Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Peter Webb Posts: 61 Registered: 10/21/12
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Oct 31, 2012 3:36 AM

Graham Cooper wrote:

> On Oct 30, 4:01 pm, "Peter Webb"
> <webbfamilyDIEspam...@optusnet.com.au> wrote:

> > Graham Cooper wrote:
> > > On Oct 30, 1:51 pm, "Peter Webb"
> > > <webbfamilyDIEspam...@optusnet.com.au> wrote:

> >
> > > > No.
> >
> > > > Do you claim to have a list of all Reals?
> >
> > > I have a listable set of all Reals.
> >
> > Great. Send it to me. I will tell you at least one missing Real.
> >

> > > Do you claim to be able to examine infinite lists?
> >
> > No, I claim to be able to examine rules which apply to infinite
> > sequences. For example, I can tell you the sequence of Reals 1, 2,
> > 3, ... where the Real in position n is n interpreted as a Real
> > number ... does not contain 0.5, without explicitly examining
> > every element in the list.
> >

> > > If so, specify the infinite stream protocol of your choice.
> >
> > > Herc
> >
> > Not needed.
> >
> > Just tell us which Real appears in position n for all n.
> >

>
>
> You want me to 'tell you' an infinite sequence?
>
> I told you which digit appears in position 1,2,3,4,5 & 6
> for reals in positions
>

Yes. But you haven't told us what the Real numbers in your list are.

What is the second Real in your list?

> R11 R12 R13 R14
> R21 R22 R23 R24
> R31 R32 R33 R34
> R41 R42 R43 R44
>
> Here are those digits again.
>
> 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.. ...
> ...
>
> Should you require any further digits then specify which ones from
> this enumerable_set_of_reals.

Its not an enumerable set of Reals. Its not even a set of Reals. It is
the first few decimal places of a few unspecified Real numbers.

What is the second Real on your list?

>
> Since you have FAILED 5 times now to provide any hint of a missing
> real from this enumerable_set_of_reals I think your claim is clearly
> debunked.

You haven't specified a single Real other than the first (0).

So you clearly haven't provided a list of all Reals. You have provided
(so far) a list with a single Real on it, 0 at posn 1.

Lets see if we can push this to two Reals ....

What is the second Real on your list?

>
> If you wish to REFINE YOUR CLAIM that given an Enumeration or
> specification thereof you have something to prove then do so.
>

Nope.

> Otherwise your claim to prove anything given any ENUMER-ABLE SET OF
> REALS clearly appears to have failed on the set provided 5 times
>
> Herc

You haven't specified an infinite list of Reals.

You haven't even specified the second Real on your list.

What is it?

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