Identity Element

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Definition

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

Examples

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

[math]45+0=45=0+45[/math]