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Date: 14-2-2017
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Let and be any sets, and let be the cardinal number of a set . Then cardinal exponentiation is defined by
(Ciesielski 1997, p. 68; Dauben 1990, p. 174; Moore 1982, p. 37; Rubin 1967, p. 275, Suppes 1972, p. 116).
It is easy to show that the cardinal number of the power set of is , since and there is a natural bijection between the subsets of and the functions from into .
REFERENCES:
Ciesielski, K. Set Theory for the Working Mathematician. Cambridge, England: Cambridge University Press, 1997.
Dauben, J. W. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton, NJ: Princeton University Press, 1990.
Moore, G. H. Zermelo's Axiom of Choice: Its Origin, Development, and Influence. New York: Springer-Verlag, 1982.
Rubin, J. E. Set Theory for the Mathematician. New York: Holden-Day, 1967.
Suppes, P. Axiomatic Set Theory. New York: Dover, 1972.
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