Editing Cardinality of the continuum (section)

==Sets with greater cardinality==

Sets with cardinality greater than <math>{\mathfrak c}</math> include:

*the set of all subsets of <math>\mathbb{R}</math> (i.e., power set <math>\mathcal{P}(\mathbb{R})</math>)
*the set [[Power set#Representing subsets as functions|2<sup>'''R'''</sup>]] of [[indicator function]]s defined on subsets of the reals (the set <math>2^{\mathbb{R}}</math> is [[isomorphic]] to <math>\mathcal{P}(\mathbb{R})</math>&nbsp;– the indicator function chooses elements of each subset to include)
*the set <math>\mathbb{R}^\mathbb{R}</math> of all functions from <math>\mathbb{R}</math> to <math>\mathbb{R}</math>
*the [[Lebesgue measure|Lebesgue σ-algebra]] of <math>\mathbb{R}</math>, i.e., the set of all [[Lebesgue measurable]] sets in <math>\mathbb{R}</math>.
*the set of all [[Lebesgue integration|Lebesgue-integrable]] functions from <math>\mathbb{R}</math> to <math>\mathbb{R}</math>
*the set of all [[Measurable function|Lebesgue-measurable]] functions from <math>\mathbb{R}</math> to <math>\mathbb{R}</math>
*the [[Stone–Čech compactification]]s of <math>\mathbb{N}</math>, <math>\mathbb{Q}</math>, and <math>\mathbb{R}</math>
*the set of all automorphisms of the (discrete) field of complex numbers.

These all have cardinality <math>2^\mathfrak c = \beth_2</math> ([[Beth number#Beth two|beth two]])