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# Antisymmetric

noting a relation in which one element’s dependence on a second implies that the second element is not dependent on the first, as the relation “greater than.”.
adjective
(logic) (of a relation) never holding between a pair of arguments x and y when it holds between y and x except when x = y, as “…is no younger than…” See nonsymmetric
(maths) symmetric except for a change of sign Compare asymmetric, symmetric (sense 1)
mathematics
A relation R is antisymmetric if,
for all x and y, x R y and y R x => x == y.
I.e. no two different elements are mutually related.
Partial orders and total orders are antisymmetric. If R is also symmetric, i.e.
x R y => y R x
then
x R y => x == y
I.e. different elements are not related.
(1995-04-18)

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