Another thing that can be done with this imaginary hotel is to double the number of people inside, again when all the rooms are already full. This is done by asking each guest to multiply their room number by two and move to that room. (If their previous room number was "n", this time they would move to room number "2n".) This would send the guest in room 1 to room 2, the guest in room 2 to room 4, the guest in room 3 to room 6, the guest in room 4 to room 8, and so on. After finishing, we find that all the rooms with the odd numbers are empty. Then we can put an infinite number of guests into these empty rooms. Now the number of guests in the hotel has been doubled without making the hotel bigger.
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