Reflexive property

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A binary relation $\mathcal R$ on a set $S$ is said to be reflexive or to have the reflexive property if $a{\mathcal R}a$ for all $a \in S$.

For example, the relation of similarity on the set of triangles in a plane is reflexive: every triangle is similar to itself. However, the relation $\mathcal R$ on the real numbers given by $x {\mathcal R} y$ if and only if $x < y$ is not reflexive because $x < x$ does not hold for at least one real value of $x$. (In fact, it does not hold for any real value of $x$, but we only need the weaker statement to disprove reflexivity.)

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