Aleph-1, denoted 
,
is the smallest uncountable cardinal number. Equivalently,
it is the cardinal number of the set
of all countable ordinal numbers. It is strictly
larger than 
(Aleph-0), the cardinal
number of every countably infinite set.
The continuum hypothesis asserts that 
, where 
is the cardinal number
of the "large" infinite set
of real numbers (called the continuum
in set theory). The continuum
hypothesis is independent of Zermelo-Fraenkel
set theory together with the axiom of choice,
provided those axioms are consistent. Consequently, those axioms alone do not determine
whether 
is the cardinal
number of the real numbers.
Curiously enough, 
-dimensional
space has the same number of points (
) as one-dimensional space, or any
finite interval of one-dimensional
space (a line segment),
as was first recognized by Georg Cantor.
