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:
“In the beautiful, man sets himself up as the standard of perfection; in select cases he worships himself in it.... Man believes that the world itself is filled with beautyhe forgets that it is he who has created it. He alone has bestowed beauty upon the worldalas! only a very human, an all too human, beauty.”
—Friedrich Nietzsche (18441900)
“... the reason I keep doing it is for the tremendous rush I get at the end of any great swim.... there is ... nothing greater than touching the shore after crossing some great body of water knowing that Ive done it with my own two arms and legs.... Im overwhelmed by the strength of my body and the power of my mind. For one moment, just one second, I feel immortal.”
—Diana Nyad (b. 1949)