Binary relations

Antisymmetric relation

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. (Wikipedia).

Antisymmetric relation
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Related pages

Binary relation | Total order | Element (mathematics) | Natural number | Mathematics | Reflexive relation | Set (mathematics) | Symmetric relation | Inequality (mathematics) | Real number | Asymmetric relation