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or antisymmetrical

[an-tee-si-me-trik or an-tee-si-me-tri-kuh l; an-tahy-] /ˌæn ti sɪˈmɛ trɪk or ˌæn ti sɪˈmɛ trɪ kəl; ˌæn taɪ-/
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.”.
Origin of antisymmetric
1920-25; anti- + symmetric Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2017.
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British Dictionary definitions for antisymmetric


(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)
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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antisymmetric in Technology

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
x R y => x == y
I.e. different elements are not related.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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