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.

Last updated: 1995-04-18

Nearby terms:

anti-aliasing ♦ antichain ♦ antisymmetric ♦ antivirus ♦ antivirus program

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