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Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

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 ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

The slicing of a three-dimensional object by a plane (or more general slice).

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

The question of whether a solution to a given problem exists. The existence problem can be solved in the affirmative without actually finding a solution to the original ...

A group action phi:G×X->X is called faithful if there are no group elements g (except the identity element) such that gx=x for all x in X. Equivalently, the map phi induces ...

The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...