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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 relations, order.


[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, repr. 1974) ISBN 0-387-90092-6 Zbl 0287.04001
How to Cite This Entry:
Reflexivity. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article