Richard's Paradox

It is possible to describe a set of positive integers that cannot be listed in a book containing a set of counting numbers on each consecutively numbered page. Another form of the paradox states that the set of all numerical functions is nondenumerable (Curry 1977).

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Church, A. "A Bibliography of Symbolic Logic." J. Symb. Logic 1, 121-218, 1936.Curry, H. B. Foundations of Mathematical Logic. New York: Dover, p. 6, 1977.Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 172-173, 1998.Richard, J. "Les principes des mathématiques et le problème des ensembles." Revue générale des sciences pures et appliquées 16, 541-543, 1905.Richard, J. "Lettre à Monsieur le rédacteur de la Revue générale des sciences." Acta Math. 30, 295-296, 1906.Richard, J. "Sur un paradoxe de la théorie des ensembles et sur l'axiome Zermelo." L'Enseignement math. 9, 94-98, 1907.

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Richard's Paradox

Cite this as:

Weisstein, Eric W. "Richard's Paradox." From MathWorld--A Wolfram Web Resource.

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