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

Revised on December 2, 2012 20:17:53 by Urs Schreiber (82.113.106.154)