antisymmetric
A {relation} R is antisymmetric if,
for all x and y, x R y and y R x ◦> x ◦◦ y.
I.e. no two different elements are mutually related.
{Partial orders} and {total orders} are antisymmetric. If R
is also {symmetric} (x R y ◦> y R x) then x R y ◦> x ◦◦ y.
I.e. different elements are not related.
(1995-04-18)