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Appendix D: List of Symbols

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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 \(y\)
    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 \(y\)
    \(x \nsim y\) \(x\) 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