Infinite Hotel Paradox - Divisions by zero

cross-posted from: https://lemmy.world/post/25703033 [https://lemmy.world/post/25703033] > https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel [https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel]

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.
If there is no vacancy then the hotel has infinite full rooms and no empty ones.