Definition:Countable Set

An infinite set is described as countable if its elements can be placed in one-to-one correspondence with the elements of $\mathbb{N}$, that is, if it can be shown that it is possible to exhaustively number its elements.

The cardinality of a countable set is denoted by the symbol $$\aleph_0$$ ("aleph null").

From Infinite Set has Countable Subset it is seen that this is the "smallest" possible cardinality of an infinite set.