Equivalence relation
This is an old revision of this page, as edited by Foxtrot (talk | contribs) at 19:44, February 17, 2008. It may differ significantly from current revision.
An equivalence relation is a mathematical relation which is reflexive, symmetric, and transitive. Equality and set membership are the most basic equivalence relations, which is why they are often called trivial equivalence relations.
Congruence relations are examples of equivalence relations, as is the j-invariant of elliptic curves.
An equivalence relation on a set S partitions S into disjoint subsets, known as equivalence classes. Two objects in the same equivalence class are said to be equivalent.
Equivalence relations are the mathematical foundation for forming quotients.