# asymmetric relation

**asymmetric relation** A relation *R* defined on a set *S* and having the property that whenever *x R y*

then it is never the case that *y R x*

where *x* and *y* are arbitrary elements of *S*. The usual “is less than” ordering defined on the integers is an asymmetric relation. See also antisymmetric relation, symmetric relation.

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**asymmetric relation**