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Hilbert Hotel


Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the current guests from room i to room i+n. Furthermore, a denumerable number of guests can be similarly accommodated by moving the existing guests from i to 2i, freeing up the denumerable number of rooms 2i-1.


See also

Cardinal Number, Denumerable Set

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References

Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 84-85, 1998.Fadiman, C. Fantasia Mathematica, Being a Set of Stories, Together with a Group of Oddments and Diversions, All Drawn from the Universe of Mathematics. New York: Simon and Schuster, p. 286, 1958.Gamow, G. One, Two, Three, ... Infinity. New York: Dover, 1988.Hilbert, D. "Lectures on the Infinite." Ch. 4 in David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933 (Ed. W. Ewald and W. Sieg). New York: Springer, pp. 668-760, 2013.Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, p. 222, 1998.Lauwerier, H. "Hilbert Hotel." In Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, p. 22, 1991.Pappas, T. "Hotel Infinity." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 37, 1989.

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Hilbert Hotel

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Weisstein, Eric W. "Hilbert Hotel." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HilbertHotel.html

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