Difference between revisions of "Well-Ordering Theorem"

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(That wasn't even a proper sentence, but I think this is what the author had in mind.)
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The '''Well-Ordering Theorem''' was proved by Zermelos in 1904, and it states:
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A place where nobody dared to go
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<blockquote>
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The love that we came to know
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''Every set can be well-ordered''.
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They call it Xanadu
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</blockquote>
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This result surprised [[mathematician]]s everywhere. The Well-Ordering Theorem is equivalent of the [[Axiom of Choice]], and no well-ordering relation has ever been explicitly constructed for [[uncountable set]]s. Thus, the mathematicians who reject the Axiom of Choice also reject this theorem.
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And now
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[[Category: set theory]]
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Open your eyes and see
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What we have made is real
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We are in Xanadu
 +
 
 +
A million lights are dancing
 +
And there you are
 +
A shooting star
 +
An everlasting world
 +
And you're here with me
 +
Eternally
 +
 
 +
Xanadu, Xanadu,
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(now we are here)
 +
In Xanadu
 +
Xanadu, Xanadu,
 +
(now we are here)
 +
In Xanadu
 +
 
 +
Xanadu, your neon lights will shine
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For you, Xanadu
 +
 
 +
The love
 +
The echoes of long ago
 +
You needed the world to know
 +
They are in Xanadu
 +
 
 +
The dream
 +
That came through a million years
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That lived on through all the tears
 +
It came to Xanadu
 +
 
 +
A million lights are dancing
 +
And there you are
 +
A shooting star
 +
An everlasting world
 +
And you're here with me
 +
Eternally
 +
 
 +
Xanadu, Xanadu,
 +
(now we are here)
 +
In Xanadu
 +
Xanadu, Xanadu,
 +
(now we are here)
 +
In Xanadu
 +
 
 +
Now that I'm here
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Now that you're near in Xanadu
 +
Now that I'm here
 +
Now that you're near in Xanadu
 +
Xanadu...

Revision as of 14:55, August 7, 2010

A place where nobody dared to go The love that we came to know They call it Xanadu

And now Open your eyes and see What we have made is real We are in Xanadu

A million lights are dancing And there you are A shooting star An everlasting world And you're here with me Eternally

Xanadu, Xanadu, (now we are here) In Xanadu Xanadu, Xanadu, (now we are here) In Xanadu

Xanadu, your neon lights will shine For you, Xanadu

The love The echoes of long ago You needed the world to know They are in Xanadu

The dream That came through a million years That lived on through all the tears It came to Xanadu

A million lights are dancing And there you are A shooting star An everlasting world And you're here with me Eternally

Xanadu, Xanadu, (now we are here) In Xanadu Xanadu, Xanadu, (now we are here) In Xanadu

Now that I'm here Now that you're near in Xanadu Now that I'm here Now that you're near in Xanadu Xanadu...

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