Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 969 — #977
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Glossary of Symbols
symbol meaning
R.X/
image of set X under binary relation R
R 1
inverse of binary relation R
R 1 .X/ inverse image of set X under relation R
surj
A surj B iff 9f W A ! B: f is a surjective function
inj
A inj B iff 9R W A ! B: R is an injective total relation
bij
A bij B iff 9f W A ! B: f is a bijection
Π1 in injective property of a relation
Π1 in surjective property of a relation
Π1 out function property of a relation
Π1 out total property of a relation
ŒD 1 out; D 1 in bijection relation
ı
relational composition operator
the empty string/list
A
the finite strings over alphabet A
A !
the infinite strings over alphabet A
rev.s/
the reversal of string s
s t concatenation of strings s; t; append.s; t/
# c .s/ number of occurrences of character c in string s
m j n
integer m divides integer n; m is a factor of n
gcd
greatest common divisor
log the base 2 logarithm, log 2
ln
the natural logarithm, log e
lcm
least common multiple
.k::n/
fi 2 Z j k < i < ng
Œk::n/
fi 2 Z j k i < ng
.k::n
fi 2 Z j k < i ng
Œk::n
P
fi 2 Z j k i ng
Q i2I r i sum of numbers r i where i ranges over set I of indices
i2I r i product of numbers r i where i ranges over set I of indices
qcnt.n; d/ quotient of n divided by d
rem.n; d/ remainder of n divided by d
.mod n/ congruence modulo n
6
not congruent
Z n
the ring of integers modulo n
C n ; n
addition and multiplication operations in Z n
Z n
the set of numbers in Œ0; n/ relatively prime to n
.n/
Euler’s totient function WWDjZ n j
hu!vi directed edge from vertex u to vertex v
Id A identity relation on set A: aId A a 0 iff a D a 0