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Comment by inportb | Hacker News Reader

    a hotel with an infinite number of rooms, all of which are currently occupied

So you have an infinite number of occupied rooms. That is, you have a one-to-one mapping between rooms and parties.

Do you have room for more guests? I don't think so, because none of the rooms are unoccupied. You could try to free up some space by consolidating parties, though.

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You don't have to consolidate, just move people: move the occupants of room n to room 2n and now you have infinitely many empty rooms (all the odd-numbered ones).

... which would consolidate the occupants of rooms n and 2n (and there are people in room 2n to begin with, if all of the rooms are indeed currently occupied).

edit: I see that the folks in 2n would now be in 4n, and so on down the chain. You'd always have some guests that are in the process of being evicted (i.e. between rooms); then again, that's negligible because we're not talking about real life (™). Clever!

If you move every guest from n to 2n, all of the odd rooms will open up, and you have room for a countably infinite number of new guests.

I believe David Hilbert was the first to describe this paradox. Source: http://en.m.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gr...

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