Re: Another Reason Why Feinstein's Proof is Incorrect

David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx> wrote:
# On 1 Jun 2006 09:18:54 -0700, "Craig Feinstein" <cafeinst@xxxxxxx>
# wrote:
#
#>But I might as well respond now as it appears that
#>more than one person believes it and I may be able to help some people
#>improve their critical thinking skills by changing their minds:
#>
#>My proof never claims that you have to treat every integer
#>individually. My proof says: let's pretend that we have a proof of
#>Collatz with L bits. It then shows that there is a specific n for which
#>any proof that Collatz halts at one with input n requires at least L+1
#>bits.
#
# As I've pointed out several times, this is exactly where the
# error is. Or rather where the essential error is - the other
# problems about how you haven't specified this or defined that
# can't be ignored but they can be fixed.
#
# What follows is not that the proof the Collatz halts with
# input n takes at least L+1 bits. What follows is that that
# proof, _including_ a specification of what n you're talking
# about, takes at least L+1 bits.
#
# And now (surprise) the contradiction goes away.


I think that's the most beautiful mistake in Feinstein's paper.

--Gerhard

___________________________________________________________
Gerhard J. Woeginger http://www.win.tue.nl/~gwoegi/

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