equivalence relation (redirected from Equivalence relations)

equivalence relation

In mathematics, a generalization of the idea of equality between elements of a set. All equivalence relations (e.g., that symbolized by the equals sign) obey three conditions: reflexivity (every element is in the relation to itself), symmetry (element A has the same relation to element B that B has to A), and transitivity (see transitive law). Congruence of triangles is an equivalence relation in geometry. Members of a set are said to be in the same equivalence class if they have an equivalence relation.

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equivalence relation [i′kwiv·ə·ləns ri′lā·shən]

(mathematics)

A relation which is reflexive, symmetric, and transitive. Also known as equals functions.

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(mathematics)

equivalence relation - A relation R on a set including elements a, b, c, which is reflexive (a R a), symmetric (a R b => b R a) and transitive (a R b R c => a R c). An equivalence relation defines an equivalence class. See also partial equivalence relation.