# Identity Element

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Definition
 Identity Element Let $S$ be a set with binary operation "*",then $e$ is said to be an identity element of $S$ if $a*e=a=e*a$ for any element $a$ of the set $S$

## Examples

Let $S$ be a set of natural numbers with addition "+" as binary operation then $0$ is the identity element of set $S$ because
$5+0=5=0+5$

$45+0=45=0+45$