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From: Hal Ruhl <hjr.domain.name.hidden>

Date: Thu, 12 Apr 2001 21:21:41 -0700

Dear Russell:

At 4/13/01, you wrote:

*>Bounded complexity does not imply bounded length. Examples include an
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*>infinite sting of '0's, and the string '1234...9101112...'
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That was part of the old debate and one of my initial mistakes. I am not

now talking about the length of theorems but the length of their proofs.

*>It must be true that the set of all theorems derivable from a finite
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*>set of axioms contains no more information (or complexity) than is
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*>contained in the set of axioms itself. However, as pointed out, this
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*>doesn't imply the theorems are bounded in length, merely that their
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*>complexity is bounded.
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*>
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*>Does this shed light on this issue?
*

With this I agree. There are however only a finite number of theorems

with a finite complexity. So number theory is either finite in theorem

count or it is infinite in complexity.

Hal

Received on Thu Apr 12 2001 - 18:26:57 PDT

Date: Thu, 12 Apr 2001 21:21:41 -0700

Dear Russell:

At 4/13/01, you wrote:

That was part of the old debate and one of my initial mistakes. I am not

now talking about the length of theorems but the length of their proofs.

With this I agree. There are however only a finite number of theorems

with a finite complexity. So number theory is either finite in theorem

count or it is infinite in complexity.

Hal

Received on Thu Apr 12 2001 - 18:26:57 PDT

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