equivalence relation

An equivalence relation is a homogeneous relation that is reflexive, transitive, and symmetric.

Formally,
a binary relation $\sim$ over set $S$ is an equivalence relation if for all $a,b,c$ in $S$,

• $a\sim a$ (reflexive)
• $a\sim b$ if and only if $b\sim a$ (symmetric)
• if $a\sim b$ and $b\sim c$ then $a\sim c$ (transitive)

An equivalence relation is a symmetric preorder.

See also
equivalence class