Re: Complexity Theory for Simpletons (Collatz)
- From: Bryan Olson <fakeaddress@xxxxxxxxxxx>
- Date: Sat, 01 Apr 2006 03:14:34 GMT
Craig Feinstein wrote:
I respect your opinion that I need to provide more explanation for the
above statement. Based on our discussion in this newsgroup, I think
it's fair to say that our entire argument in this thread is really the
question of how much explanation is required in a mathematical argument
for the argument to be considered valid.
I see the proofs as misguided; the holes unfillable.
I remember my attempt, years ago, to prove the Collatz conjecture.
I began with the line:
If the conjecture is false, then there exists a smallest
n for which the sequence does not hit 1.
The attempt did not lead to a proof, but even at this early
point it had overcome your argument. It would not try to
represent the "parity vectors" for all n. Just showing that
this smallest counterexample does not exist would be enough.
I could rule out infinite sets of numbers that could not
contain the smallest counterexample; for example, even numbers.
(The same with the P vs. NP
discussion on the other thread.)
The argument on this thread reminds me of a debate here between an
anti-evolution scientist and an evolution scientist [...]
It reminds me of other naive arguments attempting to resolve
famous mathematical problems.
--
--Bryan
.
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