Difference between revisions of "Reflexivity"
From Encyclopedia of Mathematics
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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]]. | + | A property of binary relations. A [[binary relation]] $R$ on a set $A$ is called reflexive if $aRa$ for all $a\in A$. Regarding $R$ as a subset of $A \times A$, $R$ is reflexive if it contains the diagonal or identity relation $\Delta = \{(a,a) : a \in A \}$. Examples of reflexive relations are equality (cf [[Equality axioms]]), [[equivalence relation]]s, [[Order (on a set)|order]]. |
====References==== | ====References==== | ||
Revision as of 19:46, 15 November 2014
A property of binary relations. A binary relation $R$ on a set $A$ is called reflexive if $aRa$ for all $a\in A$. Regarding $R$ as a subset of $A \times A$, $R$ is reflexive if it contains the diagonal or identity relation $\Delta = \{(a,a) : a \in A \}$. 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=34531
Reflexivity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reflexivity&oldid=34531
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article