Hilbert’s Hotel

Always room for more

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A full infinite hotel can still take new guests by shifting everyone along.
• Moving guests from room n to room 2n frees infinitely many rooms.
• Even infinitely many infinite buses fit. Infinity works differently.

Steps

1. No vacancies?
2. An infinite bus
3. The night manager’s plans
4. Which room?
5. Infinitely many buses
6. Bus 1, seat 2