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
In the Vinony graph
Within Vinony's link graph, antisymmetric relation is referenced by 158 other articles, and connects out to reflexive relation, partially ordered set and total order.
It is catalogued under the topic Properties of binary relations.
Its subject is documented across 30 Wikipedia language editions.
~4 min read
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
R
Excerpted from Wikipedia’s “antisymmetric relation” article, available under the CC BY-SA 4.0 licence.