Date: Mar 2, 2013 6:01 PM Author: Graham Cooper Subject: Re: |R| > oo On Mar 3, 7:35 am, "Ross A. Finlayson" <ross.finlay...@gmail.com>

wrote:

> On Mar 2, 12:30 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:

>

>

>

>

>

>

>

>

>

> > On Mar 2, 7:28 pm, Rupert <rupertmccal...@yahoo.com> wrote:

>

> > > On Friday, March 1, 2013 9:39:31 PM UTC+1, Graham Cooper wrote:

> > > > A LIST oo ROWS LONG!

>

> > > > 0.00...

>

> > > > 0.00...

>

> > > This post is incoherent dribble.

>

> > I showed a partial infinite list of reals.

>

> > 0.00..

> > 0;00..

> > ..

>

> > Do you have an ANTI-DIAGONAL function to support your claims it is

> > incomplete?

>

> > What is your anti-diagonal function?

>

> > Herc

>

> How would you establish that the expansions you begin to detail would

> map on to any segment of R?

>

> Well, that gets into whether the function, that makes a list these

> expansions, has as a range, an interval of reals.

>

> So, look at the equivalency function, as I call it, it's quite well-

> defined, it goes to one, and in binary there's only one anti-diagonal,

> and it's one.

>

> I'll agree that a more carefully defined function, that would have as

> each initial segment of each initial segment, of a matrix of values of

> the expansions, zeroes, with the only anti-diagonal in binary being

> ones, with real value one, may go from zero, to one.

>

> And: only one does.

>

> Then, for a conscientious mathematician, formalist year-round, that's

> compelling.

>

> There are lots who would work in foundations, but transfinite

> cardinals aren't used in real analysis, or continuum analysis for

> applications and physics. And, physics needs new methods to explain

> results of experiment. And, results in the digital are available via

> asymptotics. Good day.

>

> Regards,

>

> Ross Finlayson

>

So your argument is:

----------------------------------------

Given this sample of a list oo rows long IN BINARY

0.00..

0.00..

..

We know 0.11..

is missing from the List by Extrapolation over all digit positions.

----------------------------------------

Given this sample of a list oo rows long IN TERNARY

0.00..

0.00..

..

We know

0.11..

0.12..

0.21..

0.22..

are missing from the List by Extrapolation.

----------------------------------------

Given this sample of a list oo rows long IN BASE 4

0.00..

0.00..

..

We know

0.11..

0.12..

0.13..

0.21..

0.22..

0.23..

0.31..

0.32..

0.33...

are missing from the List by Extrapolation.

----------------------------------------

Since all above arguments must hold, the latter more absurd ones are

enough to throw doubt on Cantors Method - which is actually just

induction over ALL sizes of FINITE lists, since no_new_digit_string is

calculated in the Anti-Diagonal on some infinite lists of reals.

Herc

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