# antisymmetric relation

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## antisymmetric relation

[‚ant·i·si¦me·trik ri′lā·shən]
(mathematics)
A relation, which may be denoted ∈, among the elements of a set such that if ab and ba then a = b.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Then, it is an antisymmetric relation; that is, x [[greater than or equal to].sub.[mu]] y and y [[greater than or equal to].sub.[mu]] y implies x = y for any functions x, y on N.
All I will say is that an orthomodular lattice is a special sort of partially ordered set, where a partially ordered set is an ordered pair <A, [less than or equal to] >, where A is a non-empty set and [less than or equal to] is a reflexive, transitive, antisymmetric relation defined on A.
Lemma 2.7 Let [less than or equal to] [sub.1] and [less than or equal to] [sub.2] be two antisymmetric relations on A such that a [less than or equal to] [sub.2] b implies [[not less than or equal to].sub.1] or b = a.

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