
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 ANTIDIAGONAL function to support your claims it is > > incomplete? > > > What is your antidiagonal 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 antidiagonal, > 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 antidiagonal in binary being > ones, with real value one, may go from zero, to one. > > And: only one does. > > Then, for a conscientious mathematician, formalist yearround, 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 AntiDiagonal on some infinite lists of reals.
Herc  www.BLoCKPROLOG.com

