# Identity Element

## Identity Element

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 $$\mathbb{R}$$ :

$$5.6 × 1 = 1 × 5.6 = 5.6$$.