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.
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.
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