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 Symbol Meaning $$\to$$ Conditional statement $$\mathbb{R}$$ set of real numbers $$\mathbb{Q}$$ set of rational numbers $$\mathbb{Z}$$ set of integers $$\mathbb{N}$$ 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 $$\wedge$$ conjunction $$vee$$ disjunction $$\urcorner$$ negation $$\leftrightarrow$$ biconditional statement $$\equiv$$ logically equivalent $$m\ |\ n$$ $$m$$ divides $$n$$ $$a \equiv b$$ (mod $$n$$) $$a$$ is congruent to $$b$$ modulo $$n$$ $$|x|$$ $$m$$ divides $$n$$ $$A = B$$ $$A$$ equals $$B$$ (set equality) $$A \subseteq B$$ $$A$$ is a subset of $$B$$ $$A \not\subseteq B$$ $$A$$ is not a subset of $$B$$ $$A \subset B$$ $$A$$ is a proper subset of $$B$$ $$\mathcal{P}(A)$$ 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 $$\mathbb{R} \times \mathbb{R}$$ Cartesian plane $$\mathbb{R}^2$$ 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 $$\bigcup_{j = 1}^{n} A_j$$ union of a finite family of sets $$\bigcap_{j = 1}^{n} A_j$$ intersection of a finite family of sets $$\bigcup_{j = 1}^{\infty} B_j$$ union of an infinite family of sets $$\bigcap_{j = 1}^{\infty} B_j$$ intersection of a infinite family of sets $$\{A_{\alpha}\ |\ \alpha \in \Lambda\}$$ indexed family of sets $$\bigcup_{\alpha \in \Lambda} A_{\alpha}$$ union of an indexed family of sets $$\bigcap_{\alpha \in \Lambda} A_{\alpha}$$ 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: $$M_{2, 2} \to \mathbb{R}$$ 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 $$y$$ $$x$$ is not related to $$y$$ $$x \sim y$$ $$x$$ is related to $$y$$ $$x \nsim y$$ $$x$$ is not related to $$y$$ $$R^{-1}$$ the inverse of the relation $$R$$ $$[a]$$ equivalence class of $$a$$ $$[a]$$ congruence class of $$a$$ $$\mathbb{Z}_{n}$$ the integers modulo $$n$$ $$[a] \oplus [c]$$ addition in $$\mathbb{Z}_{n}$$ $$[a] \odot [c]$$ multiplication in $$\mathbb{Z}_{n}$$ 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 $$f$$ $$A \thickapprox B$$ $$A$$ is equivalent to $$B$$ $$A$$ and $$B$$ have the same cardinality $$\mathbb{N}_{k}$$ $$\mathbb{N}_{k} = \{1, 2, ..., k\}$$ card$$(A) = k$$ cardinality of $$A$$ is $$k$$ $$aleph_{0}$$ cardinality of $$\mathbb{N}$$ $$c$$ cardinal number of the continuum