High Quality Content by WIKIPEDIA articles! Hilbert's paradox of the Grand Hotel is a mathematical veridical paradox (a true result that is strongly counter-intuitive) about infinite sets presented by German mathematician David Hilbert (1862–1943). Consider a hypothetical hotel with countably infinitely many rooms, all of which are occupied – that is to say every room contains a guest. 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.

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