Ask all the guests in rooms >= 2 to move over one, then move into room 2.
There is always a vacancy.
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 ;)
You will eventually reach a room with a worse situation than that one, and then your entire edifice falls apart again.
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?
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?
Asking the real questions here.
i’d ask them to label their rooms with ordinal numbers instead of cardinal numbers, and then i’d move into room ∞ + 1 (i.e., ω + 1). everybody else can stay where they are.
I wonder if the world would be any different if Hilbert had never lived.
