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## Main Question or Discussion Point

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?