Antisymmetry
= Antisymmetry
{title2=$(xRy\text{ and }yRx)\implies x=y$}
The property of a <binary relation> that opposite directed relationships between two elements can hold only when those elements are equal. It does not require every pair to be comparable and does not prohibit a longer <directed cycle> whose reverse edges are initially absent. Taking <reflexive transitive closure> can therefore destroy this property.