# 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 \(n\) |

\(|x|\) | \(m\) 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 |