Cardinality of The Continuum - Sets With Greater Cardinality

Sets With Greater Cardinality

Sets with cardinality greater than include:

  • the set of all subsets of (i.e., power set )
  • the set 2R of indicator functions defined on subsets of the reals (the set is isomorphic to – the indicator function chooses elements of each subset to include)
  • the set of all functions from to
  • the Lebesgue σ-algebra of, i.e., the set of all Lebesgue measurable sets in .
  • the Stone–Čech compactifications of, and
  • the set of all automorphisms of the field of complex numbers.

They all have cardinality (Beth two).

Read more about this topic:  Cardinality Of The Continuum

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