Infinite Hotel Paradox

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

278 points · 11 comments · view on lemmy.world

11 Comments

Nougat@fedia.io · 42 pts · 1y (2 replies)

Ask all the guests in rooms >= 2 to move over one, then move into room 2.

There is always a vacancy.

tigeruppercut@lemmy.zip · 35 pts · 1y

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 ;)

marcos@lemmy.world · 13 pts · 1y

You will eventually reach a room with a worse situation than that one, and then your entire edifice falls apart again.

tetris11@lemmy.ml · 11 pts · 1y (2 replies)

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

kambusha@sh.itjust.works · 8 pts · 1y

In finite we trust.

Gloria@sh.itjust.works · 4 pts · 1y

Did you tip infinite?

jonc211@programming.dev · 9 pts · 1y (2 replies)

If they just have the guests stay in even numbered rooms, then they’ll always have an infinite number of rooms free.

palordrolap@fedia.io · 16 pts · 1y (1 reply)

Are they free if you can't put people in them?

Eheran@lemmy.world · 1 pts · 1y

Asking the real questions here.

affiliate@lemmy.world · 6 pts · 1y

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.

General_Effort@lemmy.world · 6 pts · 1y

I wonder if the world would be any different if Hilbert had never lived.