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The expected number of trials needed to collect a complete set of n different objects when picked at random with repetition is nH_n (Havil 2003, p. 131). For n=1, 2, ..., the ...

The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel set theory is replaced by 6'. Selection axiom (or "axiom of subsets"): for any set-theoretic formula A(u), ...

The rectifiable sets include the image of any Lipschitz function f from planar domains into R^3. The full set is obtained by allowing arbitrary measurable subsets of ...

A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

A subset E of a topological space S is said to be nonmeager if E is of second category in S, i.e., if E cannot be written as the countable union of subsets which are nowhere ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthogonal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. Note ...

An independent edge set (also called a matching) of a graph G is a subset of the edges such that no two edges in the subset share a vertex of G (Skiena 1990, p. 219). The ...

One of the Zermelo-Fraenkel axioms which asserts the existence of the empty set emptyset. The axiom may be stated symbolically as exists x forall y(!y in x).

A connected dominating set in a connected graph G is a dominating set in G whose vertices induce a connected subgraph, i.e., one in which there is no dominating vertex not ...