# Reflexivity

From Encyclopedia of Mathematics

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, repr. 1974) ISBN 0-387-90092-6 Zbl 0287.04001 |

**How to Cite This Entry:**

Reflexivity.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Reflexivity&oldid=54507

This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article