Examples

• Addition in the set of whole numbers is an internal composition law in [latex]\mathbb{N}[/latex].
• Division in the set of integers is not an internal composition law in [latex]\mathbb{N}[/latex] because the results obtained are not all elements of [latex]\mathbb{N}[/latex].
• The multiplication of a vector by a real number (scalar) is an external composition law with results that are vectors.