Generators of Infinite Cyclic Group

Theorem
Let $$\left \langle {g} \right \rangle = G$$ be a infinite cyclic group.

Then the only other generator of $$G$$ is $$g^{-1}$$.

Proof
The fact that $$g^{-1}$$ does indeed generate $$G$$ comes from Cyclic Group Generator is Not Unique.

Now we need to prove that $$g, g^{-1}$$ are the only elements that generate $$G$$.