List of Symbols

Appendix D List of Symbols

Symbol	Description	Location
$\to$	conditional statement	Beginning Activity
$R$	set of real numbers	Subsection
$Q$	set of rational numbers	Subsection
$Z$	set of integers	Subsection
$\land$	conjunction	Item a
$\lor$	disjunction	Item b
$\neg$	negation	Item c
$\leftrightarrow$	biconditional statement	Subsection
$\equiv$	logically equivalent	Definition
$N$	set of natural numbers	Beginning Activity
$y \in A$	$y$ is an element of $A$	Item 2.13:1
$z \notin A$	$z$ is not an element of $A$	Item 2.13:2
$A = B$	$A$ equals $B$ (set equality)	Definition
$A \subseteq B$	$A$ is a subset of $B$	Definition
${∣}$	set builder notation	Subsection
$\emptyset$	the empty set	Subsection
$\forall$	universal quantifier	Definition
$\exists$	existential quantifier	Definition
$m ∣ n$	$m$ divides $n$	Definition
$a \equiv b (\mod n)$	$a$ is congruent to $b$ modulo $n$	Definition
$\| x \|$	absolute value of $x$	Definition
$n!$	$n$ factorial	Definition
$f_{1}, f_{2}, f_{3}, \dots$	Fibonacci numbers	Beginning Activity
$A \cap B$	intersection of $A$ and $B$	Definition
$A \cup B$	union of $A$ and $B$	Definition
$A^{c}$	complement of $A$	Definition
$A - B$	set difference of $A$ and $B$	Definition
$A ⊈ B$	$A$ is not a subset of $B$	Subsection
$A \subset B$	$A$ is a proper subset of $B$	Definition
$(P) (A)$	power set of $A$	Definition
$\| A \|$	cardinality of a finite set $A$	Definition
$(a, b)$	ordered pair	Definition
$A \times B$	Cartesian product of $A$ and $B$	Definition
$R \times R$	Cartesian plane	Subsection
$R^{2}$	Cartesian plane	Subsection
$⋃_{X \in C}^{} X$	union of a family of sets	Definition
$⋂_{X \in C}^{} X$	intersection of a family of sets	Definition
$⋃_{j = 1}^{n} A_{j}$	union of a finite family of sets	Subsection
$⋂_{j = 1}^{n} A_{j}$	intersection of a finite family of sets	Subsection
$⋃_{j = 1}^{\infty} B_{j}$	union of an infinite family of sets	Subsection
$⋂_{j = 1}^{\infty} B_{j}$	intersection of an infinite family of sets	Subsection
${A_{α} ∣ α \in Λ}$	indexed family of sets	Definition
$⋃_{α \in Λ}^{} A_{α}$	union of an indexed family of sets	Definition
$⋂_{α \in Λ}^{} A_{α}$	intersection of an indexed family of sets	Definition
$s (n)$	sum of the divisors of $n$	Exercise 2
$f : A \to B$	function from $A$ to $B$	Paragraphs
$dom (f)$	domain of the function $f$	Definition
$codom (f)$	codmain of the function $f$	Definition
$f (x)$	image of $x$ under $f$	Definition
$range (f)$	range of the function $f$	Definition
$d (n)$	number of divisors of $n$	Exercise 6
$R_{n}$	$R_{n} = {0, 1, 2, \dots, n - 1}$	Subsection
$I_{A}$	identity function on the set $A$	Progress Check 6.11
$p_{1}, p_{2}$	projection functions	Exercise 5
$det (A)$	determinant of $A$	Exercise 9
$A^{T}$	transpose of $A$	Exercise 10
$det : M_{2, 2} \to R$	determinant function	Activity 37
$g \circ f : A \to C$	composition of functions $f$ and $g$	Definition
$f^{- 1}$	the inverse of the function $f$	Definition
${Sin}^{- 1}$	the inverse sine function	Activity 41
$Sin$	the restricted sine function	Activity 41
$f (A)$	image of $A$ under the function $f$	Definition
$f^{- 1} (C)$	pre-image of $C$ under the function $f$	Definition
$dom (R)$	domain of the relation $R$	Definition
$range (R)$	range of the relation $R$	Definition
$x R y$	$x$ is related to $y$	Subsection
$x ⧸ R y$	$x$ is not related to $y$	Subsection
$x \sim y$	$x$ is related to $y$	Subsection
$x ≁ y$	$x$ is not related to $y$	Subsection
$R^{- 1}$	the inverse of the relation $R$	Definition
$[a]$	equivalence class of $a$	Definition
$[a]$	congruence class of $a$	Definition
$Z_{n}$	the integers modulo $n$	Definition
$[a] \oplus [c]$	addition in $Z_{n}$	Definition
$[a] ⊙ [c]$	multiplication in $Z_{n}$	Definition
$gcd (a, b)$	greatest common divisor of $a$ and $b$	Definition
$A \approx B$	$A$ is equivalent to $B,$ $A$ and $B$ have the same cardinality	Definition
$N_{k}$	$N_{k} = {1, 2, \dots, k}$	Subsection
$card (A) = k$	cardinality of $A$ is $k$	Definition
$ℵ_{0}$	cardinality of $N$	Definition
$c$	cardinal number of the continuum	Definition

Mathematical Reasoning: Writing and Proof (PreTeXt Edition)

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Appendix D List of Symbols