Source : Free On-Line Dictionary of Computing

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)