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

Famous quotes containing the words sets and/or greater:

    “A horse, a buggy and several sets of harness, valued in all at about $250, were stolen last night from the stable of Howard Quinlan, near Kingsville. The county police are at work on the case, but so far no trace of either thieves or booty has been found.”
    —H.L. (Henry Lewis)

    “There is not a greater paradox in nature,—than that so good a religion [as Christianity] should be no better recommended by its professors.”
    —Laurence Sterne (1713–1768)