View source for Reflexivity

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A property of binary relations. A [[binary relation]] $R$ on a set $A$ is called reflexive if $aRa$ for all $a\in A$. 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====
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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>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  P. R. Halmos, ''Naive Set Theory'', Springer (1960, repr. 1974) {{ISBN|0-387-90092-6}} {{ZBL|0287.04001}}</TD></TR>
</table>

[[Category:Logic and foundations]]