Antisymmetric relation
In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle X} each of which is related by R {\displaystyle R} to the other. More formally, R {\displaystyle R} is antisymmetric precisely if for all a , b ∈ X , {\displaystyle a,b\in X,} if a R b with a ≠ b then b R a must not hold , {\displaystyle {\text{if }}\,aRb\,{\text{ with }}\,a\neq b\,{\text{ then }}\,bRa\,{\text{ must not hold}},} or equivalently, if a R b and b R a then a = b .