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Difference between revisions of "Reflexivity"

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A property of binary relations. A [[Binary relation|binary relation]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080590/r0805901.png" /> on a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080590/r0805902.png" /> is called reflexive if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080590/r0805903.png" /> for all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080590/r0805904.png" />. Examples of reflexive relations are equality, equivalence, order.
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A property of binary relations. A [[Binary relation|binary relation]] $R$ on a set $A$ is called reflexive if $aRa$ for all $a\in A$. Examples of reflexive relations are equality, equivalence, order.

Revision as of 21:04, 14 April 2014

A property of binary relations. A binary relation $R$ on a set $A$ is called reflexive if $aRa$ for all $a\in A$. Examples of reflexive relations are equality, equivalence, order.

How to Cite This Entry:
Reflexivity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reflexivity&oldid=11656
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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