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The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a and a formula A(y) of a set x consisting of all elements of a satisfying A(y), exists x ...

Let A and B be any sets, and let |X| be the cardinal number of a set X. Then cardinal exponentiation is defined by |A|^(|B|)=|set of all functions from B into A| (Ciesielski ...

The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... (OEIS A000027) or to the set of nonnegative integers 0, 1, 2, 3, ... (OEIS ...

Given a set of objects S, a binary relation is a subset of the Cartesian product S tensor S.

A set of class representatives is a subset of X which contains exactly one element from each equivalence class.

A relational system is a structure R=(S,{P_i:i in I},{f_j:j in J}) consisting of a set S, a collection of relations P_i(i in I) on S, and a collection of functions f_j(j in ...

A p-system of a set S is a sequence of subsets A_1, A_2, ..., A_p of S, among which some may be empty or coinciding with each other.

A grammar defining formal language L is a quadruple (N,T,R,S), where N is a finite set of nonterminals, T is a finite set of terminal symbols, R is a finite set of ...

The largest n such that |z_n|<4 in a Mandelbrot set. Points of different count are often assigned different colors.

The set E of edges of a loopless graph (V,E), being a set of unordered pairs of elements of V, constitutes an adjacency relation on V. Formally, an adjacency relation is any ...