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Infinite Hotel Paradox (lemmy.world)
submitted 4 months ago by cyrano@lemmy.dbzer0.com to c/science_memes@mander.xyz
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cross-posted from: https://lemmy.world/post/25703033

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

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[-] Psythik@lemm.ee 24 points 4 months ago

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.

[-] expr@programming.dev 12 points 4 months ago

It has to do with countably infinite sets.

The analysis on Wikipedia does a better job of explaining the concept: https://en.m.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel#Analysis

The whole point is that it's something we can prove mathematically that is highly unintuitive.

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this post was submitted on 17 Feb 2025
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