antisymmetric

mathematics 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)