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Topic: Peer-reviewed arguments against Cantor Diagonalization
Replies: 156   Last Post: Nov 4, 2012 3:01 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Oct 29, 2012 5:21 PM

On Oct 30, 6:30 am, Arturo Magidin <magi...@member.ams.org> wrote:
> On Monday, October 29, 2012 2:04:42 PM UTC-5, JRStern wrote:
> > On Mon, 29 Oct 2012 09:14:02 -0700 (PDT), Arturo Magidin
>
> > <magi...@member.ams.org> wrote:
>
> > >> >The government doesn't like it when I read minds without a
>
> > >> >warrant, so I try not to do it, you see.
>
> > >> There are constructivist objections to the whole enterprise.  If
>
> > >> nothing else, I was hoping to see something like these addressed
>
> > >> against the diagonal argument piecemeal.
>
> > >In a constructivist universe, you cannot have a function defined
>
> > >on the natural numbers, and you cannot have a set of real numbers at all.
>
> > >The very premise ("Suppose f:N-->(0,1) is a function") is considered
>
> > >nonsensical in the constructivist point of view.
>
> > >You can only talk about a "rule" that will allow you, in principle,
>
> > >to compute f(n) up to any degree of exactness that you care to specify.
>
> > >You can encode the procedure in the proof given assuming that the
>
> > >function f is given by Turing Machine which, when given n as an input,
>
> > >will give you the number of a Turing machine that computes f(n).
>
> > >Then you can establish the existence of a Turing machine r which,
>
> > >when given as input the number of a Turing machine that computes
>
> > >a function f as described above, will produce as an output the
>
> > >sequence b_n which is not equal to the output of any Turing machine
>
> > >whose number is produced by the Turing machine corresponding to f.
>
> > >That much is allowable within the computational universe.
>
> > Doesn't this sound rather like what some of the "cranks" hereabouts
>
> > are trying to say?
>
> Which "cranks", and what specifically do they say that you find "rather like" exactly which part of the above?
>
> Yet again: one cannot give you an exact answer if you insist on presenting nothing but vague statements that have little or no actual content. I certainly have no desire to waste my time discussing phantoms and ephemerals, so perhaps you can stop being vague and wishy-washy, and give some specifics? If you can't, then stop trying to think about math. Now. Stop. Yes. You. Stop it. There is absolutely no point in discussing mathematics on the basis of vague pronouncements, vague statements, vague "feelings", and vague impressions; because, whatever it is you end up doing, it's not mathematics.
>
> --
> Arturo Magidin

Cantor's Proof is like looking between 2 parallel mirrors and seeing
the infinite sequence of fools reflected within!

size(SET) > size( {1,2,3...} ) #term of which is now duckspeaked

based on...

inverting the diagonal of non terminating sequences!

Changing 1 digit of the diagonal does NOTHING!
Changing 1 digit at a time of the diagonal does NOTHING!
Changing all digits of the diagonal (of a non terminating list)

DOES NOTHING!

Herc

Date Subject Author
10/27/12 JRStern
10/27/12 Frederick Williams
10/27/12 JRStern
10/28/12 Tim Little
10/28/12 Peter Webb
10/28/12 JRStern
10/28/12 J. Antonio Perez M.
10/29/12 Michael Stemper
10/29/12 David C. Ullrich
10/29/12 JRStern
10/29/12 JRStern
10/30/12 David C. Ullrich
10/30/12 David C. Ullrich
10/29/12 LudovicoVan
10/27/12 J. Antonio Perez M.
10/28/12 INFINITY POWER
10/28/12 Shmuel (Seymour J.) Metz
10/28/12 Graham Cooper
10/28/12 magidin@math.berkeley.edu
10/28/12 INFINITY POWER
10/28/12 Graham Cooper
10/28/12 Virgil
10/28/12 Graham Cooper
10/28/12 JRStern
10/28/12 magidin@math.berkeley.edu
10/28/12 Graham Cooper
10/28/12 Graham Cooper
10/28/12 magidin@math.berkeley.edu
10/28/12 Graham Cooper
10/28/12 magidin@math.berkeley.edu
10/29/12 Frederick Williams
10/29/12 LudovicoVan
10/29/12 Richard Tobin
10/29/12 LudovicoVan
10/29/12 J. Antonio Perez M.
10/29/12 J. Antonio Perez M.
10/29/12 magidin@math.berkeley.edu
10/29/12 Frederick Williams
10/28/12 Graham Cooper
10/28/12 JRStern
10/28/12 Peter Webb
10/28/12 magidin@math.berkeley.edu
10/28/12 Hercules ofZeus
10/28/12 magidin@math.berkeley.edu
10/28/12 Hercules ofZeus
10/28/12 Arturo Magidin
10/28/12 Hercules ofZeus
10/28/12 Arturo Magidin
10/28/12 Hercules ofZeus
10/29/12 J. Antonio Perez M.
10/29/12 Graham Cooper
10/29/12 JRStern
10/29/12 Frederick Williams
10/29/12 magidin@math.berkeley.edu
10/29/12 Pubkeybreaker
10/29/12 JRStern
10/29/12 magidin@math.berkeley.edu
10/29/12 Graham Cooper
10/29/12 JRStern
10/29/12 magidin@math.berkeley.edu
10/30/12 Graham Cooper
10/30/12 magidin@math.berkeley.edu
10/30/12 Graham Cooper
10/30/12 J. Antonio Perez M.
10/31/12 Peter Webb
10/29/12 Peter Webb
10/29/12 magidin@math.berkeley.edu
10/29/12 Shmuel (Seymour J.) Metz
10/29/12 Virgil
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/30/12 Graham Cooper
10/30/12 Peter Webb
10/30/12 Graham Cooper
10/30/12 Peter Webb
10/30/12 Graham Cooper
10/30/12 MoeBlee
10/30/12 Peter Webb
10/30/12 Graham Cooper
10/31/12 Peter Webb
10/31/12 Graham Cooper
10/31/12 Peter Webb
10/31/12 Graham Cooper
11/2/12 Peter Webb
11/1/12 Peter Webb
11/1/12 Hercules ofZeus
11/2/12 Peter Webb
10/31/12 Peter Webb
10/30/12 Richard Tobin
10/30/12 Graham Cooper
10/30/12 MoeBlee
10/30/12 Graham Cooper
10/30/12 MoeBlee
10/30/12 Graham Cooper
10/31/12 Richard Tobin
10/31/12 Graham Cooper
10/31/12 Graham Cooper
10/31/12 Graham Cooper
10/31/12 Richard Tobin
10/31/12 Graham Cooper
10/31/12 Richard Tobin
10/31/12 Graham Cooper
10/31/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 LudovicoVan
10/29/12 J. Antonio Perez M.
10/29/12 LudovicoVan
10/29/12 Peter Webb
10/29/12 LudovicoVan
10/30/12 Peter Webb
10/30/12 LudovicoVan
10/30/12 Peter Webb
10/30/12 LudovicoVan
10/30/12 Peter Webb
10/30/12 J. Antonio Perez M.
10/30/12 LudovicoVan
10/30/12 Virgil
10/30/12 J. Antonio Perez M.
10/30/12 LudovicoVan
10/31/12 Peter Webb
10/31/12 LudovicoVan
10/31/12 J. Antonio Perez M.
10/31/12 Shmuel (Seymour J.) Metz
11/1/12 LudovicoVan
11/1/12 Jesse F. Hughes
11/2/12 Peter Webb
11/2/12 LudovicoVan
11/2/12 Graham Cooper
11/2/12 Shmuel (Seymour J.) Metz
11/2/12 Virgil
11/2/12 Peter Webb
11/2/12 Peter Webb
11/3/12 J. Antonio Perez M.
11/3/12 Shmuel (Seymour J.) Metz
11/4/12 Peter Webb
11/4/12 Virgil
11/4/12 Shmuel (Seymour J.) Metz
11/1/12 Shmuel (Seymour J.) Metz
10/31/12 Shmuel (Seymour J.) Metz
10/31/12 Shmuel (Seymour J.) Metz
10/29/12 JRStern
10/29/12 Shmuel (Seymour J.) Metz
10/28/12 Graham Cooper
10/28/12 J. Antonio Perez M.
10/29/12 David C. Ullrich
10/29/12 JRStern
10/29/12 LudovicoVan
10/29/12 Fernando Revilla
10/29/12 Shmuel (Seymour J.) Metz