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Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

Let there be three polynomials a(x), b(x), and c(x) with no common factors such that a(x)+b(x)=c(x). Then the number of distinct roots of the three polynomials is one or more ...

The Banach-Saks theorem is a result in functional analysis which proves the existence of a "nicely-convergent" subsequence for any sequence {f_n}={f_n}_(n in Z^*) of ...

A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and ...

Because even high-resolution computer monitors have a relatively small number of pixels, when graphics or text display distinguish between individual pixels. The result is ...

A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness ...

A game in which no draw is possible. Steinhaus (1999, p. 16) stated that all categorical games are unfair, but this is incorrect. For example, the game "Odds or Evens" pits ...

Let P be a finite partially ordered set. A chain in P is a set of pairwise comparable elements (i.e., a totally ordered subset). The partial order length of P is the maximum ...

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...