Hilbert's hotel: Difference between revisions
imported>Ragnar Schroder (→See also: Added link to existing article) |
imported>James Yolkowski m (sp) |
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By a similar procedure, any finite number of new arrivals may be accommodated. | By a similar procedure, any finite number of new arrivals may be accommodated. | ||
If an infinite number of strangers arrive, they may still be | If an infinite number of strangers arrive, they may still be accommodated. The procedure is similar to the finite case, except each current guest will be asked to move to the room with twice the current room number. | ||
All odd-numbered rooms will then become vacant, so the first new guest may move into the first odd-numbered room (1), the second into the second odd-numbered room (3), and so on. | All odd-numbered rooms will then become vacant, so the first new guest may move into the first odd-numbered room (1), the second into the second odd-numbered room (3), and so on. | ||
Revision as of 20:51, 3 April 2008
Hilbert's hotel is a humorous popularization of some mathematical paradoxes arising from transfinite set theory.
Introduction
The basic idea is that of a hotel with an infinite number of rooms - precisely one room for each positive integer.
It's sometimes visualized as an infinitely long corridor, with rooms numbered consecutively 1,2,3, ...
A stranger arriving at the reception when the hotel is full may get a room anyway. The management will simply send out an intercom asking every current guest to go out into the corridor, and then move into the room one step further down.
This way the first room will be left vacant for the new arrival.
By a similar procedure, any finite number of new arrivals may be accommodated.
If an infinite number of strangers arrive, they may still be accommodated. The procedure is similar to the finite case, except each current guest will be asked to move to the room with twice the current room number.
All odd-numbered rooms will then become vacant, so the first new guest may move into the first odd-numbered room (1), the second into the second odd-numbered room (3), and so on.
See also
Related topics