Moving Guests to occupied rooms Because the hotel has infinite rooms we can move any guest occupying any room n to room n 1 then fit the newcomer into room 1 No we can t Room n 1 is already occupied as are all rooms by definition Any room in the hotel has occupied as descriptor as per condition of the problem a hypothetical hotel with a countably infinite number of rooms all of which are occupied So whatever number we call any particular room be it n 1 n 2 n 3 or any other it does not change the room s occupied status Therefore we can t move a guest from an occupied room to an occupied room to make room for more guests