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Hilbert's Paradox and Time

  1. Jul 2, 2012 #1
    In Hilbert's paradox to accommodate a new guest you move guest 1 to room 2, guest 2 to room 3 and so on this will make space for a new guest. I assume that guest 1 has to wait for guest 2 to move to room 3 before he can move to room 2 thus all guests have to wait for guest n to move to room n+1. My question is that since there are infinite rooms the procedure of moving guests is infinite so does that mean that a room will never be made available?
  2. jcsd
  3. Jul 2, 2012 #2


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    Can't the hotel manager just yell out, "Attention!!! All guests out into the corridor! Quick march at my command to the room to your right - 1-2-3!!!"? :rofl:

    So the move can be synchronised perfectly without anyone needing to wait.

    You must also realise that this is purely a thought experiment, so practical considerations become meaningless. If you do manage to build a hotel with [itex]\aleph_0[/itex] rooms, let us know. :biggrin:
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