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 [latex]\mathbb{N}[/latex].
- Division on the set of integers is not an internal composition law on [latex]\mathbb{N}[/latex], since the results obtained are not all elements of [latex]\mathbb{N}[/latex].