Equivalence Relation

A relation $R$ on a set $A$ is an equivalence relation if it is reflexive, symmetric, and transitive.

Context

Equivalence relations partition a set into disjoint equivalence classes. For example, congruence modulo $n$ is an equivalence relation on the integers: it is reflexive ($a\equiv a$), symmetric ($a\equiv b\Rightarrow b\equiv a$), and transitive.

See Also

• relation
• congruent modulo
• set