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Reflexive relation
(Redirected from Irreflexive relation)
In logic and mathematics, a binary relation R over a set X is reflexive if for all a in X, a is related to itself.
In mathematical notation, this is:
A relation that is not reflexive is irreflexive.
For example, "is greater than or equal to" is a reflexive relation but "is greater than" is irreflexive.
Other examples of reflexive relations include:
- "is equal to" (equality)
- "is a subset of" (set inclusion)
- "is less than or equal to" and "is greater than or equal to" (inequality)
- "divides" (divisibility)
A reflexive relation that is also transitive is a preorder. A preorder that is antisymmetric is a partial order. A preorder that is symmetric is an equivalence relation.
The statement
is called the axiom of equality in some systems.
Last updated: 10-08-2005 03:45:52
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details