \circplus \ \doublecap Z \uplus§ \coasterisk ] \doublecup \varstar§ \coAsterisk \ltimes _ \vee \convolution © \pluscirc Y \veebarY \cup \rtimes [ \veedoublebarO \curlyvee \sqbullet ^ \wedgeMany of the above glyphs go by multiple names. \centerdot is equivalent to\sqbullet, and \ast is equivalent to *. \asterisk produces the same glyph as\ast, but as an ordinary symbol, not a binary operator. Similarly, \bigast producesa large-operator version of the \Asterisk binary operator, and \bigcoastproduces a large-operator version of the \coAsterisk binary operator.22

Table 46: MnSymbol Binary Operators∐ \amalg ⩏ \doublesqcup \righttherefore∗ \ast ⩔ \doublevee ⋌ \rightthreetimes \backslashdiv ⩕ \doublewedge \rightY⋈ \bowtie ∵ \downtherefore ⋊ \rtimes● \bullet \downY \slashdiv∩ \cap \dtimes ∏ \smallprod⩀ \capdot \fivedots ⊓ \sqcap \capplus \hbipropto \sqcapdot⋅ \cdot \hdotdot \sqcapplus○ \circ ⌜ \lefthalfcap ⊔ \sqcup \closedcurlyvee ⌞ \lefthalfcup \sqcupdot \closedcurlywedge \lefttherefore \sqcupplus∪ \cup ⋋ \leftthreetimes ∷ \squaredots⊍ \cupdot \leftY × \times⊎ \cupplus ⋉ \ltimes \udotdot⋎ \curlyvee ∖ \medbackslash ∴ \uptherefore \curlyveedot ◯ \medcircle \upY⋏ \curlywedge ∕ \medslash \utimes \curlywedgedot ∣ \medvert \vbipropto \ddotdot \medvertdot ∶ \vdotdot \diamonddots − \minus ∨ \vee÷ \div ⨪ \minusdot ⟇ \veedot \dotmedvert ∓ \mp ⧖ \vertbowtie∸ \dotminus \neswbipropto \vertdiv⋒ \doublecap \nwsebipropto ∧ \wedge⋓ \doublecup + \plus ⟑ \wedgedot \doublecurlyvee ± \pm ≀ \wreath \doublecurlywedge ⌝ \righthalfcap⩎ \doublesqcap ⌟ \righthalfcupMnSymbol defines \setminus and \smallsetminus as synonyms for\medbackslash; \Join as a synonym for \bowtie; \wr as a synonym for\wreath; \shortmid as a synonym for \medvert; \Cap as a synonym for\doublecap; \Cup as a synonym for \doublecup; and, \uplus as a synonym for\cupplus.Table 47: mathdesign Binary Operators \dtimes \udtimes \utimesThe mathdesign package additionally provides versions of each of the binary operatorsshown in Table 41 on page 21.Table 48: cmll Binary Operators` \parr & \with ∗∗ \with differs from “&” in terms of its math-mode spacing: $A \& B$ produces“A&B”, for example, while $A \with B$ produces “A & B”.23

Table 49: ulsy Geometric Binary Operators¨ \odplusTable 50: mathabx Geometric Binary Operators\blacktriangledown i \boxright a \ominusž \blacktriangleleft m \boxslash ` \oplusŸ \blacktriangleright b \boxtimes i \orightœ \blacktriangleup j \boxtop m \oslashf \boxasterisk o \boxtriangleup b \otimesn \boxbackslash l \boxvoid j \otopk \boxbot f \oasterisk o \otriangleupe \boxcirc n \obackslash l \ovoidg \boxcoasterisk k \obot \smalltriangledownc \boxdiv e \ocirc š \smalltriangleleftd \boxdot g \ocoasterisk › \smalltrianglerighth \boxleft c \odiv ˜ \smalltriangleupa \boxminus d \odot` \boxplus h \oleftTable 51: MnSymbol Geometric Binary Operators⧅ \boxbackslash ▼ \filledmedtriangledown ⊚ \ocirc⧈ \boxbox ◀ \filledmedtriangleleft ⊙ \odot⊡ \boxdot ▶ \filledmedtriangleright ⊖ \ominus⊟ \boxminus ▲ \filledmedtriangleup ⊕ \oplus⊞ \boxplus ◾ \filledsquare ⊘ \oslash⧄ \boxslash ★ \filledstar ⍟ \ostar⊠ \boxtimes ▾ \filledtriangledown ⊗ \otimes \boxvert ◂ \filledtriangleleft \otriangle \diamondbackslash ▸ \filledtriangleright ⦶ \overt \diamonddiamond ▴ \filledtriangleup \pentagram⟐ \diamonddot ◇ \meddiamond ◇ \smalldiamond \diamondminus ◻ \medsquare ◽ \smallsquare \diamondplus ☆ \medstar ☆ \smallstar \diamondslash ▽ \medtriangledown ▿ \smalltriangledown \diamondtimes ◁ \medtriangleleft ◃ \smalltriangleleft \diamondvert ▷ \medtriangleright ▹ \smalltriangleright \downslice △ \medtriangleup ▵ \smalltriangleup◆ \filleddiamond ⊛ \oast ⋆ \thinstar∎ \filledmedsquare ⦸ \obackslash \upsliceMnSymbol defines \blacksquare as a synonym for \filledmedsquare; \squareand \Box as synonyms for \medsquare; \diamond as a synonym for \smalldiamond;\Diamond as a synonym for \meddiamond; \star as a synonym for \thinstar;\circledast as a synonym for \oast; \circledcirc as a synonym for \ocirc;and, \circleddash as a synonym for \ominus.24

Table 52: Variable-sized Math Operators⋂ ⋂\bigcap⊗ ⊗\bigotimes∧ ∧\bigwedge∏ ∏\prod⋃ ⋃\bigcup⊔ ⊔\bigsqcup∐ ∐\coprod∑ ∑\sum⊙ ⊙\bigodot⊎ ⊎\biguplus∫ ∫ \int⊕ ⊕\bigoplus∨ ∨\bigvee∮ ∮ \oint∫∫Table 53: AMS Variable-sized Math Operators∫∫∫∫∫∫ ∫∫∫∫\iint\iiiint∫∫∫∫∫∫∫ ∫ ∫ ∫··· · · ·\iiint\idotsintTable 54: stmaryrd Variable-sized Math Operators \bigbox⫼ \biginterleave⊓ \bigsqcap \bigcurlyvee \bignplus \bigcurlywedge \bigparallel▽ △ \bigtriangledown\bigtriangleupTable 55: wasysym Variable-sized Math Operators \int † \iint\iiint \varint ∗ \varoint ∗ \oiintNone of the preceding symbols are defined when wasysym is passed the nointegralsoption.∗ Not defined when wasysym is passed the integrals option.† Defined only when wasysym is passed the integrals option. Otherwise, the defaultL A TEX \int glyph (as shown in Table 52) is used.25

Table 56: mathabx Variable-sized Math Operatorsœ¬\bigcurlyveeÝý\bigboxslashÉé\bigoright– ¦\bigsqcapÒò\bigboxtimesÍí\bigoslash›«\bigcurlywedgeÚú\bigboxtopÊê\bigotopÖö\bigboxasteriskßÿ\bigboxtriangleupÏï\bigotriangleupÞþ\bigboxbackslashÜü\bigboxvoidÌì\bigovoidÛû\bigboxbot’ ¢\bigcomplementop \bigplusÕõ\bigboxcircÆæ\bigoasterisk˜ ¨\bigsquplus×÷\bigboxcoasteriskÎî\bigobackslash‘¡\bigtimesÓó\bigboxdivËë\bigobotµ½\iiintÔô\bigboxdotÅå\bigocirc´ ¼\iintØø\bigboxleftÇç\bigocoasterisk³ »\intÑñ\bigboxminusÃã\bigodiv· ¿\oiintÐð\bigboxplusÈè\bigoleft ¾Ùù\bigboxrightÁá\bigominus\oint26

Table 57: txfonts/pxfonts Variable-sized Math Operators \bigsqcapplus\ointclockwise \bigsqcupplus\ointctrclockwise \fint\sqiiint \idotsint\sqiint \iiiint\sqint \iiint\varoiiintclockwise \iint\varoiiintctrclockwise \oiiintclockwise \varoiintclockwise \oiiintctrclockwise \varoiintctrclockwise \oiiint\oiintclockwise\oiintctrclockwise\oiint \varointclockwise\varointctrclockwise\varprod27

¯fflˇ˝˜%#‚˙˘˚¨&$‹Table 58: esint Variable-sized Math Operatorsjı\dotsint\ointclockwise‰\fint\ointctrclockwise” „\iiiint\sqiint“›\iiint\sqint! "\iint\varoiintfiff\landdownint\varointclockwiseffifl\landupint\varointctrclockwise\oiint28

Table 59: MnSymbol Variable-sized Math Operators⋂ ⋂ \bigcap ⊖ ⊖ \bigominus ∁ ∁ \complement⩀ ⩀ \bigcapdot ⊕ ⊕ \bigoplus ∐ ∐ \coprod \bigcapplus ⊘ ⊘ \bigoslash ∫…∫ ∫…∫ \idotsint◯ ◯ \bigcircle ⍟ ⍟ \bigostar ⨌ ⨌ \iiiint⋃ ⋃ \bigcup ⊗ ⊗ \bigotimes ∭ ∭ \iiint⊍ ⊍ \bigcupdot \bigotriangle ∬ ∬ \iint⊎ ⊎ \bigcupplus ∗ ⦶ ⦶ \bigovert ∫ ∫ \int⋎ ⋎ \bigcurlyvee + + \bigplus ⨚ ⨚ \landdownint \bigcurlyveedot ⊓ ⊓ \bigsqcap ⨙ ⨙ \landupint⋏ ⋏ \bigcurlywedge \bigsqcapdot ∲ ∲ \lcircleleftint \bigcurlywedgedot \bigsqcapplus ∲ ∲ \lcirclerightint \bigdoublecurlyvee ⊔ ⊔ \bigsqcup ∯ ∯ \oiint \bigdoublecurlywedge \bigsqcupdot ∮ ∮ \oint⩔ ⩔ \bigdoublevee \bigsqcupplus ∏ ∏ \prod⩕ ⩕ \bigdoublewedge ⨉ ⨉ \bigtimes ∳ ∳ \rcircleleftint⊛ ⊛ \bigoast ⋁ ⋁ \bigvee ∳ ∳ \rcirclerightint⦸ ⦸ \bigobackslash ⟇ ⟇ \bigveedot ⨏ ⨏ \strokedint⊚ ⊚ \bigocirc ⋀ ⋀ \bigwedge ∑ ∑ \sum⊙ ⊙ \bigodot ⟑ ⟑ \bigwedgedot ⨋ ⨋ \sumint∗ MnSymbol defines \biguplus as a synonym for \bigcupplus.Table 60: mathdesign Variable-sized Math Operators \intclockwise\ointclockwise \oiiint \ointctrclockwise \oiintThe mathdesign package provides three versions of each integral—in fact, of everysymbol—to accompany different text fonts: Utopia ( ∫ ), Garamond ( ∫ ), andCharter ( ∫ ).29

Table 61: cmll Large Math Operators˙\bigparr˘\bigwithTable 62: Binary Relations≈ \approx ≡ \equiv ⊥ \perp ⌣ \smile≍ \asymp ⌢ \frown ≺ \prec ≻ \succ⊲⊳ \bowtie \Join ∗ ≼ \preceq ≽ \succeq \cong | \mid ∝ \propto ⊢ \vdash⊣ \dashv |= \models ∼ \sim≐ \doteq ‖ \parallel ≃ \simeq∗ Not predefined in L A TEX 2ε. Use one of the packages latexsym, amsfonts, amssymb,mathabx, txfonts, pxfonts, or wasysym.Table 63: AMS Binary Relations≅ \approxeq ≖ \eqcirc \succapprox \backepsilon \fallingdotseq \succcurlyeq∽ \backsim ⊸ \multimap \succsim⋍ \backsimeq ⋔ \pitchfork ∴ \therefore∵ \because \precapprox ≈ \thickapprox≬ \between \preccurlyeq ∼ \thicksim≎ \Bumpeq \precsim ∝ \varpropto≏ \bumpeq \risingdotseq ⊩ \Vdash⊜ \circeq \shortmid \vDash \curlyeqprec \shortparallel \Vvdash \curlyeqsucc ⌢ \smallfrown \doteqdot ⌣ \smallsmileTable 64: AMS Negated Binary Relations≇ \ncong \nshortparallel \nVDash∤ \nmid \nsim \precnapprox∦ \nparallel ⊁ \nsucc \precnsim⊀ \nprec \nsucceq \succnapprox \npreceq \nvDash \succnsim \nshortmid \nvdashTable 65: stmaryrd Binary Relations \inplus \niplusTable 66: wasysym Binary Relations \invneg \leadsto \wasypropto \Join \logof30

Table 67: txfonts/pxfonts Binary Relations \circledgtr \lJoin \opentimes \circledless \lrtimes \Perp \colonapprox ⊸ \multimap \preceqq \Colonapprox \multimapboth \precneqq \coloneq \multimapbothvert \rJoin \Coloneq \multimapdot \strictfi \Coloneqq \multimapdotboth \strictif≔ \coloneqq ∗ \multimapdotbothA \strictiff \Colonsim \multimapdotbothAvert \succeqq \colonsim \multimapdotbothB \succneqq \Eqcolon \multimapdotbothBvert ∥ \varparallel \eqcolon \multimapdotbothvert \varparallelinv≕ \eqqcolon \multimapdotinv \VvDash \Eqqcolon ⟜ \multimapinv \eqsim \openJoin∗ As an alternative to using txfonts/pxfonts, a “:=” symbol can be constructed with“\mathrel{\mathop:}=”.Table 68: txfonts/pxfonts Negated Binary Relations \napproxeq \npreccurlyeq ≇ \nthickapprox \nasymp \npreceqq \ntwoheadleftarrow \nbacksim \nprecsim \ntwoheadrightarrow \nbacksimeq \nsimeq ∦ \nvarparallel \nbumpeq \nsuccapprox \nvarparallelinv \nBumpeq \nsucccurlyeq \nVdash \nequiv \nsucceqq \nprecapprox \nsuccsimTable 69: mathabx Binary Relations\between \divides \risingdotseq \botdoteq \dotseq Ç \succapprox \Bumpedeq \eqbumped ¥ \succcurlyeq \bumpedeq \eqcirc Í \succdot \circeq \eqcolon Á \succsim \coloneq \fallingdotseq 6 \therefore \corresponds Ï \ggcurly \topdoteq \curlyeqprec Î \llcurly ( \vDash· \curlyeqsucc Æ \precapprox , \Vdash) \DashV ¤ \preccurlyeq ( \VDash) \Dashv Ì \precdot , \Vvdash- \dashVv À \precsim31

Table 70: mathabx Negated Binary Relations \napprox M \notperp * \nvDash \ncong ¢ \nprec * \nVDash¸ \ncurlyeqprec È \nprecapprox . \nVdash¹ \ncurlyeqsucc ¦ \npreccurlyeq & \nvdash+ \nDashv ª \npreceq . \nVvash/ \ndashV  \nprecsim Ê \precnapprox' \ndashv \nsim ¬ \precneq+ \nDashV \nsimeq Ä \precnsim/ \ndashVv £ \nsucc Ë \succnapprox \neq É \nsuccapprox ­ \succneq \notasymp § \nsucccurlyeq Å \succnsim \notdivides « \nsucceq \notequiv à \nsuccsimThe \changenotsign command toggles the behavior of \not to produce either avertical or a diagonal slash through a binary operator. Thus, “$a \not= b$” canbe made to produce either “a = b” or “a = b”.Table 71: MnSymbol Binary Relations≈ \approx ≖ \eqcirc \nwfree ∥ \shortparallel≊ \approxeq ⩦ \eqdot \nwmodels ∼ \sim \backapprox ≂ \eqsim \nwModels ≃ \simeq \backapproxeq = \equal \nwsecrossing ≻ \succ≌ \backcong \equalclosed \nwseline ⪸ \succapprox \backeqsim ≡ \equiv \Nwseline ≽ \succcurlyeq∽ \backsim \equivclosed \nwvdash ⪰ \succeq⋍ \backsimeq ≒ \fallingdotseq \nwVdash ≿ \succsim \backtriplesim ≙ \hateq ≺ \prec \swfootline≬ \between \hcrossing ⪷ \precapprox \swfree≏ \bumpeq \leftfootline ≼ \preccurlyeq \swmodels≎ \Bumpeq \leftfree ⪯ \preceq \swModels≗ \circeq \leftmodels ≾ \precsim \swvdash \closedequal \leftModels \rightfootline \swVdash \closedprec ∝ \leftpropto \rightfree ≋ \triplesim \closedsucc \leftrightline ⊧ \rightmodels ∣ \updownline≅ \cong \Leftrightline ⊫ \rightModels ∥ \Updownline⋞ \curlyeqprec ⪦ \leftslice \rightpropto \upfootline⋟ \curlyeqsucc ⊣ \leftvdash ⪧ \rightslice \upfree≐ \doteq \leftVdash ⊢ \rightvdash \upmodels≑ \Doteq \nefootline ⊩ \rightVdash \upModels \downfootline \nefree ≓ \risingdotseq \uppropto⫝ \downfree \nemodels \sefootline ⊥ \upvdash \downmodels \neModels \sefree ⍊ \upVdash \downModels \neswline \semodels \vcrossing \downpropto \Neswline \seModels ⊪ \Vvdash⊤ \downvdash \nevdash \separated⍑ \downVdash \neVdash \sevdash \eqbump \nwfootline \seVdash32

MnSymbol additionally defines synonyms for some of the preceding symbols:⊣ \dashv (same as \leftvdash) \diagdown (same as \nwseline) \diagup (same as \neswline) \divides (same as \updownline)≑ \doteqdot (same as \Doteq)⊧ \models (same as \rightmodels)∥ \parallel (same as \Updownline)⊥ \perp (same as \upvdash)∝ \propto (same as \leftpropto) \relbar (same as \leftrightline) \Relbar (same as \Leftrightline)∝ \varpropto (same as \leftpropto)⊧ \vDash (same as \rightmodels)⊫ \VDash (same as \rightModels)⊢ \vdash (same as \rightvdash)⊩ \Vdash (same as \rightVdash)Table 72: MnSymbol Negated Binary Relations≉ \napprox ≂̸ \neqsim ̸ \nnwModels ⊁ \nsucc≊̸ \napproxeq ≠ \nequal ̸ \nnwseline ⪸̸ \nsuccapprox̸ \nbackapprox ̸ \nequalclosed ̸ \nNwseline ⋡ \nsucccurlyeq̸ \nbackapproxeq ≢ \nequiv ̸ \nnwvdash ⪰̸ \nsucceq≌̸ \nbackcong ̸ \nequivclosed ̸ \nnwVdash ≿̸ \nsuccsim̸ \nbackeqsim \neswcrossing ⊀ \nprec ̸ \nswfootline∽̸ \nbacksim ≒̸ \nfallingdotseq ⪷̸ \nprecapprox ̸ \nswfree⋍̸ \nbacksimeq ≙̸ \nhateq ⋠ \npreccurlyeq ̸ \nswmodels̸ \nbacktriplesim ̸ \nleftfootline ⪯̸ \npreceq ̸ \nswModels≏̸ \nbumpeq ̸ \nleftfree ≾̸ \nprecsim ̸ \nswvdash≎̸ \nBumpeq ̸ \nleftmodels ̸ \nrightfootline ̸ \nswVdash≗̸ \ncirceq ̸ \nleftModels ̸ \nrightfree ≋̸ \ntriplesim̸ \nclosedequal ̸ \nleftrightline ⊭ \nrightmodels ∤ \nupdownline≇ \ncong ̸ \nLeftrightline ⊯ \nrightModels ∦ \nUpdownline⋞̸ \ncurlyeqprec ⊣̸ \nleftvdash ⊬ \nrightvdash ̸ \nupfootline⋟̸ \ncurlyeqsucc ̸ \nleftVdash ⊮ \nrightVdash ̸ \nupfree≐̸ \ndoteq ̸ \nnefootline ≓̸ \nrisingdotseq ̸ \nupmodels≑̸ \nDoteq ̸ \nnefree ̸ \nsefootline ̸ \nupModels̸ \ndownfootline ̸ \nnemodels ̸ \nsefree ⊥̸ \nupvdash⫝̸ \ndownfree ̸ \nneModels ̸ \nsemodels ⍊̸ \nupVdash̸ \ndownmodels ̸ \nneswline ̸ \nseModels ⪹ \precnapprox̸ \ndownModels ̸ \nNeswline ̸ \nsevdash ⋨ \precnsim⊤̸ \ndownvdash ̸ \nnevdash ̸ \nseVdash ⪺ \succnapprox⍑̸ \ndownVdash ̸ \nneVdash ∤ \nshortmid ⋩ \succnsim̸ \neqbump ̸ \nnwfootline ∦ \nshortparallel≖̸ \neqcirc ̸ \nnwfree ≁ \nsim⩦̸ \neqdot ̸ \nnwmodels ≄ \nsimeqMnSymbol additionally defines synonyms for some of the preceding symbols:33

⊣̸ \ndashv (same as \nleftvdash)̸ \ndiagdown (same as \nnwseline)̸ \ndiagup (same as \nneswline)∤ \ndivides (same as \nupdownline)≠ \ne (same as \nequal)≠ \neq (same as \nequal)∤ \nmid (same as \nupdownline)⊭ \nmodels (same as \nrightmodels)∦ \nparallel (same as \nUpdownline)⊥̸ \nperp (same as \nupvdash)̸ \nrelbar (same as \nleftrightline)̸ \nRelbar (same as \nLeftrightline)⊭ \nvDash (same as \nrightmodels)⊬ \nvdash (same as \nrightvdash)⊮ \nVdash (same as \nrightVdash)⊯ \nVDash (same as \nrightModels)Table 73: mathtools Binary Relations::≈ \Colonapprox :− \coloneq −:: \Eqcolon:≈ \colonapprox :∼ \colonsim =: \eqqcolon:= \coloneqq ::∼ \Colonsim =:: \Eqqcolon::= \Coloneqq :: \dblcolon::− \Coloneq −: \eqcolonSimilar symbols can be defined using mathtools’s \vcentcolon, which produces acolon centered on the font’s math axis:=:= vs. =:=“=:=” “=\vcentcolon=”Table 74: turnstile Binary Relationsdefabc\dddtstile{abc}{def}defabc\nntstile{abc}{def}defabc\stdtstile{abc}{def}defabc\ddststile{abc}{def}defabc\nnttstile{abc}{def}defabc\stststile{abc}{def}defabc\ddtstile{abc}{def}defabc\nsdtstile{abc}{def}defabc\sttstile{abc}{def}defabc\ddttstile{abc}{def}defabc\nsststile{abc}{def}defabc\stttstile{abc}{def}defabc\dndtstile{abc}{def}defabc\nststile{abc}{def}defabc\tddtstile{abc}{def}defabc\dnststile{abc}{def}defabc\nsttstile{abc}{def}defabc\tdststile{abc}{def}defabc\dntstile{abc}{def}defabc\ntdtstile{abc}{def}defabc\tdtstile{abc}{def}(continued on next page)34

(continued from previous page)defabcdefabcdefabcdefabc\dnttstile{abc}{def}\dsdtstile{abc}{def}\dsststile{abc}{def}\dststile{abc}{def}defabcdefabcdefabcdefabc\ntststile{abc}{def}\nttstile{abc}{def}\ntttstile{abc}{def}\sddtstile{abc}{def}defabcdefabcdefabcdefabc\tdttstile{abc}{def}\tndtstile{abc}{def}\tnststile{abc}{def}\tntstile{abc}{def}defabcdefabcdefabcdefabcdefabcdefabcdefabcdefabcdefabc\dsttstile{abc}{def}\dtdtstile{abc}{def}\dtststile{abc}{def}\dttstile{abc}{def}\dtttstile{abc}{def}\nddtstile{abc}{def}\ndststile{abc}{def}\ndtstile{abc}{def}\ndttstile{abc}{def}defabcdefabcdefabcdefabcdefabcdefabcdefabcdefabcdefabc\sdststile{abc}{def}\sdtstile{abc}{def}\sdttstile{abc}{def}\sndtstile{abc}{def}\snststile{abc}{def}\sntstile{abc}{def}\snttstile{abc}{def}\ssdtstile{abc}{def}\ssststile{abc}{def}defabcdefabcdefabcdefabcdefabcdefabcdefabcdefabcdefabc\tnttstile{abc}{def}\tsdtstile{abc}{def}\tsststile{abc}{def}\tststile{abc}{def}\tsttstile{abc}{def}\ttdtstile{abc}{def}\ttststile{abc}{def}\tttstile{abc}{def}\ttttstile{abc}{def}defabc\nndtstile{abc}{def}defabc\sststile{abc}{def}defabc\nnststile{abc}{def}defabc\ssttstile{abc}{def}Each of the above takes an optional argument that controls the size of the upperand lower expressions. See the turnstile documentation for more information.Table 75: trsym Binary Relations¡ \InversTransformHoriz \TransformHoriz£ \InversTransformVert ¢ \TransformVert❝ .Table 76: trfsigns Binary Relations. \dfourier ❝ \Dfourier❝ \fourier ❝ \Fourier❝ \laplace ❝ \Laplace❝ \ztransf . ❝ \Ztransf35

Table 77: cmll Binary Relations¨ \coh ˝ \scoh˚ \incoh ˇ \sincohTable 78: Subset and Superset Relations⊏ \sqsubset ∗ ⊒ \sqsupseteq ⊃ \supset⊑ \sqsubseteq ⊂ \subset ⊇ \supseteq⊐ \sqsupset ∗ ⊆ \subseteq∗ Not predefined in L A TEX 2ε. Use one of the packages latexsym, amsfonts, amssymb,mathabx, txfonts, pxfonts, or wasysym.Table 79: AMS Subset and Superset Relations \nsubseteq \subseteqq \supsetneqq \nsupseteq \subsetneq \varsubsetneq \nsupseteqq \subsetneqq \varsubsetneqq⊏ \sqsubset ⋑ \Supset \varsupsetneq⊐ \sqsupset \supseteqq \varsupsetneqq⋐ \Subset \supsetneqTable 80: stmaryrd Subset and Superset Relations⪿ \subsetplus ⫀ \supsetplus \subsetpluseq \supsetpluseqTable 81: wasysym Subset and Superset Relations⊏ \sqsubset ⊐ \sqsupsetTable 82: txfonts/pxfonts Subset and Superset Relations \nsqsubset \nsqsupseteq \nSupset \nsqsubseteq \nSubset \nsqsupset \nsubseteqq36

Table 83: mathabx Subset and Superset Relations‚ \nsqsubset ƒ \nsupset … \sqsupseteq … \supseteq– \nsqSubset — \nSupset \sqsupseteqq \supseteqq† \nsqsubseteq ‡ \nsupseteq ‰ \sqsupsetneq ‰ \supsetneqŽ \nsqsubseteqq \nsupseteqq ‘ \sqsupsetneqq ‘ \supsetneqqƒ \nsqsupset € \sqsubset € \subset Š \varsqsubsetneq— \nsqSupset ” \sqSubset ” \Subset ’ \varsqsubsetneqq‡ \nsqsupseteq „ \sqsubseteq „ \subseteq ‹ \varsqsupsetneq\nsqsupseteqq Œ \sqsubseteqq Œ \subseteqq “ \varsqsupsetneqq‚ \nsubset ˆ \sqsubsetneq ˆ \subsetneq Š \varsubsetneq– \nSubset \sqsubsetneqq \subsetneqq ’ \varsubsetneqq† \nsubseteq • \sqSupset \supset ‹ \varsupsetneqŽ \nsubseteqq \sqsupset • \Supset “ \varsupsetneqqTable 84: MnSymbol Subset and Superset Relations̸ \nSqsubset ⊈ \nsubseteq ⋤ \sqsubsetneq ⊆ \subseteq⊏̸ \nsqsubset ⫅̸ \nsubseteqq \sqsubsetneqq ⫅ \subseteqq⋢ \nsqsubseteq ⋑̸ \nSupset \Sqsupset ⊊ \subsetneq̸ \nsqsubseteqq ⊅ \nsupset ⊐ \sqsupset ⫋ \subsetneqq̸ \nSqsupset ⊉ \nsupseteq ⊒ \sqsupseteq ⋑ \Supset⊐̸ \nsqsupset ⫆̸ \nsupseteqq \sqsupseteqq ⊃ \supset⋣ \nsqsupseteq \Sqsubset ⋥ \sqsupsetneq ⊇ \supseteq̸ \nsqsupseteqq ⊏ \sqsubset \sqsupsetneqq ⫆ \supseteqq⋐̸ \nSubset ⊑ \sqsubseteq ⋐ \Subset ⊋ \supsetneq⊄ \nsubset \sqsubseteqq ⊂ \subset ⫌ \supsetneqqMnSymbol additionally defines \varsubsetneq as a synonym for \subsetneq,\varsubsetneqq as a synonym for \subsetneqq, \varsupsetneq as a synonymfor \supsetneq, and \varsupsetneqq as a synonym for \supsetneqq.Table 85: Inequalities≥ \geq ≫ \gg ≤ \leq ≪ \ll \neqTable 86: AMS Inequalities \eqslantgtr ⋗ \gtrdot ⋚ \lesseqgtr ≱ \ngeq \eqslantless \gtreqless \lesseqqgtr \ngeqq≧ \geqq \gtreqqless ≶ \lessgtr \ngeqslant \geqslant ≷ \gtrless \lesssim ≯ \ngtr≫ \ggg \gtrsim ≪ \lll ≰ \nleq≩ \gnapprox \gvertneqq ≨ \lnapprox \nleqq≩ \gneq ≦ \leqq ≨ \lneq \nleqslant \gneqq \leqslant \lneqq ≮ \nless \gnsim \lessapprox \lnsim \gtrapprox ⋖ \lessdot \lvertneqq37

Table 87: wasysym Inequalities \apprge \apprleTable 88: txfonts/pxfonts Inequalities \ngg \ngtrsim \nlesssim \ngtrapprox \nlessapprox \nll \ngtrless \nlessgtrTable 89: mathabx Inequalities· \eqslantgtr ½ \gtreqless À \lesssim £ \ngtr \eqslantless ¿ \gtreqqless ! \ll É \ngtrapprox¥ \geq » \gtrless Î \lll à \ngtrsim¯ \geqq Á \gtrsim Ê \lnapprox ¦ \nleq" \gg µ \gvertneqq ¬ \lneq ° \nleqqÏ \ggg ¤ \leq ² \lneqq ¢ \nlessË \gnapprox ® \leqq Ä \lnsim È \nlessapprox­ \gneq Æ \lessapprox ´ \lvertneqq  \nlesssim³ \gneqq Ì \lessdot ¹ \neqslantgtr « \nvargeqÅ \gnsim ¼ \lesseqgtr ¸ \neqslantless ª \nvarleqÇ \gtrapprox ¾ \lesseqqgtr § \ngeq © \vargeqÍ \gtrdot º \lessgtr ± \ngeqq ¨ \varleqmathabx defines \leqslant and \le as synonyms for \leq, \geqslant and \ge assynonyms for \geq, \nleqslant as a synonym for \nleq, and \ngeqslant as asynonym for \ngeq.38

Table 90: MnSymbol Inequalities⪖ \eqslantgtr ⪌ \gtreqqless ≲ \lesssim ⋛̸ \ngtreqless⪕ \eqslantless ≷ \gtrless ≪ \ll ̸ \ngtreqlessslant≥ \geq \gtrneqqless ⋘ \lll ⪌̸ \ngtreqqless⊵ \geqclosed ≳ \gtrsim ⪉ \lnapprox ≹ \ngtrless \geqdot ≤ \leq ≨ \lneqq ≰ \nleq≧ \geqq ⊴ \leqclosed ≴ \lnsim ⋬ \nleqclosed⩾ \geqslant \leqdot ⪖̸ \neqslantgtr ̸ \nleqdot⪀ \geqslantdot ≦ \leqq ⪕̸ \neqslantless ≦̸ \nleqq≫ \gg ⩽ \leqslant ≱ \ngeq ≰ \nleqslant⋙ \ggg ⩿ \leqslantdot ⋭ \ngeqclosed ⩿̸ \nleqslantdot⪊ \gnapprox < \less ̸ \ngeqdot ≮ \nless≩ \gneqq ⪅ \lessapprox ≧̸ \ngeqq ⋪ \nlessclosed≵ \gnsim ⊲ \lessclosed ≱ \ngeqslant ⋖̸ \nlessdot> \gtr ⋖ \lessdot ⪀̸ \ngeqslantdot ⋚̸ \nlesseqgtr⪆ \gtrapprox ⋚ \lesseqgtr ≫̸ \ngg ̸ \nlesseqgtrslant⊳ \gtrclosed \lesseqgtrslant ⋙̸ \nggg ⪋̸ \nlesseqqgtr⋗ \gtrdot ⪋ \lesseqqgtr ≯ \ngtr ≸ \nlessgtr⋛ \gtreqless ≶ \lessgtr ⋫ \ngtrclosed ≪̸ \nll \gtreqlessslant \lessneqqgtr ⋗̸ \ngtrdot ⋘̸ \nlllMnSymbol additionally defines synonyms for some of the preceding symbols:⋙ \gggtr (same as \ggg)≩ \gvertneqq (same as \gneqq)⊲ \lhd (same as \lessclosed)⋘ \llless (same as \lll)≨ \lvertneqq (same as \lneqq)⋬ \ntrianglelefteq (same as \nleqclosed)⋪ \ntriangleleft (same as \nlessclosed)⋭ \ntrianglerighteq (same as \ngeqclosed)⋫ \ntriangleright (same as \ngtrclosed)⊳ \rhd (same as \gtrclosed)⊴ \trianglelefteq (same as \leqclosed)⊵ \trianglerighteq (same as \geqclosed)⊴ \unlhd (same as \leqclosed)⊵ \unrhd (same as \geqclosed)⊲ \vartriangleleft (same as \lessclosed)⊳ \vartriangleright (same as \gtrclosed)Table 91: AMS Triangle Relations◭ \blacktriangleleft \ntrianglelefteq \trianglelefteq ⊳ \vartriangleleft◮ \blacktriangleright ⋫ \ntriangleright \triangleq ⊲ \vartriangleright⋪ \ntriangleleft \ntrianglerighteq \trianglerighteq39

Table 92: stmaryrd Triangle Relations \trianglelefteqslant \trianglerighteqslant \ntrianglelefteqslant \ntrianglerighteqslantTable 93: mathabx Triangle Relationsš \ntriangleleft Ÿ \ntrianglerighteq \triangleright \vartrianglerightž \ntrianglelefteq ˜ \triangleleft \trianglerighteq› \ntriangleright œ \trianglelefteq ˜ \vartriangleleftTable 94: MnSymbol Triangle Relations▼ \filledmedtriangledown △ \largetriangleup ▿ \smalltriangledown◀ \filledmedtriangleleft ▽ \medtriangledown ◃ \smalltriangleleft▶ \filledmedtriangleright ◁ \medtriangleleft ▹ \smalltriangleright▲ \filledmedtriangleup ▷ \medtriangleright ▵ \smalltriangleup▾ \filledtriangledown △ \medtriangleup ≜ \triangleeq◂ \filledtriangleleft ≜̸ \ntriangleeq ⊴ \trianglelefteq▸ \filledtriangleright ⋪ \ntriangleleft ⊵ \trianglerighteq▴ \filledtriangleup ⋬ \ntrianglelefteq ⊲ \vartriangleleft▽ \largetriangledown ⋫ \ntriangleright ⊳ \vartriangleright◁ \largetriangleleft ⋭ \ntrianglerighteq▷ \largetriangleright \otriangleMnSymbol additionally defines synonyms for many of the preceding symbols:\triangleq is a synonym for \triangleeq; \lhd and \lessclosedare synonyms for \vartriangleleft; \rhd and \gtrclosed are synonymsfor \vartriangleright; \unlhd and \leqclosed are synonymsfor \trianglelefteq; \unrhd and \geqclosed are synonymsfor \trianglerighteq; \blacktriangledown, \blacktriangleleft,\blacktriangleright, and \blacktriangle [sic] are synonyms for,respectively, \filledmedtriangledown, \filledmedtriangleleft,\filledmedtriangleright, and \filledmedtriangleup; \trianglerightis a synonym for \medtriangleright; \triangle, \vartriangle, and\bigtriangleup are synonyms for \medtriangleup; \triangleleft is asynonym for \medtriangleleft; \triangledown and \bigtriangledown are synonymsfor \medtriangledown; \nlessclosed is a synonym for \ntriangleleft;\ngtrclosed is a synonym for \ntriangleright; \nleqclosed is a synonym for\ntrianglelefteq; and \ngeqclosed is a synonym for \ntrianglerighteq.The title “Triangle Relations” is a bit of a misnomer here as only \triangleeqand \ntriangleeq are defined as TEX relations (class 3 symbols). The\largetriangle. . . symbols are defined as TEX “ordinary” characters (class 0)and all of the remaining characters are defined as TEX binary operators (class 2).40

Table 95: Arrows⇓ \Downarrow ←− \longleftarrow ↖ \nwarrow↓ \downarrow ⇐= \Longleftarrow ⇒ \Rightarrow←↪ \hookleftarrow ←→ \longleftrightarrow → \rightarrow↩→ \hookrightarrow ⇐⇒ \Longleftrightarrow ↘ \searrow \leadsto ∗ ↦−→ \longmapsto ↙ \swarrow← \leftarrow =⇒ \Longrightarrow ↑ \uparrow⇐ \Leftarrow −→ \longrightarrow ⇑ \Uparrow⇔ \Leftrightarrow ↦→ \mapsto ↕ \updownarrow↔ \leftrightarrow ↗ \nearrow † ⇕ \Updownarrow∗ Not predefined in L A TEX 2ε. Use one of the packages latexsym, amsfonts, amssymb,txfonts, pxfonts, or wasysym.† See the note beneath Table 157 for information about how to put a diagonal arrowacross a mathematical expression (as in “✟ ✟✟✯ 0∇ · ⃗B ”) .Table 96: Harpoons↽ \leftharpoondown ⇁ \rightharpoondown ⇀↽ \rightleftharpoons↼ \leftharpoonup ⇀ \rightharpoonupTable 97: textcomp Text-mode Arrows↓ \textdownarrow → \textrightarrow← \textleftarrow ↑ \textuparrowTable 98: AMS Arrows \circlearrowleft ⇔ \leftleftarrows ⇄ \rightleftarrows \circlearrowright ⇆ \leftrightarrows ⇒ \rightrightarrows \curvearrowleft \leftrightsquigarrow \rightsquigarrow \curvearrowright ⇚ \Lleftarrow \Rsh \dashleftarrow \looparrowleft ↞ \twoheadleftarrow \dashrightarrow \looparrowright ↠ \twoheadrightarrow \downdownarrows \Lsh ⇈ \upuparrows↢ \leftarrowtail ↣ \rightarrowtailTable 99: AMS Negated Arrows \nLeftarrow \nLeftrightarrow \nRightarrow↚ \nleftarrow ↮ \nleftrightarrow ↛ \nrightarrowTable 100: AMS Harpoons⇃ \downharpoonleft ⇌ \leftrightharpoons ↿ \upharpoonleft⇂ \downharpoonright ⇋ \rightleftharpoons ↾ \upharpoonright41

Table 101: stmaryrd Arrows⇽ \leftarrowtriangle ⇐ \Mapsfrom ← \shortleftarrow \leftrightarroweq ← \mapsfrom → \shortrightarrow⇿ \leftrightarrowtriangle ⤇⇒ \Mapsto ↑ \shortuparrow \lightning \nnearrow \ssearrow⇐= \Longmapsfrom \nnwarrow \sswarrow←− \longmapsfrom ⇾ \rightarrowtriangle⤇=⇒ \Longmapsto ↓ \shortdownarrowTable 102: txfonts/pxfonts Arrows \boxdotLeft \circleddotright \Diamondleft \boxdotleft \circleleft \Diamondright \boxdotright \circleright \DiamondRight \boxdotRight \dashleftrightarrow \leftsquigarrow \boxLeft \DiamonddotLeft \Nearrow \boxleft \Diamonddotleft \Nwarrow \boxright \Diamonddotright ⇛ \Rrightarrow \boxRight \DiamonddotRight \Searrow \circleddotleft \DiamondLeft \SwarrowTable 103: mathabx Arrowsö \circlearrowleft Ð \leftarrow Ô \nwarrowó \curvearrowbotleft Ø \leftrightarrow Ñ \rightarrow÷ \circlearrowright Ð \leftleftarrows æ \restrictionõ \curvearrowbotleftright Ô \leftrightarrows Õ \rightleftarrowsô \curvearrowbotright ú \leftrightsquigarrow Ñ \rightrightarrowsð \curvearrowleft ø \leftsquigarrow ù \rightsquigarrowò \curvearrowleftright ü \lefttorightarrow ý \righttoleftarrowñ \curvearrowright î \looparrowdownleft é \Rshê \dlsh ï \looparrowdownright × \searrowÓ \downdownarrows ì \looparrowleft \swarrowÿ \downtouparrow í \looparrowright Ö \updownarrows× \downuparrows è \Lsh þ \uptodownarrowë \drsh Õ \nearrow Ò \upuparrowsTable 104: mathabx Negated Arrowsö \nLeftarrow Ü \nleftrightarrow Û \nrightarrowÚ \nleftarrow ø \nLeftrightarrow ÷ \nRightarrow42

Table 105: mathabx HarpoonsÞ \barleftharpoon à \leftharpoonup é \rightleftharpoonsß \barrightharpoon Ø \leftleftharpoons Ù \rightrightharpoonsÛ \downdownharpoons à \leftrightharpoon ê \updownharpoonså \downharpoonleft è \leftrightharpoons ä \upharpoonleftç \downharpoonright Ý \rightbarharpoon æ \upharpoonrightë \downupharpoons ã \rightharpoondown Ú \upupharpoonsÜ \leftbarharpoon á \rightharpoonupâ \leftharpoondown á \rightleftharpoonTable 106: MnSymbol Arrows \curvearrowdownup ← \longleftarrow ⤦ \rhookswarrow \curvearrowleftright ⇐ \Longleftarrow \rhookuparrow \curvearrownesw ←→ \longleftrightarrow → \rightarrow \curvearrownwse ⇐⇒ \Longleftrightarrow ⇒ \Rightarrow \curvearrowrightleft → \longmapsto ↣ \rightarrowtail \curvearrowsenw → \longrightarrow ⇄ \rightleftarrows \curvearrowswne ⇒ \Longrightarrow ↝ \rightlsquigarrow \curvearrowupdown ↫ \looparrowleft ↦ \rightmapsto⇣ \dasheddownarrow ↬ \looparrowright ⇉ \rightrightarrows⇠ \dashedleftarrow ↰ \Lsh \rightrsquigarrow \dashednearrow ↗ \nearrow ⇛ \Rrightarrow \dashednwarrow ⇗ \Nearrow ↱ \Rsh⇢ \dashedrightarrow \nearrowtail ↘ \searrow \dashedsearrow \nelsquigarrow ⇘ \Searrow \dashedswarrow \nemapsto \searrowtail⇡ \dasheduparrow \nenearrows \selsquigarrow⇓ \Downarrow \nersquigarrow \semapsto↓ \downarrow ⤡ \neswarrow \senwarrows \downarrowtail \Neswarrow \sersquigarrow⇊ \downdownarrows \neswarrows \sesearrows \downlsquigarrow ↖ \nwarrow \squigarrowdownup↧ \downmapsto ⇖ \Nwarrow ↭ \squigarrowleftright \downrsquigarrow \nwarrowtail \squigarrownesw⇵ \downuparrows \nwlsquigarrow \squigarrownwse \lcirclearrowdown \nwmapsto \squigarrowrightleft⤾ \lcirclearrowleft \nwnwarrows \squigarrowsenw⟳ \lcirclearrowright \nwrsquigarrow \squigarrowswne↻ \lcirclearrowup ⤢ \nwsearrow \squigarrowupdown⤸ \lcurvearrowdown \Nwsearrow ↙ \swarrow \lcurvearrowleft \nwsearrows ⇙ \Swarrow \lcurvearrowne ∲ \partialvardlcircleleftint ∗ \swarrowtail \lcurvearrownw ∲ \partialvardlcirclerightint ∗ \swlsquigarrow↷ \lcurvearrowright ∳ \partialvardrcircleleftint ∗ \swmapsto \lcurvearrowse ∳ \partialvardrcirclerightint ∗ \swnearrows \lcurvearrowsw ∲ \partialvartlcircleleftint ∗ \swrsquigarrow \lcurvearrowup ∲ \partialvartlcirclerightint ∗ \swswarrows⇐ \Leftarrow ∳ \partialvartrcircleleftint ∗ ↡ \twoheaddownarrow← \leftarrow ∳ \partialvartrcirclerightint ∗ ↞ \twoheadleftarrow43(continued on next page)

(continued from previous page)↢ \leftarrowtail \rcirclearrowdown \twoheadnearrow⇇ \leftleftarrows ⟲ \rcirclearrowleft \twoheadnwarrow \leftlsquigarrow ⤿ \rcirclearrowright ↠ \twoheadrightarrow↤ \leftmapsto ↺ \rcirclearrowup \twoheadsearrow↔ \leftrightarrow ⤹ \rcurvearrowdown \twoheadswarrow⇔ \Leftrightarrow ↶ \rcurvearrowleft ↟ \twoheaduparrow⇆ \leftrightarrows \rcurvearrowne ↑ \uparrow↜ \leftrsquigarrow \rcurvearrownw ⇑ \Uparrow \lhookdownarrow \rcurvearrowright \uparrowtail \lhookleftarrow \rcurvearrowse ↕ \updownarrow \lhooknearrow \rcurvearrowsw ⇕ \Updownarrow⤣ \lhooknwarrow \rcurvearrowup ⇅ \updownarrows↪ \lhookrightarrow \rhookdownarrow \uplsquigarrow⤥ \lhooksearrow ↩ \rhookleftarrow ↥ \upmapsto \lhookswarrow ⤤ \rhooknearrow \uprsquigarrow \lhookuparrow \rhooknwarrow ⇈ \upuparrows☇ \lightning \rhookrightarrow⇚ \Lleftarrow \rhooksearrowMnSymbol additionally defines synonyms for some of the preceding symbols:↺ \circlearrowleft (same as \rcirclearrowup)↻ \circlearrowright (same as \lcirclearrowup)↶ \curvearrowleft (same as \rcurvearrowleft)↷ \curvearrowright (same as \lcurvearrowright)⇠ \dashleftarrow (same as \dashedleftarrow)⇢ \dashrightarrow (same as \dashedrightarrow)↩ \hookleftarrow (same as \rhookleftarrow)↪ \hookrightarrow (same as \lhookrightarrow)↝ \leadsto (same as \rightlsquigarrow)↭ \leftrightsquigarrow (same as \squigarrowleftright)↦ \mapsto (same as \rightmapsto)↝ \rightsquigarrow (same as \rightlsquigarrow)∗ The \partialvar. . . int macros are intended to be used internally by MnSymbolto produce various types of integrals.Table 107: MnSymbol Negated Arrows̸ \ncurvearrowdownup ⤣̸ \nlhooknwarrow ⇄̸ \nrightleftarrows̸ \ncurvearrowleftright ↪̸ \nlhookrightarrow ↝̸ \nrightlsquigarrow̸ \ncurvearrownesw ⤥̸ \nlhooksearrow ↦̸ \nrightmapsto̸ \ncurvearrownwse ̸ \nlhookswarrow ⇉̸ \nrightrightarrows̸ \ncurvearrowrightleft ̸ \nlhookuparrow ̸ \nrightrsquigarrow̸ \ncurvearrowsenw ⇚̸ \nLleftarrow ⇛̸ \nRrightarrow̸ \ncurvearrowswne ↗̸ \nnearrow ⇘̸ \nSearrow̸ \ncurvearrowupdown ⇗̸ \nNearrow ↘̸ \nsearrow⇣̸ \ndasheddownarrow ̸ \nnearrowtail ̸ \nsearrowtail⇠̸ \ndashedleftarrow ̸ \nnelsquigarrow ̸ \nselsquigarrow44(continued on next page)

(continued from previous page)̸ \ndashednearrow ̸ \nnemapsto ̸ \nsemapsto̸ \ndashednwarrow ̸ \nnenearrows ̸ \nsenwarrows⇢̸ \ndashedrightarrow ̸ \nnersquigarrow ̸ \nsersquigarrow̸ \ndashedsearrow ̸ \nNeswarrow ̸ \nsesearrows̸ \ndashedswarrow ⤡̸ \nneswarrow ̸ \nsquigarrowdownup⇡̸ \ndasheduparrow ̸ \nneswarrows ̸ \nsquigarrowleftright↓̸ \ndownarrow ⇖̸ \nNwarrow ̸ \nsquigarrownesw⇓̸ \nDownarrow ↖̸ \nnwarrow ̸ \nsquigarrownwse̸ \ndownarrowtail ̸ \nnwarrowtail ̸ \nsquigarrowrightleft⇊̸ \ndowndownarrows ̸ \nnwlsquigarrow ̸ \nsquigarrowsenw̸ \ndownlsquigarrow ̸ \nnwmapsto ̸ \nsquigarrowswne↧̸ \ndownmapsto ̸ \nnwnwarrows ̸ \nsquigarrowupdown̸ \ndownrsquigarrow ̸ \nnwrsquigarrow ↙̸ \nswarrow⇵̸ \ndownuparrows ⤢̸ \nnwsearrow ⇙̸ \nSwarrow̸ \nlcirclearrowdown ̸ \nNwsearrow ̸ \nswarrowtail⤾̸ \nlcirclearrowleft ̸ \nnwsearrows ̸ \nswlsquigarrow⟳̸ \nlcirclearrowright ̸ \nrcirclearrowdown ̸ \nswmapsto↻̸ \nlcirclearrowup ⟲̸ \nrcirclearrowleft ̸ \nswnearrows⤸̸ \nlcurvearrowdown ⤿̸ \nrcirclearrowright ̸ \nswrsquigarrow̸ \nlcurvearrowleft ↺̸ \nrcirclearrowup ̸ \nswswarrows̸ \nlcurvearrowne ⤹̸ \nrcurvearrowdown ↡̸ \ntwoheaddownarrow̸ \nlcurvearrownw ↶̸ \nrcurvearrowleft ↞̸ \ntwoheadleftarrow↷̸ \nlcurvearrowright ̸ \nrcurvearrowne ̸ \ntwoheadnearrow̸ \nlcurvearrowse ̸ \nrcurvearrownw ̸ \ntwoheadnwarrow̸ \nlcurvearrowsw ̸ \nrcurvearrowright ↠̸ \ntwoheadrightarrow̸ \nlcurvearrowup ̸ \nrcurvearrowse ̸ \ntwoheadsearrow⇍ \nLeftarrow ̸ \nrcurvearrowsw ̸ \ntwoheadswarrow↚ \nleftarrow ̸ \nrcurvearrowup ↟̸ \ntwoheaduparrow↢̸ \nleftarrowtail ̸ \nrhookdownarrow ↑̸ \nuparrow⇇̸ \nleftleftarrows ↩̸ \nrhookleftarrow ⇑̸ \nUparrow̸ \nleftlsquigarrow ⤤̸ \nrhooknearrow ̸ \nuparrowtail↤̸ \nleftmapsto ̸ \nrhooknwarrow ↕̸ \nupdownarrow↮ \nleftrightarrow ̸ \nrhookrightarrow ⇕̸ \nUpdownarrow⇎ \nLeftrightarrow ̸ \nrhooksearrow ⇅̸ \nupdownarrows⇆̸ \nleftrightarrows ⤦̸ \nrhookswarrow ̸ \nuplsquigarrow↜̸ \nleftrsquigarrow ̸ \nrhookuparrow ↥̸ \nupmapsto̸ \nlhookdownarrow ↛ \nrightarrow ̸ \nuprsquigarrow̸ \nlhookleftarrow ⇏ \nRightarrow ⇈̸ \nupuparrows̸ \nlhooknearrow ↣̸ \nrightarrowtailMnSymbol additionally defines synonyms for some of the preceding symbols:45

↺̸ \ncirclearrowleft (same as \nrcirclearrowup)↻̸ \ncirclearrowright (same as \nlcirclearrowup)↶̸ \ncurvearrowleft (same as \nrcurvearrowleft)↷̸ \ncurvearrowright (same as \nlcurvearrowright)⇢̸ \ndasharrow (same as \ndashedrightarrow)⇠̸ \ndashleftarrow (same as \ndashedleftarrow)⇢̸ \ndashrightarrow (same as \ndashedrightarrow)↚ \ngets (same as \nleftarrow)↩̸ \nhookleftarrow (same as \nrhookleftarrow)↪̸ \nhookrightarrow (same as \nlhookrightarrow)↝̸ \nleadsto (same as \nrightlsquigarrow)̸ \nleftrightsquigarrow (same as \nsquigarrowleftright)↦̸ \nmapsto (same as \nrightmapsto)↝̸ \nrightsquigarrow (same as \nrightlsquigarrow)↛ \nto (same as \nrightarrow)Table 108: MnSymbol Harpoons⇂ \downharpoonccw ∗ \neswharpoons \seharpooncw⇃ \downharpooncw ∗ \neswharpoonsenw \senwharpoons⥯ \downupharpoons \nwharpoonccw \swharpoonccw↽ \leftharpoonccw ∗ \nwharpooncw \swharpooncw↼ \leftharpooncw ∗ \nwseharpoonnesw \swneharpoons⥊ \leftrightharpoondownup \nwseharpoons ⥍ \updownharpoonleftright⇋ \leftrightharpoons \nwseharpoonswne ⥌ \updownharpoonrightleft⥋ \leftrightharpoonupdown ⇀ \rightharpoonccw ∗ ⥮ \updownharpoons \neharpoonccw ⇁ \rightharpooncw ∗ ↿ \upharpoonccw ∗ \neharpooncw ⇌ \rightleftharpoons ↾ \upharpooncw ∗ \neswharpoonnwse \seharpoonccw∗ Where marked, the “ccw” suffix can be replaced with “up” and the “cw” suffixcan be replaced with “down”. (In addition, \upharpooncw can be written as\restriction.)Table 109: MnSymbol Negated Harpoons⇂̸ \ndownharpoonccw ∗ ̸ \nneswharpoons ̸ \nseharpooncw⇃̸ \ndownharpooncw ∗ ̸ \nneswharpoonsenw ̸ \nsenwharpoons⥯̸ \ndownupharpoons ̸ \nnwharpoonccw ̸ \nswharpoonccw↽̸ \nleftharpoonccw ∗ ̸ \nnwharpooncw ̸ \nswharpooncw↼̸ \nleftharpooncw ∗ ̸ \nnwseharpoonnesw ̸ \nswneharpoons⥊̸ \nleftrightharpoondownup ̸ \nnwseharpoons ⥍̸ \nupdownharpoonleftright⇋̸ \nleftrightharpoons ̸ \nnwseharpoonswne ⥌̸ \nupdownharpoonrightleft⥋̸ \nleftrightharpoonupdown ⇀̸ \nrightharpoonccw ∗ ⥮̸ \nupdownharpoons̸ \nneharpoonccw ⇁̸ \nrightharpooncw ∗ ↿̸ \nupharpoonccw ∗̸ \nneharpooncw ⇌̸ \nrightleftharpoons ↾̸ \nupharpooncw ∗̸ \nneswharpoonnwse ̸ \nseharpoonccw∗ Where marked, the “ccw” suffix can be replaced with “up” and the “cw” suffixcan be replaced with “down”. (In addition, \nupharpooncw can be written as\nrestriction.)46

Table 110: chemarrow ArrowsA\chemarrowTable 111: fge Arrows! \fgerightarrow " \fgeuparrowTable 112: MnSymbol Spoons \downfilledspoon ̸ \nnespoon \nwfilledspoon⫰ \downspoon ̸ \nnwfilledspoon \nwspoon \leftfilledspoon ̸ \nnwspoon \rightfilledspoon⟜ \leftspoon ̸ \nrightfilledspoon ⊸ \rightspoon ∗̸ \ndownfilledspoon ⊸̸ \nrightspoon ∗ \sefilledspoon⫰̸ \ndownspoon ̸ \nsefilledspoon \sespoon \nefilledspoon ̸ \nsespoon \swfilledspoon \nespoon ̸ \nswfilledspoon \swspoon̸ \nleftfilledspoon ̸ \nswspoon \upfilledspoon⟜̸ \nleftspoon ̸ \nupfilledspoon ⫯ \upspoon̸ \nnefilledspoon ⫯̸ \nupspoon∗ MnSymbol defines \multimap as a synonym for \rightspoon and \nmultimap asa synonym for \nrightspoon.Table 113: MnSymbol Pitchforks⫛ \downpitchfork ̸ \nnwpitchfork \rightpitchfork \leftpitchfork ̸ \nrightpitchfork \sepitchfork⫛̸ \ndownpitchfork ̸ \nsepitchfork \swpitchfork \nepitchfork ̸ \nswpitchfork ⋔ \uppitchfork̸ \nleftpitchfork ⋔̸ \nuppitchfork̸ \nnepitchfork \nwpitchfork∗ MnSymbol defines \pitchfork as a synonym for \uppitchfork and \npitchforkas a synonym for \nuppitchfork.47

Table 114: MnSymbol Smiles and Frowns \doublefrown ̸ \nsmileeq \smileeq \doublefrowneq ̸ \nsmileeqfrown \smileeqfrown \doublesmile ≭ \nsmilefrown ≍ \smilefrown \doublesmileeq ̸ \nsmilefrowneq \smilefrowneq \eqfrown ̸ \nsqdoublefrown \sqdoublefrown \eqsmile ̸ \nsqdoublefrowneq \sqdoublefrowneq⌢ \frown ̸ \nsqdoublesmile \sqdoublesmile \frowneq ̸ \nsqdoublesmileeq \sqdoublesmileeq \frowneqsmile ̸ \nsqeqfrown \sqeqfrown \frownsmile ̸ \nsqeqsmile \sqeqsmile \frownsmileeq ̸ \nsqfrown \sqfrown̸ \ndoublefrown ̸ \nsqfrowneq \sqfrowneq̸ \ndoublefrowneq ̸ \nsqfrowneqsmile \sqfrowneqsmile̸ \ndoublesmile ̸ \nsqfrownsmile \sqfrownsmile̸ \ndoublesmileeq ̸ \nsqsmile \sqsmile̸ \neqfrown ̸ \nsqsmileeq \sqsmileeq̸ \neqsmile ̸ \nsqsmileeqfrown \sqsmileeqfrown⌢̸ \nfrown ̸ \nsqsmilefrown \sqsmilefrown̸ \nfrowneq ̸ \nsqtriplefrown \sqtriplefrown̸ \nfrowneqsmile ̸ \nsqtriplesmile \sqtriplesmile̸ \nfrownsmile ̸ \ntriplefrown \triplefrown̸ \nfrownsmileeq ̸ \ntriplesmile \triplesmile⌣̸ \nsmile ⌣ \smile∗ MnSymbol defines \smallsmile as a synonym for \smile, \smallfrown as a synonymfor \frown, \asymp as a synonym for \smilefrown, and \nasymp as a synonymfor \nsmilefrown.Table 115: ulsy Contradiction Symbols© \blitza \blitzb \blitzc \blitzd \blitzeTable 116: Extension Characters− \relbar = \RelbarTable 117: stmaryrd Extension Characters \Arrownot \Mapsfromchar ⤇ \Mapstochar \arrownot \mapsfromcharTable 118: txfonts/pxfonts Extension Characters⤆ \Mappedfromchar \Mmappedfromchar \Mmapstochar↤ \mappedfromchar \mmappedfromchar \mmapstochar48

Table 119: mathabx Extension Charactersß \mapsfromchar Þ \mapstocharû \Mapsfromchar ú \MapstocharTable 120: Log-like Symbols\arccos \cos \csc \exp \ker \limsup \min \sinh\arcsin \cosh \deg \gcd \lg \ln \Pr \sup\arctan \cot \det \hom \lim \log \sec \tan\arg \coth \dim \inf \liminf \max \sin \tanhCalling the above “symbols” may be a bit misleading. 2 Each log-like symbol merelyproduces the eponymous textual equivalent, but with proper surrounding spacing.See Section 7.4 for more information about log-like symbols. As \bmod and\pmod are arguably not symbols we refer the reader to the Short Math Guide forL A TEX [Dow00] for samples.Table 121: AMS Log-like Symbolsinj lim \injlim lim −→\varinjlim lim \varlimsupproj lim \projlim lim \varliminf lim ←−\varprojlimLoad the amsmath package to get these symbols. See Section 7.4 for some additionalcomments regarding log-like symbols. As \mod and \pod are arguably not symbolswe refer the reader to the Short Math Guide for L A TEX [Dow00] for samples.Table 122: Greek Lettersα \alpha θ \theta o o τ \tauβ \beta ϑ \vartheta π \pi υ \upsilonγ \gamma ι \iota ϖ \varpi φ \phiδ \delta κ \kappa ρ \rho ϕ \varphiɛ \epsilon λ \lambda ϱ \varrho χ \chiε \varepsilon µ \mu σ \sigma ψ \psiζ \zeta ν \nu ς \varsigma ω \omegaη \eta ξ \xiΓ \Gamma Λ \Lambda Σ \Sigma Ψ \Psi∆ \Delta Ξ \Xi Υ \Upsilon Ω \OmegaΘ \Theta Π \Pi Φ \PhiThe remaining Greek majuscules can be produced with ordinary Latin letters. Thesymbol “M”, for instance, is used for both an uppercase “m” and an uppercase “µ”.See Section 7.5 for examples of how to produce bold Greek letters.Table 123: AMS Greek LettersϜ \digamma κ \varkappa2 Michael J. Downes prefers the more general term, “atomic math objects”.49

Table 124: txfonts/pxfonts Upright Greek Lettersα \alphaup θ \thetaup π \piup φ \phiupβ \betaup ϑ \varthetaup ϖ \varpiup ϕ \varphiupγ \gammaup ι \iotaup ρ \rhoup χ \chiupδ \deltaup κ \kappaup ϱ \varrhoup ψ \psiupɛ \epsilonup λ \lambdaup σ \sigmaup ω \omegaupε \varepsilonup µ \muup ς \varsigmaupζ \zetaup ν \nuup τ \tauupη \etaup ξ \xiup υ \upsilonupTable 125: upgreek Upright Greek Lettersα \upalpha θ \uptheta π \uppi φ \upphiβ \upbeta ϑ \upvartheta ϖ \upvarpi ϕ \upvarphiγ \upgamma ι \upiota ρ \uprho χ \upchiδ \updelta κ \upkappa ρ \upvarrho ψ \uppsiε \upepsilon λ \uplambda σ \upsigma ω \upomegaε \upvarepsilon µ \upmu σ \upvarsigmaζ \upzeta ν \upnu τ \uptauη \upeta ξ \upxi υ \upupsilonΓ \Upgamma Λ \Uplambda Σ \Upsigma Ψ \Uppsi∆ \Updelta Ξ \Upxi Υ \Upupsilon Ω \UpomegaΘ \Uptheta Π \Uppi Φ \Upphiupgreek utilizes upright Greek characters from either the PostScript Symbol font(depicted above) or Euler Roman. As a result, the glyphs may appear slightlydifferent from the above. Contrast, for example, “Γ∆Θαβγ” (Symbol) with“Γ∆Θαβγ” (Euler).Table 126: txfonts/pxfonts Variant Latin Letters \varg \varv \varw \varyPass the varg option to txfonts/pxfonts to replace g, v, w, and y with , , , and in every mathematical expression in your document.Table 127: AMS Hebrew Lettersℶ \beth ג \gimel ℸ \daleth\aleph (ℵ) appears in Table 184 on page 62.Table 128: MnSymbol Hebrew Lettersℵ \aleph ℶ \beth ℷ \gimel ℸ \daleth50

Table 129: Letter-like Symbols⊥ \bot ∀ \forall ı \imath ∋ \ni ⊤ \topl \ell \hbar ∈ \in ∂ \partial ℘ \wp∃ \exists I \Im j \jmath R \ReTable 130: AMS Letter-like Symbolsk \Bbbk ∁ \complement \hbarR \circledR Ⅎ \Finv ħ \hslashS \circledS \Game ∄ \nexistsTable 131: txfonts/pxfonts Letter-like Symbols¢ \mathcent £ \mathsterling ∗ \notin \notni∗ It’s generally preferable to use the corresponding symbol from Table 3 on page 8because the symbols in that table work properly in both text mode and math mode.Table 132: mathabx Letter-like SymbolsV \barin P \in L \nottop T \varnotinA \complement E \nexists Q \owns U \varnotownerD \exists M \notbot W \ownsbarF \Finv R \notin B \partialG \Game S \notowner C \partialslashTable 133: MnSymbol Letter-like Symbols⊥ \bot ∈ \in ∌ \nowns ∗ ⊺ \top∃ \exists ∄ \nexists ∋ \owns ℘ \wp∀ \forall ∉ \nin ∗ ℘ \powerset∗ MnSymbol provides synonyms \notin for \nin, \ni for \owns, and \intercal for\top.Table 134: trfsigns Letter-like Symbolse \e j \imTable 135: mathdesign Letter-like Symbols∉∈ \in ∋ \owns\notin \smallin \notsmallin \smallowns \notsmallownsThe mathdesign package additionally provides versions of each of the letter-likesymbols shown in Table 130.51

Table 136: fge Letter-like SymbolsA \fgeA \fgeeszett D \fgeleftB U \fgeUc \fgec F \fgeF C \fgeleftCp \fged f \fgef B \fgerightBe \fgee \fgelb ∗ s \fges∗ The fge package defines \fgeeta, \fgeN, and \fgeoverU as synonyms for \fgelb.Table 137: AMS Delimiters \ulcorner \urcorner \llcorner \lrcornerTable 138: stmaryrd Delimiters \Lbag \Rbag ⟅ \lbag ⟆ \rbag \llceil \rrceil \llfloor \rrfloor⦇ \llparenthesis ⦈ \rrparenthesisTable 139: mathabx Delimitersv \lcorners w \rcornersx \ulcornerz \llcornery \urcorner{ \lrcornerTable 140: nath Delimiters\niv\vin52

↓〈⌈⌊(/⏐↓〈\downarrow ⇓\langle 〉⌈\lceil ⌉⌊\lfloor ⌋(( )// \Table 141: Variable-sized Delimiters[⇑⇓ \Downarrow [ [ ]〉\rangle | ∣ | ‖⌉↑\rceil↑ ⏐ \uparrow ⇑⌋↑⏐\rfloor↕ ↓ \updownarrow ⇕){) { \{ }∖\backslash]]∥ \|⇑ \Uparrow⇑⇓ \Updownarrow}\}When used with \left and \right, these symbols expand to the height of theenclosed math expression. Note that \vert is a synonym for |, and \Vert is asynonym for \|.ε-TEX provides a \middle analogue to \left and \right. \middle can be used, forexample, to make an internal “|” expand to the height of the surrounding \left and\right symbols. (This capability is commonly needed when typesetting adjacentbras and kets in Dirac notation: “〈φ|ψ〉”). A similar effect can be achieved inconventional L A TEX using the braket package.⎧⎭⏐Table 142: Large, Variable-sized Delimiters⎧⎧⎫ ⎧⎫⎪⎭ \lmoustache ⎩⎫⎪ ⎩ \rmoustache ⎩ ⎪⎩ \lgroup ⎭⎫⎪ ⎭ \rgroup⏐\arrowvert⇑⇑ \Arrowvert ⎪⎪\bracevertThese symbols must be used with \left and \right. The mathabx package, however,redefines \lgroup and \rgroup so that those symbols can work without \leftand \right.Table 143: AMS Variable-sized Delimiters|∣ \lvert |∣\rvert‖∥ \lVert ‖∥\rVertAccording to the amsmath documentation [AMS99], the preceding symbols areintended to be used as delimiters (e.g., as in “|−z|”) while the \vert and \Vertsymbols (Table 141) are intended to be used as operators (e.g., as in “p|q”).Table 144: stmaryrd Variable-sized Delimiters \llbracket \rrbracket53

Table 145: mathabx Variable-sized Delimiters1 9v \ldbrack w \rdbrack7 7 \lfilet ? ? \rfilet~ \thickvert ~ \vvvertTable 146: MnSymbol Variable-sized Delimiters⌈⌊⎡⎢⎢⎣\lceil\lfloor\lwavy\lWavy⌉⌋⎤⎥⎥⎦( ( ( ) ) )⟦⎧⎪⎭\rceil ⌜ ⌜ \ulcorner ⌝ ⌝ \urcorner\rfloor ⌞ ⌞ \llcorner ⌟ ⌟ \lrcorner\rwavy ⟨ ⟨ \langle ⟩ ⟩ \rangle\rWavy \langlebar \ranglebar⎧⎪⎩⎧⎪⎩ \lgroup ⎫ ⎪⎭⎫⎪ ⎭\rgroup\lsem ⟧\rsem ⟪ ⟪ \llangle ⟫ ⟫ \rrangle⎧⎪⎭ \lmoustache ⎫ ⎪⎩⎧⎪⎫⎪⎫⎪ \rmoustache { ⎨ \lbrace } ⎬ \rbrace⎩ ⎪⎩⎪⎭/ / / / / \backslash ⟨ ⟨ < ⟩ ⟩ >[⎡⎢⎣[ ]⎤⎥⎦] \ullcorner \ulrcorner∣ | ∥ \|⎪⎪\bracevert\arrowvert\Arrowvert\vert is a synonym for |. \Vert is a synonym for \|. \mid and \mvert producethe same symbol as \vert but designated as math relations instead of ordinals.\divides produces the same symbol as \vert but designated as a binary operatorinstead of an ordinal. \parallel and \mVert produce the same symbol as \Vertbut designated as math relations instead of ordinals.54

Table 147: mathdesign Variable-sized Delimiters \leftwave \leftevaw \rightwave\rightevawThe definitions of these symbols include a preceding \left or \right. It is thereforean error to specify \left or \right explicitly. The internal, “primitive” versionsof these symbols are called \lwave, \rwave, \levaw, and \revaw.Table 148: nath Variable-sized Delimiters (Double)〈〈〈〈\lAngle 〉〉〉〉\rAngle[[[[\lBrack ]]]]\rBrack⌈⌈⌈⌈\lCeil⌉⌉⌉⌉\rCeil⌊⌊⌊⌊\lFloor⌋⌋⌋⌋\rFloor||∣ \lVert ∗ ||∣\rVert ∗∗ nath redefines all of the above to include implicit \left and \right commands.Hence, separate \lVert and \rVert commands are needed to disambiguate whether“|” is a left or right delimiter.All of the symbols in Table 148 can also be expressed using the \double macro.See the nath documentation for examples and additional information.Table 149: nath Variable-sized Delimiters (Triple)〈〈〈〈〈〈\triple< 〉〉〉〉〉〉\triple>[[[[[[\triple[ ]]]]]]\triple]|||∣ \ltriple| ∗ |||∣\rtriple| ∗∗ Similar to \lVert and \rVert in Table 148, \ltriple and \rtriple must be usedinstead of \triple to disambiguate whether “|” is a left or right delimiter.Note that \triple—and the corresponding \double—is actually a macro thattakes a delimiter as an argument.55

Table 150: textcomp Text-mode Delimiters〈 \textlangle 〉 \textrangle〚 \textlbrackdbl 〛 \textrbrackdbl⁅ \textlquill ⁆ \textrquillTable 151: metre Text-mode Delimiters} \alad } \Alad † \crux † \Crux{ \alas { \Alas ] \quadrad ] \Quadrad〉 \angud 〉 \Angud [ \quadras [ \Quadras〈 \angus 〈 \AngusTable 152: Math-mode Accentsá \acute{a} ǎ \check{a} à \grave{a} ã \tilde{a}ā \bar{a} ä \ddot{a} â \hat{a} ⃗a \vec{a}ă \breve{a} ȧ \dot{a} å \mathring{a}Also note the existence of \imath and \jmath, which produce dotless versions of“i” and “j ”. (See Table 184 on page 62.) These are useful when the accent issupposed to replace the dot. For example, “\hat{\imath}” produces a correct“ î ”, while “\hat{i}” would yield the rather odd-looking “ î ”.Table 153: AMS Math-mode Accents.......a \dddot{a} a \ddddot{a}These accents are also provided by the mathabx and accents packages and areredefined by the mathdots package if the amsmath and amssymb packages have previouslybeen loaded. All of the variations except for the original AMS ones tightenthe space between the dots (from ... a to ˙˙˙ a). The mathabx and mathdots versions alsofunction properly within subscripts and superscripts (x˙˙˙ a instead of x ... a ) .Table 154: MnSymbol Math-mode Accents⃗a\vec{a}A a Table 155: fge Math-mode Accents\spirituslenis{A}\spirituslenis{a} ∗∗ When fge is passed the crescent option, \spirituslenis instead uses a crescentaccent as in “ a ”.56

Table 156: yhmath Math-mode Accentså\ring{a}This symbol is largely obsolete, as standard L A TEX 2ε has supported \mathringsince June, 1998 [L A T98].Table 157: Extensible Accents›abc \widetilde{abc} ∗ ” abc \widehat{abc} ∗←−abc \overleftarrow{abc} † −→ abc \overrightarrow{abc}†abc \overline{abc} abc \underline{abc}{}}{abc \overbrace{abc}}{{}abc \underbrace{abc}√abc \sqrt{abc}‡As demonstrated in a 1997 TUGboat article about typesetting long-division problems[Gib97], an extensible long-division sign (“ )abc ”) can be faked by putting a“\big)” in a tabular environment with an \hline or \cline in the preceding row.The article also presents a piece of code (uploaded to CTAN as longdiv.tex) thatautomatically solves and typesets—by putting an \overline atop “\big)” andthe desired text—long-division problems. See also the polynom package, which automaticallysolves and typesets polynomial-division problems in a similar manner.∗ These symbols are made more extensible by the MnSymbol package and even moreextensible by the yhmath package.† If you’re looking for an extensible diagonal line or arrow to be used for canceling orreducing mathematical subexpressions (e.g., “✘x + ✘ −x” ✘ or “✘ 3 + ✘ ✘✿2 5”) then considerusing the cancel package.‡ With an optional argument, \sqrt typesets nth roots. For example,“\sqrt[3]{abc}” produces “ 3√ abc ” and “\sqrt[n]{abc}” produces “ n√ abc ”.Table 158: overrightarrow Extensible Accents=⇒abc \Overrightarrow{abc}Table 159: yhmath Extensible Accentsâbc \wideparen{abc} È abc \widetriangle{abc}˚âbc\widering{abc}57

Table 160: AMS Extensible Accents←→abc \overleftrightarrow{abc} abc←→abc←−\underleftarrow{abc} abc−→\underleftrightarrow{abc}\underrightarrow{abc}Table 161: MnSymbol Extensible Accentsabc \overbrace{abc} abc \underbrace{abc}abc \overgroup{abc} abc \undergroup{abc}abc \overlinesegment{abc} abc↼abc\overleftharpoon{abc}⇀abc\underlinesegment{abc}\overrightharpoon{abc}âbc \widehat{abc} ãbc \widetilde{abc}abc\wideparen{abc}Table 162: mathtools Extensible Accents{}}{abc \overbrace{abc}}{{}abc \underbrace{abc}abc \overbracket{abc} ∗ abc \underbracket{abc} ∗∗ \overbracket and \underbracket accept optional arguments that specify thebracket height and thickness. See the mathtools documentation for more information.Table 163: mathabx Extensible Accentshkikjabc \overbrace{abc}hkkjabc „ \widebar{abc}abc \overgroup{abc} abc | \widecheck{abc}lomon abc \underbrace{abc} abc Œ \wideparen{abc}loon abc \undergroup{abc}âbc\widearrow{abc}˚âbc\widering{abc}The braces shown for \overbrace and \underbrace appear in their minimum size.They can expand arbitrarily wide, however.58

Table 164: esvect Extensible Accents# ”abc \vv{abc} with package option a# „abc \vv{abc} with package option b# «abc \vv{abc} with package option c# »abc \vv{abc} with package option d# –abc \vv{abc} with package option e# —abc \vv{abc} with package option f# abc \vv{abc} with package option g# ‰abc \vv{abc} with package option hesvect also defines a \vv* macro which is used to typeset arrows over vector variableswith subscripts. See the esvect documentation for more information.Table 165: undertilde Extensible Accentsabc› \utilde{abc}Because \utilde is based on \widetilde it is also made more extensible by theyhmath package.Table 166: AMS Extensible Arrowsabc←−−\xleftarrow{abc}abc−−→\xrightarrow{abc}abc←−−↪abc↩−−→Table 167: mathtools Extensible Arrows\xhookleftarrow{abc}\xhookrightarrow{abc}abc⇐= \xLeftarrow{abc}abc↽−−abc↼−−abc←−→abc⇐=⇒\xleftharpoondown{abc}\xleftharpoonup{abc}\xleftrightarrow{abc}\xLeftrightarrow{abc}abc↼−− −−⇁abc↦−−→\xleftrightharpoons{abc}\xmapsto{abc}abc=⇒ \xRightarrow{abc}abc−−⇁abc−−⇀abc−−⇀ ↽−−\xrightharpoondown{abc}\xrightharpoonup{abc}\xrightleftharpoons{abc}Table 168: chemarr Extensible Arrowsabc−−⇀ ↽−−\xrightleftharpoons{abc}59

Table 169: chemarrow Extensible ArrowsabcDGGGGGGGdef\autoleftarrow{abc}{def}abcGGGGGGGAdef\autorightarrow{abc}{def}abcEGGGGGGGGGGGGGGCdef\autoleftrightharpoons{abc}{def}abcGGGGGGGBFGGGGGGGdef\autorightleftharpoons{abc}{def}In addition to the symbols shown above, chemarrow also provides \larrowfill,\rarrowfill, \leftrightharpoonsfill, and \rightleftharpoonsfill macros.Each of these takes a length argument and produces an arrow of the specifiedlength.Table 170: trfsigns Extensible Arrowsa \dft{a} a \DFT{a}Table 171: extarrows Extensible Arrowsabc⇐=⇒abc←−→\xLeftrightarrow{abc}\xleftrightarrow{abc}abc==== \xlongequal{abc}abc⇐==abc←−−\xLongleftarrow{abc}\xlongleftarrow{abc}abc⇐=⇒abc←−→abc==⇒abc−−→\xLongleftrightarrow{abc}\xlongleftrightarrow{abc}\xLongrightarrow{abc}\xlongrightarrow{abc}Table 172: extpfeil Extensible Arrowsabc==== \xlongequal{abc}abc↞−−−−\xtwoheadleftarrow{abc}abc↦−−→abc−−−−↠\xmapsto{abc}\xtwoheadrightarrow{abc}The extpfeil package also provides a \newextarrow command to help you defineyour own extensible arrow symbols. See the extpfeil documentation for more information.Table 173: holtpolt Non-commutative Division Symbolsabcdef\holter{abc}{def}abcdef\polter{abc}{def}60

Table 174: Dots· \cdotp : \colon ∗ . \ldotp· · · \cdots. .. \ddots†. . . \ldots. \vdots †∗ While “:” is valid in math mode, \colon uses different surrounding spacing. SeeSection 7.4 and the Short Math Guide for L A TEX [Dow00] for more information onmath-mode spacing.† The mathdots package redefines \ddots and \vdots to make them scale properlywith font size. (They normally scale horizontally but not vertically.) \fixedddotsand \fixedvdots provide the original, fixed-height functionality of L A TEX 2ε’s\ddots and \vdots macros.Table 175: AMS Dots∵ \because ∗ · · · \dotsi ∴ \therefore ∗· · · \dotsb · · · \dotsm. . . \dotsc . . . \dotso∗ \because and \therefore are defined as binary relations and therefore also appearin Table 63 on page 30.The AMS \dots symbols are named according to their intended usage: \dotsbbetween pairs of binary operators/relations, \dotsc between pairs of commas,\dotsi between pairs of integrals, \dotsm between pairs of multiplication signs,and \dotso between other symbol pairs.Table 176: wasysym Dots∴\wasythereforeTable 177: MnSymbol Dots⋅ \cdot \hdotdot ⋰ \udots \ddotdot ⋯ \hdots ∴ \uptherefore⋱ \ddots \lefttherefore ∶ \vdotdot \diamonddots \righttherefore ⋮ \vdots∵ \downtherefore ∷ \squaredots \fivedots \udotdotMnSymbol defines \therefore as \uptherefore and \because as\downtherefore. Furthermore, \cdotp and \colon produce the same glyphs as\cdot and \vdotdot respectively but serve as TEX math punctuation (class 6symbols) instead of TEX binary operators (class 2).All of the above except \hdots and \vdots are defined as binary operators andtherefore also appear in Table 46 on page 23. Also, unlike most of the other dotsymbols in this document, MnSymbol’s dots are defined as single characters insteadof as composites of multiple single-dot characters.61

Table 178: mathdots Dots. .. \iddotsTable 179: yhmath Dots. .. \adotsTable 180: mathcomp Math Symbols℃ \tccentigrade Ω \tcohm ‰ \tcperthousandµ \tcmu ‱ \tcpertenthousandTable 181: mathabx Mayan Digits0 \maya{0} 2 \maya{2} 4 \maya{4}1 \maya{1} 3 \maya{3} 5 \maya{5}Table 182: marvosym Digits0 \MVZero 2 \MVTwo 4 \MVFour 6 \MVSix 8 \MVEight1 \MVOne 3 \MVThree 5 \MVFive 7 \MVSeven 9 \MVNineTable 183: fge Digits0 \fgestruckzero 1 \fgestruckoneTable 184: Miscellaneous L A TEX 2ε Math Symbolsℵ \aleph ⋄ \Diamond ∗ ∞ \infty ′ \prime̸ \angle ♦ \diamondsuit \mho ∗ ♯ \sharp\ \backslash ∅ \emptyset ‡ ∇ \nabla ♠ \spadesuit□ \Box ∗,† ♭ \flat ♮ \natural` \surd♣ \clubsuit ♥ \heartsuit ¬ \neg △ \triangle∗ Not predefined in L A TEX 2ε. Use one of the packages latexsym, amsfonts, amssymb,txfonts, pxfonts, or wasysym. Note, however, that amsfonts and amssymb define\Diamond to produce the same glyph as \lozenge (“♦”); the other packages producea squarer \Diamond as depicted above.† To use \Box—or any other symbol—as an end-of-proof (Q.E.D.) marker, considerusing the ntheorem package, which properly juxtaposes a symbol with the end ofthe proof text.‡ Many people prefer the look of AMS’s \varnothing (“∅”, Table 185) to that ofL A TEX’s \emptyset.62

Table 185: Miscellaneous AMS Math Symbols∠ \angle \blacktriangledown \mho \backprime \diagdown ∢ \sphericalangle⋆ \bigstar \diagup □ \square \blacklozenge ð \eth ▽ \triangledown \blacksquare ♦ \lozenge ∅ \varnothing \blacktriangle ∡ \measuredangle △ \vartriangleTable 186: Miscellaneous wasysym Math Symbols \Box ⋄ \Diamond \mho ∗ \varangle∗ wasysym also defines an \agemO symbol, which is the same glyph as \mho but isintended for use in text mode.Table 187: Miscellaneous txfonts/pxfonts Math Symbols \Diamondblack ƛ \lambdaslash \varheartsuit \Diamonddot \varclubsuit \varspadesuitƛ \lambdabar \vardiamondsuitTable 188: Miscellaneous mathabx Math Symbols0 \degree 4 \fourth > \measuredangle 2 \secondå \diagdown # \hash & \pitchfork ? \sphericalangleä \diagup 8 \infty 9 \propto 3 \thirdI \diameter $ \leftthreetimes % \rightthreetimes # \varhashTable 189: Miscellaneous MnSymbol Math Symbols∠ \angle ♢ \diamondsuit ✠ \maltese ♯ \sharp⌐ \backneg ♭ \flat ∡ \measuredangle ∫ \smallint‵ \backprime ♡ \heartsuit ∇ \nabla ♠ \spadesuit✓ \checkmark ∞ \infty ♮ \natural ∢ \sphericalangle♣ \clubsuit ⨽ \invbackneg ¬ \neg∅ \diameter ⨼ \invneg ′ \primeMnSymbol defines \emptyset and \varnothing as synonyms for \diameter; \lnotand \minushookdown as synonyms for \neg; \minushookup as a synonym for\invneg; \hookdownminus as a synonym for \backneg; and, \hookupminus asa synonym for \invbackneg.63

Table 190: Miscellaneous Internal MnSymbol Math Symbols∫…∫ \partialvardint ∫…∫ \partialvartint⨚ \partialvardlanddownint ⨚ \partialvartlanddownint⨙ \partialvardlandupint ⨙ \partialvartlandupint∲ \partialvardlcircleleftint ∲ \partialvartlcircleleftint∲ \partialvardlcirclerightint ∲ \partialvartlcirclerightint∯ \partialvardoiint ∯ \partialvartoiint∮ \partialvardoint ∮ \partialvartoint∳ \partialvardrcircleleftint ∳ \partialvartrcircleleftint∳ \partialvardrcirclerightint ∳ \partialvartrcirclerightint⨏ \partialvardstrokedint ⨏ \partialvartstrokedint⨋ \partialvardsumint ⨋ \partialvartsumintThese symbols are intended to be used internally by MnSymbol to construct theintegrals appearing in Table 59 on page 29 but can nevertheless be used in isolation.Table 191: Miscellaneous textcomp Text-mode Math Symbols° \textdegree ∗ ½ \textonehalf † ¾ \textthreequarters †÷ \textdiv ¼ \textonequarter † ³ \textthreesuperior⁄ \textfractionsolidus ¹ \textonesuperior × \texttimes¬ \textlnot ± \textpm ² \texttwosuperior− \textminus √ \textsurd∗ If you prefer a larger degree symbol you might consider defining one as“\ensuremath{^\circ}” (“ ◦ ”).† nicefrac (part of the units package) can be used to construct vulgar fractions like“ 1 /2”, “ 1 /4”, “ 3 /4”, and even “ c /o”.Table 192: Miscellaneous marvosym Math SymbolsPpW \Anglesign ÷ \Squaredot \Vectorarrowhigh= \Corresponds \VectorarrowTable 193: Miscellaneous fge Math SymbolsK \fgebackslash S \fgecap R \fgecupacute h \fgelangleM \fgebaracute Q \fgecapbar P \fgecupbar L \fgeupbracketO \fgebarcap N \fgecup i \fgeinftyTable 194: Miscellaneous mathdesign Math Symbols∟\rightangleTable 195: Miscellaneous arev Math Symbols♨ \steaming ♦ \vardiamond ♤ \varspade♧ \varclub ♥ \varheart64

Table 196: Math AlphabetsFont sample Generating command Required packageABCdef123 \mathrm{ABCdef123} noneABCdef123 \mathit{ABCdef123} noneABCdef123 \mathnormal{ABCdef123} noneABC \mathcal{ABC} noneABC \mathscr{ABC} mathrsfsor \mathcal{ABC}calrsfsABC \mathcal{ABC} euscript with the mathcal optionor \mathscr{ABC}euscript with the mathscr optionABCdef123 \mathpzc{ABCdef123} none; manually defined ∗ABC \mathbb{ABC} amsfonts, § amssymb, txfonts, or pxfonts \varmathbb{ABC} txfonts or pxfontsABCdef123 \mathbb{ABCdef123} bbold or mathbbol †ABCdef123 \mathbb{ABCdef123} mbboard †ABCdef12 \mathbbm{ABCdef12} bbmABCdef12 \mathbbmss{ABCdef12} bbmABCdef12 \mathbbmtt{ABCdef12} bbmABC1 \mathds{ABC1} dsfontABC1 \mathds{ABC1} dsfont with the sans optionABCdef123 \mathfrak{ABCdef123} eufrakABCdef123 \textfrak{ABCdef123} yfonts ‡ABCdef123 \textswab{ABCdef123} yfonts ‡ABCˇf123 \textgoth{ABCdef123} yfonts ‡∗ Put “\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it}” in your document’spreamble to make \mathpzc typeset its argument in Zapf Chancery.As a similar trick, you can typeset the Calligra font’s script “ r ” (or othercalligraphic symbols) in math mode by loading the calligra package andputting “\DeclareMathAlphabet{\mathcalligra}{T1}{calligra}{m}{n}”in your document’s preamble to make \mathcalligra typeset itsargument in the Calligra font. (You may also want to specify“\DeclareFontShape{T1}{calligra}{m}{n}{s*[2.2]callig15}{}” toset Calligra at 2.2 times its design size for a better blend with typical body fonts.)† The mathbbol package defines some additional blackboard bold characters:parentheses, square brackets, angle brackets, and—if the bbgreekl optionis passed to matbbol—Greek letters. For instance, “” is producedby “\mathbb{\Langle\Lbrack\Lparen\bbalpha\bbbeta\bbgamma\Rparen\Rbrack\Rangle}”.mbboard extends the blackboard bold symbol set significantly further. Itsupports not only the Greek alphabet—including “Greek-like” symbols suchas \bbnabla (“š”)—but also all punctuation marks, various currency symbolssuch as \bbdollar (“$”) and \bbeuro (“û”), and the Hebrew alphabet(e.g., “\bbfinalnun\bbyod\bbqof\bbpe” → “ÏÉ×Ô”).‡ As their \text. . . names imply, the fonts provided by the yfonts package areactually text fonts. They are included in Table 196 because they are frequentlyused in a mathematical context.65

§ An older (i.e., prior to 1991) version of the AMS’s fonts rendered C, N, R, S,and Z as C, N, R, S, and Z. As some people prefer the older glyphs—much tothe AMS’s surprise—and because those glyphs fail to build under modern versionsof METAFONT, Berthold Horn uploaded PostScript fonts for the older blackboardboldglyphs to CTAN, to the fonts/msym10 directory. As of this writing, however,there are no L A TEX 2ε packages for utilizing the now-obsolete glyphs.66

4 Science and technology symbolsThis section lists symbols that are employed in various branches of science and engineering.Table 197: gensymb Symbols Defined to Work in Both Math and Text Mode℃ \celsius µ \micro ‰ \perthousand° \degree Ω \ohmTable 198: wasysym Electrical and Physical Symbols \AC \VHF \photon F \HF \gluonTable 199: ifsym Pulse Diagram Symbols! \FallingEdge ' \LongPulseLow % \PulseLow " \ShortPulseHigh& \LongPulseHigh $ \PulseHigh \RaisingEdge # \ShortPulseLowIn addition, within \textifsym{. . .}, the following codes are valid:l l m m h h d d < < > >L L M M H H D D = >This enables one to write “\textifsym{mmmm}” to get “mmmm” or“\textifsym{L|H|L|H|L}” to get “L|H|L|H|L”. See also the timing package,which provides a wide variety of pulse-diagram symbols within an environmentdesigned specifically for typesetting pulse diagrams.Finally, \textifsym supports the display of segmented digits, as would appearon an LCD: “\textifsym{-123.456}” produces “-123.456”. “\textifsym{b}”outputs a blank with the same width as an “8”.Table 200: ar Aspect Ratio SymbolA \ARTable 201: textcomp Text-mode Science and Engineering Symbols℃ \textcelsius ℧ \textmho µ \textmu Ω \textohm67

Table 202: wasysym Astronomical Symbols☿ \mercury ♁ \earth ♃ \jupiter ♅ \uranus ♇ \pluto♀ \venus ♂ \mars ♄ \saturn \neptune⊙ \astrosun \fullmoon ☾ \leftmoon \newmoon ☽ \rightmoon♈ \aries ♋ \cancer ♎ \libra ♒ \aquarius♉ \taurus \leo \scorpio ♑ \capricornus♊ \gemini ♍ \virgo ♐ \sagittarius ♓ \pisces \ascnode \descnode ☌ \conjunction \opposition ♈ \vernalTable 203: marvosym Astronomical Symbols \Mercury Ê \Earth Å \Jupiter Ç \Uranus É \Plutoà \Venus Ä \Mars Æ \Saturn È \NeptuneÁ \Moon À \Sunà \Aries ã \Cancer æ \Libra é \Capricorná \Taurus ä \Leo ç \Scorpio ê \Aquariusâ \Gemini å \Virgo è \Sagittarius ë \PiscesNote that \Aries . . . \Pisces can also be specified with \Zodiac{1} . . .\Zodiac{12}.A \MercuryB \VenusTable 204: mathabx Astronomical SymbolsC \Earth E \Jupiter G \UranusD \Mars F \Saturn H \NeptuneI \PlutoJ \varEarthM \fullmoon K \leftmoon N \newmoon L \rightmoon @ \SunP \Aries Q \Taurus R \Geminimathabx also defines \girl as an alias for \Venus, \boy as an alias for \Mars, and\Moon as an alias for \leftmoon.Table 205: wasysym APL Symbols \APLbox ÷ \APLinv \APLstar \APLcomment \APLleftarrowbox \APLup \APLdown \APLlog \APLuparrowbox \APLdownarrowbox − \APLminus \− \notbackslash \APLinput \APLrightarrowbox /− \notslashTable 206: wasysym APL Modifiers◦ \APLcirc{} ∼ \APLnot{} | \APLvert{}68

Table 207: marvosym Computer Hardware SymbolsÍ \ComputerMouse Ñ \ParallelPort Î \SerialInterfaceÏ \Keyboard Ò \Printer Ð \SerialPortTable 208: keystroke Computer KeysAlt \Alt Enter \Enter ∗ PrtSc \PrtSc ∗AltGr \AltGr Esc \Esc ∗ → \RArrowBreak \Break ∗ Home \Home ∗ ←↪ \Return↦−→\BSpace † Ins \Ins ∗ Scroll \Scroll ∗Ctrl \Ctrl ∗ ← \LArrow Shift ⇑ \Shift ∗↓ \DArrow Num \NumLock \SpacebarDel \Del ∗ Page ↓ \PgDown ∗−−→−−→ \Tab†End \End ∗ Page ↑ \PgUp ∗ ↑ \UArrow∗ Changes based on the language option passed to the keystroke package. For example,the german option makes \Del produce “ Entf ” instead of “ Del ”.† These symbols utilize the rotating package and therefore display improperly in mostDVI viewers.The \keystroke command draws a key with an arbitrary label.“\keystroke{F7}” produces “ F7 ”.For example,Table 209: ascii Control Characters (CP437)␁ \SOH ␈ \BS ␏ \SI ␖ \SYN ␝ \GS␂ \STX ␉ \HT ␐ \DLE ␗ \ETB ␞ \RS␃ \ETX ␊ \LF ␑ \DCa ␘ \CAN ␟ \US␄ \EOT ␋ \VT ␒ \DCb ␙ \EM␅ \ENQ ␌ \FF ␓ \DCc ␚ \SUB␆ \ACK ␍ \CR ␔ \DCd ␛ \ESC␇ \BEL ␎ \SO ␕ \NAK ␜ \FS␡ \DEL \NBSP ␀ \NUL ¦ \splitvertCode Page 437 (CP437), which was first utilized by the original IBM PC, uses thesymbols \SOH through \US to depict ASCII characters 1–31 and \DEL to depictASCII character 127. The \NUL symbol, not part of CP437, represents ASCIIcharacter 0. \NBSP, also not part of CP437, represents a nonbreaking space.\splitvert is merely the “|” character drawn as it was on the IBM PC.Table 210: marvosym Communication Symbolsk \Email t \fax v \Faxmachine E \Lightning A \Pickupz \Emailct u \FAX B \Letter H \Mobilefone T \Telefon69

Table 211: marvosym Engineering Symbols" \Beam l \Force ‘ \Octosteel \RoundedTTsteel# \Bearing ’ \Hexasteel ˜ \Rectpipe — \Squarepipe› \Circpipe & \Lefttorque ” \Rectsteel “ \Squaresteel• \Circsteel L \Lineload ' \Righttorque œ \Tsteel% \Fixedbearing $ \Loosebearing Ÿ \RoundedLsteel ∗ š \TTsteel– \Flatsteel \Lsteel \RoundedTsteel ∗∗ \RoundedLsteel and \RoundedTsteel seem to be swapped, at least in the2000/05/01 version of marvosym.Table 212: wasysym Biological Symbols♀ \female ♂ \maleTable 213: marvosym Biological Symbols~ \Female … \FemaleMale \MALE { \Neutral \FEMALE } \Hermaphrodite | \Male„ \FemaleFemale \HERMAPHRODITE ƒ \MaleMaleTable 214: marvosym Safety-related Symbolsh \Biohazard C \CEsign ` \Explosionsafe j \Radioactivityn \BSEfree J \Estatically a \Laserbeam ! \StopsignTable 215: feyn Feynman Diagram Symbols! \bigbosonloop ¡ \feyn{fu} § \feyn{gvs} h \feyn{h}a \feyn{a} ¢ \feyn{fv} ¦ \feyn{gv} l \feyn{ms}c \feyn{c} f \feyn{f} g \feyn{g} m \feyn{m}\feyn{fd} w \feyn{glu} \feyn{hd} p \feyn{p}n \feyn{fl} o \feyn{gl} i \feyn{hs} x \feyn{x}e \feyn{fs} ¥ \feyn{gu} \feyn{hu} \smallbosonloopAll other arguments to the \feyn command produce a “?” symbol.The feyn package provides various commands for composing the preceding symbolsinto complete Feynman diagrams. See the feyn documentation for examples andadditional information.70

5 DingbatsDingbats are symbols such as stars, arrows, and geometric shapes. They are commonly used as bullets initemized lists or, more generally, as a means to draw attention to the text that follows.The pifont dingbat package warrants special mention. Among other capabilities, pifont provides a L A TEXinterface to the Zapf Dingbats font (one of the standard 35 PostScript fonts). However, rather than name eachof the dingbats individually, pifont merely provides a single \ding command, which outputs the character thatlies at a given position in the font. The consequence is that the pifont symbols can’t be listed by name in thisdocument’s index, so be mindful of that fact when searching for a particular symbol.Table 216: bbding Arrowsy \ArrowBoldDownRight z \ArrowBoldRightShort x \ArrowBoldUpRight{ \ArrowBoldRightCircled w \ArrowBoldRightStrobeTable 217: pifont Arrows➔ \ding{212} ➝ \ding{221} ➦ \ding{230} ➯ \ding{239} ➹ \ding{249}→ \ding{213} ➞ \ding{222} ➧ \ding{231} ➱ \ding{241} ➺ \ding{250}↔ \ding{214} ➟ \ding{223} ➨ \ding{232} ➲ \ding{242} ➻ \ding{251}↕ \ding{215} ➠ \ding{224} ➩ \ding{233} ➳ \ding{243} ➼ \ding{252}➘ \ding{216} ➡ \ding{225} ➪ \ding{234} ➴ \ding{244} ➽ \ding{253}➙ \ding{217} ➢ \ding{226} ➫ \ding{235} ➵ \ding{245} ➾ \ding{254}➚ \ding{218} ➣ \ding{227} ➬ \ding{236} ➶ \ding{246}➛ \ding{219} ➤ \ding{228} ➭ \ding{237} ➷ \ding{247}➜ \ding{220} ➥ \ding{229} ➮ \ding{238} ➸ \ding{248}Table 218: universal Arrows \bauarrow \bauwhitearrowTable 219: marvosym Scissorss \Cutleft q \Cutright S \Leftscissorsr \Cutline R \Kutline Q \RightscissorsTable 220: bbding Scissors§ \ScissorHollowLeft ¥ \ScissorLeftBrokenTop¦ \ScissorHollowRight ¡ \ScissorRight¤ \ScissorLeft \ScissorRightBrokenBottom£ \ScissorLeftBrokenBottom ¢ \ScissorRightBrokenTopTable 221: pifont Scissors✁ \ding{33} ✂ \ding{34} ✃ \ding{35} ✄ \ding{36}71

Table 222: dingbat PencilsW \largepencilP \smallpencilTable 223: bbding Pencils and Nibs \NibLeft \PencilLeft \PencilRightDown \NibRight \PencilLeftDown \PencilRightUp\NibSolidLeft \PencilLeftUp \NibSolidRight \PencilRightTable 224: pifont Pencils and Nibs✎ \ding{46} ✏ \ding{47} ✐ \ding{48} ✑ \ding{49} ✒ \ding{50}Table 225: dingbat FistsR \leftpointright L \rightpointleft N \rightpointrightD \leftthumbsdown d \rightthumbsdownU \leftthumbsup u \rightthumbsupTable 226: bbding Fists \HandCuffLeft \HandCuffRightUp \HandPencilLeft \HandCuffLeftUp \HandLeft \HandRight \HandCuffRight \HandLeftUp \HandRightUpTable 227: pifont Fists☛ \ding{42} ☞ \ding{43} ✌ \ding{44} ✍ \ding{45}Table 228: bbding Crosses and Plusses* \Cross + \CrossOpenShadow & \PlusOutline- \CrossBoldOutline , \CrossOutline ) \PlusThinCenterOpen4 \CrossClowerTips ' \Plus. \CrossMaltese ( \PlusCenterOpenTable 229: pifont Crosses and Plusses✙ \ding{57} ✛ \ding{59} ✝ \ding{61} ✟ \ding{63}✚ \ding{58} ✜ \ding{60} ✞ \ding{62} ✠ \ding{64}72

Table 230: bbding Xs and Check Marks! \Checkmark # \XSolid % \XSolidBrush" \CheckmarkBold $ \XSolidBoldTable 231: pifont Xs and Check Marks✓ \ding{51} ✕ \ding{53} ✗ \ding{55}✔ \ding{52} ✖ \ding{54} ✘ \ding{56}Table 232: wasysym Xs and Check Marks \CheckedBox □ \Square ☒ \XBoxTable 233: universal Xs¥ \baucrossTable 234: pifont Circled Numbers1 \ding{172} ❶ \ding{182} ➀ \ding{192} ➊ \ding{202}2 \ding{173} ❷ \ding{183} ➁ \ding{193} ➋ \ding{203}3 \ding{174} ❸ \ding{184} ➂ \ding{194} ➌ \ding{204}4 \ding{175} ❹ \ding{185} ➃ \ding{195} ➍ \ding{205}5 \ding{176} ❺ \ding{186} ➄ \ding{196} ➎ \ding{206}6 \ding{177} ❻ \ding{187} ➅ \ding{197} ➏ \ding{207}7 \ding{178} ❼ \ding{188} ➆ \ding{198} ➐ \ding{208}8 \ding{179} ❽ \ding{189} ➇ \ding{199} ➑ \ding{209}9 \ding{180} ❾ \ding{190} ➈ \ding{200} ➒ \ding{210}10 \ding{181} ❿ \ding{191} ➉ \ding{201} ➓ \ding{211}pifont (part of the psnfss package) provides a dingautolist environment whichresembles enumerate but uses circled numbers as bullets. 3 See the psnfss documentationfor more information.Table 235: wasysym Stars \davidsstar \hexstar \varhexstar3 In fact, dingautolist can use any set of consecutive Zapf Dingbats symbols.73

Table 236: bbding Stars, Flowers, and Similar ShapesN \Asterisk P \FiveFlowerPetal 2 \JackStarA \AsteriskBold 8 \FiveStar 3 \JackStarBoldB \AsteriskCenterOpen ; \FiveStarCenterOpen O \SixFlowerAlternateX \AsteriskRoundedEnds ? \FiveStarConvex U \SixFlowerAltPetalC \AsteriskThin 7 \FiveStarLines M \SixFlowerOpenCenterD \AsteriskThinCenterOpen 9 \FiveStarOpen Q \SixFlowerPetalDotted0 \DavidStar : \FiveStarOpenCircled L \SixFlowerPetalRemoved/ \DavidStarSolid < \FiveStarOpenDotted [ \SixFlowerRemovedOpenPetalZ \EightAsterisk = \FiveStarOutline G \SixStarS \EightFlowerPetal > \FiveStarOutlineHeavy K \SixteenStarLightY \EightFlowerPetalRemoved @ \FiveStarShadow ` \SnowflakeH \EightStar 1 \FourAsterisk ^ \SnowflakeChevronI \EightStarBold V \FourClowerOpen _ \SnowflakeChevronBoldF \EightStarConvex W \FourClowerSolid ] \SparkleE \EightStarTaper 5 \FourStar \ \SparkleBoldR \FiveFlowerOpen 6 \FourStarOpen J \TwelweStarTable 237: pifont Stars, Flowers, and Similar Shapes✡ \ding{65} ✪ \ding{74} ✳ \ding{83} ✼ \ding{92} ❅ \ding{101}✢ \ding{66} ✫ \ding{75} ✴ \ding{84} ✽ \ding{93} ❆ \ding{102}✣ \ding{67} ✬ \ding{76} ✵ \ding{85} ✾ \ding{94} ❇ \ding{103}✤ \ding{68} ✭ \ding{77} ✶ \ding{86} ✿ \ding{95} ❈ \ding{104}✥ \ding{69} ✮ \ding{78} ✷ \ding{87} ❀ \ding{96} ❉ \ding{105}✦ \ding{70} ✯ \ding{79} ✸ \ding{88} ❁ \ding{97} ❊ \ding{106}✧ \ding{71} ✰ \ding{80} ✹ \ding{89} ❂ \ding{98} ❋ \ding{107}★ \ding{72} ✱ \ding{81} ✺ \ding{90} ❃ \ding{99}✩ \ding{73} ✲ \ding{82} ✻ \ding{91} ❄ \ding{100}Table 238: wasysym Geometric Shapes⎔ \hexagon \octagon ⬠ \pentagon ⬡ \varhexagonTable 239: MnSymbol Geometric Shapes☀ \filledlargestar ◇ \largediamond ☆ \largestar ◊ \smalllozenge⧫ \filledlozenge ◊ \largelozenge ✡ \largestarofdavid⧫ \filledmedlozenge \largepentagram ◊ \medlozenge◯ \largecircle ◻ \largesquare ✡ \medstarofdavidMnSymbol defines \bigcirc as a synonym for \largecircle; \bigstar as a synonymfor \filledlargestar; \lozenge as a synonym for \medlozenge; and,\blacklozenge as a synonym for \filledmedlozenge.74

Table 240: ifsym Geometric Shapes% \BigCircle T \FilledBigTriangleRight E \SmallCircle \BigCross Q \FilledBigTriangleUp \SmallCross& \BigDiamondshape e \FilledCircle F \SmallDiamondshape \BigHBar ¨ \FilledDiamondShadowA \SmallHBar_ \BigLowerDiamond © \FilledDiamondShadowC \SmallLowerDiamond/ \BigRightDiamond f \FilledDiamondshape O \SmallRightDiamond\BigSquare u \FilledSmallCircle @ \SmallSquare# \BigTriangleDown v \FilledSmallDiamondshape C \SmallTriangleDown" \BigTriangleLeft p \FilledSmallSquare B \SmallTriangleLeft$ \BigTriangleRight s \FilledSmallTriangleDown D \SmallTriangleRight! \BigTriangleUp r \FilledSmallTriangleLeft A \SmallTriangleUp \BigVBar t \FilledSmallTriangleRight \SmallVBar5 \Circle q \FilledSmallTriangleUp * \SpinDown \Cross ` \FilledSquare ) \SpinUp¥ \DiamondShadowA £ \FilledSquareShadowA 0 \Square¦ \DiamondShadowB ¤ \FilledSquareShadowC \SquareShadowA§ \DiamondShadowC c \FilledTriangleDown ¡ \SquareShadowB6 \Diamondshape b \FilledTriangleLeft ¢ \SquareShadowCU \FilledBigCircle d \FilledTriangleRight 3 \TriangleDownV \FilledBigDiamondshape a \FilledTriangleUp 2 \TriangleLeftP \FilledBigSquare \HBar 4 \TriangleRightS \FilledBigTriangleDown o \LowerDiamond 1 \TriangleUpR \FilledBigTriangleLeft ? \RightDiamond \VBarThe ifsym documentation points out that one can use \rlap to combinesome of the above into useful, new symbols. For example, \BigCircle and\FilledSmallCircle combine to give “ u% ”. Likewise, \Square and \Cross combineto give “0”. See Section 7.3 for more information about constructing newsymbols out of existing symbols.Table 241: bbding Geometric Shapesd \CircleShadow u \Rectangle j \SquareShadowTopLefta \CircleSolid v \RectangleBold i \SquareShadowTopRightp \DiamondSolid t \RectangleThin g \SquareSolidb \Ellipse f \Square o \TriangleDowne \EllipseShadow k \SquareCastShadowBottomRight n \TriangleUpc \EllipseSolid m \SquareCastShadowTopLefts \HalfCircleLeft l \SquareCastShadowTopRightr \HalfCircleRight h \SquareShadowBottomRightTable 242: pifont Geometric Shapes● \ding{108} ❏ \ding{111} ❒ \ding{114} ◆ \ding{117} ❙ \ding{121}❍ \ding{109} ❐ \ding{112} ▲ \ding{115} ◗ \ding{119} ❚ \ding{122}■ \ding{110} ❑ \ding{113} ▼ \ding{116} ❘ \ding{120}75

Table 243: universa Geometric Shapes¡ \baucircle \bausquare ¢ \bautriangleTable 244: universal Geometric Shapes¤ \baucircle § \bauhole † \bausquare¨ \baueclipse … \baupunct £ \bautriangleTable 245: igo Go Stones} \blackstone[\igocircle] } \whitestone[\igocircle]| \blackstone[\igocross] | \whitestone[\igocross]\blackstone[\igonone] \whitestone[\igonone]~ \blackstone[\igosquare] ~ \whitestone[\igosquare] \blackstone[\igotriangle] \whitestone[\igotriangle]In addition to the symbols shown above, igo’s \blackstone and \whitestonecommands accept numbers from 1 to 99 and display them circled as ¡, ¢, £, . . .c and ¡, ¢, £, . . . c, respectively.The igo package is intended to typeset Go boards (goban). See the igo documentationfor more information.Table 246: manfnt Dangerous Bend Symbols \dbend \lhdbend \reversedvideodbendNote that these symbols descend far beneath the baseline. manfnt also defines nondescendingversions, which it calls, correspondingly, \textdbend, \textlhdbend,and \textreversedvideodbend.Table 247: skull SymbolsA \skullTable 248: Non-Mathematical mathabx SymbolsO \ripTable 249: marvosym Information Symbols® \Bicycle o \Football Z \PointinghandV \Checkedbox x \Gentsroom w \WheelchairU \Clocklogo I \Industry b \WritinghandK \Coffeecup i \InfoX \Crossedbox y \Ladiesroom76

Table 250: Miscellaneous dingbat DingbatsO \anchor E \eye S \SborderC \carriagereturn C \filledsquarewithdots B \squarewithdotsD \checkmark I \satellitedish Z \ZborderTable 251: Miscellaneous bbding Dingbats \Envelope \Peace © \PhoneHandset T \SunshineOpenCircledq \OrnamentDiamondSolid ¨ \Phone \Plane \TapeTable 252: Miscellaneous pifont Dingbats☎ \ding{37} ✈ \ding{40} ❤ \ding{164} ❧ \ding{167} ♠ \ding{171}✆ \ding{38} ✉ \ding{41} ❥ \ding{165} ♣ \ding{168} ♦ \ding{169}✇ \ding{39} ❖ \ding{118} ❦ \ding{166} ♥ \ding{170}77

6 Other symbolsThe following are all the symbols that didn’t fit neatly or unambiguously into any of the previous sections.(Do weather symbols belong under “Science and technology”? Should dice be considered “mathematics”?)While some of the tables contain clearly related groups of symbols (e.g., musical notes), others represent motleyassortments of whatever the font designer felt like drawing.Table 253: textcomp Genealogical Symbols \textborn \textdivorced \textmarried \textdied \textleafTable 254: wasysym General Symbols \ataribox \clock \LEFTarrow ☺ \smiley␇ \bell ⌀ \diameter \lightning ☼ \sun☻ \blacksmiley \DOWNarrow ☎ \phone \UParrow \Bowtie ☹ \frownie \pointer ◊ \wasylozenge \brokenvert \invdiameter ⌕ \recorder \checked \kreuz \RIGHTarrowTable 255: wasysym Circles \CIRCLE \LEFTcircle \RIGHTcircle \rightturn \Circle \Leftcircle \Rightcircle \LEFTCIRCLE \RIGHTCIRCLE \leftturnTable 256: wasysym Musical Symbols \eighthnote \halfnote ♫ \twonotes \fullnote ♩ \quarternoteSee also \flat, \sharp, and \natural (Table 184 on page 62).Table 257: arev Musical Symbols♩ \quarternote ♪ \eighthnote ♬ \sixteenthnoteSee also \flat, \sharp, and \natural (Table 184 on page 62).78

Table 258: harmony Musical Symbols=ˇ “ ˇ “ \AAcht DD/ \DDohne ˘ “ \Halb ˇ “== \SechBR > \VMˇ “ ( \Acht D/ \Dohne < \HaPa ˇ “==\SechBr ˇ “=* \Zwdrˇ “ \AchtBL ss \Ds ‰ \Pu @ \SePa A \ZwPaˇ “=\AchtBR SS \DS ˇ “ ) \Sech < \UB? \AcPa ¯==\Ganz ˇ “ \SechBL ˇ “=\VierDD \DD < \GaPa ˇ “ \SechBl > \ViPaThe musixtex package must be installed to use harmony.Table 259: harmony Musical AccentsA ⌢ . ⌢. a \Ferli{A}\Ferli{a} ∗ A/a/ \Ohne{A}\Ohne{a} ∗⌢. ⌢.A a \Fermi{A}\Fermi{a} Ã ã \Umd{A}\Umd{a}∗A ❧ a❧ \Kr{A}\Kr{a}∗ These symbols take an optional argument which shifts the accent either horizontallyor vertically (depending on the command) by the given distance.In addition to the accents shown above, \HH is a special accent commandwhich accepts five period-separated characters and typesets them such thatb cd”.“\HH.X.a.b.c.d.” produces “X a All arguments except the first can be omitted:“\HH.X.....” produces “X”. \Takt takes two arguments and composes theminto a musical time signature. For example, “\Takt{12}{8}” produces “ 12 8 ”. Astwo special cases, “\Takt{c}{0}” produces “S ” and “\Takt{c}{1}” produces “ R ”.The musixtex package must be installed to use harmony.Table 260: Miscellaneous manfnt Symbols \manboldkidney \manpenkidney \manconcentriccircles \manquadrifolium \manconcentricdiamond \manquartercircle \mancone \manrotatedquadrifolium \mancube \manrotatedquartercircle \manerrarrow \manstar \manfilledquartercircle \mantiltpennib \manhpennib \mantriangledown \manimpossiblecube \mantriangleright \mankidney \mantriangleup \manlhpenkidney \manvpennibTable 261: marvosym Navigation Symbols· \Forward » \MoveDown ´ \RewindToIndex ¼ \ToTop¸ \ForwardToEnd º \MoveUp µ \RewindToStart¹ \ForwardToIndex \Rewind ½ \ToBottom79

Table 262: marvosym Laundry SymbolsØ \AtForty Ü \Handwash Ô \ShortNinetyFiveÓ \AtNinetyFive ¯ \IroningI Ö \ShortSixtyÕ \AtSixty ° \IroningII Û \ShortThirtyË \Bleech ± \IroningIII Ú \SpecialForty« \CleaningA Ì \NoBleech \Tumbler¾ \CleaningF ¨ \NoChemicalCleaning ‰ \WashCotton¿ \CleaningFF ² \NoIroning Š \WashSynthetics¬ \CleaningP \NoTumbler ‹ \WashWool­ \CleaningPP × \ShortFiftyÝ \Dontwash Ù \ShortFortyTable 263: Other marvosym Symbolsˆ \Ankh † \Cross Œ \Heart © \Smileyý \Bat F \FHBOlogo ÿ \MartinVogel þ \Womanface¥ \Bouquet f \FHBOLOGO m \Mundus Y \Yinyang‡ \Celtcross § \Frowny @ \MVAtª \CircledA \FullFHBO : \MVRightarrowTable 264: Miscellaneous universa Symbols¤ \bauforms £ \bauheadTable 265: Miscellaneous universal Symbols¡ \baudash „ \bauforms © \bauquarter ƒ \varQ¢ \bauequal \bauhead \bauquestion \bauface \bauplus ¦ \bauwindowTable 266: ifsym Weather Symbols \Cloud \Hail \Sleet \WeakRain\FilledCloud \HalfSun \Snow \WeakRainCloud! \FilledRainCloud \Lightning \SnowCloud $ \FilledSnowCloud# \FilledSunCloud \NoSun \Sun" \FilledWeakRainCloud \Rain \SunCloud \Fog \RainCloud \ThinFogIn addition, \Thermo{0}. . .\Thermo{6} produce thermometers that are between0/6 and 6/6 full of mercury: ¥ ¦ § ¨ © Similarly, \wind{〈sun〉}{〈angle〉}{〈strength〉} will draw wind symbols with a givenamount of sun (0–4), a given angle (in degrees), and a given strength in km/h (0–100). For example, \wind{0}{0}{0} produces “ 0 ”, \wind{2}{0}{0} produces“¢0 ”, and \wind{4}{0}{100} produces “¤: ”.80

Table 267: ifsym Alpine Symbols\SummitSign \Summit \SurveySign \HalfFilledHut\StoneMan \Mountain \Joch \VarSummit\Hut \IceMountain \Flag\FilledHut \VarMountain \VarFlag\Village \VarIceMountain \TentTable 268: ifsym Clocks\Interval \StopWatchStart \VarClock \Wecker\StopWatchEnd \Taschenuhr \VarTaschenuhrifsym also exports a \showclock macro. \showclock{〈hours〉}{〈minutes〉} outputsa clock displaying the corresponding time. For instance, “\showclock{5}{40}”produces “ ”. 〈hours〉 must be an integer from 0 to 11, and 〈minutes〉 must be aninteger multiple of 5 from 0 to 55.Table 269: Other ifsym Symbols\FilledSectioningDiamond \Letter \Radiation\Fire \PaperLandscape \SectioningDiamond\Irritant \PaperPortrait \Telephone\StrokeOne \StrokeThree \StrokeFive\StrokeTwo\StrokeFourIn addition, \Cube{1}...\Cube{6} produce dice with the corresponding number ofspots:Table 270: epsdice Dice\epsdice{1} \epsdice{3} \epsdice{5}\epsdice{2} \epsdice{4} \epsdice{6}The epsdice package does not provide a font but rather an interface to a set ofgraphics drawn in Encapsulated PostScript. Consequently, epsdice does not workwith pdfL A TEX.81

Table 271: skak Chess Informator Symbolsg \bbetter d \doublepawns N \novelty R \variousi \bdecisive L \ending F \onlymove f \wbetterb \betteris j \equal o \opposbishops h \wdecisivea \bishoppair P \etc r \passedpawn J \weakpte \bupperhand H \file M \qside w \withI \centre O \kside s \samebishops A \withattackRR \comment x \markera l \see E \withidean \compensation y \markerb q \seppawns C \withinitV \counterplay m \mate T \timelimit v \withoutt \devadvantage S \morepawns k \unclear c \wupperhandG \diagonal U \moreroom u \unitedpawns D \zugzwangThe preceding symbols are merely the named informator symbol.skak cantypeset many more chess-related symbols, including those for all of the pieces(KQRBNP/kqrbnp), but only in the context of moves and boards, notas individual, named L A TEX symbols.× \a\B˘´\bTable 272: metre Metrical Symbols\bBm \cc\Mbb \Pppp ⊗ \t¯˘¯˘´\bbm\Ccc˘¯˘¯´˙¯˘¯˘˘¯˘¯˘¯˘ \mbbx \pppp\tsbm˙¯˘¯˘ ´ \Bbm\m ◦◦ \oo \Ppppp \tsmb¯\M\p ˙ \ppppp \tsmm¯´ ˙ \pm ˙ \ps\vppm\bm\Mb¯˙\pp\pxp¯˙\vpppm˘¯´\mb ˙ \Pp˙\Pxp¯˙\x˘¯ ˙˙´ \mBb \ppm ∼ \R ˙˙¯˙˙\ppp ∼ \r\Ppp ⊗ \T˘˘´˘ \Bb \bbmb˘¯˘¯˘˘˘´ \BB ¯˘¯˘¯˘¯ \bbmx ׯ \ma˘˘ \bb ¯˘˘˘´ \bB \Bm¯˘´×˘˘ \bba \c ˘¯˘¯˘˘˘ \bbb \C ˘¯˘¯´ \mbB ˙¯˘¯˘´ \BBm \Cc ˘¯˘¯ \mbb ˙The preceding symbols are valid only within the argument to the metre command.Table 273: metre Small and Large Metrical Symbols÷ \anaclasis ÷ \Anaclasis< \antidiple < \Antidiple \Diple>·· \diple* >·· \Diple*\obelus\Obelus· \obelus* · \Obelus*∼ \respondens ∼ \Respondens⊗ \terminus ⊗ \Terminus⊕ \terminus* ⊕ \Terminus*82

Table 274: phaistos Symbols from the Phaistos DiskJ \PHarrow e \PHeagle B \PHplumedHeadh \PHbee o \PHflute d \PHramX \PHbeehive H \PHgaunlet l \PHrosetteR \PHboomerang p \PHgrater P \PHsawK \PHbow G \PHhelmet L \PHshieldb \PHbullLeg a \PHhide Y \PHshipD \PHcaptive Z \PHhorn V \PHslingS \PHcarpentryPlane Q \PHlid r \PHsmallAxec \PHcat m \PHlily q \PHstrainerE \PHchild N \PHmanacles C \PHtattooedHeadM \PHclub O \PHmattock I \PHtiaraW \PHcolumn n \PHoxBack g \PHtunnyU \PHcomb k \PHpapyrus j \PHvineT \PHdolium A \PHpedestrian s \PHwavyBandf \PHdove i \PHplaneTree F \PHwomanTable 275: protosem Proto-Semitic Charactersa \Aaleph E \AAhe k \Akaph s \Asamekh R \AAreshA \AAaleph z \Azayin K \AAkaph p \Ape S \Ashinb \Abeth w \Avav l \Alamed P \AApe v \AhelmetB \AAbeth H \Aheth L \AAlamed x \Asade V \AAhelmetg \Agimel h \AAheth m \Amem X \AAsade t \Atavd \Adaleth T \Ateth n \Anun q \AqophD \AAdaleth y \Ayod o \Aayin Q \AAqophe \Ahe Y \AAyod O \AAayin r \AreshThe protosem package defines abbreviated control sequences for each of the above.In addition, single-letter shortcuts can be used within the argument to the\textproto command (e.g., “\textproto{Pakyn}” produces “Pakyn”). Seethe protosem documentation for more information.83

Table 276: hieroglf HieroglyphicsA \HA I \HI n \Hn T \HTa \Ha i \Hi O \HO t \HtB \HB ˝ \Hibl o \Ho ˘ \Htongueb \Hb ˆ \Hibp p \Hp U \HUc \Hc ¨ \Hibs P \HP u \HuC \HC ˜ \Hibw ˙ \Hplural V \HVD \HD J \HJ + \Hplus v \Hvd \Hd j \Hj Q \HQ | \Hvbar¸ \Hdual k \Hk q \Hq w \Hwe \He K \HK ? \Hquery W \HWE \HE L \HL R \HR X \HXf \Hf l \Hl r \Hr x \HxF \HF m \Hm s \Hs Y \HYG \HG M \HM S \HS y \Hyg \Hg ˇ \Hman ¯ \Hscribe z \Hzh \Hh ´ \Hms / \Hslash Z \HZH \HH N \HN ˚ \Hsv| \Hone 3 \Hhundred 5 \HXthousand 7 \Hmillion2 \Hten 4 \Hthousand 6 \HCthousandThe hieroglf package defines alternate control sequences and single-letter shortcutsfor each of the above which can be used within the argument to the \textpmhgcommand (e.g., “\textpmhg{Pakin}” produces “Pakin”). See the hieroglfdocumentation for more information.Table 277: dictsym Dictionary Symbolsa \dsaeronautical c \dscommercial m \dsmedicalG \dsagricultural H \dsheraldical X \dsmilitaryA \dsarchitectural J \dsjuridical R \dsrailwaysB \dsbiological L \dsliterary T \dstechnicalC \dschemical M \dsmathematical84

Table 278: simpsons Characters from The Simpsons¦ \Bart ¤ \Homer \Maggie ¡ \SNPP \Burns ¢ \Lisa ¨ \MargeThe location of the characters’ pupils can be controlled with the \Goofy command.See A METAFONT of ‘Simpsons’ characters [Che97] for more information. Also,each of the above can be prefixed with \Left to make the character face left insteadof right:§ \Left\BartTable 279: staves Magical Staves \staveI \staveXXIV \staveXLVII \staveII \staveXXV \staveXLVIII \staveIII \staveXXVI \staveXLIX \staveIV \staveXXVII \staveL \staveV \staveXXVIII \staveLI \staveVI \staveXXIX \staveLII \staveVII \staveXXX \staveLIII \staveVIII \staveXXXI \staveLIV \staveIX \staveXXXII \staveLV \staveX \staveXXXIII \staveLVI \staveXI \staveXXXIV \staveLVII \staveXII \staveXXXV \staveLVIII \staveXIII \staveXXXVI \staveLIX \staveXIV \staveXXXVII \staveLX \staveXV \staveXXXVIII \staveLXI \staveXVI \staveXXXIX \staveLXII85(continued on next page)

(continued from previous page) \staveXVII \staveXL \staveLXIII \staveXVIII \staveXLI \staveLXIV \staveXIX \staveXLII \staveLXV \staveXX \staveXLIII \staveLXVI \staveXXI \staveXLIV \staveLXVII \staveXXII \staveXLV \staveLXVIII \staveXXIII \staveXLVIThe meanings of these symbols are described on the Web site for the Museumof Icelandic Sorcery and Witchcraft at http://www.galdrasyning.is/index.php?option=com content&task=category&sectionid=5&id=18&Itemid=60 (TinyURL: http://tinyurl.com/25979m). For example, \staveL (“”) isintended to ward off ghosts and evil spirits.86

7 Additional InformationUnlike the previous sections of this document, Section 7 does not contain new symbol tables. Rather, it providesadditional help in using the Comprehensive L A TEX Symbol List. First, it draws attention to symbol names usedby multiple packages. Next, it provides some guidelines for finding symbols and gives some examples regardinghow to construct missing symbols out of existing ones. Then, it comments on the spacing surrounding symbolsin math mode. After that, it presents an ASCII and Latin 1 quick-reference guide, showing how to enter all ofthe standard ASCII/Latin 1 symbols in L A TEX. And finally, it lists some statistics about this document itself.7.1 Symbol Name ClashesUnfortunately, a number of symbol names are not unique; they appear in more than one package. Dependingon how the symbols are defined in each package, L A TEX will either output an error message or replace anearlier-defined symbol with a later-defined symbol. Table 280 presents a selection of name clashes that appearin this document.Using multiple symbols with the same name in the same document—or even merely loading conflictingsymbol packages—can be tricky but, as evidenced by the existence of Table 280, not impossible. The generalprocedure is to load the first package, rename the conflicting symbols, and then load the second package.Examine the L A TEX source for this document (symbols.tex) for examples of this and other techniques forhandling symbol conflicts. Note that symbols.tex’s \savesymbol and \restoresymbol macros have beenextracted into the savesym package, which can be downloaded from CTAN.txfonts and pxfonts redefine a huge number of symbols—essentially, all of the symbols defined by latexsym,textcomp, the various AMS symbol sets, and L A TEX 2ε itself. Similarly, mathabx redefines a vast number ofmath symbols in an attempt to improve their look. The txfonts, pxfonts, and mathabx conflicts are not listedin Table 280 because they are designed to be compatible with the symbols they replace. Table 281 on page 89illustrates what “compatible” means in this context.To use the new txfonts/pxfonts symbols without altering the document’s main font, merely reset the defaultfont families back to their original values after loading one of those packages:\renewcommand\rmdefault{cmr}\renewcommand\sfdefault{cmss}\renewcommand\ttdefault{cmtt}7.2 Resizing symbolsMathematical symbols listed in this document as “variable-sized” are designed to stretch vertically. Eachvariable-sized symbol comes in one or more basic sizes plus a variation comprising both stretchable andnonstretchable segments. Table 282 on page 89 presents the symbols \} and \uparrow in their default size,in their \big, \Big, \bigg, and \Bigg sizes, in an even larger size achieved using \left/\right, and—forcontrast—in a large size achieved by changing the font size using L A TEX 2ε’s \fontsize command. Becausethe symbols shown belong to the Computer Modern family, the type1cm package needs to be loaded to supportfont sizes larger than 24.88 pt.Note how \fontsize makes the symbol wider and thicker. (The graphicx package’s \scalebox or\resizebox commands would produce a similar effect.) Also, the \fontsize-enlarged symbol is verticallycentered relative to correspondingly large text, unlike the symbols enlarged using \big et al. or \left/\right,which all use the same math axis regardless of symbol size. However, \fontsize is not limited to mathematicaldelimiters. Also, \scalebox and \resizebox are more robust to poorly composed symbols (e.g., two symbolsmade to overlap by backspacing a fixed distance) but do not work with every TEX backend and will producejagged symbols when scaling a bitmapped font.All variable-sized delimiters are defined (by the corresponding .tfm file) in terms of up to five segments, asillustrated by Figure 1 on page 89. The top, middle, and bottom segments are of a fixed size. The top-middleand middle-bottom segments (which are constrained to be the same character) are repeated as many times asnecessary to achieve the desired height.7.3 Where can I find the symbol for . . . ?If you can’t find some symbol you’re looking for in this document, there are a few possible explanations:87

Table 280: Symbol Name ClashesSymbol L A TEX 2ε AMS stmaryrd wasysym mathabx marvosym bbding ifsym dingbat wsuipa\baro▽

Table 281: Example of a Benign Name ClashSymbolDefault(Computer Modern)txfonts(Times Roman)R R R\textrecipe Table 282: Sample resized delimitersSymbol Default size \big \Big \bigg \Bigg \left / \right \fontsize}⎫} } }⎪⎬\} }⎪⎭↑↑↑ ↑ ↑ ↑\uparrow ↑ ⏐⏐⏐⏐⏐⎫⎪⎬−→⎪⎭⎫⎪⎬⎪⎭toptop-middle (extensible)middlemiddle-bottom (extensible)bottomFigure 1: Implementation of variable-sized delimiters89

• The symbol isn’t intuitively named. As a few examples, the ifsym command to draw dice is “\Cube”; aplus sign with a circle around it (“exclusive or” to computer engineers) is “\oplus”; and lightning boltsin fonts designed by German speakers may have “blitz” in their names as in the ulsy package. The moralof the story is to be creative with synonyms when searching the index.• The symbol is defined by some package that I overlooked (or deemed unimportant). If there’s somesymbol package that you think should be included in the Comprehensive L A TEX Symbol List, please sendme e-mail at the address listed on the title page.• The symbol isn’t defined in any package whatsoever.Even in the last case, all is not lost. Sometimes, a symbol exists in a font, but there is no L A TEX bindingfor it. For example, the PostScript Symbol font contains a “↵” symbol, which may be useful for representinga carriage return, but there is no package (as far as I know) for accessing that symbol. To produce anunnamed symbol, you need to switch to the font explicitly with L A TEX 2ε’s low-level font commands [L A T00]and use TEX’s primitive \char command [Knu86a] to request a specific character number in the font. 4 In fact,\char is not strictly necesssary; the character can often be entered symbolically. For example, the symbolfor an impulse train or Tate-Shafarevich group (“X”) is actually an uppercase sha in the Cyrillic alphabet.(Cyrillic is supported by the OT2 font encoding, for instance). While a sha can be defined numerically as“{\fontencoding{OT2}\selectfont\char88}” it may be more intuitive to use the OT2 font encoding’s “SH”ligature: “{\fontencoding{OT2}\selectfont SH}”.Reflecting and rotating existing symbolsA common request on comp.text.tex is for a reversed or rotated version of an existing symbol.As a last resort, these effects can be achieved with the graphicx (or graphics) package’s \reflectbox and\rotatebox macros. For example, \textsuperscript{\reflectbox{?}} produces an irony mark (“ ”;cf. http://en.wikipedia.org/wiki/Irony mark), and \rotatebox[origin=c]{180}{$\iota$} produces thedefinite-description operator (“ ”). The disadvantage of the graphicx/graphics approach is that not every TEXbackend handles graphical transformations. 5 Far better is to find a suitable font that contains the desiredsymbol in the correct orientation. For instance, if the phonetic package is available, then \textit{\riota}will yield a backend-independent “ ”. Similarly, tipa’s \textrevepsilon (“3”) or wsuipa’s \revepsilon (“”)may be used to express the mathematical notion of “such that” in a cleaner manner than with \reflectboxor \rotatebox. 6Joining and overlapping existing symbolsιSymbols that do not exist in any font can sometimes be fabricated out of existing symbols. The L A TEX 2ε sourcefile fontdef.dtx contains a number of such definitions. For example, \models (see Table 62 on page 30) isdefined in that file with:\def\models{\mathrel|\joinrel=}where \mathrel and \joinrel are used to control the horizontal spacing. \def is the TEX primitive uponwhich L A TEX’s \newcommand is based. See The TEXbook [Knu86a] for more information on all three of thosecommands.With some simple pattern-matching, one can easily define a backward \models sign (“=|”):\def\ismodeledby{=\joinrel\mathrel|}In general, arrows/harpoons, horizontal lines (“=”, “-”, “\relbar”, and “\Relbar”), and the various mathextensioncharacters can be combined creatively with miscellaneous other characters to produce a variety ofnew symbols. Of course, new symbols can be composed from any set of existing characters. For instance, L A TEXdefines \hbar (“”) as a “¯” character (\mathchar’26) followed by a backspace of 9 math units (\mkern-9mu),followed by the letter “h”:\def\hbar{{\mathchar’26\mkern-9muh}}4 pifont defines a convenient \Pisymbol command for accessing symbols in PostScript fonts by number. For example,“\Pisymbol{psy}{191}” produces “↵”.5 As an example, Xdvi ignores both \reflectbox and \rotatebox.6 More common symbols for representing “such that” include “|”, “:”, and “s.t.”.?90

We can just as easily define other barred letters:\def\bbar{{\mathchar’26\mkern-9mu b}}\def\dbar{{\mathchar’26\mkern-12mu d}}(The space after the “mu” is optional but is added for clarity.) \bbar and \dbar define “¯b” and “¯d”, respectively.Note that \dbar requires a greater backward math kern than \bbar; a −9 mu kern would have produced theless-attractive “¯d” glyph.The amsmath package provides \overset and \underset commands for placing one symbol respectivelyabove or below another. For example, \overset{G}{\sim} 7 produces “ G ∼” (sometimes used for “equidecomposablewith respect to G”).Sometimes an ordinary tabular environment can be co-opted into juxtaposing existing symbols into a newsymbol. Consider the following definition of \asterism (“ * ** ”) from a June 2007 post to comp.text.tex byPeter Flynn:\newcommand{\asterism}{\smash{%\raisebox{-.5ex}{%\setlength{\tabcolsep}{-.5pt}%\begin{tabular}{@{}cc@{}}%\multicolumn2c*\\[-2ex]*&*%\end{tabular}}}}Note how the space between columns (\tabcolsep) and rows (\\[. . . ]) is made negative to squeeze theasterisks closer together.There is a TEX primitive called \mathaccent that centers one mathematical symbol atop another. Forexample, one can define \dotcup (“ ·∪”)—the composition of a \cup and a \cdot—as follows:\newcommand{\dotcup}{\ensuremath{\mathaccent\cdot\cup}}The catch is that \mathaccent requires the accent to be a “math character”. That is, it must be a characterin a math font as opposed to a symbol defined in terms of other symbols. See The TEXbook [Knu86a] for moreinformation.Another TEX primitive that is useful for composing symbols is \vcenter. \vcenter is conceptually similarto “\begin{tabular}{l}” in L A TEX but takes a list of vertical material instead of \\-separated rows. Also,it vertically centers the result on the math axis. (Many operators, such as “+” and “−” are also verticallycentered on the math axis.) Enrico Gregorio posted the following symbol definition to comp.text.tex inMarch 2004 in response to a query about an alternate way to denote equivalence:\newcommand*{\threesim}{%\mathrel{\vcenter{\offinterlineskip\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}}The \threesim symbol, which vertically centers three \sim (“∼”) symbols with 0.35 x-heights of space betweenthem, is rendered as “∼”. \offinterlineskip is a macro that disables implicit interline spacing. Withoutit, \threesim would have a full line of vertical spacing between each \sim. Because of \vcenter, \threesimaligns properly with other math operators: a ÷ b ∼ c × d.A related L A TEX command, borrowed from Plain TEX, is \ooalign. \ooalign vertically overlaps symbolsand works both within and outside of math mode. Essentially, it creates a single-column tabular environmentwith zero vertical distance between rows. However, because it is based directly on TEX’s \ialign primitive,\ooalign uses TEX’s tabular syntax instead of L A TEX’s (i.e., with \cr as the row terminator instead of \\). Thefollowing example of \ooalign, a macro that defines a standard-state symbol (\stst, “ −◦ ”) as a superscriptedPlimsoll line (\barcirc, “−◦ ”), 8 is due to an October 2007 comp.text.tex post by Donald Arseneau:\makeatletter\providecommand\barcirc{\mathpalette\@barred\circ}\def\@barred#1#2{\ooalign{\hfil$#1-$\hfil\cr\hfil$#1#2$\hfil\cr}}\newcommand\stst{^{\protect\barcirc}}\makeatother7 LATEX’s \stackrel command is similar but is limited to placing a symbol above a binary relation.8 While \barcirc illustrates how to combine symbols using \ooalign, the stmaryrd package’s \minuso command (Table 42 onpage 21) provides a similar glyph (“”) as a single, indivisible symbol.91

In the preceding code, note the \ooalign call’s use of \hfil to horizontally center a minus sign (“−”) anda \circ (“◦”).As another example of \ooalign, consider the following code (due to Enrico Gregorio in a June 2007 postto comp.text.tex) that overlaps a \ni (“∋”) and two minus signs (“ −”) to produce “∋−”, an obscure variationon the infrequently used “3” symbol for “such that”discussed on page 90:\newcommand{\suchthat}{%\mathrel{\ooalign{$\ni$\cr\kern-1pt$-$\kern-6.5pt$-$}}}The slashed package, although originally designed for producing Feynman slashed-character notation, infact facilitates the production of arbitrary overlapped symbols. The default behavior is to overwrite a givencharacter with “/”. For example, \slashed{D} produces “ /D”. However, the \declareslashed commandprovides the flexibility to specify the mathematical context of the composite character (operator, relation,punctuation, etc., as will be discussed in Section 7.4), the overlapping symbol, horizontal and vertical adjustmentsin symbol-relative units, and the character to be overlapped. Consider, for example, the symbol forreduced quadrupole moment (“Ī”). This can be declared as follows:\newcommand{\rqm}{{%\declareslashed{}{\text{-}}{0.04}{0}{I}\slashed{I}}}\declareslashed{·}{·}{·}{·}{I} affects the meaning of all subsequent \slashed{I} commands in the samescope. The preceding definition of \rqm therefore uses an extra set of curly braces to limit that scope toa single \slashed{I}. In addition, \rqm uses amstext’s \text macro (described on the next page) to make\declareslashed use a text-mode hyphen (“-”) instead of a math-mode minus sign (“−”) and to ensure thatthe hyphen scales properly in size in subscripts and superscripts. See slashed’s documentation (located inslashed.sty itself) for a detailed usage description of the \slashed and \declareslashed commands.Somewhat simpler than slashed is the centernot package. centernot provides a single command, \centernot,which, like \not, puts a slash over the subsequent mathematical symbol. However, instead of putting the slashat a fixed location, \centernot centers the slash over its argument:̸−→−→ ̸\not\longrightarrowvs.\centernot\longrightarrowSee the centernot documentation for more information.Making new symbols work in superscripts and subscriptsTo make composite symbols work properly within subscripts and superscripts, you may need to use TEX’s\mathchoice primitive. \mathchoice evaluates one of four expressions, based on whether the current mathstyle is display, text, script, or scriptscript. (See The TEXbook [Knu86a] for a more complete description.)For example, the following L A TEX code—posted to comp.text.tex by Torsten Bronger—composesa sub/superscriptable “⊥⊤” symbol out of \top and \bot (“⊤” and “⊥”):\def\topbotatom#1{\hbox{\hbox to 0pt{$#1\bot$\hss}$#1\top$}}\newcommand*{\topbot}{\mathrel{\mathchoice{\topbotatom\displaystyle}{\topbotatom\textstyle}{\topbotatom\scriptstyle}{\topbotatom\scriptscriptstyle}}}The following is another example that uses \mathchoice to construct symbols in different math modes.The code defines a principal value integral symbol, which is an integral sign with a line through it.\def\Xint#1{\mathchoice{\XXint\displaystyle\textstyle{#1}}%{\XXint\textstyle\scriptstyle{#1}}%{\XXint\scriptstyle\scriptscriptstyle{#1}}%{\XXint\scriptscriptstyle\scriptscriptstyle{#1}}%\!\int}92

\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$}\vcenter{\hbox{$#2#3$}}\kern-.5\wd0}}\def\ddashint{\Xint=}\def\dashint{\Xint-}(The preceding code was taken verbatim from the UK TEX ∫ Users’ Group FAQ at http://www.tex.ac.uk/faq.) \dashint produces a single-dashed integral sign (“−∫ ”), while \ddashint produces a double-dashed ∫one (“= ”). The \Xint macro ∫ defined above can also be used ∫ to generate a wealth ∫ of new integrals: “”(\Xint\circlearrowright), “ ” (\Xint\circlearrowleft), “⊂” (\Xint\subset), “∞” (\Xint\infty), andso forth.L A TEX 2ε provides a simple wrapper for \mathchoice that sometimes helps produce terser symbol definitions.The macro is called \mathpalette and it takes two arguments. \mathpalette invokes the firstargument, passing it one of “\displaystyle”, “\textstyle”, “\scriptstyle”, or “\scriptscriptstyle”,followed by the second argument. \mathpalette is useful when a symbol macro must know which mathstyle is currently in use (e.g., to set it explicitly within an \mbox). Donald Arseneau posted the following\mathpalette-based definition of a probabilistic-independence symbol (“⊥”) to comp.text.tex in June 2000:\newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}}\def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}The \independent macro uses \mathpalette to pass the \independenT helper macro both the current mathstyle and the \perp symbol. \independenT typesets \perp in the current math style, moves two math units tothe right, and finally typesets a second—overlapping—copy of \perp, again in the current math style. \rlap,which enables text overlap, is described later on this page.Some people like their square-root signs with a trailing “hook” (i.e., “ √ ”) as this helps visually distinguishexpressions like “ √ 3x ” from those like “ √ 3x”. In March 2002, Dan Luecking posted a \mathpalette-baseddefinition of a hooked square-root symbol to comp.text.tex:\def\hksqrt{\mathpalette\DHLhksqrt}\def\DHLhksqrt#1#2{\setbox0=\hbox{$#1\sqrt{#2\,}$}\dimen0=\ht0\advance\dimen0-0.2\ht0\setbox2=\hbox{\vrule height\ht0 depth -\dimen0}%{\box0\lower0.4pt\box2}}Notice how \DHLhksqrt uses \mathpalette to recover the outer math style (argument #1) from within an\hbox. The rest of the code is simply using TEX primitives to position a hook of height 0.2 times the \sqrtheight at the right of the \sqrt. See The TEXbook [Knu86a] for more understanding of TEX “boxes” and“dimens”.Sometimes, however, amstext’s \text macro is all that is necessary to make composite symbols appearcorrectly in subscripts and superscripts, as in the following definitions of \neswarrow (“↗↙”) and \nwsearrow(“↖↘”): 9\newcommand{\neswarrow}{\mathrel{\text{$\nearrow$\llap{$\swarrow$}}}}\newcommand{\nwsearrow}{\mathrel{\text{$\nwarrow$\llap{$\searrow$}}}}\text resembles L A TEX’s \mbox command but shrinks its argument appropriately when used within a subscriptor superscript. \llap (“left overlap”) and its counterpart, \rlap (“right overlap”), appear frequently whencreating composite characters. \llap outputs its argument to the left of the current position, overlappingwhatever text is already there. Similarly, \rlap overlaps whatever text would normally appear to the rightof its argument. For example, “A\llap{B}” and “\rlap{A}B” each produce “AB”. However, the result of theformer is the width of “A”, and the result of the latter is the width of “B”—\llap{. . . } and \rlap{. . . } takeup zero space.In a June 2002 post to comp.text.tex, Donald Arseneau presented a general macro for aligning an arbitrarynumber of symbols on their horizontal centers and vertical baselines:\makeatletter\def\moverlay{\mathpalette\mov@rlay}9 Note that if your goal is to typeset commutative diagrams, then you should probably be using XY-pic.93

\def\mov@rlay#1#2{\leavevmode\vtop{%\baselineskip\z@skip \lineskiplimit-\maxdimen\ialign{\hfil$#1##$\hfil\cr#2\crcr}}}\makeatotherThe \makeatletter and \makeatother commands are needed to coerce L A TEX into accepting “@” aspart of a macro name. \moverlay takes a list of symbols separated by \cr (TEX’s equivalent ofL A TEX’s \\). For example, the \topbot command defined on page 92 could have been expressed as“\moverlay{\top\cr\bot}” and the \neswarrow command defined on the previous page could have beenexpressed as “\moverlay{\nearrow\cr\swarrow}”.The basic concept behind \moverlay’s implementation is that \moverlay typesets the given symbols in atable that utilizes a zero \baselineskip. This causes every row to be typeset at the same vertical position.See The TEXbook [Knu86a] for explanations of the TEX primitives used by \moverlay.Modifying L A TEX-generated symbolsOftentimes, symbols composed in the L A TEX 2ε source code can be modified with minimal effort to produceuseful variations. For example, fontdef.dtx composes the \ddots symbol (see Table 174 on page 61) out ofthree periods, raised 7 pt., 4 pt., and 1 pt., respectively:\def\ddots{\mathinner{\mkern1mu\raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern2mu\raise4\p@\hbox{.}\mkern2mu\raise\p@\hbox{.}\mkern1mu}}\p@ is a L A TEX 2ε shortcut for “pt” or “1.0pt”. The remaining commands are defined in TheTEXbook [Knu86a]. To draw a version of \ddots with the dots going along the opposite diagonal, we merelyhave to reorder the \raise7\p@, \raise4\p@, and \raise\p@:\makeatletter\def\revddots{\mathinner{\mkern1mu\raise\p@\vbox{\kern7\p@\hbox{.}}\mkern2mu\raise4\p@\hbox{.}\mkern2mu\raise7\p@\hbox{.}\mkern1mu}}\makeatother\revddots is essentially identical to the mathdots package’s \iddots command or the yhmath package’s \adotscommand.Producing complex accentsAccents are a special case of combining existing symbols to make new symbols. While various tables inthis document show how to add an accent to an existing symbol, some applications, such as transliterationsfrom non-Latin alphabets, require multiple accents per character. For instance, the creator of pdfTEXwrites his name as “Hàn Th´ê Thành”. The dblaccnt package enables L A TEX to stack accents, as in “H\‘anTh\’{\^e} Th\‘anh” (albeit not in the OT1 font encoding). In addition, the wsuipa package defines \diatopand \diaunder macros for putting one or more diacritics or accents above or below a given character. Forexample, \diaunder[{\diatop[\’|\=]}|\textsubdot{r}] produces “´¯ṙ”. See the wsuipa documentation formore information.The accents package facilitates the fabrication of accents in math mode. Its \accentset command enablesany character to be used as an accent. For instance, \accentset{\star}{f} produces “ f ⋆” and\accentset{e}{X} produces “ X”. e \underaccent does the same thing, but places the accent beneath thecharacter. This enables constructs like \underaccent{\tilde}{V}, which produces “Ṽ ”. accents providesother accent-related features as well; see the documentation for more information.Creating extensible symbolsA relatively simple example of creating extensible symbols stems from a comp.text.tex post by DonaldArseneau (June 2003). The following code defines an equals sign that extends as far to the right as possible,just like L A TEX’s \hrulefill command:94

\makeatletter\def\equalsfill{$\m@th\mathord=\mkern-7mu\cleaders\hbox{$\!\mathord=\!$}\hfill\mkern-7mu\mathord=$}\makeatotherTEX’s \cleaders and \hfill primitives are the key to understanding \equalsfill’s extensibility. Essentially,\equalsfill repeats a box containing “=” plus some negative space until it fills the maximum availablehorizontal space. \equalsfill is intended to be used with L A TEX’s \stackrel command, which stacksone mathematical expression (slightly reduced in size) atop another. Hence, “\stackrel{a}{\rightarrow}”produces “ →” a and “X \stackrel{\text{definition}}{\hbox{\equalsfill}} Y” produces “X definition======= Y ”.If all that needs to extend are horizontal and vertical lines—as opposed to repeated symbols such as the“=” in the previous example—L A TEX’s array or tabular environments may suffice. Consider the followingcode (due to a February 1999 comp.text.tex post by Donald Arseneau) for typesetting annuities:\DeclareRobustCommand{\annu}[1]{_{%\def\arraystretch{0}%\setlength\arraycolsep{1pt}%\setlength\arrayrulewidth{.2pt}%\begin{array}[b]{@{}c|}\hline\\[\arraycolsep]%\scriptstyle #1%\end{array}%}}adjust thesetwo settingsOne can then use, e.g., “$A\annu{x:n}$” to produce “A x:n ”.A more complex example of composing accents is the following definition of extensible \overbracket,\underbracket, \overparenthesis, and \underparenthesis symbols, taken from a May 2002comp.text.tex post by Donald Arseneau:\makeatletter\def\overbracket#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern3\p@}\downbracketfill\crcr\noalign{\kern3\p@\nointerlineskip}$\hfil\displaystyle{#1}\hfil$\crcr}}}\limits}\def\underbracket#1{\mathop{\vtop{\ialign{##\crcr$\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip}\upbracketfill\crcr\noalign{\kern3\p@}}}}\limits}\def\overparenthesis#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern3\p@}\downparenthfill\crcr\noalign{\kern3\p@\nointerlineskip}$\hfil\displaystyle{#1}\hfil$\crcr}}}\limits}\def\underparenthesis#1{\mathop{\vtop{\ialign{##\crcr$\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip}\upparenthfill\crcr\noalign{\kern3\p@}}}}\limits}\def\downparenthfill{$\m@th\braceld\leaders\vrule\hfill\bracerd$}\def\upparenthfill{$\m@th\bracelu\leaders\vrule\hfill\braceru$}\def\upbracketfill{$\m@th\makesm@sh{\llap{\vrule\@height3\p@\@width.7\p@}}%\leaders\vrule\@height.7\p@\hfill\makesm@sh{\rlap{\vrule\@height3\p@\@width.7\p@}}$}\def\downbracketfill{$\m@th\makesm@sh{\llap{\vrule\@height.7\p@\@depth2.3\p@\@width.7\p@}}%\leaders\vrule\@height.7\p@\hfill\makesm@sh{\rlap{\vrule\@height.7\p@\@depth2.3\p@\@width.7\p@}}$}\makeatotherTable 283 showcases these accents. The TEXbook [Knu86a] or another book on TEX primitives is indispensiblefor understanding how the preceding code works. The basic idea is that \downparenthfill, \upparenthfill,\downbracketfill, and \upbracketfill do all of the work; they output a left symbol (e.g., \braceld [“{”]for \downparenthfill), a horizontal rule that stretches as wide as possible, and a right symbol (e.g., \bracerd[“{”] for \downparenthfill). \overbracket, \underbracket, \overparenthesis, and \underparenthesis95

merely create a table whose width is determined by the given text, thereby constraining the width of thehorizontal rules.abcTable 283: Manually Composed Extensible Accents{ {\overbracket{abc} abc \overparenthesis{abc}abc \underbracket{abc} abc} }\underparenthesis{abc}Note that the simplewick package provides mechanisms for typesetting Wick contractions, which utilize\overbracket- and \underbracket-like brackets of variable width and height (or depth). For example,“\acontraction{}{A}{B}{C}\acontraction[2ex]{A}{B}{C}{D}\bcontraction{}{A}{BC}{D}ABCD”producesABCD .See the simplewick documentation for more information.Developing new symbols from scratchSometimes is it simply not possible to define a new symbol in terms of existing symbols. Fortunately, most, ifnot all, TEX distributions are shipped with a tool called METAFONT which is designed specifically for creatingfonts to be used with TEX. The METAFONTbook [Knu86b] is the authoritative text on METAFONT. If youplan to design your own symbols with METAFONT, The METAFONTbook is essential reading. Nevertheless, thefollowing is an extremely brief tutorial on how to create a new L A TEX symbol using METAFONT. Its primarypurpose is to cover the L A TEX-specific operations not mentioned in The METAFONTbook and to demonstratethat symbol-font creation is not necessarily a difficult task.Suppose we need a symbol to represent a light bulb (“A”). 10 The first step is to draw this in METAFONT.It is common to separate the font into two files: a size-dependent file, which specifies the design size andvarious font-specific parameters that are a function of the design size; and a size-independent file, which drawscharacters in the given size. Figure 2 shows the METAFONT code for lightbulb10.mf. lightbulb10.mfspecifies various parameters that produce a 10 pt. light bulb then loads lightbulb.mf. Ideally, one shouldproduce lightbulb〈size〉.mf files for a variety of 〈size〉s. This is called “optical scaling”. It enables, forexample, the lines that make up the light bulb to retain the same thickness at different font sizes, which looksmuch nicer than the alternative—and default—“mechanical scaling”. When a lightbulb〈size〉.mf file doesnot exist for a given size 〈size〉, the computer mechanically produces a wider, taller, thicker symbol:A vs. A vs. A vs. A vs.A vs.A vs.A10 pt. 20 pt. 30 pt. 40 pt. 50 pt. 60 pt. 70 pt.font identifier := "LightBulb10";font size 10pt # ;em # := 10pt # ;cap # := 7pt # ;sb # := 1 / 4 pt # ;o # := 1 / 16 pt # ;input lightbulb% Name the font.% Specify the design size.% “M” width is 10 points.% Capital letter height is 7 points above the baseline.% Leave this much space on the side of each character.% Amount that curves overshoot borders.% Load the file that draws the actual glyph.Figure 2: Sample METAFONT size-specific file (lightbulb10.mf)lightbulb.mf, shown in Figure 3, draws a light bulb using the parameters defined in lightbulb10.mf.Note that the the filenames “lightbulb10.mf” and “lightbulb.mf” do not follow the Berry font-naming10 I’m not a very good artist; you’ll have to pretend that “A” looks like a light bulb.96

scheme [Ber01]; the Berry font-naming scheme is largely irrelevant for symbol fonts, which generally lack bold,italic, small-caps, slanted, and other such variants.mode setup;define pixels(em, cap, sb);define corrected pixels(o);%% Define a light bulb at the character position for “A”%% with width 1 / 2 em # , height cap # , and depth 1pt # .beginchar("A", 1 / 2 em # , cap # , 1pt # ); "A light bulb";pickup pencircle scaled 1 / 2 pt;%% Define the points we need.top z 1 = (w/2, h + o);rt z 2 = (w + sb + o − x 4 , y 4 );bot z 3 = (z 1 − (0, w − sb − o));lft z 4 = (sb − o, 1 / 2 [y 1 , y 3 ]);path bulb;bulb = z 1 . . z 2 . . z 3 . . z 4 . . cycle;% Target a given printer.% Convert to device-specific units.% Same, but add a device-specific fudge factor.% Use a pen with a small, circular tip.% z 1 is at the top of a circle.% z 2 is at the same height as z 4 but the opposite side.% z 3 is at the bottom of the circle.% z 4 is on the left of the circle.% Define a path for the bulb itself.% The bulb is a closed path.z 5 = point 2 − 1 / 3 of bulb; % z 5 lies on the bulb, a little to the right of z 3 .z 6 = (x 5 , 0); % z 6 is at the bottom, directly under z 5 .z 7 = (x 8 , 0); % z 7 is at the bottom, directly under z 8 .z 8 = point 2 + 1 / 3 of bulb; % z 8 lies on the bulb, a little to the left of z 3 .bot z 67 = ( 1 / 2 [x 6 , x 7 ], pen bot − o − 1 / 8 pt); % z 67 lies halfway between z 6 and z 7 but a jot lower.%% Draw the bulb and the base.draw bulb;draw z 5 - - z 6 . . z 67 . . z 7 - - z 8 ;% Draw the bulb proper.% Draw the base of the bulb.%% Display key positions and points to help us debug.makegrid(0, sb, w/2, w − sb)(0, −1pt, y 2 , h); % Label “interesting” x and y coordinates.penlabels(1, 2, 3, 4, 5, 6, 67, 7, 8);% Label control points for debugging.endchar;endFigure 3: Sample METAFONT size-independent file (lightbulb.mf)The code in Figures 2 and 3 is heavily commented and should demonstrate some of the basic conceptsbehind METAFONT usage: declaring variables, defining points, drawing lines and curves, and preparing todebug or fine-tune the output. Again, The METAFONTbook [Knu86b] is the definitive reference on META-FONT programming.METAFONT can produce “proofs” of fonts—large, labeled versions that showcase the logical structure ofeach character. In fact, proof mode is METAFONT’s default mode. To produce a proof of lightbulb10.mf,issue the following commands at the operating-system prompt:prompt> mf lightbulb10.mf ⇐ Produces lightbulb10.2602gfprompt> gftodvi lightbulb10.2602gf ⇐ Produces lightbulb10.dviYou can then view lightbulb10.dvi with any DVI viewer. The result is shown in Figure 4. Observe how thegrid defined with makegrid at the bottom of Figure 3 draws vertical lines at positions 0, sb, w/2, and w − sband horizontal lines at positions 0, −1pt, y 2 , and h. Similarly, observe how the penlabels command labels allof the important coordinates: z 1 , z 2 , . . . , z 8 and z 67 , which lightbulb.mf defines to lie between z 6 and z 7 .Most, if not all, TEX distributions include a Plain TEX file called testfont.tex which is useful for testingnew fonts in a variety of ways. One useful routine produces a table of all of the characters in the font:prompt> tex testfontThis is TeX, Version 3.14159 (Web2C 7.3.1)(/usr/share/texmf/tex/plain/base/testfont.texName of the font to test = lightbulb1097

1428357676Figure 4: Proof diagram of lightbulb10.mfNow type a test command (\help for help):)*\table*\bye[1]Output written on testfont.dvi (1 page, 1516 bytes).Transcript written on testfont.log.The resulting table, stored in testfont.dvi and illustrated in Figure 5, shows every character in the font.To understand how to read the table, note that the character code for “A”—the only character defined bylightbulb10.mf—is 41 in hexadecimal (base 16) and 101 in octal (base 8).Test of lightbulb10 on March 11, 2003 at 1127´0 ´1 ´2 ´3 ´4 ´5 ´6 ´7´10x A´11x˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F˝4xFigure 5: Font table produced by testfont.texThe LightBulb10 font is now usable by TEX. L A TEX 2ε, however, needs more information before documentscan use the font. First, we create a font-description file that tells L A TEX 2ε how to map fonts in a given fontfamily and encoding to a particular font in a particular font size. For symbol fonts, this mapping is fairly simple.Symbol fonts almost always use the “U” (“Unknown”) font encoding and frequently occur in only one variant:normal weight and non-italicized. The filename for a font-description file important; it must be of the form“〈encoding〉〈family〉.fd”, where 〈encoding〉 is the lowercase version of the encoding name (typically “u” forsymbol fonts) and 〈family〉 is the name of the font family. For LightBulb10, let’s call this “bulb”. Figure 6 liststhe contents of ubulb.fd. The document “L A TEX 2ε Font Selection” [L A T00] describes \DeclareFontFamilyand \DeclareFontShape in detail, but the gist of ubulb.fd is first to declare a U-encoded version of the bulbfont family and then to specify that a L A TEX 2ε request for a U-encoded version of bulb with a (m)edium fontseries (as opposed to, e.g., bold) and a (n)ormal font shape (as opposed to, e.g., italic) should translate into aTEX request for lightbulb10.tfm mechanically scaled to the current font size.The final step is to write a L A TEX 2ε style file that defines a name for each symbol in the font. Becausewe have only one symbol our style file, lightbulb.sty (Figure 7), is rather trivial. Note that instead oftypesetting “A” we could have had \lightbulb typeset “\char65”, “\char"41”, or “\char’101” (respectively,decimal, hexadecimal, and octal character offsets into the font). For a simple, one-character symbol font98

\DeclareFontFamily{U}{bulb}{}\DeclareFontShape{U}{bulb}{m}{n}{ lightbulb10}{}Figure 6: L A TEX 2ε font-description file (ubulb.fd)such as LightBulb10 it would be reasonable to merge ubulb.fd into lightbulb.sty instead of maintainingtwo separate files. In either case, a document need only include “\usepackage{lightbulb}” to make the\lightbulb symbol available.\newcommand{\lightbulb}{{\usefont{U}{bulb}{m}{n}A}}Figure 7: L A TEX 2ε style file (lightbulb.sty)METAFONT normally produces bitmapped fonts. However, it is also possible, with the help of someexternal tools, to produce PostScript Type 1 fonts. These have the advantages of rendering better in Adobe ®Acrobat ® (at least in versions prior to 6.0) and of being more memory-efficient when handled by a PostScriptinterpreter. See http://www.tex.ac.uk/cgi-bin/texfaq2html?label=textrace for pointers to tools that canproduce Type 1 fonts from METAFONT.7.4 Math-mode spacingTerms such as “binary operators”, “relations”, and “punctuation” in Section 3 primarily regard the surroundingspacing. (See the Short Math Guide for L A TEX [Dow00] for a nice exposition on the subject.) To use a symbolfor a different purpose, you can use the TEX commands \mathord, \mathop, \mathbin, \mathrel, \mathopen,\mathclose, and \mathpunct. For example, if you want to use \downarrow as a variable (an “ordinary”symbol) instead of a delimiter, you can write “$3 x + \mathord{\downarrow}$” to get the properly spaced“3x + ↓” rather than the awkward-looking “3x+ ↓”. Similarly, to create a dotted-union symbol (“ ˙∪”) thatspaces like the ordinary set-union symbol (\cup) it must be defined with \mathbin, just as \cup is. Contrast“$A \dot{\cup} B$” (“A ˙∪B”) with “$A \mathbin{\dot{\cup}} B$” (“A ˙∪B”). See The TEXbook [Knu86a]for the definitive description of math-mode spacing.The purpose of the “log-like symbols” in Tables 120 and 121 is to provide the correct amount of spacingaround and within multiletter function names. Table 284 contrasts the output of the log-like symbols withvarious, naïve alternatives. In addition to spacing, the log-like symbols also handle subscripts properly. Forexample, “\max_{p \in P}” produces “max p∈P ” in text, but “max” as part of a displayed formula.p∈PTable 284: Spacing Around/Within Log-like SymbolsL A TEX expressionOutput$r \sin \theta$ r sin θ (best)$r sin \theta$ rsinθ$r \mbox{sin} \theta$ rsinθ$r \mathrm{sin} \theta$ rsinθThe amsmath package makes it straightforward to define new log-like symbols:\DeclareMathOperator{\atan}{atan}\DeclareMathOperator*{\lcm}{lcm}The difference between \DeclareMathOperator and \DeclareMathOperator* involves the handling of subscripts.With \DeclareMathOperator*, subscripts are written beneath log-like symbols in display style andto the right in text style. This is useful for limit operators (e.g., \lim) and functions that tend to map overa set (e.g., \min). In contrast, \DeclareMathOperator tells TEX that subscripts should always be displayedto the right of the operator, as is common for functions that take a single parameter (e.g., \log and \cos).Table 285 contrasts symbols declared with \DeclareMathOperator and \DeclareMathOperator* in both textstyle ($. . .$) and display style (\[. . .\]). 1111 Note that \displaystyle can be used to force display style within $. . .$ and \textstyle can be used to force text stylewithin \[. . .\].99

Table 285: Defining new log-like symbolsDeclaration function $\newlogsym {p \in P}$ \[ \newlogsym {p \in P} \]\DeclareMathOperator newlogsym p∈P newlogsym p∈P\DeclareMathOperator* newlogsym p∈P newlogsymp∈PIt is common to use a thin space (\,) between the words of a multiword operators, as in“\DeclareMathOperator*{\argmax}{arg\,max}”. \liminf, \limsup, and all of the log-like symbols shownin Table 121 utilize this spacing convention.7.5 Bold mathematical symbolsL A TEX does not normally use bold symbols when typesetting mathematics. However, bold symbols are occasionallyneeded, for example when naming vectors. Any of the approaches described at http://www.tex.ac.uk/cgi-bin/texfaq2html?label=boldgreek can be used to produce bold mathematical symbols. Table 286contrasts the output produced by these various techniques. As the table illustrates, these techniques exhibitvariation in their formatting of Latin letters (upright vs. italic), formatting of Greek letters (bold vs. normal),formatting of operators and relations (bold vs. normal), and spacing.Table 286: Producing bold mathematical symbolsPackage Code Outputnone $\alpha + b = \Gamma \div D$ α + b = Γ ÷ D (no bold)none $\mathbf{\alpha + b = \Gamma \div D}$ α + b = Γ ÷ Dnone \boldmath$\alpha + b = \Gamma \div D$ α + b = Γ ÷ Damsbsy $\pmb{\alpha + b = \Gamma \div D}$ α + b = Γ ÷ D (faked bold)amsbsy $\boldsymbol{\alpha + b = \Gamma \div D}$ α + b = Γ ÷ Dbm $\bm{\alpha + b = \Gamma \div D}$ α + b = Γ ÷ Dfixmath $\mathbold{\alpha + b = \Gamma \div D}$ α + b = Γ ÷ D7.6 ASCII and Latin 1 quick referenceTable 287 on the next page amalgamates data from various other tables in this document into a convenientreference for L A TEX 2ε typesetting of ASCII characters, i.e., the characters available on a typical U.S. computerkeyboard. The first two columns list the character’s ASCII code in decimal and hexadecimal. The thirdcolumn shows what the character looks like. The fourth column lists the L A TEX 2ε command to typeset thecharacter as a text character. And the fourth column lists the L A TEX 2ε command to typeset the characterwithin a \texttt{. . .} command (or, more generally, when \ttfamily is in effect).The following are some additional notes about the contents of Table 287:• “"” is not available in the OT1 font encoding.• The characters “”, and “|” do work as expected in math mode, although they produce, respectively,“¡”, “¿”, and “—” in text mode when using the OT1 font encoding. 12 The following are some alternativesfor typesetting “”, and “|”:– Specify a document font encoding other than OT1 (as described on page 7).– Use the appropriate symbol commands from Table 2 on page 8, viz. \textless, \textgreater,and \textbar.– Enter the symbols in math mode instead of text mode, i.e., $$, and $|$.12 Donald Knuth didn’t think such symbols were important outside of mathematics so he omitted them from his text fonts.100

Table 287: L A TEX 2ε ASCII TableDec Hex Char Body text \texttt33 21 ! ! !34 22 " \textquotedbl "35 23 # \# \#36 24 $ \$ \$37 25 % \% \%38 26 & \& \&39 27 ’ ’ ’40 28 ( ( (41 29 ) ) )42 2A * * *43 2B + + +44 2C , , ,45 2D - - -46 2E . . .47 2F / / /48 30 0 0 049 31 1 1 150..32..2..2..2..57 39 9 9 958 3A : : :59 3B ; ; ;60 3C < \textless \textgreater >63 3F ? ? ?64 40 @ @ @65 41 A A A66 42 B B B67 43 C C C. . . ..90 5A Z Z Z91 5B [ [ [92 5C \ \textbackslash \char‘\\93 5D ] ] ]94 5E ˆ \^{} \^{}95 5F \_ \char‘\_96 60 ‘ ‘ ‘97 61 a a a98 62 b b b99.63.c.c.c.122 7A z z z123 7B { \{ \char‘\{124 7C | \textbar |125 7D } \} \char‘\}126 7E ˜ \~{} \~{}Note that for typesetting metavariables many people prefer \textlangle and \textrangle to \textlessand \textgreater, i.e., “〈filename〉” instead of “”.• Although “/” does not require any special treatment, L A TEX additionally defines a \slash commandwhich outputs the same glyph but permits a line break afterwards. That is, “increase/decrease” isalways typeset as a single entity while “increase\slash{}decrease” may be typeset with “increase/”on one line and “decrease” on the next.• \textasciicircum can be used instead of \^{}, and \textasciitilde can be used instead of \~{}.Note that \textasciitilde and \~{} produce raised, diacritic tildes. “Text” (i.e., vertically centered)tildes can be generated with either the math-mode \sim command (shown in Table 62 on page 30),which produces a somewhat wide “∼”, or the textcomp package’s \texttildelow (shown in Table 36on page 19), which produces a vertically centered “~” in most fonts but a baseline-oriented “” inComputer Modern, txfonts, pxfonts, and various other fonts originating from the TEX world. If yourgoal is to typeset tildes in URLs or Unix filenames, your best bet is to use the url package, which has anumber of nice features such as proper line-breaking of such names.• The various \char commands within \texttt are necessary only in the OT1 font encoding. In otherencodings (e.g., T1), commands such as \{, \}, \_, and \textbackslash all work properly.• The code page 437 (IBM PC) version of ASCII characters 1 to 31 can be typeset using the ascii package.See Table 209 on page 69.• To replace “‘” and “’” with the more computer-like (and more visibly distinct) “`” and “'” withina verbatim environment, use the upquote package. Outside of verbatim, you can use \char18 and\char13 to get the modified quote characters. (The former is actually a grave accent.)Similar to Table 287, Table 288 on the next page is an amalgamation of data from other tables in thisdocument. While Table 287 shows how to typeset the 7-bit ASCII character set, Table 288 shows the Latin 1(Western European) character set, also known as ISO-8859-1.101

Table 288: L A TEX 2ε Latin 1 TableDec Hex Char L A TEX 2ε161 A1 ¡ !‘162 A2 ¢ \textcent (tc)163 A3 £ \pounds164 A4 ¤ \textcurrency (tc)165 A5 ¥ \textyen (tc)166 A6 ¦ \textbrokenbar (tc)167 A7 § \S168 A8 ¨ \textasciidieresis (tc)169 A9 © \textcopyright170 AA ª \textordfeminine171 AB « \guillemotleft (T1)172 AC ¬ \textlnot (tc)173 AD - \-174 AE ® \textregistered175 AF ¯ \textasciimacron (tc)176 B0 ° \textdegree (tc)177 B1 ± \textpm (tc)178 B2 ² \texttwosuperior (tc)179 B3 ³ \textthreesuperior (tc)180 B4 ´ \textasciiacute (tc)181 B5 µ \textmu (tc)182 B6 \P183 B7 · \textperiodcentered184 B8 ¸ \c{}185 B9 ¹ \textonesuperior (tc)186 BA º \textordmasculine187 BB » \guillemotright (T1)188 BC ¼ \textonequarter (tc)189 BD ½ \textonehalf (tc)190 BE ¾ \textthreequarters (tc)191 BF ¿ ?‘192 C0 À \‘{A}193 C1 Á \’{A}194 C2 Â \^{A}195 C3 Ã \~{A}196 C4 Ä \"{A}197 C5 Å \AA198 C6 Æ \AE199 C7 Ç \c{C}200 C8 È \‘{E}201 C9 É \’{E}202 CA Ê \^{E}203 CB Ë \"{E}204 CC Ì \‘{I}205 CD Í \’{I}206 CE Î \^{I}207 CF Ï \"{I}208 D0 Ð \DH (T1)Dec Hex Char L A TEX 2ε209 D1 Ñ \~{N}210 D2 Ò \‘{O}211 D3 Ó \’{O}212 D4 Ô \^{O}213 D5 Õ \~{O}214 D6 Ö \"{O}215 D7 × \texttimes (tc)216 D8 Ø \O217 D9 Ù \‘{U}218 DA Ú \’{U}219 DB Û \^{U}220 DC Ü \"{U}221 DD Ý \’{Y}222 DE Þ \TH (T1)223 DF ß \ss224 E0 à \‘{a}225 E1 á \’{a}226 E2 â \^{a}227 E3 ã \~{a}228 E4 ä \"{a}229 E5 å \aa230 E6 æ \ae231 E7 ç \c{c}232 E8 è \‘{e}233 E9 é \’{e}234 EA ê \^{e}235 EB ë \"{e}236 EC ì \‘{ı}237 ED í \’{ı}238 EE î \^{ı}239 EF ï \"{ı}240 F0 ð \dh (T1)241 F1 ñ \~{n}242 F2 ò \‘{o}243 F3 ó \’{o}244 F4 ô \^{o}245 F5 õ \~{o}246 F6 ö \"{o}247 F7 ÷ \textdiv (tc)248 F8 ø \o249 F9 ù \‘{u}250 FA ú \’{u}251 FB û \^{u}252 FC ü \"{u}253 FD ý \’{y}254 FE þ \th (T1)255 FF ÿ \"{y}102

The following are some additional notes about the contents of Table 288:• A “(tc)” after a symbol name means that the textcomp package must be loaded to access that symbol.A “(T1)” means that the symbol requires the T1 font encoding. The fontenc package can change thefont encoding document-wide.• Many of the \text. . . accents can also be produced using the accent commands shown in Table 18 onpage 13 plus an empty argument. For instance, \={} is essentially the same as \textasciimacron.• The commands in the “L A TEX 2ε” columns work both in body text and within a \texttt{. . .} command(or, more generally, when \ttfamily is in effect).• The “£” and “$” glyphs occupy the same slot (36) of the OT1 font encoding, with “£” appearing in italicfonts and “$” appearing in roman fonts. A problem with L A TEX’s default handling of this double-mappingis that “{\sffamily\slshape\pounds}” produces “$”, not “£”. Other font encodings use separate slotsfor the two characters and are therefore robust to the problem of “£”/”$” conflicts. Authors who use\pounds should select a font encoding other than OT1 (as explained on page 7) or use the textcomppackage, which redefines \pounds to use the TS1 font encoding.• Character 173, \-, is shown as “-” but is actually a discretionary hyphen; it appears only at the end ofa line.Microsoft ® Windows ® normally uses a superset of Latin 1 called “Code Page 1252” or “CP1252” forshort. CP1252 introduces symbols in the Latin 1 “invalid” range (characters 128–159). Table 289 presents thecharacters with which CP1252 augments the standard Latin 1 table.Table 289: L A TEX 2ε Code Page 1252 TableDec Hex Char L A TEX 2ε128 80 € \texteuro (tc)130 82 ‚ \quotesinglbase (T1)131 83 f \textit{f}132 84 „ \quotedblbase (T1)133 85 . . . \dots134 86 † \dag135 87 ‡ \ddag136 88 ˆ \textasciicircum137 89 ‰ \textperthousand (tc)138 8A Š \v{S}139 8B ‹ \guilsinglleft (T1)140 8C Œ \OE142 8E Ž \v{Z}Dec Hex Char L A TEX 2ε145 91 ‘ ‘146 92 ’ ’147 93 “ ‘‘148 94 ” ’’149 95 • \textbullet150 96 – --151 97 — ---152 98 ˜ \textasciitilde153 99 \texttrademark154 9A š \v{s}155 9B › \guilsinglright (T1)156 9C œ \oe158 9E ž \v{z}159 9F Ÿ \"{Y}The following are some additional notes about the contents of Table 289:• As in Table 288, a “(tc)” after a symbol name means that the textcomp package must be loaded to accessthat symbol. A “(T1)” means that the symbol requires the T1 font encoding. The fontenc package canchange the font encoding document-wide.• Not all characters in the 128–159 range are defined.• Look up “euro signs” in the index for alternatives to \texteuro.While too large to incorporate into this document, a listing of ISO 8879:1986 SGML/XML character entitiesand their L A TEX equivalents is available from http://www.bitjungle.com/~isoent/. Some of the characterspresented there make use of isoent, a L A TEX 2ε package (available from the same URL) that fakes some of themissing ISO glyphs using the L A TEX picture environment. 1313 isoent is not featured in this document, because it is not available from CTAN and because the faked symbols are not “true”characters; they exist in only one size, regardless of the body text’s font size.103

7.7 About this documentHistory David Carlisle wrote the first version of this document in October, 1994. It originally contained allof the native L A TEX symbols (Tables 40, 52, 62, 95, 120, 122, 141, 142, 152, 157, 184, and a few tables that havesince been reorganized) and was designed to be nearly identical to the tables in Chapter 3 of Leslie Lamport’sbook [Lam86]. Even the table captions and the order of the symbols within each table matched! The AMSsymbols (Tables 41, 63, 64, 98, 99, 123, 127, 137, and 185) and an initial Math Alphabets table (Table 196)were added thereafter. Later, Alexander Holt provided the stmaryrd tables (Tables 42, 54, 65, 101, 117, and138).In January, 2001, Scott Pakin took responsibility for maintaining the symbol list and has since implementeda complete overhaul of the document. The result, now called, “The Comprehensive L A TEX Symbol List”,includes the following new features:• the addition of a handful of new math alphabets, dozens of new font tables, and thousands of newsymbols• the categorization of the symbol tables into body-text symbols, mathematical symbols, science andtechnology symbols, dingbats, and other symbols, to provide a more user-friendly document structure• an index, table of contents, and a frequently-requested symbol list, to help users quickly locate symbols• symbol tables rewritten to list the symbols in alphabetical order• appendices to provide additional information relevant to using symbols in L A TEX• tables showing how to typeset all of the characters in the ASCII and Latin 1 font encodingsFurthermore, the internal structure of the document has been completely altered from David’s original version.Most of the changes are geared towards making the document easier to extend, modify, and reformat.Build characteristics Table 290 lists some of this document’s build characteristics. Most important isthe list of packages that L A TEX couldn’t find, but that symbols.tex otherwise would have been able to takeadvantage of. Complete, prebuilt versions of this document are available from CTAN (http://www.ctan.org/or one of its many mirror sites) in the directory tex-archive/info/symbols/comprehensive. Table 291shows the package date (specified in the .sty file with \ProvidesPackage) for each package that was used tobuild this document and that specifies a package date. Packages are not listed in any particular order in eitherTable 290 or 291.CharacteristicTable 290: Document CharacteristicsValueSource file:symbols.texBuild date: January 3, 2008Symbols documented: 4947Packages included: textcomp latexsym amssymb stmaryrd euscript wasysympifont manfnt bbding undertilde ifsym tipa tipx extraipawsuipa phonetic ulsy ar metre txfonts mathabx fclfontskak ascii dingbat skull eurosym esvect yfonts yhmathesint mathdots trsym universa upgreek overrightarrowchemarr chemarrow nath trfsigns mathtools phaistos arcsvietnam t4phonet holtpolt semtrans dictsym extarrowsprotosem harmony hieroglf cclicenses mathdesign arevMnSymbol cmll extpfeil keystroke fge turnstile simpsonsepsdice feyn universal staves igo accents nicefrac bmmathrsfs chancery calligra bbold mbboard dsfont bbmPackages omitted: none104

Table 291: Package versions used in the preparation of this documentNameDatetextcomp 2005/09/27latexsym 1998/08/17amssymb 2002/01/22stmaryrd 1994/03/03euscript 2001/10/01wasysym 2003/10/30pifont 2005/04/12manfnt 1999/07/01bbding 1996/06/21undertilde 2000/08/08ifsym 2000/04/18tipa 2002/08/08tipx 2003/01/01wsuipa 1994/07/16metre 2001/12/05txfonts 2005/01/03mathabx 2003/07/29skak 2003/09/27ascii 2006/05/30dingbat 2001/04/27skull 2002/01/23eurosym 1998/08/06yfonts 2003/01/08mathdots 2006/03/16trsym 2000/06/25universa 98/08/01upgreek 2003/02/12chemarr 2006/02/20mathtools 2004/10/10phaistos 2004/04/23arcs 2004/05/09t4phonet 2004/06/01semtrans 1998/02/10dictsym 2004/07/26extarrows 2002/03/30protosem 2005/03/18harmony 2007/05/03hieroglf 2000/09/23cclicenses 2005/05/20arev 2005/06/14MnSymbol 2007/01/21extpfeil 2006/07/27keystroke 2003/08/15fge 2007/06/03turnstile 2007/06/23epsdice 2001/02/15feyn 2002/04/23universal 97/12/24accents 2006/05/12nicefrac 1998/08/04bm 2004/02/26calligra 1996/07/18105

7.8 Copyright and licenseThe Comprehensive L A TEX Symbol ListCopyright © 2008, Scott PakinThis work may be distributed and/or modified under the conditions of the L A TEX Project Public License, eitherversion 1.3c of this license or (at your option) any later version. The latest version of this license is inhttp://www.latex-project.org/lppl.txtand version 1.3c or later is part of all distributions of L A TEX version 2006/05/20 or later.This work has the LPPL maintenance status “maintained”.The current maintainer of this work is Scott Pakin.References[AMS99] American Mathematical Society. User’s Guide for the amsmath Package (Version 2.0), December 13,1999. Available from ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf.[Ber01]Karl Berry. Fontname: Filenames for TEX fonts, June 2001. Available from http://www.ctan.org/tex-archive/info/fontname.[Che97] Raymond Chen. A METAFONT of ‘Simpsons’ characters. Baskerville, 4(4):19, September1997. ISSN 1354-5930. Available from http://tug.ctan.org/usergrps/uktug/baskervi/4 4/bask4 4.ps.[Dow00]Michael Downes. Short math guide for L A TEX, July 19, 2000. Version 1.07. Available from http://www.ams.org/tex/short-math-guide.html.[Gib97] Jeremy Gibbons. Hey—it works! TUGboat, 18(2):75–78, June 1997. Available from http://www.tug.org/TUGboat/Articles/tb18-2/tb55works.pdf.[Knu86a] Donald E. Knuth. The TEXbook, volume A of Computers and Typesetting. Addison-Wesley, Reading,MA, USA, 1986.[Knu86b] Donald E. Knuth. The METAFONTbook, volume C of Computers and Typesetting. Addison-Wesley,Reading, MA, USA, 1986.[Lam86] Leslie Lamport. L A TEX: A document preparation system. Addison-Wesley, Reading, MA, USA, 1986.[L A T98] L A TEX3 Project Team. A new math accent. L A TEX News. Issue 9, June 1998. Available fromhttp://www.ctan.org/tex-archive/macros/latex/doc/ltnews09.pdf (also included in many TEXdistributions).[L A T00] L A TEX3 Project Team. L A TEX 2ε font selection, January 30, 2000. Available from http://www.ctan.org/tex-archive/macros/latex/doc/fntguide.ps (also included in many TEX distributions).106

IndexIf you’re having trouble locating a symbol, try looking under “T” for “\text. . .”. Many text-mode commands beginwith that prefix. Also, accents are shown over/under a gray box, e.g., “ á ” for “\’”.Some symbol entries appear to be listed repeatedly. This happens when multiple packages define identical (or nearlyidentical) glyphs with the same symbol name. 14Symbols\" (ä) . . . . . . . . . . . . . . . . . 13\# (#) . . . . . . . . . . . . . 8, 101\$ ($) . . . . . . . . . . . . . . 8, 101\% (%) . . . . . . . . . . . . . 8, 101\& (&) . . . . . . . . . . . . . 8, 101\’ (á) . . . . . . . . . . . . . . . . . 13( (() . . . . . . . . . . . . . . . . . . 53( (() . . . . . . . . . . . . . . . . . . 54) ()) . . . . . . . . . . . . . . . . . . 53) ()) . . . . . . . . . . . . . . . . . . 54* (*) . . . . . . . . . . . . . . . . . . 22\, . . . . . . . . . . . . . . . . . . . 100\- (-) . . . . . . . . . . . . . 102, 103\. (ȧ) . . . . . . . . . . . . . . . . . 13/ (/) . . . . . . . . . . . . . . . . . . 53/ (/) . . . . . . . . . . . . . . . . . 54< (⟨) . . . . . . . . . . . . . . . . . . 54\AAhe (E) . . . . . . . . . . . . . . 83\AAhelmet (V) . . . . . . . . . . 83\AAheth (h) . . . . . . . . . . . . 83\AAkaph (K) . . . . . . . . . . . . 83\AAlamed (L) . . . . . . . . . . . 83\Aaleph (a) . . . . . . . . . . . . 83\AApe (P) . . . . . . . . . . . . . . 83\AAqoph (Q) . . . . . . . . . . . . 83\AAresh (R) . . . . . . . . . . . . 83\AAsade (X) . . . . . . . . . . . . 83\Aayin (o) . . . . . . . . . . . . . 83\AAyod (Y) . . . . . . . . . . . . . 83\Abeth (b) . . . . . . . . . . . . . 83absolute value . see \lvert and\rvertabzüglich . . see \textdiscount\AC () . . . . . . . . . . . . . . . . 67\acarc . . . . . . . . . . . . . . . . 15\acbar . . . . . . . . . . . . . . . . 15accents . . 13–17, 33–35, 44, 46,56–60, 68, 79, 86, 94–96any character as . . . . . . 94extensible . . 57–60, 95–96multiple per character . 94accents (package) 56, 94, 104, 105\accentset . . . . . . . . . . . . . 94[ ([) . . . . . . . . . . . . . . . . . . 53⎡[ () . . . . . . . . . . . . . . . . . 54\\ . ⎢⎣. . . . . . . . . . . . . . . . . . . 91] (]) . . . . . . . . . . . . . . . . . . 53\Acht (ˇ “ ( )= . . . . . . . . . . . . . . 79⎤\AchtBL (ˇ “) . . . . . . . . . . . . 79] () . . . . . . . . . . . . . . . . . 54\^ (â) ⎥\AchtBR (ˇ “=) . . . . . . . . . . . . 79⎦ . . . . . . . . . . . . . . . . . 13\ACK (␆) . . . . . . . . . . . . . . . 69\^{} (ˆ) . . . . . . . . . . . . . . 101\acontraction . . . . . . . . . . 96\| (‖) . . . . . . . . . . . . . . . . . 53\AcPa\| (¿a) . . . . . . . . . . . . . . . . . 13(? ) . . . . . . . . . . . . . . 79actuarial symbols . . . . . . . . 95\= (ā) . . . . . . . . . . . . . . . . . 13\acute (´) . . . . . . . . . . . . . 56\={} (¯) . . . . . . . . . . . . . . 103\acutus (á) . . . . . . . . . . . . . 16| (|) . . . . . . . . . . . . . . . . . . 53\Adaleth (d) . . . . . . . . . . . 83\_ ( ) . . . . . . . . . . . . . . 8, 101adjoint (†) . . . . . . . . . see \dag\{ ({) . . . . . . . . . . . . 8, 53, 101Adobe Acrobat . . . . . . . . . . 99\} (}) . . . . . . . . . . . . 8, 53, 101\‘ (à) . . . . . . . . . . . . . . . . . 13 \adots (. .. ) . . . . . . . . . 62, 94\~ (ã) . . . . . . . . . . . . . . . . . 13 advancing . see \textadvancing\~{} (˜) . . . . . . . . . . . . . . 101 \AE (Æ) . . . . . . . . . . . . . . . . 9\ae (æ) . . . . . . . . . . . . . . . . . 9A\agemO () . . . . . . . . . . . . . 63a (esvect package option) . . . 59 \Agimel (g) . . . . . . . . . . . . 83\a ( ×) . . . . . . . . . . . . . . . . 82 \Ahe (e) . . . . . . . . . . . . . . . 83\AA (Å) . . . . . . . . . . . . . . . . . 9 \Ahelmet (v) . . . . . . . . . . . 83\aa (å) . . . . . . . . . . . . . . . . . 9 \Aheth (H) . . . . . . . . . . . . . 83\AAaleph (A) . . . . . . . . . . . 83 \ain (s) . . . . . . . . . . . . . . . . 16\AAayin (O) . . . . . . . . . . . . 83 \Akaph (k) . . . . . . . . . . . . . 83\AAbeth (B)=. . . . . . . . . . . . 83 \Alad (}) . . . . . . . . . . . . . . 56\AAcht (ˇ “ ˇ “) . . . . . . . . . . . . . 79 \alad (}) . . . . . . . . . . . . . . 56\AAdaleth (D) . . . . . . . . . . . 83 \Alamed (l) . . . . . . . . . . . . 8314 This occurs frequently between amssymb and mathabx, for example.\Alas ({) . . . . . . . . . . . . . . 56\alas ({) . . . . . . . . . . . . . . 56\aleph (ℵ) . . . . . . . . . . 50, 62\aleph (ℵ) . . . . . . . . . . . . . 50\Alif (↪) . . . . . . . . . . . . . . . 13\alpha (α) . . . . . . . . . . . . . 49alphabetsAfrican . . . . . . . . . . . . . 9Cyrillic . . . . . . . . . . . . 90Greek . . . . . . . . 49, 50, 65Hebrew . . . . . . . . . 50, 65hieroglyphic . . . . . . . . . 84math . . . . . . . . . . . . . . 65phonetic . . . . . . . . 10–13proto-Semitic . . . . . . . . 83Vietnamese . . . . . . . . . . 9\alphaup (α) . . . . . . . . . . . . 50alpine symbols . . . . . . . . . . . 81\Alt ( Alt ) . . . . . . . . . . . . 69\AltGr ( AltGr ) . . . . . . . . . 69\amalg (∐) . . . . . . . . . . . . . 20\amalg (∐) . . . . . . . . . . . . . 23\Amem (m) . . . . . . . . . . . . . . 83ampersand . . . . . . . . . . see \&AMS 7, 8, 21, 25, 30, 36, 37, 39,41, 49–53, 56, 58, 59, 61–63,66, 87, 104amsbsy (package) . . . . . . . . 100amsfonts (package) 20, 30, 36, 41,62, 65amsmath (package) 7, 49, 56, 91,99amssymb (package) 7, 20, 30, 36,41, 56, 62, 65, 104, 105, 107amstext (package) . . . . . 92, 93\Anaclasis (÷) . . . . . . . . . . 82\anaclasis (÷) . . . . . . . . . . 82\anchor (O) . . . . . . . . . . . 77and . . . . . . . . . . . . . see \wedge\angle (∠) . . . . . . . . . . . . . 63\angle (̸ ) . . . . . . . . . . . . . 62\angle (∠) . . . . . . . . . . . . . 63angles . . . . . . . . . . . . . . 62–64\Anglesign (W) . . . . . . . . . . 64Ångström unitmath mode see \mathringtext mode . . . . . . see \AA\Angud (〉) . . . . . . . . . . . . . . 56\angud (〉) . . . . . . . . . . . . . . 56angular minutes . . . . see \primeangular seconds . . . see \second\Angus (〈) . . . . . . . . . . . . . . 56\angus (〈) . . . . . . . . . . . . . . 56107

\Ankh (ˆ) . . . . . . . . . . . . . . 80\annu ( ) . . . . . . . . . . . . . . 95annuity . . . . . . . . . . . . . . . . 95\Antidiple (

\baudash (¡) . . . . . . . . . . . 80\baueclipse (¨) . . . . . . . . . 76\bauequal (¢) . . . . . . . . . . 80\bauface () . . . . . . . . . . . 80\bauforms („) . . . . . . . . . . 80\bauforms (¤) . . . . . . . . . 80\bauhead () . . . . . . . . . . . 80\bauhead (£) . . . . . . . . . . 80\bauhole (§) . . . . . . . . . . . 76\bauplus ( ) . . . . . . . . . . . 80\baupunct (…) . . . . . . . . . . 76\bauquarter (©) . . . . . . . . . 80\bauquestion () . . . . . . . . 80\bausquare (†) . . . . . . . . . . 76\bausquare ( ) . . . . . . . . . 76\bautriangle (£) . . . . . . . . 76\bautriangle (¢) . . . . . . . . 76\bauwhitearrow () . . . . . . 71\bauwindow (¦) . . . . . . . . . . 80\BB ( ˘˘´) . . . . . . . . . . . . . . . 82\Bb ( ˘´˘) . . . . . . . . . . . . . . . 82\bB ( ˘˘´) . . . . . . . . . . . . . . . 82\bb ( ˘˘) . . . . . . . . . . . . . . . 82\bba ( ע˘) . . . . . . . . . . . . . . 82\bbalpha () . . . . . . . . . . . . 65\bbar (¯b) . . . . . . . . . . . . . . 91\bbb ( ˘˘˘) . . . . . . . . . . . . . . 82\bbbeta () . . . . . . . . . . . . . 65\Bbbk (k) . . . . . . . . . . . . . . 51bbding (package) . 71–75, 77, 88,104, 105\bbdollar ($) . . . . . . . . . . . 65\bbetter (g) . . . . . . . . . . . 82\bbeuro (û) . . . . . . . . . . . . 65\bbfinalnun (Ï) . . . . . . . . . 65\bbgamma () . . . . . . . . . . . . 65bbgreekl (mathbbol package option). . . . . . . . . . . . . 65\BBm ( ¯˘¯˘´) . . . . . . . . . . . . . . 82\Bbm ( ¯˘¯˘ ´ ) . . . . . . . . . . . . . . 82\bBm ( ¯˘¯˘´) . . . . . . . . . . . . . . 82bbm (package) . . . . . . . 65, 104\bbm ( ¯˘¯˘) . . . . . . . . . . . . . . 82\bbmb ( . . . . . . . . . . . . . 82˘¯˘¯˘)\bbmx ( ¯˘¯˘¯˘¯) . . . . . . . . . . . . 82\bbnabla (š) . . . . . . . . . . . 65bbold (package) . . . . . . 65, 104\bbpe (Ô) . . . . . . . . . . . . . . 65\bbqof (×) . . . . . . . . . . . . . 65\bbslash () . . . . . . . . . . . 21\bbyod (É) . . . . . . . . . . . . . . 65\bcontraction . . . . . . . . . . 96\bdecisive (i) . . . . . . . . . 82\Beam (") . . . . . . . . . . . . . . 70\Bearing (#) . . . . . . . . . . . 70\because (∵) . . . . . . . . 30, 61\because (∵) . . . . . . . . . . . . 61\BEL (␇) . . . . . . . . . . . . . . . 69\bell (␇) . . . . . . . . . . . . . . 78Berry, Karl . . . . . . . . . . . . 106\beta (β) . . . . . . . . . . . . . . 49\betaup (β) . . . . . . . . . . . . . 50\beth (ℶ) . . . . . . . . . . . . . . 50\beth (ℶ) . . . . . . . . . . . . . . 50\betteris (b) . . . . . . . . . . 82\between ( ) . . . . . . . . . . . . 31\between (≬) . . . . . . . . . . . . 30\between (≬) . . . . . . . . . . . 32\bibridge ( ” a”) . . . . . . . . . . . 15\Bicycle (®) . . . . . . . . . . . 76\Big . . . . . . . . . . . . . . . 87, 89\big . . . . . . . . . . . . . . . 87, 89\bigast (¦) . . . . . . . . . . . . 22\bigbosonloop (!) . . . . . . . . 70\bigbox ( ) . . . . . . . . . . . . 25\bigboxasterisk ( ) . . . . . 26\bigboxbackslash Þ ( ) . . . . 26\bigboxbot ( ) . . . . . . . . . 26\bigboxcirc ( ) . . . . . . . . 26\bigboxcoasterisk × ( ) . . . 26\bigboxdiv ( ) . . . . . . . . . 26\bigboxdot ( ) . . . . . . . . . 26\bigboxleft ( ) . . . . . . . . 26\bigboxminus Ñ ( ) . . . . . . . 26\bigboxplus ( ) . . . . . . . . 26\bigboxright ( ) . . . . . . . 26\bigboxslash ( ) . . . . . . . 26\bigboxtimes Ò ( ) . . . . . . . 26\bigboxtop ( ) . . . . . . . . . 26\bigboxtriangleup ß ( ) . . . 26\bigboxvoid ( ) . . . . . . . . 26\bigcap ( ⋂ ) . . . . . . . . . . . . 25\bigcap (⋂) . . . . . . . . . . . . 29\bigcapdot (⩀) . . . . . . . . . . 29\bigcapplus () . . . . . . . . . 29\bigcirc (○) . . . . . . . . . . . 20\bigcirc (◯) . . . . . . . . . . . 74\BigCircle (%) . . . . . . . . . 75\bigcircle (◯) . . . . . . . . . 29\bigcoast (§) . . . . . . . . . . 22\bigcomplementop ( ’ ) . . . . . 26\BigCross () . . . . . . . . . . 75\bigcup ( ⋃ ) . . . . . . . . . . . . 25\bigcup (⋃) . . . . . . . . . . . . 29\bigcupdot (⊍) . . . . . . . . . . 29\bigcupplus (⊎) . . . . . . . . 29\bigcupplus (⊎) . . . . . . . . . 29\bigcurlyvee ( œ ) . . . . . . . . 26\bigcurlyvee ( ) . . . . . . . . 25\bigcurlyvee (⋎) . . . . . . . . 29\bigcurlyveedot () . . . . . 29\bigcurlywedge ( › ) . . . . . . 26\bigcurlywedge ( ) . . . . . . 25\bigcurlywedge (⋏) . . . . . . 29\bigcurlywedgedot () . . . . 29\BigDiamondshape (&) . . . . 75\bigdoublecurlyvee () . . . 29\bigdoublecurlywedge () . 29\bigdoublevee (⩔) . . . . . . . 29\bigdoublewedge (⩕) . . . . . 29\Bigg . . . . . . . . . . . . . . 87, 89\bigg . . . . . . . . . . . . . . 87, 89\BigHBar () . . . . . . . . . . . 75\biginterleave ( ⫼ ) . . . . . . 25\BigLowerDiamond (_) . . . . 75\bignplus ( ) . . . . . . . . . . 25\bigoast (⊛) . . . . . . . . . . . 29\bigoasterisk ( Æ ) . . . . . . . 26\bigobackslash ( Î ) . . . . . . 26\bigobackslash (⦸) . . . . . . 29\bigobot ( Ë ) . . . . . . . . . . . 26\bigocirc ( Å ) . . . . . . . . . . 26\bigocirc (⊚) . . . . . . . . . . 29\bigocoasterisk ( Ç ) . . . . . 26\bigodiv ( à ) . . . . . . . . . . . 26\bigodot ( ⊙ ) . . . . . . . . . . . 25\bigodot (⊙) . . . . . . . . . . . 29\bigoleft ( È ) . . . . . . . . . . 26\bigominus ( Á ) . . . . . . . . . 26\bigominus (⊖) . . . . . . . . . 29\bigoplus ( ⊕ ) . . . . . . . . . . 25\bigoplus (⊕) . . . . . . . . . . 29\bigoright ( É ) . . . . . . . . . 26\bigoslash ( Í ) . . . . . . . . . 26\bigoslash (⊘) . . . . . . . . . 29\bigostar (⍟) . . . . . . . . . . 29\bigotimes ( ⊗ ) . . . . . . . . . 25\bigotimes (⊗) . . . . . . . . . 29\bigotop ( Ê ) . . . . . . . . . . . 26\bigotriangle () . . . . . . . 29\bigotriangleup ( Ï ) . . . . . 26\bigovert (⦶) . . . . . . . . . . 29\bigovoid ( Ì ) . . . . . . . . . . 26\bigparallel ( ) . . . . . . . . 25\bigparr (˙) . . . . . . . . . . . 30\bigplus ( ) . . . . . . . . . . . 26\bigplus (+) . . . . . . . . . . . 29\BigRightDiamond (/) . . . . 75\bigsqcap ( – ) . . . . . . . . . . 26\bigsqcap ( ⊓ ) . . . . . . . . . . 25\bigsqcap (⊓) . . . . . . . . . . . 29\bigsqcapdot () . . . . . . . . 29\bigsqcapplus ( ) . . . . . . . 27\bigsqcapplus () . . . . . . . 29\bigsqcup ( ⊔ ) . . . . . . . . . . 25\bigsqcup (⊔) . . . . . . . . . . . 29\bigsqcupdot () . . . . . . . . 29\bigsqcupplus ( ) . . . . . . . 27\bigsqcupplus () . . . . . . . 29\BigSquare ( ) . . . . . . . . . 75\bigsquplus (˜) . . . . . . . . . 26\bigstar () . . . . . . . . . . . 22\bigstar (⋆) . . . . . . . . . . . 63\bigstar (☀) . . . . . . . . . . . 74\bigtimes ( ‘ ) . . . . . . . . . . 26\bigtimes (⨉) . . . . . . . . . . . 29\BigTriangleDown (#) . . . . 75\bigtriangledown ( ▽ ) . . . . 25\bigtriangledown (▽ vs. ▽ ) 88\bigtriangledown (▽) . . . . 20\bigtriangledown (▽) . . . . 40\BigTriangleLeft (") . . . . 75\BigTriangleRight ($) . . . 75109

\BigTriangleUp (!) . . . . . . 75\bigtriangleup ( △ ) . . . . . . 25\bigtriangleup (△ vs. △ ) . 88\bigtriangleup (△) . . . . . . 20\bigtriangleup (△) . . . . . . 40\biguplus ( ⊎ ) . . . . . . . . . . 25\biguplus (⊎) . . . . . . . . . . 29\bigvarstar () . . . . . . . . . 22\BigVBar () . . . . . . . . . . . 75\bigvee ( ∨ ) . . . . . . . . . . . . 25\bigvee (⋁) . . . . . . . . . . . . 29\bigveedot (⟇) . . . . . . . . . . 29\bigwedge ( ∧ ) . . . . . . . . . . 25\bigwedge (⋀) . . . . . . . . . . . 29\bigwedgedot (⟑) . . . . . . . . 29\bigwith (˘) . . . . . . . . . . . 30\binampersand () . . . . . . . 21binary operators . . . . . . 20–24binary relations . . 30–32, 34–39,47, 48negated . . . . . . . . . 30–33\bindnasrepma () . . . . . . . 21\Biohazard (h) . . . . . . . . . 70biological symbols . . . . . . . . 70bishop . . . . . . see chess symbols\bishoppair (a) . . . . . . . . . 82blackboard boldsee alphabets,math\blackdiamond () . . . . . . . 22\blacklozenge () . . . . . . . 63\blacklozenge (⧫) . . . . . . . 74\blacksmiley (☻) . . . . . . . . 78\blacksquare () . . . . . . . . 63\blacksquare (∎) . . . . . . . . 24\blackstone . . . . . . . . . . . . 76\blacktriangle () . . . . . . 63\blacktriangle (▲) . . . . . . 40\blacktriangledown ( ) . . . 24\blacktriangledown () . . . 63\blacktriangledown (▼) . . . 40\blacktriangleleft (ž) . . . 24\blacktriangleleft (◭) . . . 39\blacktriangleleft (◀) . . . 40\blacktriangleright (Ÿ) . . 24\blacktriangleright (◮) . . 39\blacktriangleright (▶) . . 40\blacktriangleup (œ) . . . . . 24blank . . . . . . . see \textblank\Bleech (Ë) . . . . . . . . . . . . 80\blitza (©) . . . . . . . . . 20, 48\blitzb () . . . . . . . . . . . . 48\blitzc () . . . . . . . . . . . . 48\blitzd () . . . . . . . . . . . . 48\blitze () . . . . . . . . . . . . 48\Bm ( ¯˘´) . . . . . . . . . . . . . . . 82bm (package) . . . . 100, 104, 105\bm . . . . . . . . . . . . . . . . . . 100\bm ( ¯˘) . . . . . . . . . . . . . . . 82\bmod . . . . . . . . . . . . . . . . . 49body-text symbols . . . . . . 8–19bold symbols . . . . . . . . . . . 100\boldmath . . . . . . . . . . . . . 100brackets . . . . . . . see delimiters\boldsymbol . . . . . . . . . . . 100\rrparenthesis\bracevert ( ⎪ ) . . . . . . . . . 54 \Cc ( ) . . . . . . . . . . . . . . . 82born . . . . . . . . . see \textborn braket (package) . . . . . . . . . 53bosons . . . . . . . . . . . . . . . . 70 \Break ( Break ) . . . . . . . . . 69\bot (⊥) . . . . . . . . . . 20, 51, 92 breve . . . . . . . . . . see accents\bot (⊥) . . . . . . . . . . . . . . . 51 \breve (˘) . . . . . . . . . . . . . 56\botdoteq () . . . . . . . . . . 31 \breve (ă) . . . . . . . . . . . . . 16\Bouquet (¥) . . . . . . . . . . . 80 \brokenvert () . . . . . . . . . . 78\Bowtie () . . . . . . . . . . . . 78 Bronger, Torsten . . . . . . . . . 92\bowtie (⊲⊳) . . . . . . . . . . . . 30 \BS (␈) . . . . . . . . . . . . . . . . 69\bowtie (⋈) . . . . . . . . . . . . 23 \BSEfree (n) . . . . . . . . . . . 70\Box (□) . . . . . . . . . . . . . . . 62 \BSpace ( ) . . . . . . . . . 69\Box () . . . . . . . . . . . . . . . 63\bullet (•) . . . . . . . . . . . . . 20\Box (◻) . . . . . . . . . . . . . . . 24\bullet (●) . . . . . . . . . . . . . 23\boxast () . . . . . . . . . . . . 21bullseye . . . see \textbullseye\boxasterisk (f) . . . . . . . . 24\Bumpedeq () . . . . . . . . . . 31\boxbackslash (n) . . . . . . . 24\bumpedeq () . . . . . . . . . . 31\boxbackslash (⧅) . . . . . . . 24\Bumpeq (≎) . . . . . . . . . . . . 30\boxbar () . . . . . . . . . . . . 21\Bumpeq (≎) . . . . . . . . . . . . . 32\boxbot (k) . . . . . . . . . . . . 24\bumpeq (≏) . . . . . . . . . . . . 30\boxbox (⧈) . . . . . . . . . . . . 21\bumpeq (≏) . . . . . . . . . . . . . 32\boxbox (⧈) . . . . . . . . . . . . 24\bupperhand (e) . . . . . . . . . 82\boxbslash () . . . . . . . . . . 21\boxcirc (e) . . . . . . . . . . . 24\boxcircle (⧇) . . . . . . . . . . 21\boxcoasterisk (g) . . . . . . 24 \Burns () . . . . . . . . 85\boxdiv (c) . . . . . . . . . . . . 24\boxdot (d) . . . . . . . . . . . . 24C\boxdot (⊡) . . . . . . . . . . . . 21 \C ( ) . . . . . . . . . . . . . . . . . 82\boxdot (⊡) . . . . . . . . . . . . 24 c (esvect package option) . . . 59\boxdotLeft () . . . . . . . . 42 \c (¸a) . . . . . . . . . . . . . 13, 102\boxdotleft () . . . . . . . . 42 \c ( ) . . . . . . . . . . . . . . . 82\boxdotRight () . . . . . . . 42 calligra (package) . . 65, 104, 105\boxdotright () . . . . . . . 42 Calligra (font) . . . . . . . . . . . 65\boxempty () . . . . . . . . . . 21 calrsfs (package) . . . . . . . . . 65\boxLeft () . . . . . . . . . . 42 \CAN (␘) . . . . . . . . . . . . . . . 69\boxleft (h) . . . . . . . . . . . 24 cancel (package) . . . . . . . . . 57\boxleft () . . . . . . . . . . 42 \Cancer (ã) . . . . . . . . . . . . 68\boxminus (a) . . . . . . . . . . 24 \cancer (♋) . . . . . . . . . . . . 68\boxminus (⊟) . . . . . . . . . . 21 \Cap (⋓) . . . . . . . . . . . . . . . 21\boxminus (⊟) . . . . . . . . . . . 24 \Cap (⋒) . . . . . . . . . . . . . . . 23\boxplus (`) . . . . . . . . . . . 24 \cap (X) . . . . . . . . . . . . . . . 22\boxplus (⊞) . . . . . . . . . . . 21 \cap (∩) . . . . . . . . . . . . . . . 20\boxplus (⊞) . . . . . . . . . . . . 24 \cap (∩) . . . . . . . . . . . . . . . 23\boxRight () . . . . . . . . . 42 \capdot (⩀) . . . . . . . . . . . . 23\boxright (i) . . . . . . . . . . 24 \capplus () . . . . . . . . . . . . 23\boxright () . . . . . . . . . 42 \Capricorn (é) . . . . . . . . . . 68\boxslash (m) . . . . . . . . . . 24 \capricornus (♑) . . . . . . . . 68\boxslash () . . . . . . . . . . . 21 card suits . . . . . . . . . 62–64, 77\boxslash (⧄) . . . . . . . . . . . 24 cardinality . . . . . . . see \aleph\boxtimes (b) . . . . . . . . . . 24 care of ( c /o) . . . . . . . . . . . . . 64\boxtimes (⊠) . . . . . . . . . . 21 caret . . . . . . . . . . . . . . . see \^\boxtimes (⊠) . . . . . . . . . . . 24 Carlisle, David . . . . . . . 1, 104\boxtop (j) . . . . . . . . . . . . 24 caron . . . . . . . . . . see accents\boxtriangleup (o) . . . . . . 24 carriage return . 69, 77, 90, see\boxvert () . . . . . . . . . . . . 24also \hookleftarrow\boxvoid (l) . . . . . . . . . . . 24 \carriagereturn (C) . . . . . 77\boy (D) . . . . . . . . . . . . . . . 68 castle . . . . . . see chess symbolsbra . . . . . . . . . . . . . . . . . . . 53 \Catalexis ( ∧ ) . . . . . . . . . . 82\braceld ({) . . . . . . . . . . . . 95 \catalexis ( ∧) . . . . . . . . . . 82\bracerd ({) . . . . . . . . . . . . 95 catamorphism . . . . . . . . . . . . .\bracevert (⎪) . . . . . . . . . 53. see \llparenthesis and↦−→110

\cc ( ○ CC ) . . . . . . . . . . . . . 18\cc ( ) . . . . . . . . . . . . . . 82\ccby ( ○ BY: ) . . . . . . . . . . . 18\Ccc ( ) . . . . . . . . . . . . . . 82cclicenses (package) 18, 104, 105\ccnc ( ○ $\) . . . . . . . . . . . 18\ccnd ( =○ ) . . . . . . . . . . . 18\ccsa ( ○ ) . . . . . . . . . . . . . 18\cdot (·) . . . . . . . . . . . . 20, 91\cdot (⋅) . . . . . . . . . . . . 23, 61\cdotp (·) . . . . . . . . . . . . . . 61\cdotp (⋅) . . . . . . . . . . . . . . 61\cdots (· · · ) . . . . . . . . . . . . 61Cedi . see \textcolonmonetarycedilla . . . . . . . . . . see accentscelestial bodies . . . . . . . . . . 68\celsius (℃) . . . . . . . . . . . 67\Celtcross (‡) . . . . . . . . . . 80\cent (¢) . . . . . . . . . . . . . . 17\centerdot () . . . . . . . . . . 22\centerdot () . . . . . . . . . . 21centernot (package) . . . . . . . 92\centernot . . . . . . . . . . . . . 92\centre (I) . . . . . . . . . . . . 82cents . . . . . . . . . see \textcent\CEsign (C) . . . . . . . . . . . . 70chancery (package) . . . . . . . 104\changenotsign . . . . . . . . . 32\char . . . . . . . . . . . . . . . 7, 90Charter (font) . . . . . . . . 17, 29\check (ˇ) . . . . . . . . . . . . . 56check marks . . . . . . . 73, 76, 77\checked () . . . . . . . . . . . 78\CheckedBox () . . . . . . . . . 73\Checkedbox (V) . . . . . . . . . 76C\Checkmark (!) . . . . . . . . . 73\checkmark (̌) . . . . . . . . . . 8\checkmark (✓) . . . . . . . . . 63\checkmark (̌ vs. D) . . . . . 88\checkmark (D) . . . . . . . . . 77\CheckmarkBold (") . . . . . . 73chemarr (package) . 59, 104, 105chemarrow (package) 47, 60, 104\chemarrow (A) . . . . . . . . . 47Chen, Raymond . . . . . . . . 106chess symbols . . . . . . . . . . . 82\chi (χ) . . . . . . . . . . . . . . . 49\chiup (χ) . . . . . . . . . . . . . . 50\circ (◦) . . . . . . . . . 20, 64, 92\circ (○) . . . . . . . . . . . . . . 23\circeq () . . . . . . . . . . . . 31\circeq (⊜) . . . . . . . . . . . . 30\circeq (≗) . . . . . . . . . . . . . 32\CIRCLE () . . . . . . . . . . . . 78\Circle (5) . . . . . . . . . . . . 75\Circle ( vs. 5) . . . . . . . 88\Circle () . . . . . . . . . . . . 78\circlearrowleft (ö) . . . . 42\circlearrowleft () . . . . 41\circlearrowleft (↺) . . . . 44\circlearrowright (÷) . . . . 42\circlearrowright () . . . 41\circlearrowright (↻) . . . 44circled numbers . . . . . . . 73, 76\CircledA (ª) . . . . . . . . . . 80\circledast (⊛) . . . . . . . . . 21\circledast (⊛) . . . . . . . . . 24\circledbar () . . . . . . . . . 21\circledbslash () . . . . . . 21\circledcirc (⊚) . . . . . . . . 21\circledcirc (⊚) . . . . . . . . 24\circleddash (⊖) . . . . . . . . 21\circleddash (⊖) . . . . . . . . 24\circleddot . . . . . . see \odot\circleddotleft () . . . . 42\circleddotright () . . . . 42\circledgtr () . . . . . . . . . 31\circledless () . . . . . . . . 31\circledminus . . . see \ominus\circledotleft . . . . . . . . see\circleddotleft\circledotright . . . . . . . see\circleddotright\circledplus . . . . . see \oplus\circledR (R) . . . . . . . . 8, 51\circledS (S) . . . . . . . . . . 51\circledslash . . . see \oslash\circledtimes . . . see \otimes\circledvee () . . . . . . . . . 21\circledwedge () . . . . . . . 21\circleleft () . . . . . . . . 42\circleright () . . . . . . . 42circles . . . . . . . . . . . . 75, 76, 78\CircleShadow (d) . . . . . . . 75\CircleSolid (a) . . . . . . . . 75\Circpipe (›) . . . . . . . . . . 70\circplus (¨) . . . . . . . . . . 22\Circsteel (•) . . . . . . . . . 70circumflex . . . . . . . see accents\circumflexus (ã) . . . . . . . 16\CleaningA («) . . . . . . . . . . 80\CleaningF (¾) . . . . . . . . . . 80\CleaningFF (¿) . . . . . . . . . 80\CleaningP (¬) . . . . . . . . . . 80\CleaningPP (­) . . . . . . . . . 80\clickb (;) . . . . . . . . . . . . 12\clickc () . . . . . . . . . . . . . 12\clickt (R) . . . . . . . . . . . . . 12\clock () . . . . . . . . . . . . . 78clock symbols . . . . . . . . . . . 81\Clocklogo (U) . . . . . . . . . . 76\closedcurlyvee () . . . . . . 23\closedcurlywedge () . . . . 23\closedequal () . . . . . . . . 32\closedniomega (?) . . . . . . 12\closedprec () . . . . . . . . . 32\closedrevepsilon () . . . . 12\closedsucc () . . . . . . . . . 32\Cloud () . . . . . . . . . . . . . 80clovers . . . . . . . . . . . . . . . . 74clubs (suit) . . . . . . . . 62–64, 77\clubsuit (♣) . . . . . . . . . . 62\clubsuit (♣) . . . . . . . . . . . 63cmll (package) 20, 23, 30, 36, 104\coAsterisk (§) . . . . . . . . . 22\coasterisk (§) . . . . . . . . . 22code page 1252 . . . . . . . . . 103table . . . . . . . . . . . . . 103code page 437 . . . . . . . 69, 101\Coffeecup (K) . . . . . . . . . 76\coh (¨) . . . . . . . . . . . . . . . 36\colon . . . . . . . . . . . . . . . . 61\colon (: ) . . . . . . . . . . . . . 61\colon (∶) . . . . . . . . . . . . . . 61\Colonapprox () . . . . . . . 31\Colonapprox (::≈) . . . . . . . 34\colonapprox (:≈) . . . . . . . . 34\colonapprox () . . . . . . . . 31\Coloneq () . . . . . . . . . . . 31\Coloneq (::−) . . . . . . . . . . . 34\coloneq () . . . . . . . . . . . 31\coloneq (:−) . . . . . . . . . . . 34\coloneq () . . . . . . . . . . . 31\Coloneqq () . . . . . . . . . . 31\Coloneqq (::=) . . . . . . . . . . 34\coloneqq (:=) . . . . . . . . . . 34\coloneqq (≔) . . . . . . . 20, 31\Colonsim () . . . . . . . . . . 31\Colonsim (::∼) . . . . . . . . . . 34\colonsim (:∼) . . . . . . . . . . 34\colonsim () . . . . . . . . . . 31\comment (RR) . . . . . . . . . . 82communication symbols . . . . 69comp.text.tex (newsgroup) . 7,20, 90–95\compensation (n) . . . . . . . 82\complement (A) . . . . . . . . . 51\complement (∁) . . . . . . . . . 51\complement (∁) . . . . . . . . . 29complex numbers (C) . . . . seealphabets, mathComprehensive TEX Archive Network1, 7, 57, 66, 87, 103,104computer hardware symbols . 69computer keys . . . . . . . . . . . 69Computer Modern (font) 87, 89,101\ComputerMouse (Í) . . . . . . . 69\cong () . . . . . . . . . . . . . . 30\cong (≅) . . . . . . . . . . . . . . 32conjunction . . . . . . . see \wedge\conjunction (☌) . . . . . . . . 68consequence relations . . . . . . 34contradiction symbols . . 20, 48control characters . . . . . . . . 69\convolution () . . . . . . . . 22\coprod ( ∐ ) . . . . . . . . . 20, 25\coprod (∐) . . . . . . . . . . . . 29copyright . . . . . . . . . 8, 18, 102\copyright (©) . . . . . . . . . . 8\corner (k) . . . . . . . . . . . . . 16\Corresponds (=) . . . . . . . . 64\corresponds () . . . . . . . . 31\cos (cos) . . . . . . . . . . . 49, 99\cosh (cosh) . . . . . . . . . . . . 49111

\cot (cot) . . . . . . . . . . . . . . 49\coth (coth) . . . . . . . . . . . . 49\counterplay (V) . . . . . . . . 82Courier (font) . . . . . . . . . . . 17CP1252 . . . . see code page 1252CP437 . . . . . see code page 437\CR (␍) . . . . . . . . . . . . . . . . 69\cr . . . . . . . . . . . . . . . . . . . 91Creative Commons licenses . 18crescent (fge package option) 56\Cross () . . . . . . . . . . . . . 75\Cross († vs. * vs. ) . . . . . 88\Cross (*) . . . . . . . . . . . . . 72\Cross (†) . . . . . . . . . . . . . 80\crossb (¥) . . . . . . . . . . . . . 12\CrossBoldOutline (-) . . . . 72\CrossClowerTips (4) . . . . 72\crossd () . . . . . . . . . . . . . 12\Crossedbox (X) . . . . . . . . . 76crosses . . . . . . . . . . . 72, 76, 80\crossh (#) . . . . . . . . . . . . . 12\CrossMaltese (.) . . . . . . . 72\crossnilambda (3) . . . . . . 12\CrossOpenShadow (+) . . . . . 72\CrossOutline (,) . . . . . . . 72crotchet . . see musical symbols\crtilde ( ã) Ŕ . . . . . . . . . . . . 15crucifixes . . . . . . . . . . . . 72, 80\Crux (†) . . . . . . . . . . . . . . 56\crux (†) . . . . . . . . . . . . . . 56\csc (csc) . . . . . . . . . . . . . . 49CTAN see Comprehensive TEXArchive Network\Ctrl ( Ctrl ) . . . . . . . . . . . 69\Cube . . . . . . . . . . . . . . 81, 90cube root . . . . . . . . see \sqrt\Cup (⋒) . . . . . . . . . . . . . . . 21\Cup (⋓) . . . . . . . . . . . . . . . 23\cup (Y) . . . . . . . . . . . . . . . 22\cup (∪) . . . . . . . . . . 20, 91, 99\cup (∪) . . . . . . . . . . . . . . . 23\cupdot (⊍) . . . . . . . . . . . . 23\cupplus (⊎) . . . . . . . . . . . . 23\curlyc () . . . . . . . . . . . . . 12\curlyeqprec () . . . . . . . . 31\curlyeqprec () . . . . . . . . 30\curlyeqprec (⋞) . . . . . . . . 32\curlyeqsucc (·) . . . . . . . . 31\curlyeqsucc () . . . . . . . . 30\curlyeqsucc (⋟) . . . . . . . . 32\curlyesh (N) . . . . . . . . . . . 12\curlyvee (O) . . . . . . . . . . 22\curlyvee () . . . . . . . . . . 21\curlyvee (⋎) . . . . . . . . . . . 23\curlyveedot () . . . . . . . . 23\curlyveedownarrow () . . . 21\curlyveeuparrow () . . . . . 21\curlywedge (N) . . . . . . . . . 22\curlywedge () . . . . . . . . . 21\curlywedge (⋏) . . . . . . . . . 23\curlywedgedot () . . . . . . 23\curlywedgedownarrow () . 21\curlywedgeuparrow () . . . 21\curlyyogh (a) . . . . . . . . . . 12\curlyz (^) . . . . . . . . . . . . . 12\currency (¤) . . . . . . . . . . . 17currency symbols . . . . . . 17, 65\curvearrowbotleft (ó) . . 42\curvearrowbotleftright (õ). . . . . . . . . 42\curvearrowbotright (ô) . . 42\curvearrowdownup () . . . . 43\curvearrowleft (ð) . . . . . 42\curvearrowleft () . . . . . 41\curvearrowleft (↶) . . . . . 44\curvearrowleftright (ò) . 42\curvearrowleftright () . 43\curvearrownesw () . . . . . 43\curvearrownwse () . . . . . 43\curvearrowright (ñ) . . . . 42\curvearrowright () . . . . 41\curvearrowright (↷) . . . . 44\curvearrowrightleft () . 43\curvearrowsenw () . . . . . 43\curvearrowswne () . . . . . 43\curvearrowupdown () . . . . 43\Cutleft (s) . . . . . . . . . . . 71\Cutline (r) . . . . . . . . . . . 71cutoff subtraction . see \dotdiv\Cutright (q) . . . . . . . . . . 71D\D (ä) . . . . . . . . . . . . . . . . . 16d (esvect package option) . . . 59\d (ạ) . . . . . . . . . . . . . . . . . 13\dag (†) . . . . . . . . . . . . 8, 103\dagger (†) . . . . . . . . . . . . . 20\daleth (ℸ) . . . . . . . . . . . . 50\daleth (ℸ) . . . . . . . . . . . . 50dangerous bend symbols . . . 76\DArrow ( ↓ ) . . . . . . . . . . 69\dasharrow . . . . . . . . . . . . see\dashrightarrow\dasheddownarrow (⇣) . . . . . 43\dashedleftarrow (⇠) . . . . 43\dashednearrow () . . . . . . 43\dashednwarrow () . . . . . . 43\dashedrightarrow (⇢) . . . . 43\dashedsearrow () . . . . . . 43\dashedswarrow () . . . . . . 43\dasheduparrow∫(⇡) . . . . . . . 43\dashint (− ) . . . . . . . . . . . 93\dashleftarrow () . . . . . . 41\dashleftarrow (⇠) . . . . . . 44\dashleftrightarrow () . . 42\dashrightarrow () . . . . . 41\dashrightarrow (⇢) . . . . . 44\DashV ()) . . . . . . . . . . . . . 31\Dashv ()) . . . . . . . . . . . . . 31\dashv (⊣) . . . . . . . . . . . . . 30\dashv (⊣) . . . . . . . . . . . . . 33\dashVv (-) . . . . . . . . . . . . 31\davidsstar () . . . . . . . . . 73\DavidStar (0) . . . . . . . . . 74\DavidStarSolid (/) . . . . . 74\dbar (¯d) . . . . . . . . . . . . . . . 91\dbend () . . . . . . . . . . . . 76dblaccnt (package) . . . . . . . . 94\dblcolon (::) . . . . . . . . . . . 34\DCa (␑) . . . . . . . . . . . . . . . 69\DCb (␒) . . . . . . . . . . . . . . . 69\DCc (␓) . . . . . . . . . . . . . . . 69\DCd (␔) . . . . . . . . . . . . . . . 69\DD (DD) . . . . . . . . . . . . . . . 79\ddag (‡) . . . . . . . . . . . 8, 103\ddagger (‡)∫. . . . . . . . . . . . 20\ddashint (= ) . . . . . . . . . . . 93\ddddot ( .... ) . . . . . . . . . . . . 56\dddot ( ... ) . . . . . . . . . . . . . 56\dddtstile ( ) . . . . . . . . . 34\DDohne (DD/) . . . . . . . . . . . . 79\ddot (¨) . . . . . . . . . . . . . . 56\ddotdot () . . . . . . . . . 23, 61\ddots ( . . .) . . . . . . . . . 61, 94\ddots (⋱) . . . . . . . . . . . . . 61\ddststile ( ) . . . . . . . . . 34\ddtstile ( ) . . . . . . . . . . 34\ddttstile ( ) . . . . . . . . 34\DeclareFontFamily . . . . . . 98\DeclareFontShape . . . . . . . 98\DeclareMathOperator . . . . 99\DeclareMathOperator* . . . 99\declareslashed . . . . . . . . 92definite-description operator ( ). . . . . . . . . 90definition symbols . . . . . 20, 95\deg (deg) . . . . . . . . . . . . . 49\degree (0) . . . . . . . . . . . . . 63\degree (°) . . . . . . . . . . . . . 67degrees . . . . . see \textdegree\DEL (␡) . . . . . . . . . . . . . . . 69\Del ( Del ) . . . . . . . . . . . . 69\Deleatur . . . . . see \Denariusdelimiters . . . . . . . . . . . 52–56text-mode . . . . . . . . . . 56variable-sized . . . . . 53–55wavy-line . . . . . . . . 54, 55\Delta (∆) . . . . . . . . . . . . . 49\delta (δ) . . . . . . . . . . . . . 49\deltaup (δ) . . . . . . . . . . . . 50demisemiquaver . . . see musicalsymbols\Denarius (¢) . . . . . . . . . . 17\dental (ag) . . . . . . . . . . . . . 15derivitive, partial . see \partial\descnode () . . . . . . . . . . 68\det (det) . . . . . . . . . . . . . . 49\devadvantage (t) . . . . . . . 82\Dfourier (.❝ ) . . . . . . . . 35\dfourier ( ❝ .) . . . . . . . . 35\DFT ( ) . . . . . . . . . . . . . 60\dft ( ) . . . . . . . . . . . . . 60ι112

\DH (Ð) . . . . . . . . . . . . . 9, 102\DH (̷D) . . . . . . . . . . . . . . . . 12\dh (ð) . . . . . . . . . . . . . 9, 102\dh (ð) . . . . . . . . . . . . . . . . 12diacritics . . . . . . . . see accents\diaeresis (ä) . . . . . . . . . . 16diæresis . . . . . . . . see accents\diagdown (å) . . . . . . . . . . 63\diagdown () . . . . . . . . . . 63\diagdown () . . . . . . . . . . 33\diagonal (G) . . . . . . . . . . 82\diagup (ä) . . . . . . . . . . . . 63\diagup () . . . . . . . . . . . . 63\diagup () . . . . . . . . . . . . 33\diameter (I) . . . . . . . . . . 63\diameter (⌀) . . . . . . . . . . 20\diameter (∅) . . . . . . . . . . . 63\diameter (⌀) . . . . . . . . . . 78\Diamond (⋄) . . . . . . . . . . . 62\Diamond (⋄) . . . . . . . . . . . 63\Diamond (◇) . . . . . . . . . . . 24\diamond (⋄) . . . . . . . . . . . . 20\diamond (◇) . . . . . . . . . . . . 24\diamondbackslash () . . . . 24\Diamondblack () . . . . . . . 63\diamonddiamond () . . . . . 24\Diamonddot () . . . . . . . . . 63\diamonddot (⟐) . . . . . . . . . 24\DiamonddotLeft () . . . . 42\Diamonddotleft () . . . . 42\DiamonddotRight () . . . . 42\Diamonddotright () . . . . 42\diamonddots () . . . . . 23, 61\DiamondLeft () . . . . . . . 42\Diamondleft () . . . . . . . 42\diamondminus () . . . . . . . 24\diamondplus () . . . . . . . . 24\DiamondRight () . . . . . . 42\Diamondright () . . . . . . 42diamonds . . . . . . . . . . . . . . 75diamonds (suit) . . . . . 62–64, 77\DiamondShadowA (¥) . . . . . 75\DiamondShadowB (¦) . . . . . 75\DiamondShadowC (§) . . . . . 75\Diamondshape (6) . . . . . . . 75\diamondslash () . . . . . . . 24\DiamondSolid (p) . . . . . . . 75\diamondsuit (♦) . . . . . . . . 62\diamondsuit (♢) . . . . . . . . 63\diamondtimes () . . . . . . . 24\diamondvert () . . . . . . . . 24\diatop . . . . . . . . . . . . 16, 94\diaunder . . . . . . . . . . . 16, 94dice . . . . . . . . . . . . . . . 81, 90dictionary symbols . . . 10–13, 84dictsym (package) . 84, 104, 105died . . . . . . . . . see \textdieddifferential, inexact . see \dbar\digamma (Ϝ) . . . . . . . . . . . 49digits . . . . . . . . . . . . . . . . . 62LCD . . . . . . . . . . . . . . 67Mayan . . . . . . . . . . . . . 62old-style . . . . . . . . . . . . 18segmented . . . . . . . . . . 67\dim (dim) . . . . . . . . . . . . . 49\ding . . . . . . . . . . 9, 71–75, 77dingautolist . . . . . . . . . . . 73dingbat (package) 72, 77, 88, 104,105dingbat symbols . . . . . . 71–77\Diple (>) . . . . . . . . . . . . . 82\diple (>) . . . . . . . . . . . . . 82\Diple* (>·· ) . . . . . . . . . . . . 82\diple* (>·· ) . . . . . . . . . . . . 82Dirac notation . . . . . . . . . . . 53discount . . . see \textdiscountdiscretionary hyphen . . . . . 103disjoint union . . . . . . . . . . . 20disjunction . . . . . . . . see \vee\displaystyle . . 92, 93, 95, 99ditto marks . see \textquotedbl\div (÷) . . . . . . . . . . . . . . . 20\div (÷) . . . . . . . . . . . . . . . 23\divdot (£) . . . . . . . . . . . . 22\divideontimes () . . . . . . 22\divideontimes () . . . . . . 21\divides () . . . . . . . . . . . . 31\divides () . . . . . . . . . . . 33division . . . . . . . . . . . . . 20, 57non-commutative . . . . . 60division times . . . . . . . . . . see\divideontimesdivorced . . . see \textdivorced\DJ (Ð) . . . . . . . . . . . . . . . . . 9\dj (đ) . . . . . . . . . . . . . . . . . 9\dlbari (() . . . . . . . . . . . . . 12\DLE (␐) . . . . . . . . . . . . . . . 69\dlsh (ê) . . . . . . . . . . . . . . 42\dndtstile ( ) . . . . . . . . . 34\dnststile ( ) . . . . . . . . . 34\dntstile ( ) . . . . . . . . . . 34\dnttstile ( ) . . . . . . . . 35does not divide . . . . see \nmiddoes not exist . . . see \nexists\Dohne (D/) . . . . . . . . . . . . . 79dollar . . . . . . see \textdollardollar sign . . . . . . . . . . . see \$\Dontwash (Ý) . . . . . . . . . . 80\dot ( ˙ ) . . . . . . . . . . . . . . . 56dot symbols . . . . . 8, 61, 62, 94\dotcup ( ·∪) . . . . . . . . . 20, 91\dotdiv (¡) . . . . . . . . . . . . 22\Doteq . . . . . . . see \doteqdot\Doteq (≑) . . . . . . . . . . . . . 32\doteq (≐) . . . . . . . . . . . . . 30\doteq (≐) . . . . . . . . . . . . . 32\doteqdot () . . . . . . . . . . 30\doteqdot (≑) . . . . . . . . . . . 33dotless i (ı)math mode . . . . . . 56, 62text mode . . . . . . . . . . 13dotless j (j)math mode . . . . . . 56, 62text mode . . . . . . . . . . 13\dotmedvert () . . . . . . . . . 23\dotminus (∸) . . . . . . . . . . . 23\dotplus ( ) . . . . . . . . . . . 22\dotplus (∔) . . . . . . . . . . . 21\dots (. . . ) . . . . . . . . . . 8, 103dots (ellipses) . . . . 8, 61, 62, 94\dotsb (· · · ) . . . . . . . . . . . . 61\dotsc (. . .) . . . . . . . . . . . . 61\dotseq () . . . . . . . . . . . . 31\dotsi (· · · ) . . . . . . . . . . . . 61\dotsint (¯) . . . . . . . . . . 28\dotsm (· · · ) . . . . . . . . . . . . 61\dotso (. . .) . . . . . . . . . . . . 61dotted union ( ˙∪) . . . . . . . . . 99\dottedtilde ( ã) .. . . . . . . . . 15\dottimes (¢) . . . . . . . . . . 22\double . . . . . . . . . . . . . . . 55\doublebarwedge (Z) . . . . . 22\doublebarwedge () . . . . . 21\doublecap . . . . . . . . see \Cap\doublecap (\) . . . . . . . . . . 22\doublecap (⋒) . . . . . . . . . . 23\doublecup . . . . . . . . see \Cup\doublecup (]) . . . . . . . . . . 22\doublecup (⋓) . . . . . . . . . . 23\doublecurlyvee () . . . . . 23\doublecurlywedge () . . . . 23\doublefrown () . . . . . . . . 48\doublefrowneq () . . . . . . . 48\doublepawns (d) . . . . . . . . 82\doublesmile () . . . . . . . . 48\doublesmileeq () . . . . . . . 48\doublesqcap (⩎) . . . . . . . . 23\doublesqcup (⩏) . . . . . . . . 23\doubletilde (ã) . . . . . . . . 15\doublevee (⩔) . . . . . . . . . . 23\doublewedge (⩕) . . . . . . . . 23\DOWNarrow () . . . . . . . . . . 78\Downarrow (⇓) . . . . . . . 41, 53\Downarrow (⇓) . . . . . . . . . . 43\downarrow . . . . . . . . . . . . . 99\downarrow (↓) . . . . . . . 41, 53\downarrow (↓) . . . . . . . . . . 43\downarrowtail () . . . . . . . 43\downbracketfill . . . . . . . . 95\downdownarrows (Ó) . . . . . 42\downdownarrows () . . . . . 41\downdownarrows (⇊) . . . . . 43\downdownharpoons (Û) . . . . 43Downes, Michael J. . . . 49, 106\downfilledspoon () . . . . . 47\downfootline () . . . . . . . . 32\downfree (⫝) . . . . . . . . . . . 32\downharpoonccw (⇂) . . . . . . 46\downharpooncw (⇃) . . . . . . . 46\downharpoonleft (å) . . . . . 43\downharpoonleft (⇃) . . . . . 41\downharpoonright (ç) . . . . 43\downharpoonright (⇂) . . . . 41\downlsquigarrow () . . . . . 43\downmapsto (↧) . . . . . . . . . 43\downModels () . . . . . . . . . 32\downmodels () . . . . . . . . . 32113

\downp ( ) .............. 16\downparenthfill ........ 95\downpitchfork (⫛) ....... 47\downpropto () ......... 32\downrsquigarrow () ..... 43\downslice () .......... 24\downspoon (⫰) .......... 47\downt ( ) .............. 16\downtherefore (∵) . . . 23, 61\downtouparrow ( ) ...... 42\downuparrows ( ) ....... 42\downuparrows (⇵) ....... 43\downupharpoons ( ) ...... 43\downupharpoons (⥯) ...... 46\downVdash (⍑) .......... 32\downvdash (⊤) .......... 32\downY () ............. 23\drsh ( ) .............. 42\DS (SS) ................ 79\Ds (ss) ................ 79\dsaeronautical (a) ..... 84\dsagricultural (G) ..... 84\dsarchitectural (A) .... 84\dsbiological (B) ....... 84\dschemical (C) ......... 84\dscommercial (c) ....... 84\dsdtstile ( ) ......... 35dsfont (package) ..... 65,104\dsheraldical (H) ....... 84\dsjuridical (J) ........ 84\dsliterary (L) ......... 84\dsmathematical (M) ...... 84\dsmedical (m) .......... 84\dsmilitary (X) ......... 84\dsrailways (R) ......... 84\dsststile ( ) ......... 35\dstechnical (T) ........ 84\dststile ( ) .......... 35\dsttstile ( ) ........ 35\dtdtstile ( ) ......... 35\dtimes () ............ 23\dtimes () ............ 23\dtststile ( ) ......... 35\dttstile ( ) .......... 35\dtttstile ( ) ........ 35DVI ............. 18,69,97\dz ( ) ............... 12Ee (esvect package option) . . . 59\e (e) ................. 51ε-TEX ................. 53\Earth ( ) ............. 68\Earth (Ê) ............. 68\earth (♁) ............. 68\Ecommerce () ......... 17\EightAsterisk ( ) ...... 74\EightFlowerPetal ( ) ... 74\EightFlowerPetalRemoved ( )......... 74eighth note see musical symbols\eighthnote (♪) ......... 78\eighthnote () ......... 78\EightStar ( ) ......... 74\EightStarBold ( ) ...... 74\EightStarConvex ( ) .... 74\EightStarTaper ( ) ..... 74\ejective ( ) ........... 12electrical symbols . . . ..... 67electromotive force (E) .... seealphabets, math\ell (l) ............... 51\Ellipse ( ) ........... 75ellipses (dots) . . . . 8, 61, 62, 94ellipses (ovals) . . . ........ 75\EllipseShadow ( ) ...... 75\EllipseSolid ( ) ....... 75\EM (␙) ................ 69\Email (k) ............. 69\Emailct (z) ........... 69\emgma ( ) ............. 12\emptyset (∅) ........... 62\emptyset (∅) ........... 63\End ( End ) ............ 69endofproof ............ 62\ending (L) ............ 82\eng ( ) ............... 11engineering symbols . . . . 67, 70\engma ( ) ............. 12\ENQ (␅) ............... 69entails . . . ....... see \models\Enter ( Enter ) ......... 69\Envelope ( ) ........... 77\enya ( ) .............. 12\EOT (␄) ............... 69epsdice (package) . . 81, 104, 105\epsdice ( ) ..... 81\epsi ( ) .............. 12\epsilon (ɛ) ............ 49\epsilonup (ɛ) .......... 50\eqbump () ............. 32\eqbumped ( ) .......... 31\eqcirc ( ) ............ 31\eqcirc (≖) ............ 30\eqcirc (≖) ............. 32\Eqcolon () ........... 31\Eqcolon (−::) ........... 34\eqcolon ( ) ........... 31\eqcolon (−:) ........... 34\eqcolon () ........... 31\eqdot (⩦) ............. 32\eqfrown () ............ 48\Eqqcolon () .......... 31\Eqqcolon (=::) .......... 34\eqqcolon (=:) .......... 34\eqqcolon (≕) .......... 31\eqsim () ............. 31\eqsim (≂) ............. 32\eqslantgtr ( ) ......... 38\eqslantgtr () ......... 37\eqslantgtr (⪖) ......... 39\eqslantless ( ) ........ 38\eqslantless () ........ 37\eqslantless (⪕) ........ 39\eqsmile () ............ 48\equal (=) ............. 32\equal (j) ............. 82\equalclosed () ........ 32\equalsfill ......... 20,95equidecomposable ........ 91equilibrium ............ see\rightleftharpoons\equiv (≡) .......... 20,30\equiv (≡) ............. 32equivalence ............ see\equiv, \leftrightarrow,and \threesim\equivclosed () ........ 32\er ( ) ................ 11es-zet . ............ see \ss\ESC (␛) ............... 69\Esc ( Esc ) ............ 69escapable characters ....... 8\esh ( ) ............... 11\esh ( ) ............... 12esint (package) . . . .... 28,104\Estatically (J) ........ 70estimated . see \textestimatedesvect (package) ...... 59,104\eta (η) ............... 49\etaup (η) ............. 50\ETB (␗) ............... 69\etc (P) ............... 82\eth (ð) ............... 63\eth ( ) ............... 11\eth ( ) ............... 12\ETX (␃) ............... 69eufrak (package) ......... 65Euler Roman ............ 50\EUR (e ) ............... 17\EURcr (d) ............. 17\EURdig (D) ............ 17\EURhv (c) ............. 17\euro ................. 17euro signs .............. 17blackboard bold ...... 65eurosym (package) . 17, 104, 105\EURtm (e) ............. 17euscript (package) . 65, 104, 105evaluated at . . .... see \vertevil spirits . . . ........... 86exclusive or ............. 90\exists ( ) ............. 51\exists (∃) ............. 51\exists (∃) ............. 51\exp (exp) . ............ 49\Explosionsafe (`) ...... 70extarrows (package) 60, 104, 105extensible accents 57–60, 95–96extensible arrows ...... 57–60114

extensible symbols, creating 94–96extensible tildes . . . . . . . 57, 59extension characters . . . 48, 49extpfeil (package) . . 60, 104, 105extraipa (package) . . . . 15, 104\eye (E) . . . . . . . . . . . . . 77\EyesDollar (¦) . . . . . . . . . 17Ff (esvect package option) . . . 59faces . . . . . . . . . . 69, 78, 80, 85\fallingdotseq () . . . . . . 31\fallingdotseq () . . . . . . 30\fallingdotseq (≒) . . . . . . . 32\FallingEdge (!) . . . . . . . . 67\fatbslash () . . . . . . . . . . 21\fatsemi () . . . . . . . . . . . . 21\fatslash () . . . . . . . . . . . 21\FAX (u) . . . . . . . . . . . . . . 69\fax (t) . . . . . . . . . . . . . . . 69\Faxmachine (v) . . . . . . . . 69fc (package) . . . . . . . . . . 9, 13fclfont (package) . . . . . . . . 104feet . . . . . . . . . see \prime and\textquotesingle\FEMALE () . . . . . . . . . . . . 70\Female (~) . . . . . . . . . . . . 70\female (♀) . . . . . . . . . . . . . 70\FemaleFemale („) . . . . . . . 70\FemaleMale (…) . . . . . . . . . 70\Ferli (a ⌢. ) . . . . . . . . . . . . . 79\Fermi (a ⌢. ) . . . . . . . . . . . . . 79fermions . . . . . . . . . . . . . . . 70feyn (package) . . . . 70, 104, 105Feynman slashed character notation. . . . . . . . . . . . . . 92Feynman-diagram symbols . . 70\feyn{a} (a) . . . . . . . . . . . . . 70\feyn{c} (c) . . . . . . . . . . . 70\feyn{fd} ( ) . . . . . . . . . . . 70\feyn{fl} (n) . . . . . . . . 70\feyn{fs} (e) . . . . . . . . . . . 70\feyn{fu} (¡) . . . . . . . . . . . 70\feyn{fv} (¢) . . . . . . . . . . . . 70\feyn{f} (f) . . . . . . . . . . . 70\feyn{glu} (w) . . . . . . . . . . . 70\feyn{gl} (o) . . . . . . . . . . . . 70\feyn{gu} (¥) . . . . . . . . . . . 70\feyn{gvs} (§) . . . . . . . . . . . 70\feyn{gv} (¦) . . . . . . . . . . . . 70\feyn{g} (g) . . . . . . . . . . . 70\feyn{hd} () . . . . . . . . . . . 70\feyn{hs} (i) . . . . . . . . . . . 70\feyn{hu} () . . . . . . . . . . . 70\feyn{h} (h) . . . . . . . . . . . 70\feyn{ms} (l) . . . . . . . . . . . 70\feyn{m} (m) . . . . . . . . . . . 70\feyn{p} (p) . . . . . . . . . . . 70\feyn{x} (x) . . . . . . . . . . . . . 70\FF (␌) . . . . . . . . . . . . . . . . 69fge (package) . 47, 52, 56, 62, 64,104, 105fge-digits . . . . . . . . . . . . . . . 62\fgeA (A) . . . . . . . . . . . . . . 52\fgebackslash (K) . . . . . . . . 64\fgebaracute (M) . . . . . . . . 64\fgebarcap (O) . . . . . . . . . . 64\fgec (c) . . . . . . . . . . . . . . 52\fgecap (S) . . . . . . . . . . . . 64\fgecapbar (Q) . . . . . . . . . . 64\fgecup (N) . . . . . . . . . . . . 64\fgecupacute (R) . . . . . . . . 64\fgecupbar (P) . . . . . . . . . . 64\fged (p) . . . . . . . . . . . . . . 52\fgee (e) . . . . . . . . . . . . . . 52\fgeeszett () . . . . . . . . . . 52\fgeeta () . . . . . . . . . . . . 52\fgeF (F) . . . . . . . . . . . . . . 52\fgef (f) . . . . . . . . . . . . . . 52\fgeinfty (i) . . . . . . . . . . 64\fgelangle (h) . . . . . . . . . . 64\fgelb . . . . . . . . . . . . . . . . 52\fgelb () . . . . . . . . . . . . . 52\fgeleftB (D) . . . . . . . . . . . 52\fgeleftC (C) . . . . . . . . . . . 52\fgeN () . . . . . . . . . . . . . . 52\fgeoverU () . . . . . . . . . . . 52\fgerightarrow (!) . . . . . 47\fgerightB (B) . . . . . . . . . . 52\fges (s) . . . . . . . . . . . . . . . 52\fgestruckone (1) . . . . . . . . 62\fgestruckzero (0) . . . . . . . 62\fgeU (U) . . . . . . . . . . . . . . 52\fgeuparrow (") . . . . . . . . . 47\fgeupbracket (L) . . . . . . . 64\FHBOLOGO (f) . . . . . . . . . . . 80\FHBOlogo (F) . . . . . . . . . . . 80\file (H) . . . . . . . . . . . . . . 82\FilledBigCircle (U) . . . . 75\FilledBigDiamondshape (V) 75\FilledBigSquare (P) . . . . 75\FilledBigTriangleDown (S) 75\FilledBigTriangleLeft (R) 75\FilledBigTriangleRight (T). . . . . . . . . 75\FilledBigTriangleUp (Q) . 75\FilledCircle (e) . . . . . . . 75\FilledCloud ( ) . . . . . . . . 80\filleddiamond (◆) . . . . . . . 24\FilledDiamondShadowA (¨) 75\FilledDiamondShadowC (©) 75\FilledDiamondshape (f) . . 75\FilledHut () . . . . . . . . . . 81\filledlargestar (☀) . . . . 74\filledlozenge (⧫) . . . . . . . 74\filledmedlozenge (⧫) . . . . 74\filledmedsquare (∎) . . . . . 24\filledmedtriangledown (▼) 24,40\filledmedtriangleleft (◀) 24,40\filledmedtriangleright (▶). . . . . . . 24, 40\filledmedtriangleup (▲) 24,40\FilledRainCloud (!) . . . . 80\FilledSectioningDiamond (¢). . . . . . . . . 81\FilledSmallCircle (u) . . 75\FilledSmallDiamondshape (v). . . . . . . . . 75\FilledSmallSquare (p) . . 75\FilledSmallTriangleDown (s). . . . . . . . . 75\FilledSmallTriangleLeft (r). . . . . . . . . 75\FilledSmallTriangleRight(t) . . . . . . . . . . . . . . 75\FilledSmallTriangleUp (q) 75\FilledSnowCloud ($) . . . . 80\FilledSquare (`) . . . . . . . 75\filledsquare (◾) . . . . . . . . 24\FilledSquareShadowA (£) . 75\FilledSquareShadowC (¤) . 75\filledsquarewithdots (C) 77\filledstar (★) . . . . . . . . . 24\FilledSunCloud (#) . . . . . 80\FilledTriangleDown (c) . . 75\filledtriangledown (▾) 24, 40\FilledTriangleLeft (b) . . 75\filledtriangleleft (◂) 24, 40\FilledTriangleRight (d) . 75\filledtriangleright (▸) 24,40\FilledTriangleUp (a) . . . 75\filledtriangleup (▴) . 24, 40\FilledWeakRainCloud (") . 80finger, pointing . . . . . . see fists\finpartvoice (aˇ) » \finpartvoiceless (a »˚) . . . . 15\fint ( ) . . . . . . . . . . . . . . 27\fint ( ffl ) . . . . . . . . . . . . . . 28\Finv (F) . . . . . . . . . . . . . . 51\Finv (Ⅎ) . . . . . . . . . . . . . . 51\Fire () . . . . . . . . . . . . . . 81fish hook . . . . . . see \strictiffists . . . . . . . . . . . . . . . . . . 72\fivedots () . . . . . . . . 23, 61\FiveFlowerOpen (R) . . . . . 74\FiveFlowerPetal (P) . . . . 74\FiveStar (8) . . . . . . . . . . 74\FiveStarCenterOpen (;) . . 74\FiveStarConvex (?) . . . . . 74\FiveStarLines (7) . . . . . . 74\FiveStarOpen (9) . . . . . . . 74\FiveStarOpenCircled (:) . 74115

\FiveStarOpenDotted () 74\FiveStarShadow (@) . . . . . 74\Fixedbearing (%) . . . . . . . 70\fixedddots ( . . .) . . . . . . . . 61\fixedvdots ( . . .) . . . . . . . . . . 61fixmath (package) . . . . . . . 100\fj (F) . . . . . . . . . . . . . . . . 12\Flag () . . . . . . . . . . . . . . 81\flap (f) . . . . . . . . . . . . . . 12\flapr (D) . . . . . . . . . . . . . . 11\flat (♭) . . . . . . . . . . . 62, 78\flat (♭) . . . . . . . . . . . . . . . 63\Flatsteel (–) . . . . . . . . . . 70fletched arrows . . . . . . . 47, 71florin . . . . . . see \textflorinflowers . . . . . . . . . . . . . . . . 74Flynn, Peter . . . . . . . . . . . . 91\Fog () . . . . . . . . . . . . . . 80font encodings . . . . . 7, 100, 1037-bit . . . . . . . . . . . . . . . 78-bit . . . . . . . . . . . . . . . 7ASCII . . . . . . . . . . . . 104document . . . . . . . . . . 103Latin 1 . . . . . . . . . . . 104limiting scope of . . . . . . . 7LY1 . . . . . . . . . . . . . . . . 7OT1 7, 9, 13, 94, 100, 101,103OT2 . . . . . . . . . . . . . . 90T1 . . . . . 7, 9, 13, 101, 103T4 . . . . . . . . . . . 9, 13, 16T5 . . . . . . . . . . . . . . 9, 13TS1 . . . . . . . . . . . . . . 103fontdef.dtx (file) . . . . . 90, 94fontenc (package) . . 7, 9, 13, 103\fontencoding . . . . . . . . . . . 7fontsCalligra . . . . . . . . . . . . 65Charter . . . . . . . . . 17, 29Computer Modern . 87, 89,101Courier . . . . . . . . . . . . 17Garamond . . . . . . . 17, 29Helvetica . . . . . . . . . . . 17Symbol . . . . . . . . . 50, 90Times Roman . . . . 17, 89Type 1 . . . . . . . . . . . . 99Utopia . . . . . . . . . . 17, 29Zapf Chancery . . . . . . . 65Zapf Dingbats . . . . 71, 73\fontsize . . . . . . . . . . . 87, 89\Football (o) . . . . . . . . . . . 76\forall (∀) . . . . . . . . . . . . . 51\forall (∀) . . . . . . . . . . . . 51\Force (l) . . . . . . . . . . . . . 70\Forward (·) . . . . . . . . . . . . 79\ForwardToEnd (¸) . . . . . . . 79\ForwardToIndex (¹) . . . . 79\FourAsterisk (1) . . . . . . . 74\FourClowerOpen (V) . . . . . 74\FourClowerSolid (W) . . . . 74\Fourier ( ❝ ) . . . . . . . . . 35\fourier ( ❝ ) . . . . . . . . . 35Fourier transform (F) . . . . seealphabets, math\FourStar (5) . . . . . . . . . . 74\FourStarOpen (6) . . . . . . . 74\fourth (4) . . . . . . . . . . . . 63fractions . . . . . . . . . . . . . . . 64fraktur . . . see alphabets, mathFrege logic symbols 47, 52, 62, 64\frown (⌢) . . . . . . . . . . . . . 30\frown (⌢) . . . . . . . . . . . . . 48frown symbols . . . . . . . . . . . 48\frowneq () . . . . . . . . . . . . 48\frowneqsmile () . . . . . . . 48\frownie (☹) . . . . . . . . . . . 78\frownsmile () . . . . . . . . . 48\frownsmileeq () . . . . . . . 48\Frowny (§) . . . . . . . . . . . . 80\FS (␜) . . . . . . . . . . . . . . . . 69\FullFHBO () . . . . . . . . . . 80\fullmoon (M) . . . . . . . . . . 68\fullmoon () . . . . . . . . . . 68\fullnote () . . . . . . . . . . . 78G\G (Ÿa) . . . . . . . . . . . . . . . . . 13g (esvect package option) . . . 59\Game (G) . . . . . . . . . . . . . . 51\Game () . . . . . . . . . . . . . . 51\Gamma (Γ) . . . . . . . . . . . . . 49\gamma (γ) . . . . . . . . . . . . . 49\gammaup (γ) . . . . . . . . . . . . 50\Ganz (¯ ) . . . . . . . . . . . . . . 79\GaPa (

\gtreqqless () . . . . . . . . . 37\gtreqqless (⪌) . . . . . . . . . 39\gtrless (») . . . . . . . . . . . 38\gtrless (≷) . . . . . . . . . . . 37\gtrless (≷) . . . . . . . . . . . . 39\gtrneqqless () . . . . . . . . 39\gtrsim (Á) . . . . . . . . . . . . 38\gtrsim () . . . . . . . . . . . . 37\gtrsim (≳) . . . . . . . . . . . . . 39\guillemotleft («) . . . . 9, 102\guillemotright (») . . . 9, 102\guilsinglleft (‹) . . . . 9, 103\guilsinglright (›) . . . 9, 103\gvertneqq (µ) . . . . . . . . . . 38\gvertneqq () . . . . . . . . . 37\gvertneqq (≩) . . . . . . . . . . 39H\H (˝a) . . . . . . . . . . . . . . . . . 13h (esvect package option) . . . 59\h (ả) . . . . . . . . . . . . . . . . . 13\HA (A) . . . . . . . . . . . . . . 84\Ha (a) . . . . . . . . . . . . . . . 84háček . . . . . . . . . . see accents\Hail () . . . . . . . . . . . . . . 80\Halb (˘ “) . . . . . . . . . . . . . . 79half note . . see musical symbols\HalfCircleLeft (s) . . . . . . 75\HalfCircleRight (r) . . . . . 75\HalfFilledHut () . . . . . . 81\halflength (p) . . . . . . . . . 16\halfnote () . . . . . . . . . . . 78\HalfSun () . . . . . . . . . . . 80Hamiltonian (H) see alphabets,math\HandCuffLeft () . . . . . . . 72\HandCuffLeftUp () . . . . . 72\HandCuffRight () . . . . . . 72\HandCuffRightUp () . . . . 72\HandLeft () . . . . . . . . . . 72\HandLeftUp () . . . . . . . . 72\HandPencilLeft () . . . . . 72\HandRight () . . . . . . . . . 72\HandRightUp () . . . . . . . 72hands . . . . . . . . . . . . . see fists\Handwash (Ü) . . . . . . . . . . 80\HaPa (

\Hv (v) . . . . . . . . . . . . . . . 84\hv (") . . . . . . . . . . . . . . . . 12\Hvbar (|) . . . . . . . . . . . . . . 84\HW (W) . . . . . . . . . . . . . . . . 84\Hw (w) . . . . . . . . . . . . . . . 84\HX (X) . . . . . . . . . . . . . . . . 84\Hx (x) . . . . . . . . . . . . . . . . 84\HXthousand (5) . . . . . . . . . 84\HY (Y) . . . . . . . . . . . . . . . 84\Hy (y) . . . . . . . . . . . . . . . 84hyphen, discretionary . . . . . 103\HZ (Z) . . . . . . . . . . . . . . . 84\Hz (z) . . . . . . . . . . . . . . 84I\i (ı) . . . . . . . . . . . . . . . . . 13\ialign . . . . . . . . . . 91, 93, 95\ibar (ī) . . . . . . . . . . . . . . 12IBM PC . . . . . . . . . . . 69, 101Icelandic staves . . . . . . . . . . 85\IceMountain () . . . . . . . . 81\iddots (. .. ) . . . . . . . . . . . . 62\iddots () . . . . . . . . . . . . . 94\idotsint ( ∫ ··· ∫ ) . . . . . . . 25\idotsint ( ) . . . . . . . . 27\idotsint (∫…∫) . . . . . . . . . . 29\iff . see \Longleftrightarrowifsym (package) . 67, 75, 80, 81,88, 90, 104, 105igo (package) . . . . . . . . 76, 104\igocircle (}) . . . . . . . . . 76\igocircle (}) . . . . . . . . . 76\igocross (|) . . . . . . . . . . 76\igocross (|) . . . . . . . . . . 76\igonone ( ) . . . . . . . . . . . 76\igonone ( ) . . . . . . . . . . . 76\igosquare (~) . . . . . . . . . 76\igosquare (~) . . . . . . . . . 76\igotriangle () . . . . . . . . 76\igotriangle () . . . . . . . . 76\iiiint ( ∫∫∫∫ ) . . . . . . . . . 25\iiiint ( ) . . . . . . . . . . . 27\iiiint (ˇ) . . . . . . . . . . . 28\iiiint (⨌) . . . . . . . . . . . 29\iiint ( µ ) . . . . . . . . . . . . 26\iiint ( ∫∫∫ ) . . . . . . . . . . . 25\iiint ( ) . . . . . . . . . 25, 27\iiint (˝) . . . . . . . . . . . . 28\iiint (∭) . . . . . . . . . . . . . 29\iint (´) . . . . . . . . . . . . . . 26\iint ( ∫∫ ) . . . . . . . . . . . . . 25\iint ( ) . . . . . . . . . . . 25, 27\iint (˜) . . . . . . . . . . . . . . 28\iint (∬) . . . . . . . . . . . . . . 29\Im (I) . . . . . . . . . . . . . . . . 51\im (j) . . . . . . . . . . . . . . . . 51\imath (ı) . . . . . . . . . . . 51, 56\impliedby see \Longleftarrow\implies see \Longrightarrowand \vdashimpulse train . . . . . . . . see sha\in (P) . . . . . . . . . . . . . . . . 51\in (∈) . . . . . . . . . . . . . . . . 51\in (∈) . . . . . . . . . . . . . . . . 51\in (∈) . . . . . . . . . . . . . . . . 51inches . . . . . . . see \second and\textquotedbl\incoh (˚) . . . . . . . . . . . . . 36independenceprobabilistic . . . . . . . . . 93statistical . . . . . . . . . . . 93stochastic . . . . . see \bot\independent (⊥) . . . . . . . . 93\Industry (I) . . . . . . . . . . 76inequalities . . . . . . . . . 8, 37–39inexact differential . . see \dbar\inf (inf) . . . . . . . . . . . . . . 49infinity (∞) . . . . . . . see \infty\Info (i) . . . . . . . . . . . . . . 76information symbols . . . . . . 76informator symbols . . . . . . . 82\infty (8) . . . . . . . . . . . . . 63\infty (∞) . . . . . . . . . . . . . 62\infty (∞) . . . . . . . . . . . . . 63\inipartvoice (a –ˇ) . . . . . . . 15\inipartvoiceless (a –˚) . . . . 15\injlim (inj lim) . . . . . . . . . 49\inplus () . . . . . . . . . . . . 30\Ins ( Ins ) . . . . . . . . . . . . 69\int ( ) . . . . . . . . . . . . . . . 26\int ( ∫ ) . . . . . . . . . . . . . . . 25\int ( ) . . . . . . . . . . . . . . . 25\int (∫) . . . . . . . . . . . . . . . 29\intclockwise ( ) . . . . . . . 29integers (Z) see alphabets, mathintegrals . . . . . 25–29, 63, 92–93integrals (wasysym package option). . . . . . . . . . . . . 25\intercal (⊺) . . . . . . . . . . . 21\intercal (⊺) . . . . . . . . . . . 51\interleave (⫴) . . . . . . . . . 21intersection . . . . . . . . see \cap\Interval () . . . . . . . . . . 81\inva ( ) . . . . . . . . . . . . . . 12\invamp () . . . . . . . . . . . . 21\invbackneg (⨽) . . . . . . . . . 63\invdiameter () . . . . . . . . 78\inve () . . . . . . . . . . . . . . 12\InversTransformHoriz (¡) 35\InversTransformVert (£) . 35inverted symbols . 10–12, 16, 90\invf (,) . . . . . . . . . . . . . . . 12\invglotstop (d) . . . . . . . . 12\invh (&) . . . . . . . . . . . . . . 12\invlegr (I) . . . . . . . . . . . . 12\invm (5) . . . . . . . . . . . . . . 12\invneg () . . . . . . . . . . . . 30\invneg (⨼) . . . . . . . . . . . . 63\invr (G) . . . . . . . . . . . . . . 12\invscr (K) . . . . . . . . . . . . 12\invscripta (£) . . . . . . . . . 12\invv (¤) . . . . . . . . . . . . . . 12\invw (Z) . . . . . . . . . . . . . . 12\invy (\) . . . . . . . . . . . . . . 12\iota (ι) . . . . . . . . . . . . . . . 49\iotaup (ι) . . . . . . . . . . . . . 50\ipagamma ( ) . . . . . . . . . . . 12\IroningI (¯) . . . . . . . . . . 80\IroningII (°) . . . . . . . . . 80\IroningIII (±) . . . . . . . . 80irony mark ( ) . . . . . . . . . . . 90?\Irritant () . . . . . . . . . . 81\ismodeledby (=|) . . . . . . . . 90ISO character entities . . . . 103isoent (package) . . . . . . . . . 103J\j (j) . . . . . . . . . . . . . . . . . 13\JackStar (2) . . . . . . . . . . 74\JackStarBold (3) . . . . . . . 74Jewish star . . . . . . . . . . 73, 74\jmath (j) . . . . . . . . . . . 51, 56\Joch () . . . . . . . . . . . . . . 81\Join () . . . . . . . . . . . . . . 30\Join (⋈) . . . . . . . . . . . . . . 23\joinrel . . . . . . . . . . . . . . 90\Jupiter (E) . . . . . . . . . . . 68\Jupiter (Å) . . . . . . . . . . . . 68\jupiter (♃) . . . . . . . . . . . 68K\k ( ˛) . . . . . . . . . . . . . . . . . 13\kappa (κ) . . . . . . . . . . . . . 49\kappaup (κ) . . . . . . . . . . . . 50\ker (ker) . . . . . . . . . . . . . . 49ket . . . . . . . . . . . . . . . . . . . 53\Keyboard (Ï) . . . . . . . . . . 69keyboard symbols . . . . . . . . 69keys, computer . . . . . . . . . . 69keystroke (package) 69, 104, 105\keystroke ( ) . . . . . . . . 69king . . . . . . . see chess symbolsknight . . . . . . see chess symbolsKnuth, Donald E. . . 7, 100, 106symbols by . . . . . . . 76, 79\Kr ( ❧ ) . . . . . . . . . . . . . . 79\kreuz () . . . . . . . . . . . . . 78\kside (O) . . . . . . . . . . . . . 82\Kutline (R) . . . . . . . . . . . 71L\L (̷L) . . . . . . . . . . . . . . . . . . 9\l (̷l) . . . . . . . . . . . . . . . . . . 9\labdentalnas (4) . . . . . . . 11\labvel . . . . . . . . . . . . . . . 15\Ladiesroom (y) . . . . . . . . . 76Lagrangian (L) . see alphabets,math\Lambda (Λ) . . . . . . . . . . . . 49\lambda (λ) . . . . . . . . . . . . 49\lambdabar (ƛ) . . . . . . . . . . 63118

\lambdaslash (ƛ) . . . . . . . . 63\lambdaup (λ) . . . . . . . . . . . 50Lamport, Leslie . . . . . . 104, 106\land . . . . . . . . . . . see \wedge\landdownint ( % ) . . . . . . . . 28\landdownint (⨚) . . . . . . . . 29\landupint ( # ) . . . . . . . . . . 28\landupint (⨙) . . . . . . . . . . 29\Langle (

\leqdot () . . . . . . . . . . . . . 39\leqq (®) . . . . . . . . . . . . . . 38\leqq (≦) . . . . . . . . . . . . . . 37\leqq (≦) . . . . . . . . . . . . . . 39\leqslant () . . . . . . . . . . 37\leqslant (⩽) . . . . . . . . . . . 39\leqslantdot (⩿) . . . . . . . . 39\less (

\lrcorner (⌟) . . . . . . . . . . . 54\lrJoin . . . . . . . . . see \Join\lrtimes () . . . . . . . . . . . . 31\lsem () . . . . . . . . . . . . . 54\lsemantic . . . . . see \ldbrack\Lsh (è) . . . . . . . . . . . . . . . 42\Lsh () . . . . . . . . . . . . . . . 41\Lsh (↰) . . . . . . . . . . . . . . . 43\Lsteel () . . . . . . . . . . . . 70\ltimes () . . . . . . . . . . . . 22\ltimes (⋉) . . . . . . . . . . . . 21\ltimes (⋉) . . . . . . . . . . . . 23\ltriple . . . . . . . . . . . . . . 55Luecking, Dan . . . . . . . . . . . 93\lVert (‖) . . . . . . . . . . . . . 53\lVert (||) . . . . . . . . . . . . . . 55\lvert (|) . . . . . . . . . . . . . . 53\lvertneqq (´) . . . . . . . . . . 38\lvertneqq () . . . . . . . . . 37\lvertneqq (≨) . . . . . . . . . . 39\lwave ( ) . . . . . . . . . . . . . 55\lWavy () . . . . . . . . . . . . 54\lwavy () . . . . . . . . . . . . . 54\lz (1) . . . . . . . . . . . . . . . . 11M\M . . . . . . . . . . . . . . . . . . . . . 9\M ( ¯´) . . . . . . . . . . . . . . . . 82\m . . . . . . . . . . . . . . . . . . . . . 9\m ( ¯) . . . . . . . . . . . . . . . . 82\ma ( ׯ) . . . . . . . . . . . . . . . 82macron . . . . . . . . . see accents\macron (ā) . . . . . . . . . . . . . 16\Maggie ( ) . . . . . . . . . 85magical signs . . . . . . . . . . . . 85majuscules . . . . . . . . . . . . . 49\makeatletter . . . . . . . . . . 94\makeatother . . . . . . . . . . . 94\MALE ( ) . . . . . . . . . . . . . . 70\Male (|) . . . . . . . . . . . . . . 70\male (♂) . . . . . . . . . . . . . . 70\MaleMale (ƒ) . . . . . . . . . . 70\maltese (✠) . . . . . . . . . . . . 8\maltese (✠) . . . . . . . . . . . 63\manboldkidney () . . . . . . . 79\manconcentriccircles () 79\manconcentricdiamond () 79\mancone () . . . . . . . . . . . 79\mancube () . . . . . . . . . . . 79\manerrarrow () . . . . . . . 79\manfilledquartercircle () 79manfnt (package) 76, 79, 104, 105\manhpennib () . . . . . . . . . 79\manimpossiblecube () . . . 79\mankidney () . . . . . . . . . . 79\manlhpenkidney () . . . . . . 79\manpenkidney () . . . . . . . 79\manquadrifolium () . . . . 79\manquartercircle () . . . . 79\manrotatedquadrifolium (). . . . . . . . . 79\manrotatedquartercircle (). . . . . . . . . 79\manstar () . . . . . . . . . . . 79\mantiltpennib () . . . . . . 79\mantriangledown () . . . . . 79\mantriangleright () . . . . 79\mantriangleup () . . . . . . 79\manvpennib () . . . . . . . . . . 79\Mappedfromchar (⤆) . . . . . . . 48\mappedfromchar (↤) . . . . . . . 48\Mapsfrom (⇐) . . . . . . . . . . 42\mapsfrom (←) . . . . . . . . . . 42\Mapsfromchar (û) . . . . . . . . 49\Mapsfromchar () . . . . . . . . 48\mapsfromchar (ß) . . . . . . . . 49\mapsfromchar () . . . . . . . . 48\Mapsto (⤇⇒) . . . . . . . . . . . . 42\mapsto (↦→) . . . . . . . . . . . . 41\mapsto (↦) . . . . . . . . . . . . 44\Mapstochar (ú) . . . . . . . . . . 49\Mapstochar (⤇) . . . . . . . . . . 48\mapstochar (Þ) . . . . . . . . . . 49\Marge (¨) . . . . . . . . . 85\markera (x) . . . . . . . . . . . 82\markerb (y) . . . . . . . . . . . 82married . . . . . see \textmarried\Mars (D) . . . . . . . . . . . . . . 68\Mars (Ä) . . . . . . . . . . . . . . 68\mars (♂) . . . . . . . . . . . . . . 68\MartinVogel (ÿ) . . . . . . . . 80marvosym (package) . 17, 62, 64,68–71, 76, 79, 80, 88matbbol (package) . . . . . . . . 65\mate (m) . . . . . . . . . . . . . . 82material biconditional . . . . . . .. see \leftrightarrow and\equivmaterial conditional . . . . . . see\rightarrow and \supsetmaterial equivalence . . . . . . . .. see \leftrightarrow and\equivmaterial implication . . . . . . see\rightarrow and \supsetmath alphabets . . . . . . . . . . 65math-text . . . . . . . . . . . . . . 20mathabx (package) . . 22, 24, 26,30–32, 36–38, 40, 42, 43, 49,51–54, 56, 58, 62, 63, 68, 76,87, 88, 104, 105, 107\mathaccent . . . . . . . . . . . . 91\mathbb . . . . . . . . . . . . . . . 65\mathbbm . . . . . . . . . . . . . . 65\mathbbmss . . . . . . . . . . . . . 65\mathbbmtt . . . . . . . . . . . . . 65mathbbol (package) . . . . . . . 65\mathbf . . . . . . . . . . . . . . 100\mathbin . . . . . . . . . . . . . . 99\mathbold . . . . . . . . . . . . . 100mathcal (euscript package option). . . . . . . . . 65\mathcal . . . . . . . . . . . . . . 65\mathcent (¢) . . . . . . . . . . . 51\mathchoice . . . . . . . . . 92, 93\mathclose . . . . . . . . . . . . . 99mathcomp (package) . . . . . . 62mathdesign (package) 17, 23, 29,51, 55, 64, 104\mathdollar ($) . . . . . . . . . 20mathdots (package) . 56, 61, 62,94, 104, 105\mathds . . . . . . . . . . . . . . . 65\mathellipsis (. . .) . . . . . . 20mathematical symbols . . 20–66\mathfrak . . . . . . . . . . . . . . 65\mathit . . . . . . . . . . . . . . . 65\mathnormal . . . . . . . . . . . . 65\mathop . . . . . . . . . . . . . . . 99\mathopen . . . . . . . . . . . . . . 99\mathord . . . . . . . . . . . . . . 99\mathpalette . . . . . . . . . . . 93\mathparagraph () . . . . . . 20\mathpunct . . . . . . . . . . . . . 99\mathpzc . . . . . . . . . . . . . . 65\mathrel . . . . . . . . . . . 90, 99\mathring (˚) . . . . . . . . 56, 57\mathrm . . . . . . . . . . . . . . . 65mathrsfs (package) . . . . 65, 104mathscr (euscript package option). . . . . . . . . 65\mathscr . . . . . . . . . . . . . . 65\mathsection (§) . . . . . . . . 20\mathsterling (£) . . . . . 20, 51mathtools (package) . 34, 58, 59,104, 105\mathunderscore ( ) . . . . . . 20\max (max) . . . . . . . . . . . . . 49Maxwell-Stefan diffusion coefficient. . . . . . . . . . . . see\DH\maya . . . . . . . . . . . . . . . . . 62\Mb ( ˘¯´) . . . . . . . . . . . . . . . 82\mb ( ˘¯) . . . . . . . . . . . . . . . 82\Mbb ( ˘¯˘¯´) . . . . . . . . . . . . . . 82\mBb ( ˘¯˘¯ ´ ) . . . . . . . . . . . . . . 82\mbB ( ˘¯˘¯´) . . . . . . . . . . . . . . 82\mbb ( ˘¯˘¯) . . . . . . . . . . . . . . 82mbboard (package) . . . . 65, 104\mbbx ( ˘¯˘¯˘¯˘) . . . . . . . . . . . . 82\mbox . . . . . . . . . . . . . . . . . 93\measuredangle (>) . . . . . . 63\measuredangle (∡) . . . . . . 63\measuredangle (∡) . . . . . . 63mechanical scaling . . . . . 96, 98\medbackslash (∖) . . . . . . . 23\medbullet () . . . . . . . . . . 21121

\medcirc () . . . . . . . . . . . . 21\medcircle (◯) . . . . . . . . . . 23\meddiamond (◇) . . . . . . . . . 24\medlozenge (◊) . . . . . . . . . 74\medslash (∕) . . . . . . . . . . . 23\medsquare (◻) . . . . . . . . . . 24\medstar (☆) . . . . . . . . . . . 24\medstarofdavid (✡) . . . . . 74\medtriangledown (▽) . 24, 40\medtriangleleft (◁) . 24, 40\medtriangleright (▷) . 24, 40\medtriangleup (△) . . . 24, 40\medvert (∣) . . . . . . . . . . . . 23\medvertdot () . . . . . . . . . 23\Mercury (A) . . . . . . . . . . . . 68\Mercury (Â) . . . . . . . . . . . . 68\mercury (☿) . . . . . . . . . . . . 68\merge () . . . . . . . . . . . . . 21METAFONT . . . . . 66, 96, 97, 99METAFONTbook symbols . . . 79metre (package) . 16, 56, 82, 104,105metre . . . . . . . . . . . . . . . . . 82metrical symbols . . . . . . . . . 82\mho () . . . . . . . . . . . . 62, 63micro . . . . . . . . . . see \textmu\micro (µ) . . . . . . . . . . . . . 67Microsoft ® Windows ® . . . 103\mid (|) . . . . . . . . . . . . . 30, 54\middle . . . . . . . . . . . . . . . 53\midtilde ({) . . . . . . . . . . . 16millesimal sign . . . . . . . . . see\textperthousand\min (min) . . . . . . . . . . 49, 99minim . . . . see musical symbolsminus . . . . . . . see \textminus\minus (−) . . . . . . . . . . . . . 23\minusdot (⨪) . . . . . . . . . . . 23\minushookdown (¬) . . . . . . 63\minushookup (⨼) . . . . . . . . 63\minuso () . . . . . . . . . 21, 91minutes, angular . . . see \primemiscellaneous symbols . . 62–64,77–86“Missing $ inserted” . . . . 20\Mmappedfromchar () . . . . . . 48\mmappedfromchar () . . . . . . 48\Mmapstochar () . . . . . . . . . 48\mmapstochar () . . . . . . . . . 48MnSymbol (package) 23, 24, 29,32, 33, 37, 39, 40, 43–48, 50,51, 54, 56–58, 61, 63, 64, 74,104, 105\Mobilefone (H) . . . . . . . . . 69\mod . . . . . . . . . . . . . . . . . . 49\models (|=) . . . . . . . . . 30, 90\models (⊧) . . . . . . . . . . . . 33moduli space . . . see alphabets,mathmonetary symbols . . . . . 17, 65\moo () . . . . . . . . . . . . . . . 21\Moon (K) . . . . . . . . . . . . . . 68\Moon (Á) . . . . . . . . . . . . . . 68\morepawns (S) . . . . . . . . . . 82\moreroom (U) . . . . . . . . . . 82\Mountain () . . . . . . . . . . 81mouse . . . . see \ComputerMouse\MoveDown (») . . . . . . . . . . . 79\moverlay . . . . . . . . . . . . . . 94\MoveUp (º) . . . . . . . . . . . . 79\mp (∓) . . . . . . . . . . . . . . . . 20\mp (∓) . . . . . . . . . . . . . . . . 23\mu (µ) . . . . . . . . . . . . . . . . 49\multimap (⊸) . . . . . . . 30, 31\multimap (⊸) . . . . . . . . . . 47\multimapboth () . . . . . . 31\multimapbothvert () . . . . 31\multimapdot () . . . . . . . . 31\multimapdotboth () . . . . 31\multimapdotbothA () . . . 31\multimapdotbothAvert () . 31\multimapdotbothB () . . . 31\multimapdotbothBvert () . 31\multimapdotbothvert () . . 31\multimapdotinv () . . . . . 31\multimapinv (⟜) . . . . . . . . 31multiple accents per character 94\Mundus (m) . . . . . . . . . . . . 80Museum of Icelandic Sorcery andWitchcraft . . . . . . . . . 86musical symbols 19, 62, 63, 78,79musixtex (package) . . . . . . . . 79\muup (µ) . . . . . . . . . . . . . . 50\MVAt (@) . . . . . . . . . . . . . . 80\MVEight (8) . . . . . . . . . . . . 62\MVFive (5) . . . . . . . . . . . . 62\MVFour (4) . . . . . . . . . . . . 62\MVNine (9) . . . . . . . . . . . . 62\MVOne (1) . . . . . . . . . . . . . 62\MVRightarrow (:) . . . . . . . 80\MVSeven (7) . . . . . . . . . . . . 62\MVSix (6) . . . . . . . . . . . . . 62\MVThree (3) . . . . . . . . . . . . 62\MVTwo (2) . . . . . . . . . . . . . 62\MVZero (0) . . . . . . . . . . . . 62N\nabla (∇) . . . . . . . . . . . . . 62\nabla (∇) . . . . . . . . . . . . . 63\NAK (␕) . . . . . . . . . . . . . . . 69\napprox () . . . . . . . . . . . 32\napprox (≉) . . . . . . . . . . . . 33\napproxeq () . . . . . . . . . . 31\napproxeq (≊̸) . . . . . . . . . . 33\nasymp () . . . . . . . . . . . . 31\nasymp (≭) . . . . . . . . . . . . . 48nath (package) . . . . . 52, 55, 104\natural (♮) . . . . . . . . . 62, 78\natural (♮) . . . . . . . . . . . . 63natural numbers (N) . . . . . seealphabets, mathnavigation symbols . . . . . . . 79\nbackapprox (̸) . . . . . . . . 33\nbackapproxeq (̸) . . . . . . . 33\nbackcong (≌̸) . . . . . . . . . . 33\nbackeqsim (̸) . . . . . . . . . 33\nbacksim () . . . . . . . . . . . 31\nbacksim (∽̸) . . . . . . . . . . . 33\nbacksimeq () . . . . . . . . . 31\nbacksimeq (⋍̸) . . . . . . . . . 33\nbacktriplesim (̸) . . . . . . 33\NBSP ( ) . . . . . . . . . . . . . . 69\nBumpeq () . . . . . . . . . . . . 31\nBumpeq (≎̸) . . . . . . . . . . . . 33\nbumpeq () . . . . . . . . . . . . 31\nbumpeq (≏̸) . . . . . . . . . . . . 33\ncirceq (≗̸) . . . . . . . . . . . . 33\ncirclearrowleft (↺̸) . . . 46\ncirclearrowright (↻̸) . . 46\nclosedequal (̸) . . . . . . . 33\ncong () . . . . . . . . . . . . . 32\ncong (≇) . . . . . . . . . . . . . 30\ncong (≇) . . . . . . . . . . . . . 33\ncurlyeqprec (¸) . . . . . . . 32\ncurlyeqprec (⋞̸) . . . . . . . 33\ncurlyeqsucc (¹) . . . . . . . 32\ncurlyeqsucc (⋟̸) . . . . . . . 33\ncurvearrowdownup (̸) . . . 44\ncurvearrowleft (↶̸) . . . . 46\ncurvearrowleftright (̸) 44\ncurvearrownesw (̸) . . . . 44\ncurvearrownwse (̸) . . . . 44\ncurvearrowright (↷̸) . . . . 46\ncurvearrowrightleft (̸) 44\ncurvearrowsenw (̸) . . . . 44\ncurvearrowswne (̸) . . . . 44\ncurvearrowupdown (̸) . . . 44\ndasharrow (⇢̸) . . . . . . . . . 46\ndasheddownarrow (⇣̸) . . . . 44\ndashedleftarrow (⇠̸) . . . . 44\ndashednearrow (̸) . . . . . 45\ndashednwarrow (̸) . . . . . 45\ndashedrightarrow (⇢̸) . . . 45\ndashedsearrow (̸) . . . . . 45\ndashedswarrow (̸) . . . . . 45\ndasheduparrow (⇡̸) . . . . . . 45\ndashleftarrow (⇠̸) . . . . . 46\ndashrightarrow (⇢̸) . . . . 46\nDashV (+) . . . . . . . . . . . . 32\nDashv (+) . . . . . . . . . . . . 32\ndashV (/) . . . . . . . . . . . . 32\ndashv (') . . . . . . . . . . . . 32\ndashv (⊣̸) . . . . . . . . . . . . 34\ndashVv (/) . . . . . . . . . . . 32\nddtstile ( ) . . . . . . . . . 35\ndiagdown (̸) . . . . . . . . . 34\ndiagup (̸) . . . . . . . . . . . 34\ndivides (∤) . . . . . . . . . . . 34\nDoteq (≑̸) . . . . . . . . . . . . . 33\ndoteq (≐̸) . . . . . . . . . . . . . 33\ndoublefrown (̸) . . . . . . . 48\ndoublefrowneq (̸) . . . . . . 48\ndoublesmile (̸) . . . . . . . 48\ndoublesmileeq (̸) . . . . . . 48\nDownarrow (⇓̸) . . . . . . . . . 45\ndownarrow (↓̸) . . . . . . . . . 45122

\ndownarrowtail (̸) . . . . . . 45\ndowndownarrows (⇊̸) . . . . . 45\ndownfilledspoon (̸) . . . . 47\ndownfootline (̸) . . . . . . . 33\ndownfree (⫝̸) . . . . . . . . . . 33\ndownharpoonccw (⇂̸) . . . . . 46\ndownharpooncw (⇃̸) . . . . . . 46\ndownlsquigarrow (̸) . . . . 45\ndownmapsto (↧̸) . . . . . . . . 45\ndownModels (̸) . . . . . . . . 33\ndownmodels (̸) . . . . . . . . 33\ndownpitchfork (⫛̸) . . . . . 47\ndownrsquigarrow (̸) . . . . 45\ndownspoon (⫰̸) . . . . . . . . . 47\ndownuparrows (⇵̸) . . . . . . 45\ndownupharpoons (⥯̸) . . . . . 46\ndownVdash (⍑̸) . . . . . . . . . 33\ndownvdash (⊤̸) . . . . . . . . . 33\ndststile ( ) . . . . . . . . . 35\ndtstile ( ) . . . . . . . . . . 35\ndttstile ( ) . . . . . . . . . 35\ne . . . . . . . . . . . . . . see \neq\ne (≠) . . . . . . . . . . . . . . . . 34\Nearrow () . . . . . . . . . . . 42\Nearrow (⇗) . . . . . . . . . . . 43\nearrow (Õ) . . . . . . . . . . . 42\nearrow (↗) . . . . . . 41, 93, 94\nearrow (↗) . . . . . . . . . . . 43\nearrowtail () . . . . . . . . 43\nefilledspoon () . . . . . . 47\nefootline () . . . . . . . . . 32\nefree () . . . . . . . . . . . . 32\neg (¬) . . . . . . . . . . . . . . . 62\neg (¬) . . . . . . . . . . . . . . . 63negation . . . see \neg and \sim\neharpoonccw () . . . . . . . 46\neharpooncw () . . . . . . . . 46\nelsquigarrow () . . . . . . 43\nemapsto () . . . . . . . . . . 43\neModels () . . . . . . . . . . 32\nemodels () . . . . . . . . . . 32\nenearrows () . . . . . . . . 43\nepitchfork () . . . . . . . . 47\Neptune (H) . . . . . . . . . . . 68\Neptune (È) . . . . . . . . . . . 68\neptune () . . . . . . . . . . . . 68\neq () . . . . . . . . . . . . . . . 32\neq () . . . . . . . . . . . . . . . 37\neq (≠) . . . . . . . . . . . . . . . 34\neqbump (̸) . . . . . . . . . . . . 33\neqcirc (≖̸) . . . . . . . . . . . . 33\neqdot (⩦̸) . . . . . . . . . . . . . 33\neqfrown (̸) . . . . . . . . . . . 48\neqsim (≂̸) . . . . . . . . . . . . . 33\neqslantgtr (¹) . . . . . . . . 38\neqslantgtr (⪖̸) . . . . . . . . 39\neqslantless (¸) . . . . . . . 38\neqslantless (⪕̸) . . . . . . . 39\neqsmile (̸) . . . . . . . . . . . 48\nequal (≠) . . . . . . . . . . . . . 33\nequalclosed (̸) . . . . . . . 33\nequiv () . . . . . . . . . . . . 31\nequiv (≢) . . . . . . . . . . . . . 33\nequivclosed (̸) . . . . . . . 33\nersquigarrow () . . . . . . 43\nespoon () . . . . . . . . . . . 47\Neswarrow () . . . . . . . . . 43\neswarrow (↗↙) . . . . . . 93, 94\neswarrow (⤡) . . . . . . . . . 43\neswarrows () . . . . . . . . 43\neswbipropto () . . . . . . . 23\neswcrossing () . . . . . . . 33\neswharpoonnwse () . . . . 46\neswharpoons () . . . . . . . 46\neswharpoonsenw () . . . . 46\Neswline () . . . . . . . . . . 32\neswline () . . . . . . . . . . 32\Neutral ({) . . . . . . . . . . . 70\neVdash () . . . . . . . . . . . 32\nevdash () . . . . . . . . . . . 32\newextarrow . . . . . . . . . . . 60\newmoon (N) . . . . . . . . . . . 68\newmoon () . . . . . . . . . . . 68\newtie (a) . . . . . . . . . . . . . 13\nexists (E) . . . . . . . . . . . . 51\nexists (∄) . . . . . . . . . . . . 51\nexists (∄) . . . . . . . . . . . . 51\nfallingdotseq (≒̸) . . . . . . 33\nfrown (⌢̸) . . . . . . . . . . . . . 48\nfrowneq (̸) . . . . . . . . . . . 48\nfrowneqsmile (̸) . . . . . . . 48\nfrownsmile (̸) . . . . . . . . 48\nfrownsmileeq (̸) . . . . . . . 48\NG (Ŋ) . . . . . . . . . . . . . . . . . 9\ng (ŋ) . . . . . . . . . . . . . . . . . 9\ngeq (§) . . . . . . . . . . . . . . 38\ngeq (≱) . . . . . . . . . . . 37, 38\ngeq (≱) . . . . . . . . . . . . . . 39\ngeqclosed (⋭) . . . . . . 39, 40\ngeqdot (̸) . . . . . . . . . . . . 39\ngeqq (±) . . . . . . . . . . . . . 38\ngeqq () . . . . . . . . . . . . . 37\ngeqq (≧̸) . . . . . . . . . . . . . 39\ngeqslant () . . . . . . . . . 37\ngeqslant (≱) . . . . . . . . . . 39\ngeqslantdot (⪀̸) . . . . . . . 39\ngets (↚) . . . . . . . . . . . . . 46\ngg () . . . . . . . . . . . . . . 38\ngg (≫̸) . . . . . . . . . . . . . . . 39\nggg (⋙̸) . . . . . . . . . . . . . 39\ngtr (£) . . . . . . . . . . . . . . 38\ngtr (≯) . . . . . . . . . . . . . . 37\ngtr (≯) . . . . . . . . . . . . . . 39\ngtrapprox (É) . . . . . . . . . 38\ngtrapprox () . . . . . . . . . 38\ngtrclosed (⋫) . . . . . . 39, 40\ngtrdot (⋗̸) . . . . . . . . . . . . 39\ngtreqless (⋛̸) . . . . . . . . . 39\ngtreqlessslant (̸) . . . . . 39\ngtreqqless (⪌̸) . . . . . . . . 39\ngtrless () . . . . . . . . . . . 38\ngtrless (≹) . . . . . . . . . . . 39\ngtrsim (Ã) . . . . . . . . . . . 38\ngtrsim () . . . . . . . . . . . . 38\nhateq (≙̸) . . . . . . . . . . . . . 33\nhookleftarrow (↩̸) . . . . . 46\nhookrightarrow (↪̸) . . . . 46\ni (∋) . . . . . . . . . . . . . 51, 92\ni (∋) . . . . . . . . . . . . . . . . 51\nialpha (¢) . . . . . . . . . . . . 12\nibar . . . . . . . . see \ownsbar\nibeta (©) . . . . . . . . . . . . . 12\NibLeft () . . . . . . . . . . . 72\NibRight () . . . . . . . . . . 72nibs . . . . . . . . . . . . . . . . . . 72\NibSolidLeft ( ) . . . . . . . 72\NibSolidRight () . . . . . . 72nicefrac (package) . 64, 104, 105\nichi ([) . . . . . . . . . . . . . 12\niepsilon () . . . . . . . . . . 12\nigamma () . . . . . . . . . . . . 12\niiota ()) . . . . . . . . . . . . . 12\nilambda (2) . . . . . . . . . . . 12\nin (∉) . . . . . . . . . . . . . . . 51\niomega (>) . . . . . . . . . . . . 12\niphi (C) . . . . . . . . . . . . . 12\niplus () . . . . . . . . . . . . 30\nisigma (O) . . . . . . . . . . . . 12\nitheta (S) . . . . . . . . . . . . 12\niupsilon (V) . . . . . . . . . . 12\niv ( ) . . . . . . . . . . . . . . . 52\nj (7) . . . . . . . . . . . . . . . . 12\nlcirclearrowdown (̸) . . 45\nlcirclearrowleft (⤾̸) . . 45\nlcirclearrowright (⟳̸) . 45\nlcirclearrowup (↻̸) . . . . 45\nlcurvearrowdown (⤸̸) . . . . 45\nlcurvearrowleft (̸) . . . . 45\nlcurvearrowne (̸) . . . . . 45\nlcurvearrownw (̸) . . . . . 45\nlcurvearrowright (↷̸) . . . 45\nlcurvearrowse (̸) . . . . . 45\nlcurvearrowsw (̸) . . . . . 45\nlcurvearrowup (̸) . . . . . . 45\nleadsto (↝̸) . . . . . . . . . . 46\nLeftarrow (ö) . . . . . . . . 42\nLeftarrow () . . . . . . . . 41\nLeftarrow (⇍) . . . . . . . . 45\nleftarrow (Ú) . . . . . . . . 42\nleftarrow (↚) . . . . . . . . 41\nleftarrow (↚) . . . . . . . . . 45\nleftarrowtail (↢̸) . . . . . 45\nleftfilledspoon (̸) . . . 47\nleftfootline (̸) . . . . . . 33\nleftfree (̸) . . . . . . . . . . 33\nleftharpoonccw (↽̸) . . . . 46\nleftharpooncw (↼̸) . . . . . 46\nleftleftarrows (⇇̸) . . . . 45\nleftlsquigarrow (̸) . . . . 45\nleftmapsto (↤̸) . . . . . . . . 45\nleftModels (̸) . . . . . . . . 33\nleftmodels (̸) . . . . . . . . 33\nleftpitchfork (̸) . . . . . 47\nLeftrightarrow (ø) . . . . 42123

\nLeftrightarrow () . . . . 41\nLeftrightarrow (⇎) . . . . 45\nleftrightarrow (Ü) . . . . 42\nleftrightarrow (↮) . 20, 41\nleftrightarrow (↮) . . . . 45\nleftrightarrows (⇆̸) . . . . 45\nleftrightharpoondownup (⥊̸). . . . . . . . . 46\nleftrightharpoons (⇋̸) . . 46\nleftrightharpoonupdown (⥋̸). . . . . . . . . 46\nLeftrightline (̸) . . . . . 33\nleftrightline (̸) . . . . . 33\nleftrightsquigarrow (̸) 46\nleftrsquigarrow (↜̸) . . . . 45\nleftspoon (⟜̸) . . . . . . . . 47\nleftVdash (̸) . . . . . . . . . 33\nleftvdash (⊣̸) . . . . . . . . . 33\nleq (¦) . . . . . . . . . . . . . . 38\nleq (≰) . . . . . . . . . . . 37, 38\nleq (≰) . . . . . . . . . . . . . . 39\nleqclosed (⋬) . . . . . . 39, 40\nleqdot (̸) . . . . . . . . . . . . 39\nleqq (°) . . . . . . . . . . . . . 38\nleqq () . . . . . . . . . . . . . 37\nleqq (≦̸) . . . . . . . . . . . . . 39\nleqslant () . . . . . . . . . 37\nleqslant (≰) . . . . . . . . . . 39\nleqslantdot (⩿̸) . . . . . . . 39\nless (¢) . . . . . . . . . . . . . 38\nless (≮) . . . . . . . . . . . . . 37\nless (≮) . . . . . . . . . . . . . 39\nlessapprox (È) . . . . . . . . 38\nlessapprox () . . . . . . . . 38\nlessclosed (⋪) . . . . . 39, 40\nlessdot (⋖̸) . . . . . . . . . . . 39\nlesseqgtr (⋚̸) . . . . . . . . . 39\nlesseqgtrslant (̸) . . . . . 39\nlesseqqgtr (⪋̸) . . . . . . . . 39\nlessgtr () . . . . . . . . . . . 38\nlessgtr (≸) . . . . . . . . . . . 39\nlesssim (Â) . . . . . . . . . . 38\nlesssim () . . . . . . . . . . . 38\nlhookdownarrow (̸) . . . . . 45\nlhookleftarrow (̸) . . . . 45\nlhooknearrow (̸) . . . . . . 45\nlhooknwarrow (⤣̸) . . . . . . 44\nlhookrightarrow (↪̸) . . . . 44\nlhooksearrow (⤥̸) . . . . . . 44\nlhookswarrow (̸) . . . . . . 44\nlhookuparrow (̸) . . . . . . . 44\nll () . . . . . . . . . . . . . . 38\nll (≪̸) . . . . . . . . . . . . . . . 39\nLleftarrow (⇚̸) . . . . . . . . 44\nlll (⋘̸) . . . . . . . . . . . . . 39\nmapsto (↦̸) . . . . . . . . . . . 46\nmid (∤) . . . . . . . . . . . . . . . 30\nmid (∤) . . . . . . . . . . . . . . 34\nmodels (⊭) . . . . . . . . . . . . 34\nmultimap (⊸̸) . . . . . . . . . 47\nndtstile ( ) . . . . . . . . . 35\nNearrow (⇗̸) . . . . . . . . . . 44\nnearrow () . . . . . . . . . . . 42\nnearrow (↗̸) . . . . . . . . . . 44\nnearrowtail (̸) . . . . . . . 44\nnefilledspoon (̸) . . . . . 47\nnefootline (̸) . . . . . . . . 33\nnefree (̸) . . . . . . . . . . . 33\nneharpoonccw (̸) . . . . . . 46\nneharpooncw (̸) . . . . . . . 46\nnelsquigarrow (̸) . . . . . 44\nnemapsto (̸) . . . . . . . . . 45\nneModels (̸) . . . . . . . . . 33\nnemodels (̸) . . . . . . . . . 33\nnenearrows (̸) . . . . . . . 45\nnepitchfork (̸) . . . . . . . 47\nnersquigarrow (̸) . . . . . 45\nnespoon (̸) . . . . . . . . . . 47\nNeswarrow (̸) . . . . . . . . 45\nneswarrow (⤡̸) . . . . . . . . 45\nneswarrows (̸) . . . . . . . 45\nneswharpoonnwse (̸) . . . 46\nneswharpoons (̸) . . . . . . 46\nneswharpoonsenw (̸) . . . 46\nNeswline (̸) . . . . . . . . . 33\nneswline (̸) . . . . . . . . . 33\nneVdash (̸) . . . . . . . . . . 33\nnevdash (̸) . . . . . . . . . . 33\nnststile ( ) . . . . . . . . . 35\nntstile ( ) . . . . . . . . . . 34\nnttstile ( ) . . . . . . . . . 34\nNwarrow (⇖̸) . . . . . . . . . . 45\nnwarrow () . . . . . . . . . . . 42\nnwarrow (↖̸) . . . . . . . . . . 45\nnwarrowtail (̸) . . . . . . . 45\nnwfilledspoon (̸) . . . . . 47\nnwfootline (̸) . . . . . . . . 33\nnwfree (̸) . . . . . . . . . . . 33\nnwharpoonccw (̸) . . . . . . 46\nnwharpooncw (̸) . . . . . . . 46\nnwlsquigarrow (̸) . . . . . 45\nnwmapsto (̸) . . . . . . . . . 45\nnwModels (̸) . . . . . . . . . 33\nnwmodels (̸) . . . . . . . . . 33\nnwnwarrows (̸) . . . . . . . 45\nnwpitchfork (̸) . . . . . . . 47\nnwrsquigarrow (̸) . . . . . 45\nNwsearrow (̸) . . . . . . . . 45\nnwsearrow (⤢̸) . . . . . . . . 45\nnwsearrows (̸) . . . . . . . 45\nnwseharpoonnesw (̸) . . . 46\nnwseharpoons (̸) . . . . . . 46\nnwseharpoonswne (̸) . . . 46\nNwseline (̸) . . . . . . . . . 33\nnwseline (̸) . . . . . . . . . 33\nnwspoon (̸) . . . . . . . . . . 47\nnwVdash (̸) . . . . . . . . . . 33\nnwvdash (̸) . . . . . . . . . . 33\NoBleech (Ì) . . . . . . . . . . 80\NoChemicalCleaning (¨) . . 80nointegrals (wasysym package option). . . . . . . . . . . . . 25\NoIroning (²) . . . . . . . . . 80non-commutative division . . 60nonbreaking space . . . . . . . . 69norm . . see \lVert and \rVert\NoSun () . . . . . . . . . . . . . 80not . . . . . . . . . . . . . . see \neg\not . . . . . . . . . . . . . . . 32, 92not equal (= vs. =) . . . . . . . 32\notasymp () . . . . . . . . . . 32\notbackslash ( \−) . . . . . . . 68\notbot (M) . . . . . . . . . . . . 51\notdivides () . . . . . . . . . 32\notequiv () . . . . . . . . . . 32\notin (R) . . . . . . . . . . . . . 51\notin () . . . . . . . . . . . . . 51\notin (∉) . . . . . . . . . . . . . 51\notin (∉) . . . . . . . . . . . . . . 51\notni () . . . . . . . . . . . . . 51\notowner (S) . . . . . . . . . . . 51\notowns . . see \notowner and\notni\notperp (M) . . . . . . . . . . . 32\notslash ( /−) . . . . . . . . . . 68\notsmallin () . . . . . . . . . 51\notsmallowns () . . . . . . . . 51\nottop (L) . . . . . . . . . . . . 51\NoTumbler () . . . . . . . . . . 80\novelty (N) . . . . . . . . . . . 82\nowns (∌) . . . . . . . . . . . . . . 51\nparallel (∦) . . . . . . . . . . 30\nparallel (∦) . . . . . . . . . . 34\nperp (⊥̸) . . . . . . . . . . . . . 34\npitchfork (⋔̸) . . . . . . . . . 47\nplus () . . . . . . . . . . . . . 21\nprec (¢) . . . . . . . . . . . . . 32\nprec (⊀) . . . . . . . . . . . . . 30\nprec (⊀) . . . . . . . . . . . . . 33\nprecapprox (È) . . . . . . . . 32\nprecapprox () . . . . . . . . 31\nprecapprox (⪷̸) . . . . . . . . 33\npreccurlyeq (¦) . . . . . . . 32\npreccurlyeq () . . . . . . . 31\npreccurlyeq (⋠) . . . . . . . 33\npreceq (ª) . . . . . . . . . . . 32\npreceq () . . . . . . . . . . . 30\npreceq (⪯̸) . . . . . . . . . . . . 33\npreceqq () . . . . . . . . . . . 31\nprecsim (Â) . . . . . . . . . . 32\nprecsim () . . . . . . . . . . . 31\nprecsim (≾̸) . . . . . . . . . . . 33\nrcirclearrowdown (̸) . . 45\nrcirclearrowleft (⟲̸) . . 45\nrcirclearrowright (⤿̸) . 45\nrcirclearrowup (↺̸) . . . . 45\nrcurvearrowdown (⤹̸) . . . . 45\nrcurvearrowleft (↶̸) . . . . 45\nrcurvearrowne (̸) . . . . . 45\nrcurvearrownw (̸) . . . . . 45\nrcurvearrowright (̸) . . . 45\nrcurvearrowse (̸) . . . . . 45\nrcurvearrowsw (̸) . . . . . 45\nrcurvearrowup (̸) . . . . . . 45124

\nRelbar (̸) . . . . . . . . . . . 34\nrelbar (̸) . . . . . . . . . . . 34\nrestriction (↾̸) . . . . . . . 46\nrhookdownarrow (̸) . . . . . 45\nrhookleftarrow (↩̸) . . . . 45\nrhooknearrow (⤤̸) . . . . . . 45\nrhooknwarrow (̸) . . . . . . 45\nrhookrightarrow (̸) . . . . 45\nrhooksearrow (̸) . . . . . . 45\nrhookswarrow (⤦̸) . . . . . . 45\nrhookuparrow (̸) . . . . . . . 45\nRightarrow (÷) . . . . . . . . 42\nRightarrow () . . . . . . . 41\nRightarrow (⇏) . . . . . . . . 45\nrightarrow (Û) . . . . . . . . 42\nrightarrow (↛) . . . . . . . 41\nrightarrow (↛) . . . . . . . . 45\nrightarrowtail (↣̸) . . . . 45\nrightfilledspoon (̸) . . 47\nrightfootline (̸) . . . . . 33\nrightfree (̸) . . . . . . . . . 33\nrightharpoonccw (⇀̸) . . . . 46\nrightharpooncw (⇁̸) . . . . 46\nrightleftarrows (⇄̸) . . . . 44\nrightleftharpoons (⇌̸) . . 46\nrightlsquigarrow (↝̸) . . . 44\nrightmapsto (↦̸) . . . . . . . 44\nrightModels (⊯) . . . . . . . 33\nrightmodels (⊭) . . . . . . . 33\nrightpitchfork (̸) . . . . 47\nrightrightarrows (⇉̸) . . . 44\nrightrsquigarrow (̸) . . . 44\nrightspoon (⊸̸) . . . . . . . . 47\nrightsquigarrow (↝̸) . . . . 46\nrightVdash (⊮) . . . . . . . . 33\nrightvdash (⊬) . . . . . . . . 33\nrisingdotseq (≓̸) . . . . . . . 33\nRrightarrow (⇛̸) . . . . . . . 44\nsdtstile ( ) . . . . . . . . . 34\nSearrow (⇘̸) . . . . . . . . . . 44\nsearrow (↘̸) . . . . . . . . . . 44\nsearrowtail (̸) . . . . . . . 44\nsefilledspoon (̸) . . . . . 47\nsefootline (̸) . . . . . . . . 33\nsefree (̸) . . . . . . . . . . . 33\nseharpoonccw (̸) . . . . . . 46\nseharpooncw (̸) . . . . . . . 46\nselsquigarrow (̸) . . . . . 44\nsemapsto (̸) . . . . . . . . . 45\nseModels (̸) . . . . . . . . . 33\nsemodels (̸) . . . . . . . . . 33\nsenwarrows (̸) . . . . . . . 45\nsenwharpoons (̸) . . . . . . 46\nsepitchfork (̸) . . . . . . . 47\nsersquigarrow (̸) . . . . . 45\nsesearrows (̸) . . . . . . . 45\nsespoon (̸) . . . . . . . . . . 47\nseVdash (̸) . . . . . . . . . . 33\nsevdash (̸) . . . . . . . . . . 33\nshortmid () . . . . . . . . . . 30\nshortmid (∤) . . . . . . . . . . 33\nshortparallel () . . . . . . 30\nshortparallel (∦) . . . . . . 33\nsim () . . . . . . . . . . . . . . 32\nsim () . . . . . . . . . . . . . . 30\nsim (≁) . . . . . . . . . . . . . . 33\nsimeq () . . . . . . . . . . . . 32\nsimeq () . . . . . . . . . . . . 31\nsimeq (≄) . . . . . . . . . . . . . 33\nsmile (⌣̸) . . . . . . . . . . . . . 48\nsmileeq (̸) . . . . . . . . . . . 48\nsmileeqfrown (̸) . . . . . . . 48\nsmilefrown (≭) . . . . . . . . 48\nsmilefrowneq (̸) . . . . . . . 48\nsqdoublefrown (̸) . . . . . . 48\nsqdoublefrowneq (̸) . . . . 48\nsqdoublesmile (̸) . . . . . . 48\nsqdoublesmileeq (̸) . . . . 48\nsqeqfrown (̸) . . . . . . . . . 48\nsqeqsmile (̸) . . . . . . . . . 48\nsqfrown (̸) . . . . . . . . . . . 48\nsqfrowneq (̸) . . . . . . . . . 48\nsqfrowneqsmile (̸) . . . . . 48\nsqfrownsmile (̸) . . . . . . . 48\nsqsmile (̸) . . . . . . . . . . . 48\nsqsmileeq (̸) . . . . . . . . . 48\nsqsmileeqfrown (̸) . . . . . 48\nsqsmilefrown (̸) . . . . . . . 48\nSqsubset (̸) . . . . . . . . . . 37\nsqSubset (–) . . . . . . . . . . 37\nsqsubset (‚) . . . . . . . . . . 37\nsqsubset () . . . . . . . . . . 36\nsqsubset (⊏̸) . . . . . . . . . . 37\nsqsubseteq (†) . . . . . . . . 37\nsqsubseteq () . . . . . . . . 36\nsqsubseteq (⋢) . . . . . . . . 37\nsqsubseteqq (Ž) . . . . . . . 37\nsqsubseteqq (̸) . . . . . . . 37\nSqsupset (̸) . . . . . . . . . . 37\nsqSupset (—) . . . . . . . . . . 37\nsqsupset (ƒ) . . . . . . . . . . 37\nsqsupset () . . . . . . . . . . 36\nsqsupset (⊐̸) . . . . . . . . . . 37\nsqsupseteq (‡) . . . . . . . . 37\nsqsupseteq () . . . . . . . . 36\nsqsupseteq (⋣) . . . . . . . . 37\nsqsupseteqq ( ) . . . . . . . 37\nsqsupseteqq (̸) . . . . . . . 37\nsqtriplefrown (̸) . . . . . . 48\nsqtriplesmile (̸) . . . . . . 48\nsquigarrowdownup (̸) . . 45\nsquigarrowleftright (̸) 45\nsquigarrownesw (̸) . . . . 45\nsquigarrownwse (̸) . . . . . 45\nsquigarrowrightleft (̸) 45\nsquigarrowsenw (̸) . . . . 45\nsquigarrowswne (̸) . . . . 45\nsquigarrowupdown (̸) . . . 45\nsststile ( ) . . . . . . . . . 34\nststile ( ) . . . . . . . . . . 34\nsttstile ( ) . . . . . . . . . 34\nSubset (–) . . . . . . . . . . . 37\nSubset () . . . . . . . . . . . . 36\nSubset (⋐̸) . . . . . . . . . . . . 37\nsubset (‚) . . . . . . . . . . . 37\nsubset (⊄) . . . . . . . . . . . . 37\nsubseteq (†) . . . . . . . . . . 37\nsubseteq () . . . . . . . . . 36\nsubseteq (⊈) . . . . . . . . . . 37\nsubseteqq (Ž) . . . . . . . . . 37\nsubseteqq () . . . . . . . . . 36\nsubseteqq (⫅̸) . . . . . . . . . 37\nsucc (£) . . . . . . . . . . . . . 32\nsucc (⊁) . . . . . . . . . . . . . 30\nsucc (⊁) . . . . . . . . . . . . . 33\nsuccapprox (É) . . . . . . . . 32\nsuccapprox () . . . . . . . . 31\nsuccapprox (⪸̸) . . . . . . . . 33\nsucccurlyeq (§) . . . . . . . 32\nsucccurlyeq () . . . . . . . 31\nsucccurlyeq (⋡) . . . . . . . 33\nsucceq («) . . . . . . . . . . . 32\nsucceq () . . . . . . . . . . . 30\nsucceq (⪰̸) . . . . . . . . . . . . 33\nsucceqq () . . . . . . . . . . . 31\nsuccsim (Ã) . . . . . . . . . . 32\nsuccsim () . . . . . . . . . . . 31\nsuccsim (≿̸) . . . . . . . . . . . 33\nSupset (—) . . . . . . . . . . . 37\nSupset () . . . . . . . . . . . . 36\nSupset (⋑̸) . . . . . . . . . . . . 37\nsupset (ƒ) . . . . . . . . . . . 37\nsupset (⊅) . . . . . . . . . . . . 37\nsupseteq (‡) . . . . . . . . . . 37\nsupseteq () . . . . . . . . . 36\nsupseteq (⊉) . . . . . . . . . . 37\nsupseteqq ( ) . . . . . . . . . 37\nsupseteqq () . . . . . . . . . 36\nsupseteqq (⫆̸) . . . . . . . . . 37\nSwarrow (⇙̸) . . . . . . . . . . 45\nswarrow (↙̸) . . . . . . . . . . 45\nswarrowtail (̸) . . . . . . . 45\nswfilledspoon (̸) . . . . . 47\nswfootline (̸) . . . . . . . . 33\nswfree (̸) . . . . . . . . . . . 33\nswharpoonccw (̸) . . . . . . 46\nswharpooncw (̸) . . . . . . . 46\nswlsquigarrow (̸) . . . . . 45\nswmapsto (̸) . . . . . . . . . 45\nswModels (̸) . . . . . . . . . 33\nswmodels (̸) . . . . . . . . . 33\nswnearrows (̸) . . . . . . . 45\nswneharpoons (̸) . . . . . . 46\nswpitchfork (̸) . . . . . . . 47\nswrsquigarrow (̸) . . . . . 45\nswspoon (̸) . . . . . . . . . . 47\nswswarrows (̸) . . . . . . . 45\nswVdash (̸) . . . . . . . . . . 33\nswvdash (̸) . . . . . . . . . . 33\ntdtstile ( ) . . . . . . . . . 34ntheorem (package) . . . . . . . 62\nthickapprox (≇) . . . . . . . 31\nto (↛) . . . . . . . . . . . . . . . 46\ntriangleeq (≜̸) . . . . . . . . 40\ntriangleleft (š) . . . . . . 40125

\ntriangleleft (⋪) . . . . . . 39\ntriangleleft (⋪) . . . . 39, 40\ntrianglelefteq (ž) . . . . 40\ntrianglelefteq () . . . . 39\ntrianglelefteq (⋬) . . 39, 40\ntrianglelefteqslant () 40\ntriangleright (›) . . . . . 40\ntriangleright (⋫) . . . . . 39\ntriangleright (⋫) . . . 39, 40\ntrianglerighteq (Ÿ) . . . . 40\ntrianglerighteq () . . . 39\ntrianglerighteq (⋭) . 39, 40\ntrianglerighteqslant () 40\ntriplefrown (̸) . . . . . . . 48\ntriplesim (≋̸) . . . . . . . . . 33\ntriplesmile (̸) . . . . . . . 48\ntststile ( ) . . . . . . . . . 35\nttstile ( ) . . . . . . . . . . 35\ntttstile ( ) . . . . . . . . . 35\ntwoheaddownarrow (↡̸) . . . 45\ntwoheadleftarrow () . . . 31\ntwoheadleftarrow (↞̸) . . 45\ntwoheadnearrow (̸) . . . . 45\ntwoheadnwarrow (̸) . . . . 45\ntwoheadrightarrow () . . 31\ntwoheadrightarrow (↠̸) . . 45\ntwoheadsearrow (̸) . . . . 45\ntwoheadswarrow (̸) . . . . 45\ntwoheaduparrow (↟̸) . . . . . 45\nu (ν) . . . . . . . . . . . . . . . . 49nuclear power plant . see \SNPP\NUL (␀) . . . . . . . . . . . . . . . 69null set . . . . . . . . . . . . . 62, 63number . . . . . see \textnumeronumber sets see alphabets, mathnumbers . . . . . . . . . . see digitscircled . . . . . . . . . . 73, 76\NumLock ( Num ) . . . . . . . . 69\nUparrow (⇑̸) . . . . . . . . . . . 45\nuparrow (↑̸) . . . . . . . . . . . 45\nuparrowtail (̸) . . . . . . . 45\nUpdownarrow (⇕̸) . . . . . . . 45\nupdownarrow (↕̸) . . . . . . . 45\nupdownarrows (⇅̸) . . . . . . 45\nupdownharpoonleftright (⥍̸). . . . . . . . . 46\nupdownharpoonrightleft (⥌̸). . . . . . . . . 46\nupdownharpoons (⥮̸) . . . . . 46\nUpdownline (∦) . . . . . . . . 33\nupdownline (∤) . . . . . . . . 33\nupfilledspoon (̸) . . . . . . 47\nupfootline (̸) . . . . . . . . 33\nupfree (̸) . . . . . . . . . . . . 33\nupharpoonccw (↿̸) . . . . . . . 46\nupharpooncw (↾̸) . . . . . . . 46\nuplsquigarrow (̸) . . . . . . 45\nupmapsto (↥̸) . . . . . . . . . . 45\nupModels (̸) . . . . . . . . . 33\nupmodels (̸) . . . . . . . . . . 33\nuppitchfork (⋔̸) . . . . . . . 47\nuprsquigarrow (̸) . . . . . . 45\nupspoon (⫯̸) . . . . . . . . . . . 47\nupuparrows (⇈̸) . . . . . . . . 45\nupVdash (⍊̸) . . . . . . . . . . 33\nupvdash (⊥̸) . . . . . . . . . . . 33\nuup (ν) . . . . . . . . . . . . . . 50\nvargeq («) . . . . . . . . . . . 38\nvarleq (ª) . . . . . . . . . . . 38\nvarparallel (∦) . . . . . . . 31\nvarparallelinv () . . . . . 31\nVDash (*) . . . . . . . . . . . . 32\nVDash () . . . . . . . . . . . . 30\nVDash (⊯) . . . . . . . . . . . . 34\nVdash (.) . . . . . . . . . . . . 32\nVdash () . . . . . . . . . . . . 31\nVdash (⊮) . . . . . . . . . . . . 34\nvDash (*) . . . . . . . . . . . . 32\nvDash () . . . . . . . . . . . . 30\nvDash (⊭) . . . . . . . . . . . . 34\nvdash (&) . . . . . . . . . . . . 32\nvdash () . . . . . . . . . . . . 30\nvdash (⊬) . . . . . . . . . . . . 34\nVvash (.) . . . . . . . . . . . . 32\Nwarrow () . . . . . . . . . . . 42\Nwarrow (⇖) . . . . . . . . . . . 43\nwarrow (Ô) . . . . . . . . . . . 42\nwarrow (↖) . . . . . . . . 41, 93\nwarrow (↖) . . . . . . . . . . . 43\nwarrowtail () . . . . . . . . 43\nwfilledspoon () . . . . . . 47\nwfootline () . . . . . . . . . 32\nwfree () . . . . . . . . . . . . 32\nwharpoonccw () . . . . . . . 46\nwharpooncw () . . . . . . . . 46\nwlsquigarrow () . . . . . . 43\nwmapsto () . . . . . . . . . . 43\nwModels () . . . . . . . . . . 32\nwmodels () . . . . . . . . . . 32\nwnwarrows () . . . . . . . . 43\nwpitchfork () . . . . . . . . 47\nwrsquigarrow () . . . . . . 43\Nwsearrow () . . . . . . . . . 43\nwsearrow (↖↘) . . . . . . . . . 93\nwsearrow (⤢) . . . . . . . . . 43\nwsearrows () . . . . . . . . 43\nwsebipropto () . . . . . . . 23\nwsecrossing () . . . . . . . 32\nwseharpoonnesw () . . . . 46\nwseharpoons () . . . . . . . 46\nwseharpoonswne () . . . . 46\Nwseline () . . . . . . . . . . 32\nwseline () . . . . . . . . . . 32\nwspoon () . . . . . . . . . . . 47\nwVdash () . . . . . . . . . . . 32\nwvdash () . . . . . . . . . . . 32O\O (Ø) . . . . . . . . . . . . . . . . . 9\o (ø) . . . . . . . . . . . . . . . . . . 9o (o) . . . . . . . . . . . . . . . . . . 49\oast (⊛) . . . . . . . . . . . . . . 24\oasterisk (f) . . . . . . . . . . 24\obackslash (n) . . . . . . . . . 24\obackslash (⦸) . . . . . . . . . 24\obar (ɵ) . . . . . . . . . . . . . . 21\Obelus ( ) . . . . . . . . . . . 82\obelus ( ) . . . . . . . . . . . 82\Obelus* ( · ) . . . . . . . . . . . 82\obelus* ( · ) . . . . . . . . . . . 82\oblong () . . . . . . . . . . . . 21\obot (k) . . . . . . . . . . . . . . 24\obslash (⦸) . . . . . . . . . . . 21\oc () . . . . . . . . . . . . . . . . . 20\ocirc (e) . . . . . . . . . . . . . 24\ocirc (⊚) . . . . . . . . . . . . . 24\ocircle () . . . . . . . . . . . 21\ocoasterisk (g) . . . . . . . . 24\octagon () . . . . . . . . . . . 74\Octosteel (‘) . . . . . . . . . . 70\od (å) . . . . . . . . . . . . . . . . 15\odiv (c) . . . . . . . . . . . . . . 24\odot (d) . . . . . . . . . . . . . . 24\odot (⊙) . . . . . . . . . . . . . . 20\odot (⊙) . . . . . . . . . . . . . . 24\odplus (¨) . . . . . . . . . . . . 24\OE (Œ) . . . . . . . . . . . . 9, 103\oe (œ) . . . . . . . . . . . . . 9, 103\officialeuro (e) . . . . . . . 17\offinterlineskip . . . . . . . 91ogonek . . . . . . . . . see accents\ogreaterthan (⧁) . . . . . . . 21\ohill ( a) { . . . . . . . . . . . . . 15ohm . . . . . . . . . . see \textohm\ohm (Ω) . . . . . . . . . . . . . . . 67\Ohne (a/) . . . . . . . . . . . . . . 79\OHORN (Ơ) . . . . . . . . . . . . . . 9\ohorn (ơ) . . . . . . . . . . . . . . 9\oiiint ( ) . . . . . . . . . . . 27\oiiint ( ) . . . . . . . . . . . 29\oiiintclockwise ( ) . . . . 27\oiiintctrclockwise ( ) . 27\oiint (·) . . . . . . . . . . . . . 26\oiint ( ) . . . . . . . . . . 25, 27\oiint ( ‚ ) . . . . . . . . . . . . . 28\oiint ( ) . . . . . . . . . . . . . 29\oiint (∯) . . . . . . . . . . . . . 29\oiintclockwise ( ) . . . . . 27\oiintctrclockwise ( ) . . 27\oint ( ) . . . . . . . . . . . . . . 26\oint ( ∮ ) . . . . . . . . . . . . . . 25\oint (∮) . . . . . . . . . . . . . . 29\ointclockwise ( ) . . . . . . 27\ointclockwise ( ı ) . . . . . . . 28\ointclockwise ( ) . . . . . . . 29\ointctrclockwise ( ) . . . . 27\ointctrclockwise ( ) . . . . 28\ointctrclockwise ( ) . . . . 29old-style digits . . . . . . . . . . . 18\oldstylenums . . . . . . . . . . 18\oleft (h) . . . . . . . . . . . . . 24\olessthan (⧀) . . . . . . . . . . 21126

\Omega (Ω) . . . . . . . . . . . . . 49\omega (ω) . . . . . . . . . . . . . 49\omegaup (ω) . . . . . . . . . . . 50\ominus (a) . . . . . . . . . . . . 24\ominus (⊖) . . . . . . . . . . . . 20\ominus (⊖) . . . . . . . . . . . . 24\onlymove (F) . . . . . . . . . . 82\oo ( ◦◦) . . . . . . . . . . . . . . . 82\oo (@) . . . . . . . . . . . . . . . 12\ooalign . . . . . . . . . . . 91, 92\open (z) . . . . . . . . . . . . . . 16open unit disk (D) . . . . . . seealphabets, math\openJoin () . . . . . . . . . . . 31\openo (=) . . . . . . . . . . . . . . 12\openo (c) . . . . . . . . . . . . . 12\openo () . . . . . . . . . . . . . 12\opentimes () . . . . . . . . . . 31operatorsbinary . . . . . . . . . . 20–24logical see logical operatorsset . . . . . see set operatorsunary . . . . . . . . . . . . . 20\oplus (`) . . . . . . . . . . . . . 24\oplus (⊕) . . . . . . . . . . 20, 90\oplus (⊕) . . . . . . . . . . . . . 24\opposbishops (o) . . . . . . . 82\opposition () . . . . . . . . 68optical scaling . . . . . . . . . . . 96options . . . see package optionsor . . . . . . . . . . . . . . . see \vee\oright (i) . . . . . . . . . . . . 24\OrnamentDiamondSolid (q) 77orthogonal to . . . . . . see \bot\oslash (m) . . . . . . . . . . . . 24\oslash (⊘) . . . . . . . . . . . . 20\oslash (⊘) . . . . . . . . . . . . 24\ostar (⍟) . . . . . . . . . . . . . 24\otimes (b) . . . . . . . . . . . . 24\otimes (⊗) . . . . . . . . . . . . 20\otimes (⊗) . . . . . . . . . . . . 24\otop (j) . . . . . . . . . . . . . . 24\otriangle () . . . . . . . 24, 40\otriangleup (o) . . . . . . . . 24ovals . . . . . . . . . . . . . . . . . . 75\ovee () . . . . . . . . . . . . . . 21\overarc (a ⌢ ) . . . . . . . . . . . . 16\overbrace (hkikj) . . . . . . . 58\overbrace ( ) . . . . . . . . . . 58\overbrace ( {}}{ ) . . . . . . . . 58\overbrace ( {}}{ ) . . . . . . . . 57\overbracket ( ) . . . . . . . . 58\overbracket ( ) . . . . . 95, 96\overbridge ( ” a) . . . . . . . . . 15\overgroup (hkkj) . . . . . . . . 58\overgroup ( ) . . . . . . . . . 58\overleftarrow ( ←− ) . . . . . . 57\overleftharpoon ( ↼ ) . . . . 58\overleftrightarrow ( ←→ ) . 58\overline ( ) . . . . . . . . 20, 57\overlinesegment ( ) . . . . 58\overparenthesis ( {{ ) . 95, 96\Overrightarrow ( =⇒ ) . . . . . 57overrightarrow (package) 57, 104\overrightarrow ( −→ ) . . . . . 57\overrightharpoon ( ⇀ ) . . . . 58\overring (x) . . . . . . . . . . 16\overset . . . . . . . . . . . . . . 91\overt (⦶) . . . . . . . . . . . . . 24\ovoid (l) . . . . . . . . . . . . . 24\owedge () . . . . . . . . . . . . 21\owns . . . . . . . . . . . . . see \ni\owns (Q) . . . . . . . . . . . . . . 51\owns (∋) . . . . . . . . . . . . . . 51\owns (∋) . . . . . . . . . . . . . . 51\ownsbar (W) . . . . . . . . . . . . 51P\P () . . . . . . . . . . . . . . 8, 102\p ( . . . . . . . . . . . . . . . . . 82\p@ ˙). . . . . . . . . . . . . . . . . . . 94package optionsa (esvect) . . . . . . . . . . . 59b (esvect) . . . . . . . . . . . 59bbgreekl (mathbbol) . . . 65c (esvect) . . . . . . . . . . . 59crescent (fge) . . . . . . . . 56d (esvect) . . . . . . . . . . . 59e (esvect) . . . . . . . . . . . 59f (esvect) . . . . . . . . . . . 59g (esvect) . . . . . . . . . . . 59german (keystroke) . . . . 69h (esvect) . . . . . . . . . . . 59integrals (wasysym) . . . . 25mathcal (euscript) . . . . . 65mathscr (euscript) . . . . . 65nointegrals (wasysym) . . 25sans (dsfont) . . . . . . . . . 65varg (txfonts/pxfonts) . . 50packageslongdiv . . . . . . . . . . . . . 57accents . . . 56, 94, 104, 105amsbsy . . . . . . . . . . . . 100amsfonts 20, 30, 36, 41, 62,65amsmath . 7, 49, 56, 91, 99amssymb . 7, 20, 30, 36, 41,56, 62, 65, 104, 105, 107amstext . . . . . . . . . 92, 93ar . . . . . . . . . . . . 67, 104arcs . . . . . . . . 16, 104, 105arev . . . . . 64, 78, 104, 105ascii . . . . 69, 101, 104, 105bbding . 71–75, 77, 88, 104,105bbm . . . . . . . . . . . 65, 104bbold . . . . . . . . . . 65, 104bm . . . . . . . 100, 104, 105braket . . . . . . . . . . . . . 53calligra . . . . . . 65, 104, 105calrsfs . . . . . . . . . . . . . 65cancel . . . . . . . . . . . . . 57cclicenses . . . . 18, 104, 105centernot . . . . . . . . . . . 92chancery . . . . . . . . . . . 104chemarr . . . . . 59, 104, 105chemarrow . . . . 47, 60, 104cmll . . . 20, 23, 30, 36, 104dblaccnt . . . . . . . . . . . . 94dictsym . . . . . 84, 104, 105dingbat 72, 77, 88, 104, 105dsfont . . . . . . . . . 65, 104epsdice . . . . . . 81, 104, 105esint . . . . . . . . . . 28, 104esvect . . . . . . . . . 59, 104eufrak . . . . . . . . . . . . . 65eurosym . . . . . 17, 104, 105euscript . . . . . 65, 104, 105extarrows . . . . 60, 104, 105extpfeil . . . . . . 60, 104, 105extraipa . . . . . . . . 15, 104fc . . . . . . . . . . . . . . 9, 13fclfont . . . . . . . . . . . . 104feyn . . . . . . . . 70, 104, 105fge . 47, 52, 56, 62, 64, 104,105fixmath . . . . . . . . . . . 100fontenc . . . . . 7, 9, 13, 103gensymb . . . . . . . . . . . . 67graphics . . . . . . . . . . . . 90graphicx . . . . . . . 16, 87, 90harmony . . . . . 79, 104, 105hieroglf . . . . . 84, 104, 105holtpolt . . . . . . . . 60, 104ifsym 67, 75, 80, 81, 88, 90,104, 105igo . . . . . . . . . . . . 76, 104isoent . . . . . . . . . . . . . 103keystroke . . . . 69, 104, 105latexsym . 20, 30, 36, 41, 62,87, 104, 105manfnt . . . 76, 79, 104, 105marvosym 17, 62, 64, 68–71,76, 79, 80, 88matbbol . . . . . . . . . . . . 65mathabx . . . . . . 22, 24, 26,30–32, 36–38, 40, 42, 43, 49,51–54, 56, 58, 62, 63, 68, 76,87, 88, 104, 105, 107mathbbol . . . . . . . . . . . 65mathcomp . . . . . . . . . . 62mathdesign . 17, 23, 29, 51,55, 64, 104mathdots 56, 61, 62, 94, 104,105mathrsfs . . . . . . . . 65, 104mathtools . . 34, 58, 59, 104,105mbboard . . . . . . . . 65, 104metre . 16, 56, 82, 104, 105MnSymbol . . . . 23, 24, 29,32, 33, 37, 39, 40, 43–48, 50,51, 54, 56–58, 61, 63, 64, 74,104, 105127

musixtex . . . . . . . . . . . . 79nath . . . . . . . . . 52, 55, 104nicefrac . . . . . 64, 104, 105ntheorem . . . . . . . . . . . 62overrightarrow . . . . 57, 104phaistos . . . . . 83, 104, 105phonetic . . . 12, 15, 90, 104pifont 9, 71–75, 77, 90, 104,105polynom . . . . . . . . . . . . 57protosem . . . . 83, 104, 105psnfss . . . . . . . . . . . . . 73pxfonts . . 20, 21, 27, 30, 31,36, 38, 41, 42, 48, 50, 51, 62,63, 65, 87, 101rotating . . . . . . . . . 18, 69savesym . . . . . . . . . . . . 87semtrans . 13, 16, 104, 105simplewick . . . . . . . . . . 96simpsons . . . . . . . 85, 104skak . . . . . . . . 82, 104, 105skull . . . . . . . . 76, 104, 105slashed . . . . . . . . . . . . . 92staves . . . . . . . . . 85, 104stmaryrd . . . . . . 21, 25, 30,36, 40, 42, 48, 52, 53, 88, 91,104, 105t4phonet . 13, 16, 104, 105textcomp . . . . . . . . . . . 7,8, 13, 17–19, 41, 56, 64, 67,78, 87, 101, 103–105timing . . . . . . . . . . . . . 67tipa . 10, 11, 13, 15, 16, 90,104, 105tipx . . . . . . . . 11, 104, 105trfsigns . . . . 35, 51, 60, 104trsym . . . . . . . 35, 104, 105turnstile . . 34, 35, 104, 105txfonts 20, 21, 27, 30, 31, 36,38, 41, 42, 48, 50, 51, 62, 63,65, 87, 89, 101, 104, 105type1cm . . . . . . . . . . . . 87ulsy . . . . . . 24, 48, 90, 104underscore . . . . . . . . . . . 8undertilde . . . . 59, 104, 105units . . . . . . . . . . . . . . 64universa . . 76, 80, 104, 105universal 71, 73, 76, 80, 104,105upgreek . . . . . 50, 104, 105upquote . . . . . . . . . . . 101url . . . . . . . . . . . . . . . 101vietnam . . . . . . . . . . . 104vntex . . . . . . . . . . . . 9, 13wasysym . 12, 17, 19–21, 25,30, 36, 38, 41, 61–63, 67, 68,70, 73, 74, 78, 88, 104, 105wsuipa 11, 15, 16, 88, 90, 94,104, 105yfonts . . . . . . 65, 104, 105yhmath 57, 59, 62, 94, 104Pakin, Scott . . . . . . . . . 1, 104\PaperLandscape (¤) . . . . . 81\PaperPortrait (£) . . . . . . 81par . . . . . . . . . . . . see \invampparagraph mark . . . . . . . see \Pparallel . see also \varparallel\parallel (‖) . . . . . . . . 30, 54\parallel (∥) . . . . . . . . . . . 33\ParallelPort (Ñ) . . . . . . . 69\parr (`) . . . . . . . . . . . . . . 23\partial (B) . . . . . . . . . . . . 51\partial (∂) . . . . . . . . . . . . 51\partialslash (C) . . . . . . . 51\partialvardint (∫…∫) . . . . 64\partialvardlanddownint (⨚) 64\partialvardlandupint (⨙) 64\partialvardlcircleleftint(∲) . . . . . . . . . . . . . . 43\partialvardlcircleleftint(∲) . . . . . . . . . . . . . . 64\partialvardlcirclerightint(∲) . . . . . . . . . . . . . . 43\partialvardlcirclerightint(∲) . . . . . . . . . . . . . . 64\partialvardoiint (∯) . . . 64\partialvardoint (∮) . . . . . 64\partialvardrcircleleftint(∳) . . . . . . . . . . . . . . 43\partialvardrcircleleftint(∳) . . . . . . . . . . . . . . 64\partialvardrcirclerightint(∳) . . . . . . . . . . . . . . 43\partialvardrcirclerightint(∳) . . . . . . . . . . . . . . 64\partialvardstrokedint (⨏) 64\partialvardsumint (⨋) . . . 64\partialvartint (∫…∫) . . . . . 64\partialvartlanddownint (⨚) 64\partialvartlandupint (⨙) 64\partialvartlcircleleftint(∲) . . . . . . . . . . . . . . 43\partialvartlcircleleftint(∲) . . . . . . . . . . . . . . 64\partialvartlcirclerightint(∲) . . . . . . . . . . . . . . 43\partialvartlcirclerightint(∲) . . . . . . . . . . . . . . 64\partialvartoiint (∯) . . . 64\partialvartoint (∮) . . . . . 64\partialvartrcircleleftint(∳) . . . . . . . . . . . . . . 43\partialvartrcircleleftint(∳) . . . . . . . . . . . . . . 64\partialvartrcirclerightint(∳) . . . . . . . . . . . . . . 43\partialvartrcirclerightint(∳) . . . . . . . . . . . . . . 64\partialvartstrokedint (⨏) 64\partialvartsumint (⨋) . . . 64particle-physics symbols . . . . 70parts per thousand . . . . . . see\textperthousand\partvoice (a –ˇ) » \partvoiceless (a – »˚) . . . . . . . 15\passedpawn (r) . . . . . . . . . 82pawn . . . . . . see chess symbols\Peace () . . . . . . . . . . . . . 77\PencilLeft () . . . . . . . . 72\PencilLeftDown () . . . . . 72\PencilLeftUp () . . . . . . . 72\PencilRight () . . . . . . . 72\PencilRightDown () . . . . 72\PencilRightUp () . . . . . . 72pencils . . . . . . . . . . . . . . . . 72\pentagon (⬠) . . . . . . . . . . 74\pentagram () . . . . . . . . . . 24people . . . . . . . . . . . . see facespercent sign . . . . . . . . . see \%\permil () . . . . . . . . . . . . 19\Perp () . . . . . . . . . . . . . . 31\perp (⊥) . . . . . . . . . . . 30, 93\perp (⊥) . . . . . . . . . . . . . . 33\perthousand (‰) . . . . . . . 67\Pfund (£) . . . . . . . . . . . . . 17\PgDown ( Page ↓ ) . . . . . . . 69\PgUp ( Page ↑ ) . . . . . . . . . 69phaistos (package) . 83, 104, 105Phaistos disk . . . . . . . . . . . . 83pharmaceutical prescription see\textrecipe\PHarrow (J) . . . . . . . . . . . . 83\PHbee (h) . . . . . . . . . . . . 83\PHbeehive (X) . . . . . . . . 83\PHboomerang (R) . . . . . . . 83\PHbow (K) . . . . . . . . . . . . . . 83\PHbullLeg (b) . . . . . . . . . . 83\PHcaptive (D) . . . . . . . . . 83\PHcarpentryPlane (S) . . . 83\PHcat (c) . . . . . . . . . . . . 83\PHchild (E) . . . . . . . . . . . 83\PHclub (M) . . . . . . . . . . . . . 83\PHcolumn (W) . . . . . . . . . . . 83\PHcomb (U) . . . . . . . . . . . . 83\PHdolium (T) . . . . . . . . . . 83\PHdove (f) . . . . . . . . . . . 83\PHeagle (e) . . . . . . . . . . . 83\PHflute (o) . . . . . . . . . . . 83\PHgaunlet (H) . . . . . . . . . 83\PHgrater (p) . . . . . . . . . . 83\PHhelmet (G) . . . . . . . . . . 83\PHhide (a) . . . . . . . . . . . 83128

\PHhorn (Z) . . . . . . . . . . . . . 83\Phi (Φ) . . . . . . . . . . . . . . . 49\phi (φ) . . . . . . . . . . . . . . . 49\phiup (φ) . . . . . . . . . . . . . 50\PHlid (Q) . . . . . . . . . . . . . 83\PHlily (m) . . . . . . . . . . . . 83\PHmanacles (N) . . . . . . . . 83\PHmattock (O) . . . . . . . . . 83\Phone (¨) . . . . . . . . . . . . . 77\phone (☎) . . . . . . . . . . . . . 78\PhoneHandset (©) . . . . . . . 77phonetic (package) 12, 15, 90, 104phonetic symbols . . . . . . 10–13\photon () . . . . . . . . . 67photons . . . . . . . . . . . . . . . 70\PHoxBack (n) . . . . . . . . . . 83\PHpapyrus (k) . . . . . . . . . . 83\PHpedestrian (A) . . . . . . 83\PHplaneTree (i) . . . . . . . . 83\PHplumedHead (B) . . . . . 83\PHram (d) . . . . . . . . . . . . 83\PHrosette (l) . . . . . . . . . 83\PHsaw (P) . . . . . . . . . . . . . 83\PHshield (L) . . . . . . . . . . 83\PHship (Y) . . . . . . . . . . . 83\PHsling (V) . . . . . . . . . . . 83\PHsmallAxe (r) . . . . . . . . 83\PHstrainer (q) . . . . . . . 83\PHtattooedHead (C) . . . . 83\PHtiara (I) . . . . . . . . . . . 83\PHtunny (g) . . . . . . . . . . 83\PHvine (j) . . . . . . . . . . . . 83\PHwavyBand (s) . . . . . . . . . 83\PHwoman (F) . . . . . . . . . . . 83physical symbols . . . . . . . . . 67\Pi (Π) . . . . . . . . . . . . . . . . 49\pi (π) . . . . . . . . . . . . . . . . 49\Pickup (A) . . . . . . . . . . . . 69pifont (package) 9, 71–75, 77, 90,104, 105pilcrow . . . . . . . . . . . . . see \Ppipe . . . . . . . . . see \textpipe\Pisces (ë) . . . . . . . . . . . . 68\pisces (♓) . . . . . . . . . . . . 68\Pisymbol . . . . . . . . . . . . . . 90\pitchfork (&) . . . . . . . . . . 63\pitchfork (⋔) . . . . . . . . . . 30\pitchfork (⋔) . . . . . . . . . . 47pitchfork symbols . . . . . . . . 47\piup (π) . . . . . . . . . . . . . . 50\planck (¯h) . . . . . . . . . . . . 12\Plane () . . . . . . . . . . . . . 77planets . . . . . . . . . . . . . . . . 68playing cards . . . . see card suitsPlimsoll line 91, see also \minuso\Plus (') . . . . . . . . . . . . . . 72\plus (+) . . . . . . . . . . . . . . 23plus-or-minus sign . . . . see \pm\PlusCenterOpen (() . . . . . 72\pluscirc (©) . . . . . . . . . . 22\PlusOutline (&) . . . . . . . . 72plusses . . . . . . . . . . . . . . . . 72\PlusThinCenterOpen ()) . . 72\Pluto (I) . . . . . . . . . . . . . 68\Pluto (É) . . . . . . . . . . . . . 68\pluto (♇) . . . . . . . . . . . . . 68\pm (±) . . . . . . . . . . . . . . . . 20\pm (±) . . . . . . . . . . . . . . . . 23\pm ( ¯˙) . . . . . . . . . . . . . . . 82\pmb . . . . . . . . . . . . . . . . . 100\pmod . . . . . . . . . . . . . . . . . 49\pod . . . . . . . . . . . . . . . . . . 49\pointer () . . . . . . . . . . . . 78pointing finger . . . . . . . see fists\Pointinghand (Z) . . . . . . . 76\polishhook (~) . . . . . . . . . 16\polter ( ) . . . . . . . . . . . 60polygons . . . . . . . . . . . . . . . 74polynom (package) . . . . . . . . 57polynomial division . . . . . . . 57PostScript 50, 66, 71, 81, 90, 99PostScript fonts . . . . . . . 71, 90\pounds (£) . . . . . . 8, 102, 103power set (P) . .see alphabets,math\powerset (℘) . . . . . . . . . . . 51\Pp ( ˙) . . . . . . . . . . . . . . . . 82\pp ( ˙ ) . . . . . . . . . . . . . . 82\ppm ( ¯˙˙) . . . . . . . . . . . . . . 82\Ppp (˙) . . . . . . . . . . . . . . . 82\ppp ( ) . . . . . . . . . . . . . . 82\Pppp ( ˙˙) . . . . . . . . . . . . . . 82\pppp ( ) . . . . . . . . . . . . . 82\Ppppp ( ˙˙) . . . . . . . . . . . . . 82\ppppp (˙ ) . . . . . . . . . . . . 82\Pr (Pr) . . . . . . . . . . . . . . . 49\prec (≺) . . . . . . . . . . . . . . 30\prec (≺) . . . . . . . . . . . . . . 32\precapprox (Æ) . . . . . . . . . 31\precapprox () . . . . . . . . . 30\precapprox (⪷) . . . . . . . . . 32\preccurlyeq (¤) . . . . . . . . 31\preccurlyeq () . . . . . . . . 30\preccurlyeq (≼) . . . . . . . . 32\precdot (Ì) . . . . . . . . . . . 31\preceq (≼) . . . . . . . . . . . . 30\preceq (⪯) . . . . . . . . . . . . . 32\preceqq () . . . . . . . . . . . . 31\precnapprox (Ê) . . . . . . . . 32\precnapprox () . . . . . . . . 30\precnapprox (⪹) . . . . . . . . 33\precneq (¬) . . . . . . . . . . . 32\precneqq () . . . . . . . . . . 31\precnsim (Ä) . . . . . . . . . . 32\precnsim () . . . . . . . . . . 30\precnsim (⋨) . . . . . . . . . . . 33\precsim (À) . . . . . . . . . . . 31\precsim () . . . . . . . . . . . 30\precsim (≾) . . . . . . . . . . . . 32prescription . . see \textrecipe\prime (′) . . . . . . . . . . . . . . 62\prime (′) . . . . . . . . . . . . . . 63\Printer (Ò) . . . . . . . . . . . 69printer’s fist . . . . . . . . see fistsprobabilistic independence . . 93\prod ( ∏ ) . . . . . . . . . . . . . 25\prod (∏) . . . . . . . . . . . . . . 29\projlim (proj lim) . . . . . . . 49pronunciation symbols . . . .seephonetic symbolsproof, end of . . . . . . . . . . . . 62\propto (9) . . . . . . . . . . . . 63\propto (∝) . . . . . . . . . . . . 30\propto (∝) . . . . . . . . . . . . 33proto-Semitic symbols . . . . . 83protosem (package) 83, 104, 105\ProvidesPackage . . . . . . . 104\PrtSc ( PrtSc ) . . . . . . . . . 69\ps ( ) . . . . . . . . . . . . . . 82\Psi (Ψ) . . . . . . . . . . . . . . . 49\psi (ψ) . . . . . . . . . . . . . . . 49\psiup (ψ) . . . . . . . . . . . . . 50psnfss (package) . . . . . . . . . . 73\Pu (‰ ) . . . . . . . . . . . . . . . . 79pulse diagram symbols . . . . . 67\PulseHigh ($) . . . . . . . . . 67\PulseLow (%) . . . . . . . . . 67punctuation . . . . . . . . . . . . . 9\pwedge (U) . . . . . . . . . . . . 12pxfonts (package) 20, 21, 27, 30,31, 36, 38, 41, 42, 48, 50, 51,62, 63, 65, 87, 101\Pxp (˙) . . . . . . . . . . . . . . . 82\pxp (˙ ) . . . . . . . . . . . . . . 82QQ.E.D. . . . . . . . . . . . . . . . . 62\qside (M) . . . . . . . . . . . . . 82\Quadrad (]]) . . . . . . . . . . . . 56\quadrad ( ]) . . . . . . . . . . . . 56\Quadras ([[) . . . . . . . . . . . . 56\quadras ( [) . . . . . . . . . . . . 56quarter note see musical symbols\quarternote (♩) . . . . . . . . 78\quarternote (♩) . . . . . . . . . 78quaternions (H) see alphabets,mathquaver . . . see musical symbolsqueen . . . . . . see chess symbols\quotedblbase („) . . . . . 9, 103\quotesinglbase (‚) . . . 9, 103129

R\R ( ∼) . . . . . . . . . . . . . . . . 82\r (å) . . . . . . . . . . . . . . . . . 13\r ( ∼) . . . . . . . . . . . . . . . . 82\Radiation () . . . . . . . . . 81radicals . . see \sqrt and \surd\Radioactivity (j) . . . . . . 70\Rain () . . . . . . . . . . . . . . 80\RainCloud () . . . . . . . . . 80raising . . . . . see \textraising\RaisingEdge ( ) . . . . . . . . 67\Rangle (>) . . . . . . . . . . . . 65\rAngle (〉〉) . . . . . . . . . . . . . 55\rangle (〉) . . . . . . . . . . 20, 53\rangle (⟩) . . . . . . . . . . . . . 54\ranglebar () . . . . . . . . . . 54\RArrow ( → ) . . . . . . . . . . 69\rarrowfill . . . . . . . . . . . . 60rational numbers (Q) . . . . . seealphabets, mathrationalized Planck constant see\hbar\Rbag () . . . . . . . . . . . . . . 52\rbag (⟆) . . . . . . . . . . . . . . . 52⎫⎪\Rbrack (]) . . . . . . . . . . . . . 65\rbrace ( ⎬) ⎪⎭. . . . . . . . . . . 54\rBrack (]]) . . . . . . . . . . . . . 55\rc (©a) . . . . . . . . . . . . . . . . 15\rCeil (⌉⌉) . . . . . . . . . . . . . . 55\rceil (⌉) . . . . . . . . . . . . . . 53⎤\rceil () . . . . . . . . . . . . . 54\rcirclearrowdown ⎥ () . . . 44\rcirclearrowleft (⟲) . . . 44\rcirclearrowright (⤿) . . 44\rcirclearrowup (↺) . . . . . 44\rcircleleftint (∳) . . . . . . 29\rcirclerightint (∳) . . . . . 29\rcorners (w) . . . . . . . . . . . 52\rcurvearrowdown (⤹) . . . . . 44\rcurvearrowleft (↶) . . . . 44\rcurvearrowne () . . . . . . 44\rcurvearrownw () . . . . . . 44\rcurvearrowright () . . . . 44\rcurvearrowse () . . . . . . 44\rcurvearrowsw () . . . . . . 44\rcurvearrowup () . . . . . . . 44\rdbrack (w) . . . . . . . . . . . . 54\Re (R) . . . . . . . . . . . . . . . . 51real numbers (R) see alphabets,mathrecipe . . . . . . see \textrecipe\recorder (⌕) . . . . . . . . . . . 78\Rectangle (u) . . . . . . . . . . 75\RectangleBold (v) . . . . . . . 75rectangles . . . . . . . . . . . . . . 75\RectangleThin (t) . . . . . . . 75\Rectpipe (˜) . . . . . . . . . . . 70\Rectsteel (”) . . . . . . . . . . 70reduced quadrupole moment see\rqm\reflectbox . . . . . . . . . . . . 90registered trademark . . . . . see\textregisteredrelational symbols . . . . . . . . 30binary 30–32, 34–39, 47, 48negated binary . . . . 30–33triangle . . . . . . . . . 39, 40\Relbar (=) . . . . . . . . . 48, 90\Relbar () . . . . . . . . . . . . 33\relbar (−) . . . . . . . . . 48, 90\relbar () . . . . . . . . . . . . 33\resizebox . . . . . . . . . . . . . 87\Respondens (∼) . . . . . . . . . 82\respondens (∼) . . . . . . . . . 82\restoresymbol . . . . . . . . . 87\restriction . . . . . . . . . . see\upharpoonright\restriction (æ) . . . . . . . . 42\restriction (↾) . . . . . . . . 46retracting see \textretracting\Return ( ←↪ ) . . . . . . . . . . 69return . . . . . see carriage return\revaw ( ) . . . . . . . . . . . . . 55\revD (¢) . . . . . . . . . . . . . . 12\revddots (. .. ) . . . . . . . . . . 94\reve () . . . . . . . . . . . . . . 12\reveject (f) . . . . . . . . . . . 12\revepsilon () . . . . . . 12, 90reverse solidus . . . . . . . . . . see\textbackslashreversed symbols . . . . . . . . . 90\reversedvideodbend () . 76\revglotstop (c) . . . . . . . . 12\Rewind () . . . . . . . . . . . . 79\RewindToIndex (´) . . . . . 79\RewindToStart (µ) . . . . . . 79\rfilet ( ? ) . . . . . . . . . . . . . 54\rFloor (⌋⌋) . . . . . . . . . . . . . 55\rfloor (⌋) . . . . . . . . . . . . . 53\rfloor (⎫) . . . . . . . . . . . . 54⎥\rgroup ( ⎭ ⎦ ) . . . . . . . . . . . . 53\rgroup (⎫⎪⎭ ) . . . . . . . . . . . 54\RHD () . . . . . . . . . . . . . . . 21\rhd (⊲) . . . . . . . . . . . . 20, 21\rhd (⊳) . . . . . . . . . . . . 39, 40\rho (ρ) . . . . . . . . . . . . . . . 49\rhookdownarrow () . . . . . . 44\rhookleftarrow (↩) . . . . . 44\rhooknearrow (⤤) . . . . . . . 44\rhooknwarrow () . . . . . . . 44\rhookrightarrow () . . . . 44\rhooksearrow () . . . . . . . 44\rhookswarrow (⤦) . . . . . . . 43\rhookuparrow () . . . . . . . . 43\rhoup (ρ) . . . . . . . . . . . . . 50\right . . . . . . . . 53, 55, 87, 89\rightangle (∟) . . . . . . . . . 64\RIGHTarrow () . . . . . . . . . 78\Rightarrow (⇒) . . . . . 20, 41\Rightarrow (⇒) . . . . . . . . 43\rightarrow (Ñ) . . . . . . . . 42\rightarrow (→) . . . . . . . . 41\rightarrow (→) . . . . . . . . . 43\rightarrowtail (↣) . . . . . 41\rightarrowtail (↣) . . . . . 43\rightarrowtriangle (⇾) . . 42\rightbarharpoon (Ý) . . . . 43\RIGHTCIRCLE () . . . . . . . . 78\RIGHTcircle () . . . . . . . . 78\Rightcircle () . . . . . . . . 78\RightDiamond (?) . . . . . . . 75\rightevaw ( ) . . . . . . . . . . 55\rightfilledspoon () . . . 47\rightfootline () . . . . . . 32\rightfree () . . . . . . . . . . 32\righthalfcap (⌝) . . . . . . . 23\righthalfcup (⌟) . . . . . . . 23\rightharpoonccw (⇀) . . . . 46\rightharpooncw (⇁) . . . . . 46\rightharpoondown (ã) . . . 43\rightharpoondown (⇁) . . . 41\rightharpoonup (á) . . . . . 43\rightharpoonup (⇀) . . . . . 41\rightleftarrows (Õ) . . . . 42\rightleftarrows (⇄) . . . . 41\rightleftarrows (⇄) . . . . 43\rightleftharpoon (á) . . . 43\rightleftharpoons (é) . . 43\rightleftharpoons (⇋) . . 41\rightleftharpoons (⇀↽) . . 41\rightleftharpoons (⇌) . . . 46\rightleftharpoonsfill . . . 60\rightlsquigarrow (↝) . . . . 43\rightmapsto (↦) . . . . . . . . 43\rightModels (⊫) . . . . . . . . 32\rightmodels (⊧) . . . . . . . . 32\rightmoon (L) . . . . . . . . . . 68\rightmoon (☽) . . . . . . . . . . 68\rightp (w) . . . . . . . . . . . . . 16\rightpitchfork () . . . . . 47\rightpointleft (L) . . . . 72\rightpointright (N) . . . 72\rightpropto () . . . . . . . . 32\rightrightarrows (Ñ) . . . 42\rightrightarrows (⇒) . . . 41\rightrightarrows (⇉) . . . . 43\rightrightharpoons (Ù) . . 43\rightrsquigarrow () . . . . 43\Rightscissors (Q) . . . . . . 71\rightslice () . . . . . . . . . 21\rightslice (⪧) . . . . . . . . . 32\rightspoon (⊸) . . . . . . . . 47\rightsquigarrow (ù) . . . 42\rightsquigarrow () . . . . 41\rightsquigarrow (↝) . . . . 44130

\rightt (o) . . . . . . . . . . . . . 16\righttherefore () . . . 23, 61\rightthreetimes (%) . . . . 63\rightthreetimes (⋌) . . . . 21\rightthreetimes (⋌) . . . . . 23\rightthumbsdown (d) . . . 72\rightthumbsup (u) . . . . . 72\righttoleftarrow (ý) . . . 42\Righttorque (') . . . . . . . . 70\rightturn () . . . . . . . . . 78\rightVdash (⊩) . . . . . . . . . 32\rightvdash (⊢) . . . . . . . . . 32\rightwave ( ) . . . . . . . . . . 55\rightY () . . . . . . . . . . . . 23\ring (˚) . . . . . . . . . . . . . . 57ring equal to . . . . . see \circeqring in equal to . . . see \eqcirc\riota ( ) . . . . . . . . . . . . . . 12\rip (O) . . . . . . . . . . . . . . . 76\risingdotseq () . . . . . . . 31\risingdotseq () . . . . . . . 30\risingdotseq (≓) . . . . . . . 32\rJoin () . . . . . . . . . . . . . 31\rlap . . . . .⎫. . . . . . . . . 75, 93\rmoustache ( ⎩ ) . . . . . . . . 53\rmoustache (⎫⎪⎩ ) . . . . . . . . 54rook . . . . . . . see chess symbolsroots . . . . . . . . . . . . see \sqrt\rotatebox . . . . . . . . . . 16, 90rotated symbols . . 10–12, 16, 90rotating (package) . . . . . 18, 69\rotm (m) . . . . . . . . . . . . . . 12\rotOmega () . . . . . . . . . . . 12\rotr (r) . . . . . . . . . . . . . . 12\rotvara (A) . . . . . . . . . . . . 12\rotw (w) . . . . . . . . . . . . . . 12\roty (y) . . . . . . . . . . . . . . 12\RoundedLsteel (Ÿ) . . . . . . 70\RoundedTsteel () . . . . . . . 70\RoundedTTsteel () . . . . . . 70\Rparen ()) . . . . . . . . . . . . . 65\rqm (Ī) . . . . . . . . . . . . . . . 92\rrangle (⟫) . . . . . . . . . . . 54\rrbracket () . . . . . . . . . . 53\rrceil () . . . . . . . . . . . . . 52\rrfloor () . . . . . . . . . . . . 52\Rrightarrow (⇛) . . . . . . . 42\Rrightarrow (⇛) . . . . . . . . 43\rrparenthesis (⦈) . . . . . . . 52\RS (␞) . . . . . . . . . . . . . . . . 69\rsem () . . . . . . . . . . . . . 54\rsemantic . . . . . see \rdbrack\Rsh (é) . . . . . . . . . . . . . . . 42\Rsh () . . . . . . . . . . . . . . . 41\Rsh (↱) . . . . . . . . . . . . . . . 43\rtimes () . . . . . . . . . . . . 22\rtimes (⋊) . . . . . . . . . . . . 21\rtimes (⋊) . . . . . . . . . . . . 23\rtriple . . . . . . . . . . . . . . 55\rVert (||) . . . . . . . . . . . . . . 55\rVert (‖) . . . . . . . . . . . . . 53\rvert (|) . . . . . . . . . . . . . . 53\rwave ( ) . . . . . . . . . . . . . 55\rWavy () . . . . . . . . . . . . 54\rwavy () . . . . . . . . . . . . . 54S\S (§) . . . . . . . . . . . . . . 8, 102safety-related symbols . . . . . 70\Sagittarius (è) . . . . . . . . 68\sagittarius (♐) . . . . . . . . 68\samebishops (s) . . . . . . . . 82sans (dsfont package option) . 65\satellitedish (I) . . . . . . 77\Saturn (F) . . . . . . . . . . . . 68\Saturn (Æ) . . . . . . . . . . . . 68\saturn (♄) . . . . . . . . . . . . 68savesym (package) . . . . . . . . 87\savesymbol . . . . . . . . . . . . 87\Sborder (S) . . . . . . . . . . . 77\scalebox . . . . . . . . . . . . . . 87scalingmechanical . . . . . . . 96, 98optical . . . . . . . . . . . . . 96\scd () . . . . . . . . . . . . . . . 12\scg () . . . . . . . . . . . . . . . 12\schwa () . . . . . . . . . . . . . . 11\schwa (e) . . . . . . . . . . . . . 12Schwartz distribution spaces seealphabets, math\sci (*) . . . . . . . . . . . . . . . 11scientific symbols . . . . . . 67–70\ScissorHollowLeft (§) . . 71\ScissorHollowRight (¦) . 71\ScissorLeft (¤) . . . . . . . 71\ScissorLeftBrokenBottom (£). . . . . . . . . 71\ScissorLeftBrokenTop (¥) 71\ScissorRight (¡) . . . . . . . 71\ScissorRightBrokenBottom( ) . . . . . . . . . . . . . . 71\ScissorRightBrokenTop (¢) 71scissors . . . . . . . . . . . . . . . . 71\scn (:) . . . . . . . . . . . . . . . 11\scoh (˝) . . . . . . . . . . . . . . 36\Scorpio (ç) . . . . . . . . . . . 68\scorpio () . . . . . . . . . . . 68\scr (J) . . . . . . . . . . . . . . . 11script letters see alphabets, math\scripta (¡) . . . . . . . . . . . . 11\scriptg () . . . . . . . . . . . . 12\scriptscriptstyle . . . 92, 93\scriptstyle . . . . . . . . 92, 93\scriptv (Y) . . . . . . . . . . . . 12\Scroll ( Scroll ) . . . . . . . . 69\scu (W) . . . . . . . . . . . . . . . 12\scy (]) . . . . . . . . . . . . . . . 12\sddtstile ( ) . . . . . . . . . 35\sdststile ( ) . . . . . . . . . 35\sdtstile ( ) . . . . . . . . . . 35\sdttstile ( ) . . . . . . . . . 35seagull . . . . . see \textseagull\Searrow () . . . . . . . . . . . 42\Searrow (⇘) . . . . . . . . . . . 43\searrow (×) . . . . . . . . . . . 42\searrow (↘) . . . . . . . . 41, 93\searrow (↘) . . . . . . . . . . . 43\searrowtail () . . . . . . . . 43\sec (sec) . . . . . . . . . . . . . . 49==) . . . . . . . . . . . . 79\Sech (ˇ “ ) ) . . . . . . . . . . . . . . 79\SechBL (ˇ “= =)\SechBl (ˇ “ . . . . . . . . . . . . 79\SechBR (ˇ “==) . . . . . . . . . . . . 79\SechBr (ˇ “ =) =. . . . . . . . . . . . 79\second (2) . . . . . . . . . . . . . 63seconds, angular . . see \second\secstress (i) . . . . . . . . . . . 16section mark . . . . . . . . . see \S\SectioningDiamond (¡) . . 81\see (l) . . . . . . . . . . . . . . 82\sefilledspoon () . . . . . . 47\sefootline () . . . . . . . . . 32\sefree () . . . . . . . . . . . . 32segmented digits . . . . . . . . . 67\seharpoonccw () . . . . . . . 46\seharpooncw () . . . . . . . . 46\selectfont . . . . . . . . . . . . . 7\selsquigarrow () . . . . . . 43semantic valuation . . . . . . . see\llbracket/\rrbracketand \ldbrack/\rdbrack\semapsto () . . . . . . . . . . 43semibreve . see musical symbolssemidirect products . . 21, 22, 63semiquaver see musical symbolssemitic transliteration . . 13, 16\seModels () . . . . . . . . . . 32\semodels () . . . . . . . . . . 32semtrans (package) . 13, 16, 104,105\senwarrows () . . . . . . . . 43\senwharpoons () . . . . . . . 46\SePa (@ ) . . . . . . . . . . . . . . 79\separated () . . . . . . . . . . 32\sepitchfork () . . . . . . . . 47\seppawns (q) . . . . . . . . . . 82\SerialInterface (Î) . . . . 69\SerialPort (Ð) . . . . . . . . . 69\sersquigarrow () . . . . . . 43\sesearrows () . . . . . . . . 43\sespoon () . . . . . . . . . . . 47set operatorsintersection . . . . see \capunion . . . . . . . . . see \cup\setminus (\) . . . . . . . . . . . 20131

\setminus (∖) . . . . . . . . . . . 23\seVdash () . . . . . . . . . . . 32\sevdash () . . . . . . . . . . . 32SGML . . . . . . . . . . . . . . . 103sha (X) . . . . . . . . . . . . . . . 90\sharp (♯) . . . . . . . . . . . 62, 78\sharp (♯) . . . . . . . . . . . . . . 63\Shift ( Shift ⇑ ) . . . . . . . . 69\shift (˜) . . . . . . . . . . . . . 20\Shilling (¡) . . . . . . . . . . . 17\shneg (ˆ) . . . . . . . . . . . . . 20\shortdownarrow (↓) . . . . . . 42\ShortFifty (×) . . . . . . . . 80\ShortForty (Ù) . . . . . . . . 80\shortleftarrow (←) . . . . . 42\shortmid () . . . . . . . . . . . 30\shortmid (∣) . . . . . . . . . . . 23\ShortNinetyFive (Ô) . . . . 80\shortparallel () . . . . . . . 30\shortparallel (∥) . . . . . . 32\ShortPulseHigh (") . . . . . 67\ShortPulseLow (#) . . . . . . 67\shortrightarrow (→) . . . . 42\ShortSixty (Ö) . . . . . . . . 80\ShortThirty (Û) . . . . . . . 80\shortuparrow (↑) . . . . . . . 42\showclock . . . . . . . . . . . . . 81\shpos (´) . . . . . . . . . . . . . 20\SI (␏) . . . . . . . . . . . . . . . . 69\Sigma (Σ) . . . . . . . . . . . . . 49\sigma (σ) . . . . . . . . . . . . . 49\sigmaup (σ) . . . . . . . . . . . . 50\sim (∼) . . . . . . . . . 30, 91, 101\sim (∼) . . . . . . . . . . . . . . . 32\simeq (≃) . . . . . . . . . . . . . 30\simeq (≃) . . . . . . . . . . . . . 32simplewick (package) . . . . . . 96simpsons (package) . . . . 85, 104Simpsons characters . . . . . . . 85\sin (sin) . . . . . . . . . . . . . . 49\sincoh (ˇ) . . . . . . . . . . . . 36\sinh (sinh) . . . . . . . . . . . . 49\SixFlowerAlternate (O) . . 74\SixFlowerAltPetal (U) . . 74\SixFlowerOpenCenter (M) . 74\SixFlowerPetalDotted (Q) 74\SixFlowerPetalRemoved (L) 74\SixFlowerRemovedOpenPetal([) . . . . . . . . . . . . . . 74\SixStar (G) . . . . . . . . . . . 74\SixteenStarLight (K) . . . 74sixteenth note . . . . see musicalsymbols\sixteenthnote (♬) . . . . . . 78skak (package) . . . . 82, 104, 105skull (package) . . . . 76, 104, 105\skull (A) . . . . . . . . . . . . . 76\slash (/) . . . . . . . . . . . . 101\slashb (§) . . . . . . . . . . . . . 12\slashc () . . . . . . . . . . . . . 12\slashd () . . . . . . . . . . . . . 12\slashdiv () . . . . . . . . . . . 23slashed (package) . . . . . . . . . 92\slashed . . . . . . . . . . . . . . 92slashed letters . . . . . . . . . . . 92slashed.sty (file) . . . . . . . . 92\slashu (U) . . . . . . . . . . . . . 12\Sleet () . . . . . . . . . . . . . 80\sliding (ā) . . . . . . . . . . . . 15\smallbosonloop ( ) . . . . . . . 70\SmallCircle (E) . . . . . . . . 75\SmallCross () . . . . . . . . 75\smalldiamond (◇) . . . . . . . 24\SmallDiamondshape (F) . . 75\smallfrown (⌢) . . . . . . . . . 30\smallfrown (⌢) . . . . . . . . . 48\SmallHBar () . . . . . . . . . 75\smallin () . . . . . . . . . . . . 51\smallint (∫) . . . . . . . . . . . 63\SmallLowerDiamond () . . 75\smalllozenge (◊) . . . . . . . . 74\smallowns () . . . . . . . . . . 51\smallpencil (P) . . . . . . 72\smallprod (∏) . . . . . . . . . . 23\SmallRightDiamond (O) . . 75\smallsetminus () . . . . . . 21\smallsetminus (∖) . . . . . . 23\smallsmile (⌣) . . . . . . . . . 30\smallsmile (⌣) . . . . . . . . . 48\SmallSquare (@) . . . . . . . . 75\smallsquare (◽) . . . . . . . . 24\smallstar (☆) . . . . . . . . . . 24\SmallTriangleDown (C) . . 75\smalltriangledown () . . . 24\smalltriangledown (▿) 24, 40\SmallTriangleLeft (B) . . 75\smalltriangleleft (š) . . . 24\smalltriangleleft (◃) 24, 40\SmallTriangleRight (D) . . 75\smalltriangleright (›) . . 24\smalltriangleright (▹) 24, 40\SmallTriangleUp (A) . . . . 75\smalltriangleup (˜) . . . . . 24\smalltriangleup (▵) . . 24, 40\SmallVBar () . . . . . . . . . 75\smile (⌣) . . . . . . . . . . . . . 30\smile (⌣) . . . . . . . . . . . . . 48smile symbols . . . . . . . . . . . 48\smileeq () . . . . . . . . . . . . 48\smileeqfrown () . . . . . . . 48\smilefrown (≍) . . . . . . . . . 48\smilefrowneq () . . . . . . . 48\Smiley (©) . . . . . . . . . . . . 80\smiley (☺) . . . . . . . . . . . . 78smiley faces . . . . . . . . 69, 78, 80\sndtstile ( ) . . . . . . . . . 35\Snow () . . . . . . . . . . . . . . 80\SnowCloud () . . . . . . . . . 80\Snowflake (`) . . . . . . . . . 74\SnowflakeChevron (^) . . . 74\SnowflakeChevronBold (_) 74snowflakes . . . . . . . . . . . . . . 74\SNPP (¡) . . . . . . . . . . . . . 85\snststile ( ) . . . . . . . . . 35\sntstile ( ) . . . . . . . . . . 35\snttstile ( ) . . . . . . . . . 35\SO (␎) . . . . . . . . . . . . . . . . 69\SOH (␁) . . . . . . . . . . . . . . . 69spacethin . . . . . . . . . . . . . . 100space, visible . . . . . . . . . . . . . 8\Spacebar ( ) . . . . 69spades (suit) . . . . . . . 62–64, 77\spadesuit (♠) . . . . . . . . . . 62\spadesuit (♠) . . . . . . . . . . 63\Sparkle (]) . . . . . . . . . . . 74\SparkleBold (\) . . . . . . . . 74sparkles . . . . . . . . . . . . . . . 74“special” characters . . . . . . . . 8\SpecialForty (Ú) . . . . . . 80\sphericalangle (?) . . . . . 63\sphericalangle (∢) . . . . . 63\sphericalangle (∢) . . . . . 63\SpinDown (*) . . . . . . . . . . . . 75\SpinUp () . . . . . . . . . . . . . 75\spirituslenis (a ) . . . . . . . 56\spirituslenis ( ) . . . . . . . 56\splitvert (¦) . . . . . . . . . . 69spoon symbols . . . . . . . . . . . 47\spreadlips (ȧ) . . . . . . . . . 15\sqbullet () . . . . . . . . . . . 22\sqcap ([) . . . . . . . . . . . . . 22\sqcap (⊓) . . . . . . . . . . . . . 20\sqcap (⊓) . . . . . . . . . . . . . 23\sqcapdot () . . . . . . . . . . . 23\sqcapplus () . . . . . . . . . . 21\sqcapplus () . . . . . . . . . . 23\sqcup (\) . . . . . . . . . . . . . 22\sqcup (⊔) . . . . . . . . . . . . . 20\sqcup (⊔) . . . . . . . . . . . . . 23\sqcupdot () . . . . . . . . . . . 23\sqcupplus () . . . . . . . . . . 21\sqcupplus () . . . . . . . . . . 23\sqdoublecap (^) . . . . . . . . 22\sqdoublecup (_) . . . . . . . . 22\sqdoublefrown () . . . . . . . 48\sqdoublefrowneq () . . . . . 48\sqdoublesmile () . . . . . . . 48\sqdoublesmileeq () . . . . . 48\sqeqfrown () . . . . . . . . . . 48\sqeqsmile () . . . . . . . . . . 48\sqfrown () . . . . . . . . . . . . 48\sqfrowneq () . . . . . . . . . . 48\sqfrowneqsmile () . . . . . . 48\sqfrownsmile () . . . . . . . 48\sqiiint ( ) . . . . . . . . . . 27\sqiint ( ) . . . . . . . . . . . . 27\sqiint ( ” ) . . . . . . . . . . . . 28\sqint ( ) . . . . . . . . . . . . . 27\sqint ( › ) . . . . . . . . . . . . . . 28132

\sqrt ( √ ) . . . . . . . . . . 57, 93\sqsmile () . . . . . . . . . . . . 48\sqsmileeq () . . . . . . . . . . 48\sqsmileeqfrown () . . . . . . 48\sqsmilefrown () . . . . . . . 48\Sqsubset () . . . . . . . . . . . 37\sqSubset (”) . . . . . . . . . . 37\sqsubset (€) . . . . . . . . . . 37\sqsubset (⊏) . . . . . . . . . . 36\sqsubset (⊏) . . . . . . . . . . . 37\sqsubseteq („) . . . . . . . . . 37\sqsubseteq (⊑) . . . . . . . . . 36\sqsubseteq (⊑) . . . . . . . . . 37\sqsubseteqq (Œ) . . . . . . . . 37\sqsubseteqq () . . . . . . . . 37\sqsubsetneq (ˆ) . . . . . . . . 37\sqsubsetneq (⋤) . . . . . . . . 37\sqsubsetneqq ( ) . . . . . . . 37\sqsubsetneqq () . . . . . . . 37\Sqsupset () . . . . . . . . . . . 37\sqSupset (•) . . . . . . . . . . 37\sqsupset ( ) . . . . . . . . . . 37\sqsupset (⊐) . . . . . . . . . . 36\sqsupset (⊐) . . . . . . . . . . . 37\sqsupseteq (…) . . . . . . . . . 37\sqsupseteq (⊒) . . . . . . . . . 36\sqsupseteq (⊒) . . . . . . . . . 37\sqsupseteqq ( ) . . . . . . . . 37\sqsupseteqq () . . . . . . . . 37\sqsupsetneq (‰) . . . . . . . . 37\sqsupsetneq (⋥) . . . . . . . . 37\sqsupsetneqq (‘) . . . . . . . 37\sqsupsetneqq () . . . . . . . 37\sqtriplefrown () . . . . . . . 48\sqtriplesmile () . . . . . . . 48\Square (0) . . . . . . . . . . . . 75\Square (□ vs. f vs. 0) . . . 88\Square (□) . . . . . . . . . . . . 73\Square (f) . . . . . . . . . . . . 75\square (¥) . . . . . . . . . . . . . 22\square (□) . . . . . . . . . . . . 63\square (◻) . . . . . . . . . . . . 24square root . . . . . . . see \sqrthooked . . . . . see \hksqrt\SquareCastShadowBottomRight(k) . . . . . . . . . . . . . . 75\SquareCastShadowTopLeft (m). . . . . . . . . 75\SquareCastShadowTopRight(l) . . . . . . . . . . . . . . 75\Squaredot (÷) . . . . . . . . . . 64\squaredots (∷) . . . . . . 23, 61\Squarepipe (—) . . . . . . . . . 70squares . . . . . . . . . . . . . 75, 76\SquareShadowA ( ) . . . . . . 75\SquareShadowB (¡) . . . . . . 75\SquareShadowBottomRight (h). . . . . . . . . 75\SquareShadowC (¢) . . . . . . 75\SquareShadowTopLeft (j) . 75\SquareShadowTopRight (i) 75\SquareSolid (g) . . . . . . . . 75\Squaresteel (“) . . . . . . . . 70\squarewithdots (B) . . . . . 77\squigarrowdownup () . . . 43\squigarrowleftright (↭) . 43\squigarrownesw () . . . . . 43\squigarrownwse () . . . . . . 43\squigarrowrightleft () . 43\squigarrowsenw () . . . . . 43\squigarrowswne () . . . . . 43\squigarrowupdown () . . . . 43\squplus (]) . . . . . . . . . . . 22\SS (SS) . . . . . . . . . . . . . . . . 9\ss (ß) . . . . . . . . . . . . . . . . . 9\ssdtstile ( ) . . . . . . . . . 35\ssearrow () . . . . . . . . . . . 42\sslash (⫽) . . . . . . . . . . . . 21\ssststile ( ) . . . . . . . . . 35\sststile ( ) . . . . . . . . . . 35\ssttstile ( ) . . . . . . . . . 35\sswarrow () . . . . . . . . . . . 42\stackrel . . . . . . . . . 20, 91, 95standard state . . . . . . . . . . . 91\star (⋆) . . . . . . . . . . . 20, 94\star (⋆) . . . . . . . . . . . . . . 24Star of David . . . . . . . . 73, 74stars . . . . . . . . . . . . . 63, 73, 74statistical independence . . . . 93\staveI () . . . . . . . . . . 85\staveII () . . . . . . . . . . 85\staveIII () . . . . . . . . 85\staveIV () . . . . . . . . . 85\staveIX () . . . . . . . . . . 85\staveL () . . . . . . . 85, 86\staveLI () . . . . . . . . . 85\staveLII () . . . . . . . . 85\staveLIII () . . . . . . . . 85\staveLIV () . . . . . . . . 85\staveLIX () . . . . . . . . 85\staveLV () . . . . . . . . . . 85\staveLVI () . . . . . . . . . 85\staveLVII () . . . . . . . . 85\staveLVIII () . . . . . . . 85\staveLX () . . . . . . . 85\staveLXI () . . . . . . . . . 85\staveLXII () . . . . . . . . 85\staveLXIII () . . . . . . . 86\staveLXIV () . . . . . . . . . 86\staveLXV () . . . . . . . . . 86\staveLXVI () . . . . . . . . 86\staveLXVII () . . . . . . . . 86\staveLXVIII () . . . . . . . 86staves . . . . . . . . . . . . . . . . . 85staves (package) . . . . . . 85, 104\staveV () . . . . . . . . . . 85\staveVI () . . . . . . . . . 85\staveVII () . . . . . . . . 85\staveVIII () . . . . . . . 85\staveX () . . . . . . . . . . 85\staveXI () . . . . . . . . . . 85\staveXII () . . . . . . . . . 85\staveXIII () . . . . . . . . 85\staveXIV () . . . . . . . . 85\staveXIX () . . . . . . . . 86\staveXL () . . . . . . . . . . 86\staveXLI () . . . . . . . . . 86\staveXLII () . . . . . . . 86\staveXLIII () . . . . . . . . 86\staveXLIV () . . . . . . . 86\staveXLIX () . . . . . . . . 85\staveXLV () . . . . . . . . 86\staveXLVI () . . . . . . . . 86\staveXLVII () . . . . . . . 85\staveXLVIII () . . . . . 85\staveXV () . . . . . . . . . 85\staveXVI () . . . . . . . . . 85\staveXVII () . . . . . . . . 86\staveXVIII () . . . . . . . 86\staveXX () . . . . . . . . . 86\staveXXI () . . . . . . . . 86\staveXXII () . . . . . . . . 86\staveXXIII () . . . . . 86\staveXXIV () . . . . . . . . 85\staveXXIX () . . . . . . . 85\staveXXV () . . . . . . . . 85\staveXXVI () . . . . . . . 85\staveXXVII () . . . . . . . 85133

dot . . . . . . . . 8, 61, 62, 94electrical . . . . . . . . . . . 67engineering . . . . . . 67, 70extensible 57–60, 89, 94–96Feynman diagram . . . . . 70Frege logic . . 47, 52, 62, 64frown . . . . . . . . . . . . . . 48genealogical . . . . . . . . . 78general . . . . . . . . . . . . 78Go stones . . . . . . . . . . 76information . . . . . . . . . 76informator . . . . . . . . . . 82inverted . . . . 10–12, 16, 90keyboard . . . . . . . . . . . 69Knuth’s . . . . . . . . . 76, 79laundry . . . . . . . . . . . . 80legal . . . . . . . . . 8, 18, 102letter-like . . . . . . . . 51, 52life insurance . . . . . . . . 95linear logic . . . . . 20, 30, 36linguistic . . . . . . . . 10–13log-like . . . . . . . . 49, 100magical signs . . . . . . . . 85mathematical . . . . . 20–66METAFONTbook . . . . . 79metrical . . . . . . . . . . . . 82miscellaneous 62–64, 77–86monetary . . . . . . . . 17, 65musical . 19, 62, 63, 78, 79navigation . . . . . . . . . . 79non-commutative division 60particle physics . . . . . . 70Phaistos disk . . . . . . . . 83phonetic . . . . . . . . 10–13physical . . . . . . . . . . . . 67pitchfork . . . . . . . . . . . 47proto-Semitic . . . . . . . . 83pulse diagram . . . . . . . 67relational . . . . . . . . . . . 30reversed . . . . . . . . . . . . 90rotated . . . . 10–12, 16, 90safety-related . . . . . . . . 70scientific . . . . . . . . 67–70Simpsons characters . . . 85smile . . . . . . . . . . . . . . 48spoon . . . . . . . . . . . . . 47staves . . . . . . . . . . . . . 85subset and superset 36, 37technological . . . . . 67–70TEXbook . . . . . . . . 76, 79transliteration . . . . . . . 13upside-down . 10–12, 16, 90,100–101variable-sized 25–29, 87, 89weather . . . . . . . . . . . . 80zodiacal . . . . . . . . . . . . 68symbols.tex (file) . . . . 87, 104\SYN (␖) . . . . . . . . . . . . . . . 69T\T . . . . . . . . . . . . . . . . . . . . . 9\T ( ) . . . . . . . . . . . . . . . . . 16\T ( ⊗) . . . . . . . . . . . . . . . . 82a−−→−−→\t (a) . . . . . . . . . . . . . . . . . 13\t ( ⊗) . . . . . . . . . . . . . . . . 82t4phonet (package) . 13, 16, 104,105\Tab ( ) . . . . . . . . . . . 69\tabcolsep . . . . . . . . . . . . . 91tacks . . . . . . . . . . . . . . . 30, 51\taild () . . . . . . . . . . . . . 12\tailinvr (H) . . . . . . . . . . . 12\taill (0) . . . . . . . . . . . . . . 12\tailn (9) . . . . . . . . . . . . . 12\tailr (F) . . . . . . . . . . . . . . 12\tails (L) . . . . . . . . . . . . . . 12\tailt (P) . . . . . . . . . . . . . . 12\tailz (_) . . . . . . . . . . . . . 12\Takt . . . . . . . . . . . . . . . . . 79\talloblong (⫾) . . . . . . . . . 21tally markers . . . . . . . . . . . . 81\tan (tan) . . . . . . . . . . . . . . 49\tanh (tanh) . . . . . . . . . . . . 49\Tape () . . . . . . . . . . . . . . 77\Taschenuhr (–) . . . . . . . . 81Tate-Shafarevich group see sha\tau (τ) . . . . . . . . . . . . . . . 49\Taurus (Q) . . . . . . . . . . . . 68\Taurus (á) . . . . . . . . . . . . 68\taurus (♉) . . . . . . . . . . . . 68\tauup (τ) . . . . . . . . . . . . . . 50\tccentigrade (℃) . . . . . . . 62\tcmu (µ) . . . . . . . . . . . . . . 62\tcohm (Ω) . . . . . . . . . . . . . 62\tcpertenthousand (‱) . . 62\tcperthousand (‰) . . . . . . 62\td (ạ.) . . . . . . . . . . . . . . . . 15\tddtstile ( ) . . . . . . . . 34\tdststile ( ) . . . . . . . . . 34\tdtstile ( ) . . . . . . . . . 34\tdttstile ( ) . . . . . . . . 35technological symbols . . 67–70\Telefon (T) . . . . . . . . . . . 69\Telephone (() . . . . . . . . 81Tennent, Bob . . . . . . . . . . . 20\Tent () . . . . . . . . . . . . . . 81\Terminus (⊗) . . . . . . . . . . 82\terminus (⊗) . . . . . . . . . . . 82\Terminus* (⊕) . . . . . . . . . . 82\terminus* (⊕) . . . . . . . . . . 82\tesh (Q) . . . . . . . . . . . . . . 12testfont.dvi (file) . . . . . . . 98testfont.tex (file) . . . . 97, 98TEX 40, 61, 87, 90–99, 101, 106TEXbook, The . . . . . . 90–95, 99symbols from . . . . . 76, 79\text . . . . . . . . . . . . 20, 92, 93\textacutedbl (˝) . . . . . . . 17\textacutemacron (´ā) . . . . . 13\textacutewedge (´ˇa) . . . . . . 13\textadvancing (a ffi ) . . . . . . . 14\textaolig (") . . . . . . . . . . 11\textasciiacute (´) . . 17, 102\textasciibreve (˘) . . . . . . 17\textasciicaron (ˇ) . . . . . . 17\textasciicircum (ˆ) . . 8, 101,103\textasciidieresis (¨) 17, 102\textasciigrave (`) . . . . . . 17\textasciimacron . . . . . . . 103\textasciimacron (¯) 17, 102\textasciitilde (˜) 8, 101, 103\textasteriskcentered (∗) . 8,19\textbabygamma (È) . . . . . . . 10\textbackslash (\) . . . . 8, 101\textbaht (฿) . . . . . . . . . . . 17\textbar (|) . . . . . . 8, 100, 101\textbarb (b) . . . . . . . . . . . 10\textbarc (c) . . . . . . . . . . . 10\textbard (d) . . . . . . . . . . . 10\textbardbl (‖) . . . . . . . . . 19\textbardotlessj (é) . . . . . 10\textbarg (g) . . . . . . . . . . . 10\textbarglotstop (Ü) . . . . . 10\textbari (1) . . . . . . . . . . . 10\textbarl (ł) . . . . . . . . . . . 10\textbaro (8) . . . . . . . . . . . 10\textbarrevglotstop (Ý) . . 10\textbaru (0) . . . . . . . . . . . 10\textbeltl (ì) . . . . . . . . . . 10\textbenttailyogh (B) . . . . 11\textbeta (B) . . . . . . . . . . . 10\textbigcircle (○) . . . . . . 19\textbktailgamma (.) . . . . . 11\textblank (␢) . . . . . . . . . . 19\textborn () . . . . . . . . . . . 78\textbottomtiebar (a

\textordfeminine (ª) 8, 19, 102\textordmasculine (º) . . 8, 19,102\textovercross (‰a) . . . . . . . 14\textoverw ( — a) . . . . . . . . . . 14\textpalhook (%) . . . . . . . . . 10\textpalhooklong (ˆ) . . . . . 11\textpalhookvar (˜) . . . . . . 11\textparagraph () . . . . 8, 19\textperiodcentered (·) . 8, 19,102\textpertenthousand (‱) . 19\textperthousand (‰) 19, 103\textpeso (₱) . . . . . . . . . . . 17\textphi (F) . . . . . . . . . . . . 10\textpilcrow () . . . . . . . . 19\textpipe (|) . . . . . . . . . . . 10\textpipe (|) . . . . . . . . . . . 13\textpipevar (F) . . . . . . . . . 11\textpm (±) . . . . . . . . 64, 102\textpmhg . . . . . . . . . . . . . . 84\textpolhook (ą) . . . . . . . . 14\textprimstress (") . . . . . . 10\textproto . . . . . . . . . . . . . 83\textqplig (=) . . . . . . . . . 11\textquestiondown (¿) . . . . . 8\textquotedbl (") . . . . 9, 100\textquotedblleft (“) . . . . . 8\textquotedblright (”) . . . . 8\textquoteleft (‘) . . . . . . . . 8\textquoteright (’) . . . . . . . 8\textquotesingle (') . . . . . 19\textquotestraightbase (‚) 19\textquotestraightdblbase („). . . . . . . . . 19\textraiseglotstop (ij) . . . 10\textraisevibyi (ğ) . . . . . . 10\textraising (a fi ) . . . . . . . . 14\textramshorns (7) . . . . . . . 10\textrangle (〉) . . . . . 56, 101\textrbrackdbl (〛) . . . . . . . 56\textrecipe () . . . . . . 19, 89\textrectangle (¨) . . . . . . . 11\textreferencemark (※) 19, 20\textregistered (®) 8, 18, 102\textretracting (a ffl ) . . . . . . 14\textretractingvar (˚) . . . 11\textrevapostrophe (\) . . . . 10\textreve (9) . . . . . . . . . . . 10\textrevepsilon (3) . . . 10, 90\textreversedvideodbend ( ). . . . . . . . . 76\textrevglotstop (Q) . . . . . 10\textrevscl (v) . . . . . . . . . 11\textrevscr (z) . . . . . . . . . 11\textrevyogh (ź) . . . . . . . . 10\textrhooka (␣) . . . . . . . . . 11\textrhooke (*) . . . . . . . . . 11\textrhookepsilon (+) . . . . 11\textrhookopeno (:) . . . . . . 11\textrhookrevepsilon (Ç) . 10\textrhookschwa (Ä) . . . . . . 11\textrhoticity (~) . . . . . . . 11\textrightarrow (→) . . . . . 41\textringmacron (˚ā) . . . . . . 14\textroundcap (“a) . . . . . . . 14\textrptr (¿) . . . . . . . . . . . 11\textrquill (⁆) . . . . . . . . . 56\textrtaild (ã) . . . . . . . . . 11\textrtaild (ð) . . . . . . . . . 13\textrtailhth (/) . . . . . . . 11\textrtaill (í) . . . . . . . . . . 11\textrtailn (ï) . . . . . . . . . 10\textrtailr (ó) . . . . . . . . . 10\textrtails (ù) . . . . . . . . . 10\textrtailt (ú) . . . . . . . . . 10\textrtailt (») . . . . . . . . . 13\textrtailz (ü) . . . . . . . . . 10\textrthook ($) . . . . . . . . . . 10\textrthooklong (´) . . . . . . 11\textsca (À) . . . . . . . . . . . . 10\textscaolig (q) . . . . . . . . 11\textscb (à) . . . . . . . . . . . . 10\textscdelta (r) . . . . . . . . 11\textsce (ď) . . . . . . . . . . . . 10\textscf (s) . . . . . . . . . . . . 11\textscg (å) . . . . . . . . . . . . 10\textsch (Ë) . . . . . . . . . . . . 10\textschwa (@) . . . . . . . . . . 10\textschwa (¡) . . . . . . . . . . 13\textsci (I) . . . . . . . . . . . . 10\textscj (ĺ) . . . . . . . . . . . . 10\textsck (t) . . . . . . . . . . . . 11\textscl (Ï) . . . . . . . . . . . . 10\textscm (w) . . . . . . . . . . . 11\textscn (ð) . . . . . . . . . . . . 10\textscoelig (Œ) . . . . . . . . 10\textscomega (ś) . . . . . . . . 10\textscp (x) . . . . . . . . . . . . 11\textscq (y) . . . . . . . . . . . . 11\textscr (ö) . . . . . . . . . . . . 10\textscripta (A) . . . . . . . . 10\textscriptg (g) . . . . . . . . 10\textscriptv (V) . . . . . . . . 10\textscriptv (¬) . . . . . . . . . 13\textscu (Ú) . . . . . . . . . . . . 10\textscy (Y) . . . . . . . . . . . . 10\textseagull (a) . . . . . . . . 14\textsecstress (­) . . . . . . . 10\textsection (§) . . . . . . 8, 19\textservicemark (℠) . . . . . 18\textsevenoldstyle (7) . . . 18\textsixoldstyle (6) . . . . . 18\textsoftsign (ž) . . . . . . . . 10\textspleftarrow (˝) . . . . . 11\textsterling (£) . . . . . 8, 17\textstretchc (Â) . . . . . . . 10\textstretchcvar ($) . . . . . 11\textstyle . . . . . . . . 92, 93, 99\textsubacute (a) . . . . . . . 14\textsubarch (a) ›. . . . . . . . 14\textsubbar (ā) “. . . . . . . . . 14\textsubbridge (a”) . . . . . . . 14\textsubcircum (aˆ) . . . . . . . 14\textsubdot (ȧ) . . . . . . . . . 14\textsubdoublearrow (˙) . . 11\textsubgrave (a) . . . . . . . 14\textsublhalfring ‹(a – ) . . . . 14\textsubplus (a ff ) . . . . . . . . 14\textsubrhalfring (a » ) . . . . 14\textsubrightarrow (¯) . . . 11\textsubring (å) . . . . . . . . 14\textsubsquare (a«) . . . . . . . 14\textsubtilde (ã) . . . . . . . 14\textsubumlaut (ä) . . . . . . . 14\textsubw (a—) . . . . . . . . . . . 14\textsubwedge (aˇ) . . . . . . . 14\textsuperimposetilde (a &) . 14\textsuperscript . . . . . . . . 15\textsurd (√) . . . . . . . . . . . 64\textswab . . . . . . . . . . . . . . 65\textsyllabic (a) . . . . . . . 15\texttctclig (tC) ". . . . . . . . 10\textteshlig (Ù) . . . . . . . . 10\textteshlig (œ) . . . . . . . . 13\texttheta (T) . . . . . . . . . . 10\textthorn (þ) . . . . . . . . . . 10\textthornvari (P) . . . . . . . 11\textthornvarii (Q) . . . . . . 11\textthornvariii (R) . . . . . 11\textthornvariv (S) . . . . . . 11\textthreeoldstyle (3) . . . 18\textthreequarters (¾) 64, 102\textthreequartersemdash (—). . . . . . . . . 19\textthreesuperior (³) 64, 102\texttildedot (˜ȧ) . . . . . . . 15\texttildelow () . . . 19, 101\texttimes (×) . . . . . . . . . . 64\texttoneletterstem (£) . . . 10\texttoptiebar ( > a) . . . . . . . 15\texttrademark () . 8, 18, 103\texttslig (ţ) . . . . . . . . . . 10\textturna (5) . . . . . . . . . . 10\textturncelig (ŕ) . . . . . . 10\textturnglotstop (E) . . . . 11\textturnh (4) . . . . . . . . . . 10\textturnk (ľ) . . . . . . . . . . 10\textturnlonglegr (Õ) . . . . 10\textturnm (W) . . . . . . . . . 10\textturnmrleg (î) . . . . . . 10\textturnr (ô) . . . . . . . . . . 10\textturnrrtail (õ) . . . . . . 10\textturnsck (u) . . . . . . . . 11\textturnscripta (6) . . . . . 10\textturnscu ({) . . . . . . . . 11\textturnt (Ø) . . . . . . . . . . 10\textturnthree (C) . . . . . . . 11\textturntwo (A) . . . . . . . . 11\textturnv (2) . . . . . . . . . . 10\textturnw (û) . . . . . . . . . . 10\textturny (L) . . . . . . . . . . 10\texttwelveudash () . . . . . 19\texttwooldstyle . . . . . . . . 18\texttwooldstyle (2) . . . . . 18\texttwosuperior (²) . 64, 102\textuncrfemale (8) . . . . . . 11137

\textunderscore ( ) . . . . . . . 8\textuparrow (↑) . . . . . . . . 41\textupfullarrow (˘) . . . . . 11\textupsilon (U) . . . . . . . . 10\textupstep (Ţ) . . . . . . . . . 10\textvbaraccent (IJa) . . . . . . 15\textvbaraccent (¿a) . . . . . . 16\textvertline (Š) . . . . . . . . 10\textvibyi (ğ) . . . . . . . . . . 11\textvibyy (ů) . . . . . . . . . . 11\textvisiblespace ( ) . . . . . 8\textwon (₩) . . . . . . . . . . . 17\textwynn (ß) . . . . . . . . . . . 11\textyen (¥) . . . . . . . 17, 102\textyogh (Z) . . . . . . . . . . . 11\textyogh () . . . . . . . . . . . 13\textzerooldstyle (0) . . . . 18\TH (Þ) . . . . . . . . . . . . . 9, 102\th (þ) . . . . . . . . . . . . . 9, 102Thành, Hàn Th´ê . . . . . . . . . 94\therefore (6) . . . . . . . . . . 31\therefore (∴) . . . . . . . 30, 61\therefore (∴) . . . . . . . . . . 61\Thermo . . . . . . . . . . . . . . . 80\Theta (Θ) . . . . . . . . . . . . . 49\theta (θ) . . . . . . . . . . . . . 49\thetaup (θ) . . . . . . . . . . . . 50\thickapprox (≈) . . . . . . . . 30\thicksim (∼) . . . . . . . . . . 30\thickvert (~) . . . . . . . . . . 54thin space . . . . . . . . . . . . . 100\ThinFog () . . . . . . . . . . . 80\thinstar (⋆) . . . . . . . . . . . 24\third (3) . . . . . . . . . . . . . 63thirty-second note . see musicalsymbols\Thorn (Þ) . . . . . . . . . . . . . 12\thorn (B) . . . . . . . . . . . . . 12\thorn (p) . . . . . . . . . . . . . 12\thorn (þ) . . . . . . . . . . . . . 12thousandths . . . . . . . . . . . see\textperthousand\threesim (∼) . . . . . . . . . . 91tilde 8, 10, 11, 13, 16, 19, 56, 57,59, 94, 101extensible . . . . . . . 57, 59vertically centered . . . 101\tilde (˜) . . . . . . . . . . 56, 94\tildel (-) . . . . . . . . . . . . 12time of day . . . . . . . . . . . . . 81\timelimit (T) . . . . . . . . . 82\times (×) . . . . . . . . . . . . . 20\times (×) . . . . . . . . . . . . . 23Times Roman (font) . . . 17, 89timing (package) . . . . . . . . . 67tipa (package) 10, 11, 13, 15, 16,90, 104, 105tipx (package) . . . . 11, 104, 105\tndtstile ( ) . . . . . . . . 35\tnststile ( ) . . . . . . . . . 35\tntstile ( ) . . . . . . . . . 35\tnttstile ( ) . . . . . . . . 35\to . . . . . . . . see \rightarrow\ToBottom (½) . . . . . . . . . . . 79\tone . . . . . . . . . . . . . . . . . 11\top (⊤) . . . . . . . . . . . . 51, 92\top (⊺) . . . . . . . . . . . . . . . 51\topbot (⊥⊤) . . . . . . . . . 92, 94\topdoteq () . . . . . . . . . . 31torus (T) . see alphabets, math\ToTop (¼) . . . . . . . . . . . . . 79trademark . see \texttrademark\TransformHoriz ( ) . . . . 35transforms . . . . 35, 60, see alsoalphabets, math\TransformVert (¢) . . . . . . 35transliterationsemitic . . . . . . . . . . 13, 16transliteration symbols . . . . 13transversality . see \pitchforktrfsigns (package) 35, 51, 60, 104\triangle (△) . . . . . . . . . . 62\triangle (△) . . . . . . . . . . 40triangle relations . . . . . . 39, 40\TriangleDown (3) . . . . . . . 75\TriangleDown (o vs. 3) . . 88\TriangleDown (o) . . . . . . . 75\triangledown (▽) . . . . . . . 63\triangledown (▽) . . . . . . . 40\triangleeq (≜) . . . . . . . . . 40\TriangleLeft (2) . . . . . . . 75\triangleleft (˜) . . . . . . . 40\triangleleft (⊳) . . . . . . . 20\triangleleft (◁) . . . . . . . 40\trianglelefteq (œ) . . . . . 40\trianglelefteq () . . . . . 39\trianglelefteq (⊴) . . . 39, 40\trianglelefteqslant () . 40\triangleq () . . . . . . 20, 39\triangleq (≜) . . . . . . . . . . 40\TriangleRight (4) . . . . . . 75\triangleright () . . . . . . 40\triangleright (⊲) . . . . . . . 20\triangleright (▷) . . . . . . 40\trianglerighteq ( ) . . . . 40\trianglerighteq () . . . . 39\trianglerighteq (⊵) . . 39, 40\trianglerighteqslant () 40triangles . . . . . . . . . . 63, 75, 76\TriangleUp (1) . . . . . . . . 75\TriangleUp (n vs. 1) . . . . 88\TriangleUp (n) . . . . . . . . 75\triple . . . . . . . . . . . . . . . 55\triplefrown () . . . . . . . . 48\triplesim (≋) . . . . . . . . . . 32\triplesmile () . . . . . . . . 48trsym (package) . . . 35, 104, 105\tsbm ( ) . . . . . . . . . . . . . 82\tsdtstile ( ) . . . . . . . . 35\tsmb ( ) . . . . . . . . . . . . . 82\tsmm ( ) . . . . . . . . . . . . . 82\tsststile ( ) . . . . . . . . . 35\Tsteel (œ) . . . . . . . . . . . . 70\tststile ( ) . . . . . . . . . 35\tsttstile ( ) . . . . . . . . 35\ttdtstile ( ) . . . . . . . . 35\TTsteel (š) . . . . . . . . . . . 70\ttststile ( ) . . . . . . . . . 35\tttstile ( ) . . . . . . . . . 35\ttttstile ( ) . . . . . . . . 35TUGboat . . . . . . . . . . . . . . 57\Tumbler () . . . . . . . . . . . 80turnstile (package) . 34, 35, 104,105\TwelweStar (J) . . . . . . . . 74\twoheaddownarrow (↡) . . . . 43\twoheadleftarrow (↞) . . . 41\twoheadleftarrow (↞) . . . 43\twoheadnearrow () . . . . . 44\twoheadnwarrow () . . . . . 44\twoheadrightarrow (↠) . . 41\twoheadrightarrow (↠) . . 44\twoheadsearrow () . . . . . 44\twoheadswarrow () . . . . . 44\twoheaduparrow (↟) . . . . . . 44\twonotes (♫) . . . . . . . . . . . 78txfonts (package) 20, 21, 27, 30,31, 36, 38, 41, 42, 48, 50, 51,62, 63, 65, 87, 89, 101, 104,105type1cm (package) . . . . . . . . 87Type 1 (font) . . . . . . . . . . . 99U\U (ă) . . . . . . . . . . . . . . . . . 16\U (¼a) . . . . . . . . . . . . . . . . . 13\u (ă) . . . . . . . . . . . . . . . . . 13\UArrow ( ↑ ) . . . . . . . . . . 69\UB (

\unclear (k) . . . . . . . . . . . 82\underaccent . . . . . . . . . . . 94\underarc (a ⌣) . . . . . . . . . . . 16\underarch (a) . . . . . . . . . . 15\underbrace (lomon) . . . . . . 58\underbrace ( ) . . . . . . . . . 58\underbrace ( }{{} ) . . . . . . . 58\underbrace ( }{{}) . . . . . . . 57\underbracket ( ) . . . . . . . 58\underbracket ( ) . . . . 95, 96\underdots (r) . . . . . . . . . . 16\undergroup (loon) . . . . . . . 58\undergroup ( ) . . . . . . . . 58\underleftarrow ( ←−) . . . . . 58\underleftrightarrow ( ←→) 58\underline ( ) . . . . . . . . . . 57\underlinesegment ( ) . . . . 58\underparenthesis ( }}) 95, 96\underrightarrow ( −→) . . . . 58\underring (y) . . . . . . . . . . 16underscore . . . . . . . . . . see \_underscore (package) . . . . . . . 8\underset . . . . . . . . . . . . . . 91undertilde (package) 59, 104, 105\undertilde (|) . . . . . . . . . 16\underwedge (}) . . . . . . . . . 16union . . . . . . . . . . . . see \cupunit disk (D) . . . see alphabets,math\unitedpawns (u) . . . . . . . . 82units (package) . . . . . . . . . . 64unity (1) . . see alphabets, mathuniversa (package) . 76, 80, 104,105universal (package) 71, 73, 76, 80,104, 105\unlhd () . . . . . . . . . . 20, 21\unlhd (⊴) . . . . . . . . . . 39, 40\unrhd () . . . . . . . . . . 20, 21\unrhd (⊵) . . . . . . . . . . 39, 40\upalpha (α) . . . . . . . . . . . . 50\UParrow () . . . . . . . . . . . . 78\Uparrow (⇑) . . . . . . . . . 41, 53\Uparrow (⇑) . . . . . . . . . . . . 44\uparrow (↑) . . . . . . . 41, 53, 87\uparrow (↑) . . . . . . . . . . . . 44\uparrowtail () . . . . . . . . 44\upbar . . . . . . . . . . . . . . . . 15\upbeta (β) . . . . . . . . . . . . . 50\upbracketfill . . . . . . . . . 95\upchi (χ) . . . . . . . . . . . . . 50\Updelta (∆) . . . . . . . . . . . . 50\updelta (δ) . . . . . . . . . . . . 50\Updownarrow (⇕) . . . . . 41, 53\Updownarrow (⇕) . . . . . . . . 44\updownarrow (↕) . . . . . 41, 53\updownarrow (↕) . . . . . . . . 44\updownarrows (Ö) . . . . . . . 42\updownarrows (⇅) . . . . . . . 44\updownharpoonleftright (⥍) 46\updownharpoonrightleft (⥌) 46\updownharpoons (ê) . . . . . . 43\updownharpoons (⥮) . . . . . . 46\Updownline (∥) . . . . . . . . . 32\updownline (∣) . . . . . . . . . 32\upepsilon (ε) . . . . . . . . . . 50\upeta (η) . . . . . . . . . . . . . 50\upfilledspoon () . . . . . . . 47\upfootline () . . . . . . . . . 32\upfree () . . . . . . . . . . . . 32\Upgamma (Γ) . . . . . . . . . . . . 50\upgamma (γ) . . . . . . . . . . . . 50upgreek (package) . 50, 104, 105\upharpoonccw (↿) . . . . . . . . 46\upharpooncw (↾) . . . . . . . . 46\upharpoonleft (ä) . . . . . . . 43\upharpoonleft (↿) . . . . . . . 41\upharpoonright (æ) . . . . . . 43\upharpoonright (↾) . . . . . . 41\upiota (ι) . . . . . . . . . . . . . 50\upkappa (κ) . . . . . . . . . . . . 50\Uplambda (Λ) . . . . . . . . . . . 50\uplambda (λ) . . . . . . . . . . . 50\uplett . . . . . . . . . . . . . . . 15\uplsquigarrow () . . . . . . . 44\uplus (Z) . . . . . . . . . . . . . 22\uplus (⊎) . . . . . . . . . . . . . 20\uplus (⊎) . . . . . . . . . . . . . 23\upmapsto (↥) . . . . . . . . . . . 44\upModels () . . . . . . . . . . . 32\upmodels () . . . . . . . . . . . 32\upmu (µ) . . . . . . . . . . . . . . 50\upnu (ν) . . . . . . . . . . . . . . 50\Upomega (Ω) . . . . . . . . . . . 50\upomega (ω) . . . . . . . . . . . 50\upp (t) . . . . . . . . . . . . . . . 16\upparenthfill . . . . . . . . . 95\Upphi (Φ) . . . . . . . . . . . . . 50\upphi (φ) . . . . . . . . . . . . . 50\Uppi (Π) . . . . . . . . . . . . . . 50\uppi (π) . . . . . . . . . . . . . . 50\uppitchfork (⋔) . . . . . . . . 47\uppropto () . . . . . . . . . . . 32\Uppsi (Ψ) . . . . . . . . . . . . . 50\uppsi (ψ) . . . . . . . . . . . . . 50upquote (package) . . . . . . . 101\uprho (ρ) . . . . . . . . . . . . . 50upright Greek letters . . . . . . 50\uprsquigarrow () . . . . . . . 44upside-down symbols . . 100–101upside-down symbols 10–12, 16,90\Upsigma (Σ) . . . . . . . . . . . . 50\upsigma (σ) . . . . . . . . . . . . 50\Upsilon (Υ) . . . . . . . . . . . 49\upsilon (υ) . . . . . . . . . . . . 49\upsilonup (υ) . . . . . . . . . . 50\upslice () . . . . . . . . . . . 24\upspoon (⫯) . . . . . . . . . . . . 47\upt (l) . . . . . . . . . . . . . . . 16\uptau (τ) . . . . . . . . . . . . . . 50\uptherefore (∴) . . . . . 23, 61\Uptheta (Θ) . . . . . . . . . . . 50\uptheta (θ) . . . . . . . . . . . . 50\uptodownarrow (þ) . . . . . . 42\upuparrows (Ò) . . . . . . . . . 42\upuparrows (⇈) . . . . . . . . 41\upuparrows (⇈) . . . . . . . . . 44\upupharpoons (Ú) . . . . . . . 43\Upupsilon (Υ) . . . . . . . . . . 50\upupsilon (υ) . . . . . . . . . . 50\upvarepsilon (ε) . . . . . . . . 50\upvarphi (ϕ) . . . . . . . . . . . 50\upvarpi (ϖ) . . . . . . . . . . . 50\upvarrho (ρ) . . . . . . . . . . . 50\upvarsigma (σ) . . . . . . . . . 50\upvartheta (ϑ) . . . . . . . . . 50\upVdash (⍊) . . . . . . . . . . . 32\upvdash (⊥) . . . . . . . . . . . . 32\Upxi (Ξ) . . . . . . . . . . . . . . 50\upxi (ξ) . . . . . . . . . . . . . . 50\upY () . . . . . . . . . . . . . . . 23\upzeta (ζ) . . . . . . . . . . . . . 50\Uranus (G) . . . . . . . . . . . . 68\Uranus (Ç) . . . . . . . . . . . . . 68\uranus (♅) . . . . . . . . . . . . . 68\urcorner (y) . . . . . . . . . . . 52\urcorner () . . . . . . . . . . . 52\urcorner (⌝) . . . . . . . . . . . 54url (package) . . . . . . . . . . . 101\US (␟) . . . . . . . . . . . . . . . . 69\usepackage . . . . . . . . . . . . . 7\ut (ã) . . . . . . . . . . . . . . . . 15\utilde (˜) . . . . . . . . . . . . . 59\utimes () . . . . . . . . . . . . 23\utimes () . . . . . . . . . . . . 23Utopia (font) . . . . . . . . . 17, 29V\v (ǎ) . . . . . . . . . . . . . . . . . 13\vara (a) . . . . . . . . . . . . . . 12\varangle () . . . . . . . . . . 63\varbigcirc () . . . . . . . . 21\VarClock (›) . . . . . . . . . . 81\varclub (♧) . . . . . . . . . . . 64\varclubsuit () . . . . . . . . 63\varcurlyvee () . . . . . . . . 21\varcurlywedge () . . . . . . 21\vardiamond (♦) . . . . . . . . . 64\vardiamondsuit () . . . . . . 63\varEarth (J) . . . . . . . . . . . 68\varepsilon (ε) . . . . . . . . . 49\varepsilonup (ε) . . . . . . . . 50\VarFlag () . . . . . . . . . . . 81varg (txfonts/pxfonts package option). . . . . . . . . . . . . 50\varg () . . . . . . . . . . . . . . 50\varg (G) . . . . . . . . . . . . . . 12\vargeq (©) . . . . . . . . . . . . 38\varhash (#) . . . . . . . . . . . 63\varheart (♥) . . . . . . . . . . 64\varheartsuit () . . . . . . . 63139

\varhexagon (⬡) . . . . . . . . . 74\varhexstar () . . . . . . . . . 73\vari (i) . . . . . . . . . . . . . . . 12variable-sized symbols 25–29, 87,89\VarIceMountain () . . . . . 81\varinjlim (lim) . . . . . . . . . 49−→\varint ( ) . . . . . . . . . . . . 25\various (R) . . . . . . . . . . . 82\varkappa (κ) . . . . . . . . . . 49\varleq (¨) . . . . . . . . . . . . 38\varliminf (lim) . . . . . . . . . 49\varlimsup (lim) . . . . . . . . . 49\varmathbb . . . . . . . . . . . . . 65\VarMountain () . . . . . . . . 81\varnothing (∅) . . . . 20, 62, 63\varnothing (∅) . . . . . . . . . 63\varnotin (T) . . . . . . . . . . . 51\varnotowner (U) . . . . . . . . 51\varoast () . . . . . . . . . . . 21\varobar () . . . . . . . . . . . 21\varobslash () . . . . . . . . . 21\varocircle () . . . . . . . . . 21\varodot () . . . . . . . . . . . 21\varogreaterthan () . . . . 21\varoiiintclockwise ( ) . 27\varoiiintctrclockwise ( ). . . . . . . . . 27\varoiint ( ! ) . . . . . . . . . . 28\varoiintclockwise ( ) . . 27\varoiintctrclockwise ( ) 27\varoint ( ) . . . . . . . . . . . 25\varointclockwise ( ) . . . . 27\varointclockwise ( ff ) . . . . 28\varointctrclockwise ( ) . 27\varointctrclockwise ( fl ) . . 28\varolessthan () . . . . . . . 21\varomega (¨) . . . . . . . . . . . 12\varominus () . . . . . . . . . . 21\varopeno (C) . . . . . . . . . . . 12\varoplus () . . . . . . . . . . 21\varoslash () . . . . . . . . . . 21\varotimes () . . . . . . . . . . 21\varovee () . . . . . . . . . . . 21\varowedge () . . . . . . . . . . 21\varparallel (∥) . . . . . . . . 31\varparallelinv () . . . . . . 31\varphi (ϕ) . . . . . . . . . . . . 49\varphiup (ϕ) . . . . . . . . . . . 50\varpi (ϖ) . . . . . . . . . . . . . 49\varpiup (ϖ) . . . . . . . . . . . 50\varprod ( ) . . . . . . . . . . . 27\varprojlim (lim) . . . . . . . . ←−49\varpropto (∝) . . . . . . . . . 30\varpropto (∝) . . . . . . . . . . 33\varQ (ƒ) . . . . . . . . . . . . . . 80\varrho (ϱ) . . . . . . . . . . . . . 49\varrhoup (ϱ) . . . . . . . . . . . 50\varsigma (ς) . . . . . . . . . . . 49\varsigmaup (ς) . . . . . . . . . 50\varspade (♤) . . . . . . . . . . 64\varspadesuit () . . . . . . . 63\varsqsubsetneq (Š) . . . . . 37\varsqsubsetneqq (’) . . . . 37\varsqsupsetneq (‹) . . . . . 37\varsqsupsetneqq (“) . . . . 37\varstar () . . . . . . . . . . . . 22\varsubsetneq (Š) . . . . . . . 37\varsubsetneq () . . . . . . . 36\varsubsetneq (⊊) . . . . . . . 37\varsubsetneqq (’) . . . . . . 37\varsubsetneqq () . . . . . . 36\varsubsetneqq (⫋) . . . . . . . 37\VarSummit () . . . . . . . . . 81\varsupsetneq (‹) . . . . . . . 37\varsupsetneq () . . . . . . . 36\varsupsetneq (⊋) . . . . . . . 37\varsupsetneqq (“) . . . . . . 37\varsupsetneqq () . . . . . . 36\varsupsetneqq (⫌) . . . . . . . 37\VarTaschenuhr (”) . . . . . . 81\vartheta (ϑ) . . . . . . . . . . . 49\varthetaup (ϑ) . . . . . . . . . 50\vartimes () . . . . . . . . . . . 21\vartriangle (△) . . . . . . . . 63\vartriangle (△) . . . . . . . . 40\vartriangleleft (˜) . . . . 40\vartriangleleft (⊳) . . . . 39\vartriangleleft (⊲) . . 39, 40\vartriangleright () . . . . 40\vartriangleright (⊲) . . . 39\vartriangleright (⊳) . 39, 40\varv () . . . . . . . . . . . . . . 50\varw () . . . . . . . . . . . . . . 50\vary () . . . . . . . . . . . . . . 50\VBar () . . . . . . . . . . . . . . 75\vbipropto () . . . . . . . . . . 23\vcentcolon (:) . . . . . . . . . . 34\vcenter . . . . . . . . . . . . . . 91\vcrossing () . . . . . . . . . . 32\VDash (() . . . . . . . . . . . . . 31\VDash (⊫) . . . . . . . . . . . . . 33\Vdash (,) . . . . . . . . . . . . . 31\Vdash (⊩) . . . . . . . . . . . . . 30\Vdash (⊩) . . . . . . . . . . . . . 33\vDash (() . . . . . . . . . . . . . 31\vDash () . . . . . . . . . . . . . 30\vDash (⊧) . . . . . . . . . . . . . 33\vdash (⊢) . . . . . . . . . . . . . 30\vdash (⊢) . . . . . . . . . . . . . 33\vdotdot (∶) . . . . . . . . . 23, 61\vdots ( . .) . . . . . . . . . . . . . . 61\vdots (⋮) . . . . . . . . . . . . . . 61\vec (⃗) . . . . . . . . . . . . . . . 56\vec (⃗) . . . . . . . . . . . . . . . 56\Vectorarrow (p) . . . . . . . . . 64\Vectorarrowhigh (P) . . . . . . 64\vee (_) . . . . . . . . . . . . . . . 22\vee (∨) . . . . . . . . . . . . . . . 20\vee (∨) . . . . . . . . . . . . . . . 23\veebar (Y) . . . . . . . . . . . . 22\veebar () . . . . . . . . . . . . 21\veedot (⟇) . . . . . . . . . . . . 23\veedoublebar ([) . . . . . . . 22\Venus (B) . . . . . . . . . . . . . 68\Venus (Ã) . . . . . . . . . . . . . 68\venus (♀) . . . . . . . . . . . . . 68\vernal (♈) . . . . . . . . . . . . 68\Vert (‖) . . . . . . . . . . . 53, 54\vert (|) . . . . . . . . . . . . 53, 54\vertbowtie (⧖) . . . . . . . . . 23\vertdiv () . . . . . . . . . . . . 23\VHF () . . . . . . . . . . . . . . . 67\Vier (ˇ “) . . . . . . . . . . . . . . 79vietnam (package) . . . . . . . 104\Village ( ) . . . . . . . . 81\vin ( ) . . . . . . . . . . . . . . . 52vinculum . . . . . . see \overline\ViPa (> ) . . . . . . . . . . . . . . 79\Virgo (å) . . . . . . . . . . . . . 68\virgo (♍) . . . . . . . . . . . . 68\VM (>) . . . . . . . . . . . . . . . . 79vntex (package) . . . . . . . . 9, 13\vod (v˚) . . . . . . . . . . . . . . . 12\voicedh (h) . . . . . . . . . . . . 12\vppm ( ¯˙) . . . . . . . . . . . . . . 82\vpppm ( ¯˙) . . . . . . . . . . . . . 82\VT (␋) . . . . . . . . . . . . . . . . 69\vv ( #» ) . . . . . . . . . . . . . . . 59\VvDash () . . . . . . . . . . . . 31\Vvdash (,) . . . . . . . . . . . . 31\Vvdash () . . . . . . . . . . . . 30\Vvdash (⊪) . . . . . . . . . . . . 32\vvvert (~) . . . . . . . . . . . . 54W\WashCotton (‰) . . . . . . . . 80\WashSynthetics (Š) . . . . 80\WashWool (‹) . . . . . . . . . . 80\wasylozenge (◊) . . . . . . . . 78\wasypropto () . . . . . . . . . 30wasysym (package) . . . . . . . 12,17, 19–21, 25, 30, 36, 38, 41,61–63, 67, 68, 70, 73, 74, 78,88, 104, 105\wasytherefore (∴) . . . . . . 61wavy-line delimiters . . . . 54, 55\wbetter (f) . . . . . . . . . . . 82\wdecisive (h) . . . . . . . . . 82\weakpt (J) . . . . . . . . . . . . 82\WeakRain () . . . . . . . . . . 80\WeakRainCloud () . . . . . . 80weather symbols . . . . . . . . . 80\Wecker (š) . . . . . . . . . . . 81\wedge (^) . . . . . . . . . . . . . 22\wedge (∧) . . . . . . . . . . . . . 20\wedge (∧) . . . . . . . . . . . . . 23\wedgedot (⟑) . . . . . . . . . . . 23Weierstrass ℘ function . see \wp\Wheelchair (w) . . . . . . . . . 76\whistle (aŢ) . . . . . . . . . . . . 15\whitestone . . . . . . . . . . . . 76whole note see musical symbols140

Wick contractions . . . . . . . . 96\widearrow (t) . . . . . . . . . . 58\widebar (s) . . . . . . . . . . . . 58\widecheck (q) . . . . . . . . . . 58\widehat (̂) . . . . . . . . . . . . 58\widehat (̂) . . . . . . . . . . . . 57\wideparen (u) . . . . . . . . . . 58\wideparen () . . . . . . . . . . 58\wideparen (Û) . . . . . . . . . . 57\widering (˚Û) . . . . . . . . . . . 58\widering (˚Û) . . . . . . . . . . . 57\widetilde (̃) . . . . . . . . . . 58\widetilde (˜) . . . . . . . 57, 59\widetriangle (Ê) . . . . . . . 57\wind . . . . . . . . . . . . . . . . . 80window . . . . . . . . . . . . . . . . 80Windows ® . . . . . . . . . . . . 103\with (&) . . . . . . . . . . . . . . 23\with (w) . . . . . . . . . . . . . . 82\withattack (A) . . . . . . . . . 82\withidea (E) . . . . . . . . . . 82\withinit (C) . . . . . . . . . . . 82\without (v) . . . . . . . . . . . 82\wn (?) . . . . . . . . . . . . . . . . 20\Womanface (þ) . . . . . . . . . 80won . . . . . . . . . . see \textwon\wp (℘) . . . . . . . . . . . . . . . . 51\wp (℘) . . . . . . . . . . . . . . . . 51\wr (≀) . . . . . . . . . . . . . . . . 20\wr (≀) . . . . . . . . . . . . . . . . 23\wreath (≀) . . . . . . . . . . . . . 23wreath product . . . . . . see \wr\Writinghand (b) . . . . . . . . 76wsuipa (package) 11, 15, 16, 88,90, 94, 104, 105\wupperhand (c) . . . . . . . . . 82X\x ( ˙˙) . . . . . . . . . . . . . . . . 82\XBox (☒) . . . . . . . . . . . . . . 73Xdvi . . . . . . . . . . . . . . . . . . 90\xhookleftarrow (←−↪) . . . . . 59\xhookrightarrow (↩−→) . . . . 59\Xi (Ξ) . . . . . . . . . . . . . . . . 49\xi (ξ) . . . . . . . . . . . . . . . . 49\xiup (ξ) . . . . . . . . . . . . . . 50\xLeftarrow (⇐=) . . . . . . . . 59\xleftarrow (←−) . . . . . . . . 59\xleftharpoondown (↽−) . . . 59\xleftharpoonup (↼−) . . . . . 59\xLeftrightarrow (⇐⇒) . . . 60\xLeftrightarrow (⇐⇒) . . . 59\xleftrightarrow (←→) . . . 60\xleftrightarrow (←→) . . . 59\xleftrightharpoons (↼− −⇁) . 59\xlongequal ( =) . . . . . . . . 60\xlongequal ( =) . . . . . . . . 60\xLongleftarrow (⇐=) . . . . 60\xlongleftarrow (←−) . . . . 60\xLongleftrightarrow (⇐=⇒). . . . . . . . . 60\xlongleftrightarrow (←−→). . . . . . . . . 60\xLongrightarrow (=⇒) . . . 60\xlongrightarrow (−→) . . . 60\xmapsto (↦−→) . . . . . . . . . . 59\xmapsto (↦−→) . . . . . . . . . . 60XML . . . . . . . . . . . . . . . . 103\xRightarrow (=⇒) . . . . . . . . 59\xrightarrow (−→) . . . . . . . 59\xrightharpoondown (−⇁) . . 59\xrightharpoonup (−⇀) . . . . 59\xrightleftharpoons (−⇀↽−) . 59\xrightleftharpoons (−⇀↽−) . 59Xs . . . . . . . . . . . . . . . . 73, 76\XSolid (#) . . . . . . . . . . . . 73\XSolidBold ($) . . . . . . . . 73\XSolidBrush (%) . . . . . . . . 73\xtwoheadleftarrow (↞−−−) 60\xtwoheadrightarrow (−−−↠) 60XY-pic . . . . . . . . . . . . . . . . . 93Y\Ydown () . . . . . . . . . . . . . 21yen . . . . . . . . . . . see \textyenyfonts (package) . . . 65, 104, 105yhmath (package) 57, 59, 62, 94,104\Yinyang (Y) . . . . . . . . . . . 80\Yleft () . . . . . . . . . . . . . 21\yogh (`) . . . . . . . . . . . . . . 12\yogh (x) . . . . . . . . . . . . . . 12\Yright () . . . . . . . . . . . . 21\Yup (⅄) . . . . . . . . . . . . . . . 21ZZapf Chancery (font) . . . . . . 65Zapf Dingbats (font) . . . 71, 73\Zborder (Z) . . . . . . . . . . . 77\zeta (ζ) . . . . . . . . . . . . . . 49\zetaup (ζ) . . . . . . . . . . . . . 50\Zodiac . . . . . . . . . . . . . . . 68zodiacal symbols . . . . . . . . . 68\Ztransf ( . ❝ ) . . . . . . . . . 35\ztransf ( ❝ . ) . . . . . . . . . 35\zugzwang (D) . . . . . . . . . . 82\Zwdr (ˇ “ * ) . . . . . . . . . . . . . . 79\ZwPa (A ) . . . . . . . . . . . . . . 79141