The Free On-line Dictionary of Computing (30 December 2018):

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, i.e.

    x R y  =>  y R x

   then

    x R y  =>  x == y

   I.e. different elements are not related.

   (1995-04-18)