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A requirement necessary for a given statement or theorem to hold. Also called a criterion.

The formal term in propositional calculus for the connective implies.

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.

A topological structure which interpolates between contact structures and codimension-one foliations.

An equation of the form f(x)=b (mod m), (1) where the values of 0<=x<m for which the equation holds are sought. Such an equation may have none, one, or many solutions. There ...

Two square matrices A and B are called congruent if there exists a nonsingular matrix P such that B=P^(T)AP, where P^(T) is the transpose.

A number h which satisfies the conditions of the congruum problem: x^2+h=a^2 and x^2-h=b^2, where x,h,a,b are integers. The list of congrua is given by 24, 96, 120, 240, 336, ...

Functions which can be expressed in terms of Legendre functions of the first and second kinds. See Abramowitz and Stegun (1972, p. 337). P_(-1/2+ip)(costheta) = (1) = ...

A proposition which is consistent with known data, but has neither been verified nor shown to be false. It is synonymous with hypothesis.