On: Does infinity exist?

[inportb]

... 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!

[soccerniru → inportb]

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...