# 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 $\mu$, we denote the $\mu$th aleph as $\aleph_\mu$.

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

Revised on October 17, 2012 11:05:39 by Toby Bartels (75.88.85.197)