nLab
irreflexive relation
A (binary) relation on a set is irreflexive if no element of is related to itself:
\forall (x: A),\; x \nsim x
In the language of the -poset Rel of sets and relations, a relation is irreflexive if it is disjoint from the identity relation on :
\id_A \cap R \subseteq \empty
Of course, this containment is in fact an equality.
Revised on June 29, 2009 01:41:39
by
Toby Bartels
(71.104.230.172)