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The theorem in set theory and logic that for all sets A and B, B=(A intersection B^_) union (B intersection A^_)<=>A=emptyset, (1) where A^_ denotes complement set of A and ...

The term "porism" is an archaic type of mathematical proposition whose historical purpose is not entirely known. It is used instead of "theorem" by some authors for a small ...

Two triangles are said to be poristic triangles if they share the same incircle and circumcircle. More specifically, in the plane of a reference triangle, a triangle is said ...

Let A be a C^*-algebra. An element a in A is called positive if a=a* and sp(a) subset= R^+, or equivalently if there exists an element b in A such that a=bb^*. For example, ...

A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be positive lightlike if it has zero (Lorentzian) norm and if its first ...

A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be positive timelike if it has imaginary (Lorentzian) norm and if its first ...

A power mean is a mean of the form M_p(a_1,a_2,...,a_n)=(1/nsum_(k=1)^na_k^p)^(1/p), (1) where the parameter p is an affinely extended real number and all a_k>=0. A power ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...

Let f:A->B be a map between sets A and B. Let Y subset= B. Then the preimage of Y under f is denoted by f^(-1)(Y), and is the set of all elements of A that map to elements in ...

For X a topological space, the presheaf F of Abelian groups (rings, ...) on X is defined such that 1. For every open subset U subset= X, an Abelian group (ring, ...) F(U), ...