Cantor's Theorem -- from Wolfram MathWorld
- ️Weisstein, Eric W.
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The cardinal number of any set is lower than the cardinal number of the set of all its subsets.
A corollary is that there is no highest 
(aleph).
See also
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References
Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, pp. 257 and 295, 1997.Suppes, P. Axiomatic Set Theory. New York: Dover, p. 97, 1972.
Cite this as:
Weisstein, Eric W. "Cantor's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CantorsTheorem.html