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 \(n\) |
\(|x|\) |
the absolute value of \(x\) |
\(A = B\) |
\(A\) 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 |