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: But... by Gamer)

Even if all the room numbers are finite, you can always choose a number that will make it unreasonable. Let's say a million kilometers is unreasonable? And we'll say that the distance between each room is a meter. In that case, the guy living in room #1000000000 needs to travel a million kilometers to room #2000000000, which we've decided is unreasonable.

So unless this hotel is equipped with teleportation technology, I'm afraid we have a problem.

Posted by TamTam on 2007-01-28 04:56:46