On Fri, 2007-02-16 at 14:55 -0600, Mike McCarty wrote: > Celejar wrote: > > > > In Hilbert's hotel, when all the rooms are full and a new guest > > arrives, the management just moves everyone down one room and places > > the newcomer into the first room, which is now vacant. > > When a countably infinite number of new guests arrive, he accomodates > them by moving each current guest into the room with the number > 2x his current, so guest in room 1 goes to room 2, guest in room > 2 goes to room 4, etc. This frees up rooms 1, 3, 5, 7, etc., > into which he places the new guests, by placing guest n into > room with number 2n-1, so guest 1 goes into room 1, guest 2 > goes into room 3, etc. > > Ask me about the machine and the ping pong balls some time.
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