SB Notation

Appendix A Notation

The following table defines the notation used in this book. Page numbers or references refer to the first appearance of each symbol.

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Symbol	Description	Location
$a \in A$	$a$ is in the set $A$	Paragraph
$N$	the natural numbers	Paragraph
$Z$	the integers	Paragraph
$Q$	the rational numbers	Paragraph
$R$	the real numbers	Paragraph
$C$	the complex numbers	Paragraph
$A \subset B$	$A$ is a subset of $B$	Paragraph
$\emptyset$	the empty set	Paragraph
$A \cup B$	the union of sets $A$ and $B$	Paragraph
$A \cap B$	the intersection of sets $A$ and $B$	Paragraph
$A^{'}$	complement of the set $A$	Paragraph
$A ∖ B$	difference between sets $A$ and $B$	Paragraph
$A \times B$	Cartesian product of sets $A$ and $B$	Paragraph
$A^{n}$	$A \times \dots \times A$ ( $n$ times)	Paragraph
$i d$	identity mapping	Paragraph
$f^{- 1}$	inverse of the function $f$	Paragraph
$a \equiv b (\mod n)$	$a$ is congruent to $b$ modulo $n$	Example 1.2.30
$n!$	$n$ factorial	Example 2.1.4
$(\binom{n}{k})$	binomial coefficient $n! / (k! (n - k)!)$	Example 2.1.4
$a ∣ b$	$a$ divides $b$	Paragraph
$gcd (a, b)$	greatest common divisor of $a$ and $b$	Paragraph
$P (X)$	power set of $X$	Exercise 2.4.12
$lcm (m, n)$	the least common multiple of $m$ and $n$	Exercise 2.4.23
$Z_{n}$	the integers modulo $n$	Paragraph
$U (n)$	group of units in $Z_{n}$	Example 3.2.4
$M_{n} (R)$	the $n \times n$ matrices with entries in $R$	Example 3.2.7
$det A$	the determinant of $A$	Example 3.2.7
$G L_{n} (R)$	the general linear group	Example 3.2.7
$Q_{8}$	the group of quaternions	Example 3.2.8
$C^{*}$	the multiplicative group of complex numbers	Example 3.2.9
$\| G \|$	the order of a group	Paragraph
$R^{*}$	the multiplicative group of real numbers	Example 3.3.1
$Q^{*}$	the multiplicative group of rational numbers	Example 3.3.1
$S L_{n} (R)$	the special linear group	Example 3.3.3
$Z (G)$	the center of a group	Exercise 3.5.48
$⟨ a ⟩$	cyclic group generated by $a$	Theorem 4.1.3
$\| a \|$	the order of an element $a$	Paragraph
$cis θ$	$\cos θ + i \sin θ$	Paragraph
$T$	the circle group	Paragraph

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