Definition:Equivalence Relation/Definition 1

Definition
Let $\mathcal R$ be a relation on a set $S$.

Let $\mathcal R$ be:


 * $(1): \quad$ reflexive
 * $(2): \quad$ symmetric
 * $(3): \quad$ transitive

Then $\mathcal R$ is an equivalence relation on $S$.

Also known as
An equivalence relation is frequently referred to just as an equivalence.

Also see

 * Equivalence of Definitions of Equivalence Relation