For simultaneously reflexive, symmetric and transitive relations. Use it with the tag (relations).
An equivalence relation is a binary relation $R$ on a set $A$ that is reflexive, symmetric and transitive:
- $(\forall a\in A):aRa$ (reflexive)
- $(\forall a,b\in A):aRb \implies bRa$ (symmetric)
- $(\forall a,b,c\in A):aRb\wedge bRc \implies aRc$ (transitive)