Antisymmetric

1 definition found

From The Free On-line Dictionary of Computing (27 SEP 03) [foldoc]:

  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)