# Godel Numbering

• Jan 14th 2010, 10:10 AM
jgrylls
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?
• Jan 14th 2010, 12:59 PM
HallsofIvy
Quote:

Originally Posted by jgrylls
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.
• Jan 15th 2010, 02:24 AM
jgrylls
yeah my bad, it had been a long day. So all it does is mean that nothing can be mistaken for anything else?
• Jan 16th 2010, 01:06 AM
HallsofIvy
"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.