Definition
Hilbert's paradox of the Grand Hotel is a thought experiment which illustrates a counterintuitive property of infinite sets. It shows that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924–1925 lecture "Über das Unendliche", and was popularized through George Gamow's 1947 book One Two Three... Infinity.
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