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The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex ...

In nonstandard analysis, the limitation to first-order analysis can be avoided by using a construction known as a superstructure. Superstructures are constructed in the ...

This problem is NP-complete (Garey and Johnson 1983).

Let X be an arbitrary topological space. Denote the set closure of a subset A of X by A^- and the complement of A by A^'. Then at most 14 different sets can be derived from A ...

Let X be a set of urelements that contains the set N of natural numbers, and let V(X) be a superstructure whose individuals are in X. Let V(^*X) be an enlargement of V(X), ...

For any sets A and B, their cardinal numbers satisfy |A|<=|B| iff there is a one-to-one function f from A into B (Rubin 1967, p. 266; Suppes 1972, pp. 94 and 116). It is easy ...

The largest value of a set, function, etc. The maximum value of a set of elements A={a_i}_(i=1)^N is denoted maxA or max_(i)a_i, and is equal to the last element of a sorted ...

The smallest value of a set, function, etc. The minimum value of a set of elements A={a_i}_(i=1)^N is denoted minA or min_(i)a_i, and is equal to the first element of a ...

Consider a Boolean algebra of subsets b(A) generated by a set A, which is the set of subsets of A that can be obtained by means of a finite number of the set operations ...

A partial derivative of second or greater order with respect to two or more different variables, for example f_(xy)=(partial^2f)/(partialxpartialy). If the mixed partial ...