Notation

Appendix A Notation

Symbol	Description	Location
$x \in S$	$x$ is an element of $S$	Paragraph
$x \notin S$	$x$ is not an element of $S$	Paragraph
${x \in S : P (x)}$	$x$ in $S$ such that $x$ has property $P$	Paragraph
$A \subseteq S$	$A$ is a subset of $S$	Definition 1.2.2
$A ⊈ S$	$A$ is not a subset of $S$	Paragraph
$R$	the set of real numbers	Item
$Z$	the set of integers	Item
$Q$	the set of rational numbers	Item
$N$	the set of natural numbers	Item
$Z^{+}$	the set of positive integers	Item
$Z^{n o n n e g}$	the set of nonnegative integers	Item
$R^{+}$	the set of positive real numbers	Item
$R^{n o n n e g}$	the set of nonnegative real numbers	Item
$A \times B$	the product of $A$ and $B;$ ${(a, b) : a \in A, b \in B}$	Definition 1.2.6
$a R b$	$a$ is related to $b$	Paragraph
$\sim p$	not $p$	Item
$p \land q$	$p$ and $q$	Item
$p \lor q$	$p$ or $q$	Item
$t$	a statement that is always true; tautology	Paragraph
$c$	a statement that is always false; contradiction	Paragraph
$P \equiv Q$	$P$ is logically equivalent to $Q$	Definition 2.1.10
$p \to q$	if $p$ then $q$	Item
$∴$	therefore	Assemblage
$\forall$	for all; universal quantifier	Item
$\exists$	there exists; existential quantifier	Item
$Q$	the set of ratioanl numbers	Definition 4.2.1
$R ∖ Q$	the set of irratioanl numbers	Definition 4.2.2
$d ∣ n$	$d$ divides $n$	Paragraph
	$d$ does not divide $n$	Paragraph
$n div d$	quotient when $n$ is divided by $d$	Paragraph
$n mod d$	remainder when $n$ is divided by $d$	Paragraph
$\sum_{k = 1}^{n} a_{k}$	the sum of $a_{k}$ from $k = 1$ to $n$	Assemblage
$\prod_{k = 1}^{n} a_{k}$		Paragraph
$(\binom{n}{r})$	$n$ choose $r$	Definition 5.1.6
$A \cup B$	$A$ union $B$	Definition 6.1.4
$A \cap B$	$A$ intersect $B$	Definition 6.1.6
$A - B$	$A$ minus $B;$ the difference of set $A$ and $B$	Definition 6.1.8
$A^{C}$	the complement of $A$	Definition 6.1.10
$⋃_{i = 1}^{n} A_{i}$	the union $A_{1} \cup A_{2} \cup \dots \cup A_{n}$	Paragraph
$⋂_{i = 1}^{n} A_{i}$	the intersection $A_{1} \cap A_{2} \cap \dots \cap A_{n}$	Paragraph
$P (A)$	the power set of $A$	Definition 6.1.13
$\Leftrigharrow$	if and only if in proofs	Paragraph
$\| S \|$	the number of elements in $S$	Paragraph
$Im (f)$	the image of $f$	Definition 7.1.6
$f^{- 1} (x)$	the inverse of function $f$	Theorem 7.2.13
$x R y$	$x$ is related to $y$	Paragraph
$m \equiv n \mod d$	$m$ is congruent to $n$ mod $d;$ $d ∣ (m - n)$	Paragraph
$[a]$	the equivalence class of $a$	Paragraph
$P (n, r)$	the number of $r$ -permutations from a set of $n$ elements	Definition 9.2.8
$(\binom{n}{r})$	$n$ choose $r$	Definition 9.5.1

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