If an operation * is defined on a set E, then

*n*is a neutral element of the operation * if and only if*x * n = x*for all*x*in E.### Properties

- The number 0 is the identity element for addition on the set of whole numbers.

\(3 + 0 = 3\)

\(0 + 12 = 12\)

- The number 1 is the identity element for multiplication on the set of whole numbers.

\(3 × 1 = 3\)

\(12 × 1 = 12\)

### Examples

- The whole number 0 is the identity element for addition in \(\mathbb{R}\) :

\(5.6 + 0 = 0 + 5.6 = 5.6\).

- The whole number 1 is the identity element for multiplication in \(\mathbb{R}\) :

\(5.6 × 1 = 1 × 5.6 = 5.6\).