Reflexive relation

Definition

Let $R$ be a binary relation on a set $A$. The relation $R$ is reflexive when $a \mathrel{R} a$ for each $a \in A$.

Remarks

On $\mathbb{R}$, the relation $\le$ is reflexive and the relation $<$ is not. A relation is irreflexive when no element is related to itself. Reflexivity is one of the conditions for an equivalence relation and for a partial order.

Explanations

L1 human

In the graph of a reflexive relation, each point has a loop to itself. "Has the same birthday as" is reflexive, because each person has the same birthday as themselves.