nLab
reflexive relation

Contents

Definition

A (binary) relation \sim on a set AA is reflexive if every element of AA is related to itself:

(x:A),xx\forall (x: A),\; x \sim x

In the language of the 22-poset Rel of sets and relations, a relation R:AAR: A \to A is reflexive if it contains the identity relation on AA:

id AR\id_A \subseteq R

Last revised on December 2, 2012 at 20:17:53. See the history of this page for a list of all contributions to it.