An equivalence class is defined as a subset of the form , where is an element of and the notation "" is used to mean that there is an equivalence relation between and . It can be shown that any two equivalence classes are either equal or disjoint, hence the collection of equivalence classes forms a partition of . For all , we have iff and belong to the same equivalence class.
A set of class representatives is a subset of which contains exactly one element from each equivalence class.
For a positive integer, and integers, consider the congruence , then the equivalence classes are the sets , etc. The standard class representatives are taken to be 0, 1, 2, ..., .