Re: Collatz conjecture

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 06/11/04 

Date: 11 Jun 2004 17:48:18 +0200

ath77@aol.com (Alexander T. Hamming) writes:

> See http://arxiv.org/abs/math.GM/0312309
> I checked it and believe it.

  The author tries to "show that any proof of the Collatz 3n+1
Conjecture must have an infinite number of lines". His argument is of
course incorrect, and it's a good example of its kind. I have in mind
arguments with a startling conclusion which an ordinary mathematical
reader will immediately recognize as suspect because they don't use
any particulars of the problem they deal with. Consider Theorem 3: the
argument is that to show that there exists an m such that T_(m)(n)=1,
we need to perform at least m_0 computations, where m_0 is the
smallest m such that T_(m)(n)=1, "since the value of T_(m_0)(n) is
determined in showing that there exists an m in N such that
T_(m)(n)=1". What would you say about an argument to the effect that
to show that there exists an m>10^100 such that m is a prime, we must
at least perform the work needed to show that m_0 is a prime, where
m_0 is the smallest prime > 10^100, since "the (boolean) value of 'm_0
is a prime' is determined in showing that there exists an m>10^100
such that m is a prime"?

Relevant Pages

  • Re: Collatz conjecture
    ... > Conjecture must have an infinite number of lines". ... > course incorrect, and it's a good example of its kind. ... > is a prime' is determined in showing that there exists an m>10^100 ... The people who still try to prove the Collatz Conjecture ...
    (sci.math)
  • Re: paths through binary trees in ZF
    ... infinite paths ... depth nodes under 1 root)  has ... only countably many infinite branches through it,  thereby showing  ZF ...
    (sci.logic)
  • Re: .99999999999999 = 1 and formally real fields
    ... This is not what I was showing. ... infinite number of dimensions used in the analysis. ... a finite way within about 16 significant figures in the series. ... I have already shown that Partial Sums is inaccurate like for example with ...
    (sci.math)
  • Re: paths through binary trees in ZF
    ... only countably many infinite branches through it,  thereby showing  ZF ... inconsistent since it also ... In fact, in any complete infinite binary tree, each node "distinguishes" ...
    (sci.logic)
  • Re: .99999999999999 = 1 and formally real fields
    ... > This is not what I was showing. ... > infinite number of dimensions used in the analysis. ... > series showing that it could converge but it would be inaccurate or have some ... > I have already shown that Partial Sums is inaccurate like for example with ...
    (sci.math)
Loading