A given [[Binary Operation|binary operation]] $\circ$ on a [[Set|set]] $S$ has the [[Identity Property]] if [[Existential Quantifier|there exists]] en identity element $e$ such that $\circ$ with any $a\in S$ yields $a$. $\huge \forall a \in S ; a\circ e = a $ The identity element $e$ is considered the left-identity if it is the identity when being applied to the left, $\huge e \circ a = a $ While it is considered the right-identity if it works to the right, $\huge a \circ e = a $