Mind-Bending Math & GamesInfinity
Hilbert's Hotel
A full hotel with infinitely many rooms can always fit more guests
The sign says NO VACANCY: infinitely many rooms, all taken. A new guest walks in, then an endless busload. Where does everyone sleep?
You'll find out
- How a full hotel still has room
- Where an endless busload sleeps
- Whether every infinity is the same size
Why it matters
Infinity isn't just philosophy: it proves some problems can never be solved by any computer, however fast.
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