# Internal Composition Law on a Set E

## Internal Composition Law on a Set E

Consider a set E; any application of E × E on E is called an internal composition law on E.

The results of an internal composition law are also elements of E.

### Examples

• Addition on the set of whole numbers is an internal composition law on $$\mathbb{N}$$.
• Division on the set of integers is not an internal composition law on $$\mathbb{N}$$, since the results obtained are not all elements of $$\mathbb{N}$$.