# Equivalence relation

An equivalence relation is a binary relation on set (that is, a subset of ) that is reflexive, symmetric, and transitive, that is, the following three properties hold:

Given an equivalence relation , we define the set of equivalence classes by

The equivalence classes of a non-empty set form a partition of .

Conversely, given a partition of set , the relation defined by

is an equivalence relation such that .