In the universe Roomeron, there are infinitely many planets. Each planet has an infinite number of hotels, and each hotel has an infinite number of rooms. Since the business is so great, you decide to build a hotel of your own, also with an infinite number of rooms. To keep track of the rooms, each is numbered starting at 1. The hotels and planets are similarly numbered.

During the current tourist season, every room of every hotel, (including yours) on every planet is full. A freak catastrophe occurs in every other hotel besides yours and their rooms become trashed. The guests from those hotels ask to stay in your unwrecked hotel.

How can you put the infinitely many guests from infinitely many hotels from infinitely many planets in your already full hotel?

(In reply to re(3): But... by Gamer)

Why, then you'll need an infinite amount of them, to enable your infinite guests to travel in a finite amount of time. And since each elevator takes up space, together they'll take up an infinite amount of space, leaving no room for guests. =(
Or maybe there will still be room? Infinity minus infinity is an unknown amount, right? Argh...

But anyway, you can't have infinitely fast elevators - they can never move faster than the speed of light!
Great, now I'm trying too hard to make sense, which rather defeats the purpose of the problem. Okay, you win. =P

Posted by TamTam on 2007-01-29 17:33:49