antisymmetric

antisymmetric

[an-tee-si-me-trik, an-tahy-]
adjective Mathematics.
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.”
Also, antisymmetrical.


Origin:
1920–25; anti- + symmetric

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antisymmetric (ˌæntɪsɪˈmɛtrɪk)
 
adj
1.  logic See nonsymmetric (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…"
2.  maths asymmetric Compare symmetric symmetric except for a change of sign

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Computing Dictionary

antisymmetric definition

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)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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