Reflexive closure

In mathematics, the reflexive closure of a binary relation${\displaystyle R}$ on a set${\displaystyle X}$ is the smallest reflexive relation on ${\displaystyle X}$ that contains ${\displaystyle R}$, i.e. the set ${\displaystyle R\cup \{(x,x)\mid x\in X\}}$.

For example, if ${\displaystyle X}$ is a set of distinct numbers and ${\displaystyle xRy}$ means "${\displaystyle x}$ is less than ${\displaystyle y}$", then the reflexive closure of ${\displaystyle R}$ is the relation "${\displaystyle x}$ is less than or equal to ${\displaystyle y}$".