Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Matheology � 154: Consistency Proof!
Posted:
Nov 23, 2012 4:17 PM
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In article
<2ceaeaba-fad1-4520-a7f1-0ac776eed623@u9g2000vbm.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 23 Nov., 17:09, William Hughes <wpihug...@gmail.com> wrote:
> > On Nov 23, 11:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >
> > > On 23 Nov., 15:42, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Nov 23, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > On 23 Nov., 15:16, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > > > On Nov 23, 10:11 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > > > On 23 Nov., 13:27, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > > > > > So to summarize:
> >
> > > > > > > > Analysis:
> > > > > > > > limit in real numbers: unbounded
> > > > > > > > (oo in extended reals)
> >
> > > > > > > > limit of set of 1's:
> >
> > > > > oo = Limit[n-->oo] SUM[k=0 to n] 10^k
> > > > > = 1*10^0 + 1*10^1 + 1*10^2 + 1*10^3 + ...
> > > > > = ...111
> >
> > > > this piece of nonsense has nothing to do
> > > > with the limit of the sequence
> >
> > > > 1
> > > > 10
> > > > 100
> > > > ...
> >
> > > > which is oo = Limit[n-->oo] 10^k
> > > > and it not represented by any numeral.
> >
> > > That is of little interest!
> >
> > On the contrary, the fact that the analytic *limit*
> > cannot be described in terms of digits is
> > the point.-
>
> No, that is not a point.
The analytic limit can be calculated.
Agreed, but that it can be expressed as a real number seems to be a
delusion that WM cannot shake. Even if one extends the reals by a one or
two point compactification so that there is a value in the extended
reals, that value is not representable as a digit string.
> Analysis infers from the limit the number of required digits, namely
> oo.
Which 'number' of digits preceding a radix point is not allowed.
So WM is off daydreaming in his Wolkenmuekenheim again!
--
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