Set in which an internal composition law.

### Examples

- The set of whole numbers is closed under addition and multiplication.

Any sum or product of whole numbers is a whole number.

Let*n*∈ \(\mathbb{N}\) and*p*∈ \(\mathbb{N}\). Then : ∀*n, p*∈ \(mathbb{N}\) : (*n*+*p*) ∈ \(\mathbb{N}\) and (*n × p*) ∈ \(\mathbb{N}\). - The set of whole numbers is not closed under subtraction and division.

Not all differences and quotients of whole numbers are whole numbers.

Let*n*∈ \(\mathbb{N}\) and*p*∈ \(\mathbb{N}\). Then : ∃*n, p*∈ \(\mathbb{N}\) : (*n*–*p*) ∉ \(\mathbb{N}\) and (*n ÷ p*) ∉ \(\mathbb{N}\).