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Infinite Hotel Paradox
(lemmy.world)
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this post was submitted on 17 Feb 2025
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I've always hated this supposed paradox, because how is it possible for a hotel with infinite rooms to be full? Even with infinite guests, there will always be room for more. Because, you know, there are infinite rooms.
It's not always discussed as such, but Hilbert's Hotel is a mathematically well defined topic and can be proved rigorously. An infinite set of rooms can be the set x1, x2,...xinf, and people can be y1, y2...yinf. You can pair every entry in these two sets. x1&y1, x2&y2,...xinf&yinf. You can't number a room without having a person in the room, and you can't find a person who doesn't have a room.