equivalence relation


equivalence relation

noun

Definition of EQUIVALENCE RELATION

:  a relation (as equality) between elements of a set (as the real numbers) that is symmetric, reflexive, and transitive and for any two elements either holds or does not hold

First Known Use of EQUIVALENCE RELATION

circa 1949

equivalence relation

noun    (Concise Encyclopedia)

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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