A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers. In other words, one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.

Are all infinite sets countably infinite?

An infinite set that can be put into a one-to-one correspondence with N is countably infinite. Finite sets and countably infinite are called countable. An infinite set that cannot be put into a one-to-one correspondence with N is uncountably infinite.

Is Z countably infinite?

The set Z of integers is countably infinite.