Hilbert's Infinite Hotel

Every room is full. A new guest arrives. No problem. Then a bus pulls up with infinitely many more.

David Hilbert's hotel has infinitely many rooms and no vacancies, yet it can always take more guests. Check in a new guest, unload an infinite bus, and find the one bus that will never fit.

Steps

1. A Full Hotel
2. The Infinite Bus
3. Infinitely Many Buses
4. What Cantor Saw
5. The Bus That Doesn't Fit
6. Bigger Infinities