Hilbert Hotel

Let a hotel have a Denumerable set of rooms numbered 1, 2, 3, .... Then any finitenumber of guests can be accommodated without evicting the current guests by moving the current guests from room to room . Furthermore, a Denumerable number of guests can be similarlyaccommodated by moving the existing guests from to , freeing up a Denumerablenumber of rooms .

References

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.

• Omega Function
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