Appendix D: List of Symbols
- Page ID
- 7094
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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 \(n\) |
\(|x|\) | 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 |