If they just have the guests stay in even numbered rooms, then they’ll always have an infinite number of rooms free.
Are they free if you can’t put people in them?
I wonder if the world would be any different if Hilbert had never lived.
Ask all the guests in rooms >= 2 to move over one, then move into room 2.
There is always a vacancy.
You will eventually reach a room with a worse situation than that one, and then your entire edifice falls apart again.
Then housekeeping has to re-clean infinite rooms before everyone can resettle, which only works if you have infinite cleaners. Just walk down to the infinite + 1 room and no one has to move ;)
I once brought infinite* baggage to the infinite hotel. I was told to leave an infinite** amount of times, but I have an infinite** amount of time to wait in at the hotel lobby bar, drinking infinite** beers, until the infinite* taxi’s arrive.
* = levels of infinity
In finite we trust.
Did you tip infinite?
