Identity Relation

If a relation on A is given by $aRa$ for EVERY $a\in A$ — that is, the relation consists exactly of the pairs $\{(a,a)/a\in A\}$ (sometimes called the DIAGONAL subset of $A\times A$) — this is called the IDENTITY RELATION on A. In words: $aRb$ exactly when $b=a$, and nothing else. It relates every element only to itself, and to no other element. …