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Definition

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

$\forall \left(x:A\right),\phantom{\rule{thickmathspace}{0ex}}x\sim x$\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