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Math Help - Godel Numbering

  1. #1
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    Godel Numbering

    Im am trying to give a brief descrition to the proof of godels in completeness theorems. How did the use of godel numbering help with the proof. I know its got something to do with the fundmentle theorem of arithmetic and the fact every number can be written as a sum of primes but how did this help?
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  2. #2
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    Quote Originally Posted by jgrylls View Post
    Im am trying to give a brief descrition to the proof of godels in completeness theorems. How did the use of godel numbering help with the proof. I know its got something to do with the fundmentle theorem of arithmetic and the fact every number can be written as a sum of primes but how did this help?
    Writing a number as a "sum of primes" has nothing at all to do with this! The fundamental theorem of arithmetic says that every positive integer can be written, in a unique way, as a product of primes. And the point of that is to show that every symbol in your symbolic logic, every statement, every, proof of a statement, can be assigned a unique positive integer.
    Last edited by HallsofIvy; January 16th 2010 at 02:05 AM.
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    yeah my bad, it had been a long day. So all it does is mean that nothing can be mistaken for anything else?
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  4. #4
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    "All" is a large term. I will repeat what I said before: every symbol in your symbolic logic, every statement, every, proof of a statement, can be assigned a unique positive integer.
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