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A problem related to the continuum hypothesis which was solved by Solovay (1970) using the inaccessible cardinals axiom. It has been proven by Shelah and Woodin (1990) that ...

There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of the ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point ...

Machin's formula is given by 1/4pi=4cot^(-1)5-cot^(-1)239. There are a whole class of Machin-like formulas with various numbers of terms (although only four such formulas ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

Given a smooth manifold M with an open cover U_i, a partition of unity subject to the cover U_i is a collection of smooth, nonnegative functions psi_i, such that the support ...