Date: Nov 1, 2012 3:56 AM
Author: Hercules ofZeus
Subject: Re: Peer-reviewed arguments against Cantor Diagonalization

On Nov 1, 5:41 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.. ...
> >  ...
>
> Its not a set of Reals. It is set of the 7 leading digits of 16
> different Reals.
>
> We know the first Real is 0, because you told us.
>
> What is the value of the second Real?
>
>
>
> > 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 what, exactly?






> 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