Editing Beth number (section)

=== Beth one ===

{{main|cardinality of the continuum}}

Sets with cardinality <math>\beth_1</math> include:

* the [[transcendental numbers]]
* the [[irrational number]]s
* the [[real number]]s <math>\mathbb{R}</math>
* the [[complex number]]s <math>\mathbb{C}</math>
* the [[uncomputable real number]]s
* [[Euclidean space]] <math>\mathbb{R}^n</math>
* the [[power set]] of the [[natural number]]s <math>2^\mathbb{N}</math> (the set of all subsets of the natural numbers)
* the set of [[sequence]]s of integers (i.e., <math>\mathbb{Z}^\mathbb{N}</math>, which includes all functions from <math>\mathbb{N}</math> to <math>\mathbb{Z}</math>)
* the set of sequences of real numbers, <math>\mathbb{R}^\mathbb{N}</math> 
* the set of all [[real analytic function]]s from <math>\mathbb{R}</math> to <math>\mathbb{R}</math>
* the set of all [[continuous function]]s from <math>\mathbb{R}</math> to <math>\mathbb{R}</math>
* the set of all functions from <math>\mathbb{R}</math> to <math>\mathbb{R}</math> with at most countable discontinuities <ref name=":3">{{cite journal |last=Soltanifar |first=Mohsen |year=2023 |title= A classification of elements of function space F(R,R) |journal=Mathematics |volume=11 |issue=17 |page=3715 |doi=10.3390/math11173715 |doi-access=free |arxiv=2308.06297 }}</ref>
*the set of finite subsets of real numbers
*the set of all [[analytic function]]s from <math>\mathbb{C}</math> to <math>\mathbb{C}</math> (the [[holomorphic]] functions)
*the set of all functions from the natural numbers to the natural numbers (<math>\mathbb{N}^\mathbb{N}</math>).