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'Hilbert's Hotel'
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| Title of object: |
Hilbert's Hotel |
| Canonical Name: |
HilbertsHotel |
| Type: |
Topic |
| Created on: |
2004-04-19 03:27:25 |
| Modified on: |
2004-04-19 16:03:08 |
| Classification: |
msc:26A12 |
Revision comment (for changes between this and next version):
| Changes for correction #4284 ('Minor stuff'). |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
The hotel manager D. Hilbert had a very large hotel, in fact, there were an infinite number of rooms. The hotel was very popular and every room was occupied. One day a new guest arrived.
-Is there any \PMlinkescapeword{free} room?
-No ..., said Mr Hilbert.
-Oh, what a pitty, the guest said and started to walk away.
-But you can still get a room.
The new guest was very confused by this and asked how that could be possible.
-I'll just ask the guest in room number 1 to move to room number 2, the guest in number 2 moves to room 3, the guest in room 3 moves to room number 4, and so on and so forth, and then you can have room number 1.
The guest was very happy with this and called all his friends to tell them all about this fantastic hotel. Then one day they all arrived at the same time.
-Hello, we are an infinite number of people, and we wish a room each.
Mr Hilbert felt reluctant to ask each guest to move to a new room an infinite number of times, that would be very unplessant, and they will never finish either.
But he got a brilliant idea,
-I'll let guest in number 1 move into number 2, guest in number 2 move into number 4, guest in number 3 move into number 6, number 4 to number 8 and so on.
Then you can move into any room with an odd number, they will all be \PMlinkescapeword{free}, and there will be sufficient with rooms for all of you.
And all the new guests got a room on their own. |
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