Irreflexive relation
= Irreflexive relation
{title2=$\forall x\,\neg R(x,x)$}
A <binary relation> is irreflexive when no element is related to itself. An <irreflexive relation> that is also a <transitive relation> is a <strict partial order>. Transitivity then excludes every finite directed cycle, since a cycle would imply $R(x,x)$ at its starting element.