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Appendix D: List of Symbols

Last updated

Aug 4, 2022
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- Appendix C: Answers and Hints for Selected Exercises
- Detailed Licensing

( \newcommand{\kernel}{\mathrm{null}\,}\)

Symbol	Meaning
$\to$	Conditional statement
$R$	set of real numbers
$Q$	set of rational numbers
$Z$	set of integers
$N$	set of natural numbers
$y \in A$	$y$ is an element of $A$
$z \notin A$	$z$ is not an element of $A$
{ \| }	set builder notation
$\forall$	universal quantifier
$\exists$	existential quantifier
$\emptyset$	the empty set
$\land$	conjunction
$v e e$	disjunction
$⌝$	negation
$\leftrightarrow$	biconditional statement
$\equiv$	logically equivalent
$m \| n$	$m$ divides $n$
$a \equiv b$ (mod $n$ )	$a$ is congruent to $b$ modulo $n$
$\| x \|$	the absolute value of $x$
$A = B$	$A$ equals $B$ (set equality)
$A \subseteq B$	$A$ is a subset of $B$
$A ⊈ B$	$A$ is not a subset of $B$
$A \subset B$	$A$ is a proper subset of $B$
$P (A)$	power set of $A$
$\| A \|$	cardinality of a finite set $A$
$A \cap B$	intersection of $A$ and $B$
$A^{c}$	complement of $A$
$A - B$	set difference of $A$ and $B$
$A \times B$	Cartesian product of $A$ and $B$
$(a, b)$	ordered pair
$R \times R$	Cartesian plane
$R^{2}$	Cartesian plane
$\bigcup_{X \in \mathcal{C} X$	union of a family of sets
$\bigcap_{X \in \mathcal{C} X$	intersection of a finite family of sets
$⋃_{j = 1}^{n} A_{j}$	union of a finite family of sets
$⋂_{j = 1}^{n} A_{j}$	intersection of a finite family of sets
$⋃_{j = 1}^{\infty} B_{j}$	union of an infinite family of sets
$⋂_{j = 1}^{\infty} B_{j}$	intersection of a infinite family of sets
${A_{α} \| α \in Λ}$	indexed family of sets
$⋃_{α \in Λ} A_{α}$	union of an indexed family of sets
$⋂_{α \in Λ} A_{α}$	intersection of an indexed family of sets
$n!$	$n$ factorial
$f_{1}, f_{2}, f_{3}, . . .$	Fibonacci numbers
$s (n)$	sum of the divisors of $n$
$f : A \to B$	function from $A$ to $B$
dom( $f$ )	domain of the function $f$
codom( $f$ )	codmain of the function $f$
$f (x)$	inage of $x$ under $f$
range( $f$ )	range of the function $f$
$d (n)$	number of divisors of $n$
$I_{A}$	identity function on the set $A$
$p_{1}, p_{2}$	projection functions
det $(A)$	determinant of $A$
$A^{T}$	transpose of $A$
det: $M_{2, 2} \to R$	determinant function
$g \circ f : A \to C$	composition of function $f$ and $g$
$f^{- 1}$	the inverse of the function $f$
Sin	the restricted sine function
Sin $^{- 1}$	the inverse sine function
dom( $R$ )	domain of the relation $R$
range( $R$ )	range of the relation $R$
$x R y$	$x$ is related to $y$
$屏幕快照 2019-05-02 下午3.04.43.png$	$x$ is not related to $y$
$x \sim y$	$x$ is related to $y$
$x ≁ y$	$x$ is not related to $y$
$R^{- 1}$	the inverse of the relation $R$
$[a]$	equivalence class of $a$
$[a]$	congruence class of $a$
$Z_{n}$	the integers modulo $n$
$[a] \oplus [c]$	addition in $Z_{n}$
$[a] ⊙ [c]$	multiplication in $Z_{n}$
gcd( $a$ , $b$ )	greatest common divisor of $a$ and $b$
$f (A)$	image of $A$ under the function $f$
$f^{- 1} (C)$	pre-image of $C$ under the funtion $f$
$A \approx B$	$A$ is equivalent to $B$ $A$ and $B$ have the same cardinality
$N_{k}$	$N_{k} = {1, 2, . . ., k}$
card $(A) = k$	cardinality of $A$ is $k$
$a l e p h_{0}$	cardinality of $N$
$c$	cardinal number of the continuum

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