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A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

A theorem in game theory which guarantees the existence of a set of mixed strategies for finite, noncooperative games of two or more players in which no player can improve ...

A condition which must hold for a result to be true, but which does not guarantee it to be true. If a condition is both necessary and sufficient, then the result is said to ...

The symbol ¬ used to denote the negation operation ("NOT") in symbolic logic, also called "logical not."

A negative matrix is a real or integer matrix (a)_(ij) for which each matrix element is a negative number, i.e., a_(ij)<0 for all i, j. Negative matrices are therefore a ...

An algebra, also called a nilalgebra, consisting only of nilpotent Elements.

Let M be a finitely generated module over a commutative Noetherian ring R. Then there exists a finite set {N_i|1<=i<=l} of submodules of M such that 1. intersection ...

A geometry in which Archimedes' axiom does not hold.

An algebra which does not satisfy a(bc)=(ab)c is called a nonassociative algebra.

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).