An antisymmetric relation is a relation where no two distinct elements are related in both directions. In other words. is antisymmetric iff
or, equivalently,
Antisymmetry isn't quite the compliment of Symmetry. Due to the fact that is allowed in an antisymmetric relation, the equivalence relation, is both symmetric and antisymmetric.
Examples of antisymmetric relations also include the successor relation, , or this relation linking numbers to their prime factors