The cardinality of the integers, whole numbers, and rationals. See SetTheory and/or TransfiniteCardinality for more.

http://jeff560.tripod.com/aleph.gif is also known as aleph-null, aleph-zero.

See also SurrealNumbers by DonaldErvinKnuth
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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.

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CategoryMath