antisymmetric

from The Free On-line Dictionary of Computing (8 July 2008)

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)