# Identity

The Identity or Identity element is a special element of a set under a binary operation which when combined with any element of a set results in the same element.

Normally denoted by e.

If in a set A under a binary operation * there exists an element e such that for all a $\in\$ A then a * e = a then e is called the identity element.

Some care has to be taken if the operation is non-commutative when the definition above specifically defines what is called the right-identity.

The left identity is defined as that element such that for all a $\in\$ A then e * a = a.

The identity element of the set of integers under the binary operation of addition is the number zero.