The mathematician David Hilbert is credited with the concept of an infinite hotel (or Grand Hotel, as he called it), a hotel with an infinite number of rooms. One afternoon, a man went to the desk and asked whether he could book a room for the night. As it turned out, all the rooms in the hotel were taken. The concierge, being a clever fellow, devised a scheme whereby the guest was given a room so that each guest had his or her own room. How did the concierge manage this?