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The golden ratio has decimal expansion phi=1.618033988749894848... (OEIS A001622). It can be computed to 10^(10) digits of precision in 24 CPU-minutes on modern hardware and ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...

A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is brought ...

The tetrahedral group T_d is the point group of symmetries of the tetrahedron including the inversion operation. It is one of the 12 non-Abelian groups of order 24. The ...

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

A coequalizer of a pair of maps f,g:X->Y in a category is a map c:Y->C such that 1. c degreesf=c degreesg, where degrees denotes composition. 2. For any other map c^':Y->C^' ...

The compact-open topology is a common topology used on function spaces. Suppose X and Y are topological spaces and C(X,Y) is the set of continuous maps from f:X->Y. The ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...