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Meaning of ANTISYMMETRIC

 
Computing Dictionary
 
 Definition: 

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.

 

 

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