nLab aleph

An aleph (ℵ) is the cardinality of an infinite well-ordered (or well-orderable) set. Assuming the axiom of choice (in the guise of the well-ordering theorem), every cardinal number is either a natural number or an aleph.

The alephs are themselves well-ordered; for an ordinal number μ\mu, we denote the μ\muth aleph as μ\aleph_\mu.

In particular 0\aleph_0 is the the cardinality of the set of natural numbers.

Last revised on October 17, 2012 at 11:05:39. See the history of this page for a list of all contributions to it.