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