antisymmetric relation
Sign in to saveAlso known as antisymmetric property, anti-symmetric property, anti-symmetric relation
binary relation such that if A is related to B and is different from it then B is not related to A
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Encyclopedic overview
Y indicates that the column's property is always true for the row's term (at the very left), while ✗ indicates that the property is not guaranteed in general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively. All definitions tacitly require the homogeneous relation
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Excerpted from Wikipedia’s “antisymmetric relation” article, available under the CC BY-SA 4.0 licence.