Exhibit a bijective function $\Bbb Z \to \Bbb Z$ with infinitely many orbits I've the following exercise:

Give an example of a bijective function $\Bbb Z\rightarrow\Bbb Z$ with infinitely many orbits.

What would be its infinite orbits?

HINT: Recall that there is a bijection between $\Bbb Z$ and $\Bbb{Z\times Z}$. Can you find a bijection $f\colon\Bbb{Z\times Z\to Z\times Z}$ with infinitely many infinite orbits?
