Hilbert’s hotel
The hotel has infinitely many rooms, all of them taken. Choose what to ask the guests so that you can fit in the newcomers.
The experiment starts as soon as the page has loaded (JavaScript is required).
Try the experiment: your result will appear here, next to what most people do.
What just happened (read it after the experiment)
What most people do: Most people first suggest the “last room.” There isn’t one.
One visitor? Every guest moves to the next room: room 1 is freed up. An infinite busload? Every guest moves to the room with double their number: all the odd-numbered rooms are freed up.
David Hilbert told this story in 1924 to show that an infinite set can have as many elements as one of its parts: there are as many even numbers as there are whole numbers.
Infinity doesn’t behave like a very large number.
More experiments
Sources
- David Hilbert, 1924 lecture; George Gamow, One Two Three… Infinity, 1947.