Generators of Additive Group of Integers

Theorem
The only generators of the additive group of integers $$\left({\mathbb{Z}, +}\right)$$ are $$1$$ and $$-1$$.

Proof
From Integers Infinite Cyclic Group, $$\left({\mathbb{Z}, +}\right)$$ is an infinite cyclic group generated by $$1$$.

From Generators of Infinite Cyclic Group, there is only one other generator of such a group, and that is the inverse of that generator.

The result follows.