| a relation that is reflexive, symmetrical, and transitive, as equality. |
| equivalence relation n. A reflexive, symmetric, and transitive relationship between elements of a set, such as congruence for the set of all triangles in a plane. |
equivalence relation mathematics
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.
(1996-05-13)