Identity element

In mathematics, an identity element, or neutral element, of a binary operation operating on a set is an element of the set that leaves unchanged every element of the set when the operation is applied.[1][2] 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 and multiplicative identity)[3] when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.

Contents
1 Definitions
2 Examples
3 Properties
4 See also