this post was submitted on 17 Feb 2025
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Infinite Hotel Paradox (lemmy.world)
submitted 6 days ago by [email protected] to c/[email protected]
39 comments fedilink hide all child comments
 

cross-posted from: https://lemmy.world/post/25703033

https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

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[–] [email protected] 15 points 5 days ago

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.