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(4): But...
atheron originally had the intention of posting this under the category of 'Paradoxes'.
I'm not suggesting that I am versed in this area of Maths in the least, but this arises from the work of the mathematicians Cantor and Hilbert. You might care to follow this further by researching their names.
Yes, it does seem somewhat paradoxical that you can perform operations on an infinite amount which yields yet another infinite amount.
I leave this to you, and/or those more versed to offer explanations short of the official solution.
Posted by brianjn
on 2007-01-31 01:01:52