The cardinality of the integers, whole numbers, and rationals. See SetTheory and/or TransfiniteCardinality for more.
is also known as aleph-null, aleph-zero.
See also SurrealNumbers by DonaldErvinKnuth
An old math joke related to the concept:
AlephNought bottles of beer on the wall, AlephNought bottles of beer,
Take one down, pass it around, AlephNought bottles of beer on the wall.