Aleph-one

Aleph-one is the set theory symbol \(\aleph_1\) for the smallest infinite set larger than \(\aleph_0\) (Aleph-zero), which in turn is equal to the cardinal number of the set of countable ordinal numbers. Retrieved 2021-07-31.
The continuum hypothesis asserts that \(\aleph_1=c\), where \(c\) is the cardinal number of the "large" infinite set of real numbers (called the continuum in set theory). However, the truth of the continuum hypothesis depends on the version of set theory you are using and so is undecidable.
Curiously enough, \(n\)-dimensional space has the same number of points (\(c\)) as one-dimensional space, or any finite interval of one-dimensional space (a line segment), as was first recognized by Georg Cantor.
== Sources ==
Category:Aleph numbers
Category:Transfinite ordinals