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

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Graham Cooper

Posts: 4,252
Registered: 5/20/10
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Oct 31, 2012 1:12 AM
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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 ...
...


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.. ...
...


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



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

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