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, ..., .

**References**

Shanks, D. *Solved and Unsolved Problems in Number Theory, 4th ed.* New York: Chelsea, pp. 56-57, 1993.

© 1996-9

1999-05-25