Definition:Equivalence Relation/Definition 2

Definition
Let $\RR \subseteq S \times S$ be a relation on a set $S$.

$\RR$ is an equivalence relation :


 * $\Delta_S \cup \RR^{-1} \cup \RR \circ \RR \subseteq \RR$

where:
 * $\Delta_S$ denotes the diagonal relation on $S$
 * $\RR^{-1}$ denotes the inverse relation
 * $\circ$ denotes composition of relations

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

Also see

 * Equivalence of Definitions of Equivalence Relation