Antisymmetric relation
Binary relation such that if A is related to B and is different from it then B is not related to A / From Wikipedia, the free encyclopedia
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In mathematics, a binary relation on a set
is antisymmetric if there is no pair of distinct elements of
each of which is related by
to the other. More formally,
is antisymmetric precisely if for all
or equivalently,
The definition of antisymmetry says nothing about whether
actually holds or not for any
. An antisymmetric relation
on a set
may be reflexive (that is,
for all
), irreflexive (that is,
for no
), or neither reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.
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![]() ![]() All definitions tacitly require the homogeneous relation |