 For example, consider a hotel with a countably infinite number of rooms. One night when the hotel is completely occupied, a traveler shows up and asks for a room. “No problem,” the receptionist replies, “there’s plenty of space!” The first occupant then moves to the second room, the second to the third room, the third to the fourth room, and so on all the way up. The result is a hotel that has gone from being completely occupied to having one room free, and the traveler can stay the night after all. This supertask was described in a 1924 lecture by David Hilbert, as reported by Gamow (1947).