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.
[latex]3 + 0 = 3[/latex]
[latex]0 + 12 = 12[/latex]
- The number 1 is the identity element for multiplication on the set of whole numbers.
[latex]3 × 1 = 3[/latex]
[latex]12 × 1 = 12[/latex]
Examples
- The whole number 0 is the identity element for addition in [latex]\mathbb{R}[/latex] :
[latex]5.6 + 0 = 0 + 5.6 = 5.6[/latex].
- The whole number 1 is the identity element for multiplication in [latex]\mathbb{R}[/latex] :
[latex]5.6 × 1 = 1 × 5.6 = 5.6[/latex].