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Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

The categorical notion which is dual to product. The coproduct of a family {X_i}_(i in I) of objects of a category is an object C=coproduct_(i in I)X_i, together with a ...

Given a weighted, undirected graph G=(V,E) and a graphical partition of V into two sets A and B, the cut of G with respect to A and B is defined as cut(A,B)=sum_(i in A,j in ...

Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...

Each of the sets forming a direct product is said to be a direct factor. A group G is said to be a direct factor of the group G^' if G^' is isomorphic to the group direct ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space ...

A dot plot, also called a dot chart, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete ...

A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, ...

Two statements in logic are said to be equipollent if they are deducible from each other. Two sets A and B are said to be equipollent iff there is a one-to-one correspondence ...