Definition:Additive Group of Integers

Theorem
The additive group of integers $\left({\Z, +}\right)$ is the set of integers under the operation of addition.

Also see

 * Integers under Addition form Countably Infinite Abelian Group

Thus integer addition is:


 * Well-defined on $\Z$
 * Closed on $\Z$
 * Associative on $\Z$
 * Commutative on $\Z$
 * The identity of $\left({\Z, +}\right)$ is $0$
 * Each element of $\left({\Z, +}\right)$ has an inverse.