Search Results for ""

Every Boolean algebra is isomorphic to the Boolean algebra of sets. The theorem is equivalent to the maximal ideal theorem, which can be proved without using the axiom of ...

The Banach-Steinhaus theorem is a result in the field of functional analysis which relates the "size" of a certain subset of points defined relative to a family of linear ...

A theorem in set theory stating that, for all sets A and B, the following equivalences hold, A subset B<=>A intersection B=A<=>A union B=B.

A theorem stated in 1882 which cannot be derived from Euclid's postulates. Given points a, b, c, and d on a line, if it is known that the points are ordered as (a,b,c) and ...

Dini's theorem is a result in real analysis relating pointwise convergence of sequences of functions to uniform convergence on a closed interval. For an increasing sequence ...

Iff p is a prime, then (p-1)!+1 is a multiple of p, that is (p-1)!=-1 (mod p). (1) This theorem was proposed by John Wilson and published by Waring (1770), although it was ...

If ABB^' and AC^'C are straight lines with BC and B^'C^' intersecting at D and AB+BD=AC^'+C^'D, then AB^'+B^'D=AC+CD. The origin and some history of this theorem are ...

Mann's theorem is a theorem widely circulated as the "alpha-beta conjecture" that was subsequently proven by Mann (1942). It states that if A and B are sets of integers each ...

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

Any motion of a rigid body in space at every instant is a screw motion. This theorem was proved by Mozzi and Cauchy.