Notation

Appendix B Notation

Symbol	Description	Location
$A \subseteq B$	set inclusion	Definition 1.1.1
$N$	natural numbers	Paragraph
$Z$	integers	Paragraph
$Q$	rational numbers	Paragraph
$R$	real numbers	Paragraph
$(a, b), [a, b], etc.$	intervals of real numbers	Paragraph
$f : A \to B$	function	Definition 1.1.4
$(g \circ f) (x)$	function composition	Definition 1.1.7
$\| A \| = \| B \|$	cardinality, equal	Definition 1.1.10
$\| A \| \leq \| B \|$	cardinality, less than or equal	Definition 1.1.10
$P (A)$	power set	Definition 1.1.12
$b ∣ a$	divides; divisible by	Definition 1.3.1
$gcd (a, b)$	greatest common divisor	Definition 1.3.4
$n!$	factorial	Definition 2.1.14
$P (n, k),_{n} P_{k}$	$k$ -permutation of an $n$ -set	Proposition 2.2.5
$(\binom{n}{k}), C (n, k),_{n} C_{k}$	$k$ -combination of an $n$ -set	Definition 2.2.15
$⌊ n ⌋$	floor function	Example 3.2.1
$D_{n}$	number of derangements of ${1, 2, \dots, n}$	Exploration 3.3.1
$[x]$	equivalence class of $x$	Definition 4.1.7
$a \equiv b (\mod n)$	congruence modulo $n$	Definition 4.2.1
$Z_{n}$	Set of congruence classes mod $n$	Definition 4.2.6
$a \mod n$	modulo operation	Definition 4.2.12
$ϕ (n)$	Euler's totient function	Definition 4.4.1
$d (v)$	degree of a vertex	Definition 5.2.6
$V (G)$	vertex set of $G$	Remark 5.2.11
$E (G)$	edge set of $G$	Remark 5.2.11
$C_{n}$	cycle on $n$ vertices	Definition 5.3.12
$K_{n}$	complete graph on $n$ vertices	Definition 5.3.13
$G_{1} ≅ G_{2}$	graph isomorphism	Definition 5.4.3
$\overset{―}{G}$	graph complement of $G$	Definition 5.4.15
$P_{n}$	path graph on $n$ vertices	Definition 5.5.1
$K_{m, n}$	complete bipartite graph on $m$ and $n$ vertices	Definition 5.6.8