At Wiki, we have:
The cardinality of the natural numbers is $\aleph_0$.
Also from Wiki, we have:
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets.
Q: Which axioms of ZFC are required to prove the existence of the cardinal number $\aleph _ 0$?