Editing Beth number (section)

=== Beth two ===
<math>\beth_2</math> (pronounced ''beth two'') is also referred to as <math>2^\mathfrak{c}</math> (pronounced ''two to the power of <math>\mathfrak{c}</math>'').

Sets with cardinality <math>\beth_2</math> include:

* the [[power set]] of the set of [[real number]]s, so it is the number of [[subset]]s of the [[real line]], or the number of sets of real numbers
* the power set of the power set of the set of natural numbers
* the set of all [[function (mathematics)|functions]] from <math>\mathbb{R}</math> to <math>\mathbb{R}</math> (<math>\mathbb{R}^\mathbb{R}</math>)
* the set of all functions from <math>\mathbb{R}^m</math> to <math>\mathbb{R}^n</math>
* the set of all functions from <math>\mathbb{R}</math> to <math>\mathbb{R}</math> with uncountably many discontinuities <ref name=":3"/>
* the power set of the set of all functions from the set of natural numbers to itself, or the number of sets of sequences of natural numbers
* the [[Stone–Čech compactification]]s of <math>\mathbb{R}</math>, <math>\mathbb{Q}</math>, and <math>\mathbb{N}</math>
* the set of deterministic [[fractal]]s in <math>\mathbb{R}^n</math> <ref name=":4">{{cite journal  |last=Soltanifar |first=Mohsen |year=2021 |title=A generalization of the Hausdorff dimension theorem for deterministic fractals |journal=Mathematics |volume=9 |issue=13 |page=1546 |arxiv=2007.07991 |doi=10.3390/math9131546 |doi-access=free }}</ref>
* the set of random [[fractal]]s in <math>\mathbb{R}^n</math>.<ref name=":5">{{cite journal |last=Soltanifar |first=Mohsen |year=2022 |title=The second generalization of the Hausdorff dimension theorem for random fractals |journal=Mathematics |volume=10 |issue=5 |page=706 |hdl=1807/110291 |hdl-access=free |doi=10.3390/math10050706 |doi-access=free }}</ref>