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 $0$.