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Hilbert's paradox of the Grand Hotel
Hilbert's paradox of the Grand 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 and was popularized through George Gamow's 1947 book ''One Two Three... Infinity''.
==The paradox==
Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms, where the pigeonhole principle would apply.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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