Math Investigation eTwinning. Mission: Infinity...Affairs! Volume: Infinity | Page 6

Hilbert’s Hotel
The Hilbert is the largest hotel in the world: it has infinitely many
rooms. We could imagine that it consists of just a single, never-ending
corridor, with the rooms numbered 1, 2, 3, 4 and so on. On the day we
arrive at the Hilbert, every single room in the Hotel is full. (Business is
going very well indeed…)
In any other Hotel, the reception would have to turn us away: if all the rooms are full there simply
isn’t space for us. Very surprisingly, this is not the case in the Hilbert…
Once we arrive and ask for a room, the hotel makes a loudspeaker announcement that can be heard
everywhere in the hotel: they ask all their guests to move up into the next room. Now the guest in
room 1 moves into room 2, the guest in room 2 moves into room 3, and the guest in any
room n moves into room n + 1. Since there is no last room in the hotel, every guest will get a new
room.

l

LYKEIO SCHIMATARIOY, GREECE

- VALLAURI FOSSANO, ITALY

Σελίδα 6