nLab
reflexive relation

Definition

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

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

In the language of the $2$-poset Rel of sets and relations, a relation $R:A\to A$ is reflexive if it contains the identity relation on $A$:

$${id}_A\subseteq R$$\id_A \subseteq R

Related concepts

• relation

  • reflexive relation, irreflexive relation

  • symmetric relation