Hilbert’s hotel has rooms numbered 1, 2, 3, 4, 5, . . . – one room for each positive integer. Guests are sometimes asked to move rooms, but never more than once a day. Guests are never asked to share a room with anyone else, and guests are never turned away. Guests often arrive to Hilbert’s hotel in one of his special buses. Each bus holds passengers numbered 1, 2, 3, 4, 5, . . . – one passenger for each positive integer. 1. Our story opens with Hilbert’s hotel empty. A bus full of guests arrive at Hilbert’s hotel. (a) How can Hilbert assign people to rooms?