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Topic: |R| > oo
Replies: 26   Last Post: Mar 8, 2013 8:55 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,421 Registered: 5/20/10
Re: |R| > oo
Posted: Mar 2, 2013 6:01 PM

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
>

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

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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