Monday, February 28, 2011

In a hotel with infinite occupied rooms : Hilbert's paradox of the Grand Hotel

While watching BBC Horizon : To Infinity and Beyond a question is mentioned:
In a hotel with infinite rooms all of which are occupied. Can you accomodate a newly arriving guest?

The answer is yes. Since you can move guest in room 1 to room 2, Previous guest in room 2 to room 3, room 3 guest to room 4 and so on ... Ad infinitum.

What the episode on youtube. It is fun. 

I would assume that this would be fairly apparent to math majors:
http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

But nonetheless was new to me and and answer is easily discoverable if you have a firm grasp of infinity.