Search Results for ""

A triple (a,b,c) of positive integers satisfying a<b<c is said to be geometric if ac=b^2. In particular, such a triple is geometric if its terms form a geometric sequence ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be harmonic if 1/a+1/c=2/b. In particular, such a triple is harmonic if the reciprocals of its terms form an ...

Teichmüller's theorem asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence ...

Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given ...

Consider the local behavior of a map f:R^m->R^n by choosing a point x in R^m and an open neighborhood U subset R^m such that x in U. Now consider the set of all mappings ...

A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...

Analytic continuation gives an equivalence relation between function elements, and the equivalence classes induced by this relation are called global analytic functions.

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

Universal algebra studies common properties of all algebraic structures, including groups, rings, fields, lattices, etc. A universal algebra is a pair A=(A,(f_i^A)_(i in I)), ...

There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator. The only ...