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, i.e. x R y => y R x then x R y => x == y I.e. different elements are not related. (1995-04-18)