I checked out your website, it’s full of a bunch of nonsense and technical jargon thrown together in an apparent attempt to blind the reader, and awful grammar, mixed with whimsical, irrelevant analogies. In the particular case of your comment here, no, that does not follow at all from Godel’s Incompleteness Theorem. What you are saying is ambiguous, or seems so to me. No, there are no additional dependencies, all the dependencies are laid out in the axioms that define Peano Arithmetic. Yes, there are additional interesting mutual connection such as the prime numbers, however all of these interesting connections are built up from the basic axioms. We define new operations that are distinct and consistent that are based on the axioms to make things more convenient for us, but we could write it out using just the operators and properties used to define the axioms if we really had the desire to. Godel’s work on incompleteness requires self-reference, which is absent in Peano Arithmetic, and doesn’t arise until we define new operations upon the set defined by Peano Arithmetic. Perhaps you are groping towards the fact that the Natural Numbers are not a complete set of the Real Numbers because of the existence of the Division operation, i.e. 4/7 is not a Natural Number?

]]>Anatraj, there are only countably many (polynomial time or not) computable functions. Because there are only countably many Turing Machines that compute them.

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