Definition:Additive Monoid of Natural Numbers

Definition

The additive monoid of natural numbers $\left({\N, +}\right)$ is the set of natural numbers under the operation of addition.

Also see

• Natural Numbers under Addition form Commutative Monoid

Thus natural number addition is:

• Well-defined on $\N$
• Closed on $\N$
• Associative on $\N$
• Commutative on $\N$
• The identity of $\left({\N, +}\right)$ is $0$.