Hilbert’s Infinite Hotel Paradox

Hilbert’s paradox of the Grand Hotel, or simply Hilbert’s hotel, is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and that this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924 lecture

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