- Page 4: ll:JQ1@ HINDUS TAN Ul!!.rU BOOK AGE
- Page 9: viii 4.4 Gaps in the rational numbe
- Page 12 and 13: CONTENTS 15 Power series 15.1 Forma
- Page 14 and 15: Preface This text originated from t
- Page 16 and 17: Preface XV more advanced facts abou
- Page 18 and 19: Preface xvii tive; much of the key
- Page 21 and 22: 2 1. Introduction 1. What is a real
- Page 24 and 25: 1.2. Why do analysis? 5 At this poi
- Page 26: 1.2. Why do analysis? 7 However, de
- Page 33 and 34: Chapter 2 Starting at the beginning
- Page 36 and 37: 2.1. The Pean? axioms However, we s
- Page 39: 20 2. The natuml numbers Now we can
- Page 42 and 43: 2.1. The Peano axioms 23 from appea
- Page 45 and 46: 26 2. The natural numbers understoo
- Page 48 and 49: 2.2. Addition 29 m)++· But by defi
- Page 52 and 53: 2.3. Multiplication 33 Exercise 2.2
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36 2. The natural numbers Proof. Se
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38 3. Set theory that some of the a
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40 3. Set theory A.7). Because of t
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3.1. Fundamentals 43 proof We prove
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3.1. Fundamentals We have now accum
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54 3. Set theory Instead, we shall
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3.3. Functions 57 One common way to
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60 3. Set theory Proof. Since g o h
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9.4. Images and inverse images 67 N
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70 3. Set theory This should be com
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4 .1. The integers 85 tage of our f
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4.1. The integers 87 Lemma 4.1.3 (A
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4.1. The integers 89 Jfn is a posit
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92 4. Integers and rationals Proof.
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96 4. Integers and rationals xx-1 =
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4-4· Gaps in the rational numbers
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108 5. The real numbers or more of
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5.5. The least upper bound property
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5.6. Real exponentiation, part I 14
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164 6. Limits of sequences Example
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8.1. Countability 209 Jtelllark 8.1
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216 8. Infinite sets Exercise 8.1.4
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8.5. Ordered sets 241 yet another c
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9.2. The algebra of real-valued fun
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g, 1. The intermediate value theore
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Chapter 10 Differentiation of funct
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292 10. Differentiation of function
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300 10. Differentiation of function
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308 11. The Riemann integral (a) X
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318 11. The Riemann integral Proof.
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322 11. The Riemann integral Proof.
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324 11. The Riemann integral for ev
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11.5. Riemann integrability of cont
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Chapter A Appendix: the basics of m
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A.1. Mathematical statements 351 :E
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A.2. Implication 357 Sometimes it i
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364 A. Appendix: the basics of math
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;1.4. Variables and quantifiers 367
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A.4· Variables and quantifiers 371
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374 A. Appendix: the basics of math
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A. 7. Equality 377 takes the value
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A. 7. Equality 379 sin(y) = sin(z2)
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B.l. The decimal representation of
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Index ++ (increment), 18, 56 on int
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INDEX C, C 0 , C 1 , C 2 , Ck, 556
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INDEX of functions, 75, 425 discont
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VIII equivalence of in finite dimen
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X negative: see negation, positive
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INDEX sup norm: see supremum as nor