Neutral element

In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often shortened to identity (as in the case of additive identity for 0 and multiplicative identity for 1) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.