Now, a very clever or annoying student asks, “What happens if an

00 185 Now, a very clever or annoying student asks, “What happens if an infinite number of infinitely large buses arrive at the hotel. Can they all fit in?” The mathematical question is “does infinity times infinity, equal infinity?” Let us ask all the guests to get out of the bus and line up in the parking lot in neat rows. Passengers from bus one in line 1, those from bus 2 in line 2, and so on. All the guests now form a two-dimensional grid. We already know how to map a two-dimensional grid to one- dimension using the zigzag method. We can fit them all in the hotel and we are done! Is Anything Larger than Infinity? Is there any bus or combination of buses that would cause the manager of Hilbert’s Hotel a problem. The answer is yes and it involves a subtle change to the contents of the bus. An infinite number of buses turn up but this time the buses are filled with men and women. The hotel manager is asked to put everyone in a room and once again he obliges using the zigzag method. At the end of the process the tour guide comes to him. “I think you have missed some people,’ he says. “Since I am just one person, I know you can fit me in. But, I have a whole bus in the car park you completely missed.” “No,” says the manager. “I did every bus.” Infinity Plus Infinity Equals Infinity HOUSE_OVERSIGHT_015875