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Re: Peer-reviewed arguments against Cantor Diagonalization
Posted:
Nov 2, 2012 6:09 AM
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Hercules ofZeus wrote:
> 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
pi - 3
Turns out you don't have a list of all Reals after all. And I didn't
even need Cantor to find it.
Surely you know that the proposed set contains only rational numbers,
and some numbers are irrational?
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