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A subspace A of X is called a deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X and a in A, 1. F(x,0)=x, 2. F(x,1) in A, ...

Differential entropy differs from normal or absolute entropy in that the random variable need not be discrete. Given a continuous random variable X with a probability density ...

Efron's dice are set of four nontransitive dice such that the probabilities of A winning against B, B against C, C against D, and D against A are all the same. The images ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

An equalizer of a pair of maps f,g:X->Y in a category is a map e:E->X such that 1. f degreese=g degreese, where degrees denotes composition. 2. For any other map e^':E^'->X ...

A number n is called equidigital if the number of digits in the prime factorization of n (including powers) uses the same number of digits as the number of digits in n. The ...

A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

An equivalence relation on a set X is a subset of X×X, i.e., a collection R of ordered pairs of elements of X, satisfying certain properties. Write "xRy" to mean (x,y) is an ...

A univariate function f(x) is said to be even provided that f(x)=f(-x). Geometrically, such functions are symmetric about the y-axis. Examples of even functions include 1 ...

An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to +1. For initial set {1,2,3,4}, ...