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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 31, 2012 3:45 AM

On Oct 31, 5:39 pm, "Peter Webb"
<webbfamilyDIEspam...@optusnet.com.au> wrote:
> Graham Cooper wrote:
> > On Oct 31, 2:34 pm, "Peter Webb"
> > <webbfamilyDIEspam...@optusnet.com.au> wrote:

> > > Graham Cooper wrote:
> > > > On Oct 31, 1:37 pm, "Peter Webb"
> > > > <webbfamilyDIEspam...@optusnet.com.au> wrote:

> > > > > Graham Cooper wrote:
> > > > > > On Oct 30, 6:24 pm, "Peter Webb" wrote:
>
> > > > > > > You do claim to have a list of all Reals, don't you?
>
> > > > > > I have a listable set of all reals.
>
> > > > > > 0.000000.. 0.110000.. 0.111010.. 0.111110.. ...
> > > > > > 0.000111.. 0.101000.. 0.000010.. 0.001100.. ...
> > > > > > 0.111000.. 0.010010.. 0.001010.. 0.101010.. ...
> > > > > > 0.111100.. 0.001011.. 0.000011.. 0.111111.. ...
> > > > > > ...

>
> > > > > > > You haven't specified the list yet.
>
> > > > > > AHA! Peter is on the ball!
>
> > > > > > No enumeration function! Just a good ole countable SET of all
> > > > > > reals!

>
> > > > > > The order is arbitrary isn't it?
>
> > > > > > > > Otherwise your claim to prove anything given any
> > > > > > > > ENUMER-ABLE SET OF REALS clearly appears to have failed
> > > > > > > > on the set provided 5 times already.

>
> > > > > > > > Herc
>
> > > > > > > I made no such claim. To start off with, its nonsense.
>
> > > > > > Nonetheless it was the topic before you took over from
> > > > > > Moeblee.

>
> > > > > > On Oct 30, 9:18 am, MoeBlee <modem...@gmail.com> wrote:
> > > > > > > I just proved that given any enumerable set S of denumerable
> > > > > > > binary sequences there is denumerable binary sequence not
> > > > > > > in S.

>
> > > > > > If you do not wish to apply any mathematical approach to the
> > > > > > given countable set of reals,

>
> > > > > > 0.000000.. 0.110000.. 0.111010.. 0.111110.. ...
> > > > > > 0.000111.. 0.101000.. 0.000010.. 0.001100.. ...
> > > > > > 0.111000.. 0.010010.. 0.001010.. 0.101010.. ...
> > > > > > 0.111100.. 0.001011.. 0.000011.. 0.111111.. ...
> > > > > > ...

>
> > > > > That's not a given countable set of Reals.
>
> > > > > Its not even a list of a few Reals, or even a single Real.
>
> > > > > Lets start with the first Real on your list. Just the first
> > > > > one. I don't care about the others for the time being. What is
> > > > > the first Real on your list?

>
> > > > 0!  Top left corner!
>
> > > OK, what is the second Real on the list?
>
> > > > Maybe you should DEFINE what you mean by countable set before
> > > > asking for one.

>
> > > You don't know what a countable set is?
>
> > > For the purposes of this thread, you can treat it as a set which
> > > can be bijected with N.

>
> > > Which means you have to specify which values in R correspond to
> > > which values in N.

>
> > > You have already told us that the Real corresponding to n=1 is 0.
>
> > > Now you can tell us the Real corresponding to n=2.
>
> > > Eventually you will need to specify the Reals corresponding to all
> > > natural numbers n, but I figure the values for n=1 (given) and n=2
> > > (next) will be a good start.

>
> > This set can be bijected with N
>
> > 1/1  1/2  1/3  1/4 ...
> > 2/1  2/2  2/3  2/4 ...
> > 3/1  3/2  3/3  3/4 ...
> > 4/1  4/2  4/3  4/4 ...
> > ...

>
> Yes.
>
>
>

> > similarly this set of reals CAN-BE bijected with N
>
> >  0.000000.. 0.110000.. 0.111010.. 0.111110.. ...
> >  0.000111.. 0.101000.. 0.000010.. 0.001100.. ...
> >  0.111000.. 0.010010.. 0.001010.. 0.101010.. ...
> >  0.111100.. 0.001011.. 0.000011.. 0.111111.. ...
> >  ...

>
> But this isn't a list of Reals.
>
> It is a list of the first few decimal digits of a few unspecified Reals.
>
> You need to produce a list of Reals.
>
> Lets do this in steps.
>
> What is the second Real on your list?
>
>
>

> > Hence, you CANNOT prove a COUNTABLE SET OF REALS is incomplete.
>
> > PROOF:  This is the 10th time asking.
>
> > In fact, I call this  THE UNANSWERABLE QUESTION  for a reason!
>
> > Herc
>
> And the second Real on your list is?

OK use this countable set of reals.

1/10  1/20  1/30  1/40 ...
2/11  2/21  2/31  2/41 ...
3/31  3/32  3/33  3/34 ...
4/17  4/27  4/37  4/47 ...
...

what's missing?

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
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