A (binary) relation on a set is antisymmetric if any two elements that are related in both orders are equal:
In the language of the -poset-with-duals Rel of sets and relations, a relation is antisymmetric if its intersection with its reverse is contained in the identity relation on :
If an antisymmetric relation is also reflexive (as most are in practice), then this containment becomes an equality.
Revised on August 24, 2012 20:04:12
by Urs Schreiber