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The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection of Stiefel-Whitney classes such that their cup ...

Let (K,|·|) be a complete non-Archimedean valuated field, with valuation ring R, and let f(X) be a power series with coefficients in R. Suppose at least one of the ...

A set of moves which a player plans to follow while playing a game.

X subset= R^n is subanalytic if, for all x in R^n, there is an open set U and a bounded semianalytic set Y subset R^(n+m) such that X intersection U is the projection of Y ...

If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, ...

For a subgroup H of a group G, the index of H, denoted (G:H), is the cardinal number of the set of left cosets of H in G (which is equal to the cardinal number of the set of ...

A condition which, if true, guarantees that a result is also true. (However, the result may also be true if the condition is not met.) If a condition is both necessary and ...

Two angles alpha and beta for which alpha+beta=pi are said to be supplementary. In other words, alpha and beta are supplementary angles if they produce a straight angle when ...

Given a sequence of real numbers a_n, the supremum limit (also called the limit superior or upper limit), written lim sup and pronounced 'lim-soup,' is the limit of ...

A symmetric design is a block design (v, k, lambda, r, b) with the same number of blocks as points, so b=v (or, equivalently, r=k). An example of a symmetric block design is ...