The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.
Cantor's Paradox
See also
Cantor's Theorem, Power SetExplore with Wolfram|Alpha
References
Curry, H. B. Foundations of Mathematical Logic. New York: Dover, p. 5, 1977.Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 32-33, 1998.Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, pp. 257 and 295, 1997.Suppes, P. Axiomatic Set Theory. New York: Dover, pp. 9 and 118, 1972.Cite this as:
Weisstein, Eric W. "Cantor's Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CantorsParadox.html