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Difference between revisions of "Reflexivity"

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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 (cf [[Equality axioms]]), [[equivalence relation]]s, [[Order (on a set)|order]].
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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 (cf [[Equality axioms]]), [[equivalence relation]]s, [[Order (on a set)|order]].
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====References====
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  R. Fraïssé, ''Theory of Relations'', Studies in Logic and the Foundations of Mathematics, Elsevier (2011) ISBN 0080960413</TD></TR>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  P. R. Halmos, ''Naive Set Theory'', Springer (1960) ISBN 0-387-90092-6</TD></TR>
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</table>
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[[Category:Logic and foundations]]

Revision as of 18:46, 19 October 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 (cf Equality axioms), equivalence relations, order.

References

[a1] R. Fraïssé, Theory of Relations, Studies in Logic and the Foundations of Mathematics, Elsevier (2011) ISBN 0080960413
[a2] P. R. Halmos, Naive Set Theory, Springer (1960) ISBN 0-387-90092-6
How to Cite This Entry:
Reflexivity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reflexivity&oldid=33961
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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