Dear Russell: At 4/13/01, you wrote: >Bounded complexity does not imply bounded length. Examples include an >infinite sting of '0's, and the string '1234...9101112...'
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 >set of axioms contains no more information (or complexity) than is >contained in the set of axioms itself. However, as pointed out, this >doesn't imply the theorems are bounded in length, merely that their >complexity is bounded. > >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
