Equivalence Class
An equivalence class is defined as a Subset of the form 
, where 
is an element of 
and theNotation ``
'' is used to mean that there is an Equivalence Relation between 
and 
. It can be shownthat 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 Oneelement 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.
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