Rel, bicategory of relations, allegory
left and right euclidean;
extensional, well-founded relations.
A (binary) relation on a set is asymmetric if no two elements are related in both orders:
In the language of the -poset-with-duals Rel of sets and relations, a relation is asymmetric if it is disjoint from its dual:
Of course, this containment is in fact an equality.
An asymmetric relation is necessarily irreflexive.
Last revised on August 24, 2012 at 20:04:19. See the history of this page for a list of all contributions to it.