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Topic: Matheology § 154: Consistency Proof!
Replies: 101   Last Post: Nov 25, 2012 5:08 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 154: Consistency Proof!
Posted: Nov 25, 2012 3:36 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Nov., 21:34, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 23 Nov., 22:37, Virgil <vir...@ligriv.com> wrote:
> >
> > > > Analysis can show that the limit VALUE is oo in the extended reals, but
> > > > does not presume to claim that there is a decimal, or any other place
> > > > value based numeral, representing that limit value.

> >
> > > If the limit value
> > > Limit[n-->oo] SUM[k=0 to n] a_k*10^k = oo
> > > is accepted in the extended reals, then it is simply ridiculous to
> > > claim that the abbreviation
> > > ..., a_k, ..., a_3, a_2, a_1, a_0
> > > is not in the abbreviations of the extended reals.

> >
> > The only such "abbreviations" in standard use for "extended reals  are
> > oo for the one point compactification or +oo and -oo for the two point
> > compactification.

>
> My proof does not need this abbreviation. My proof only needs the
> facts
> that the set { a_k | k in |N } of coefficients of the series is not
> empty and the number |{ a_k | k in |N }| of coefficients of the
> series is not zero. More is not required.

In standard mathematics, series and sequences do not have coefficients
at all, but only terms, though sometimes, as in power series, the terms
can have coefficients.

But WMatheology has very little in common with standard mathematics.

> > > But William had agreed: "On the contrary, the fact that the analytic
> > > *limit* cannot be described in terms of digits is the point."

> >
> > > And he stated proudly:
> >
> > > Analysis:
> > >    limit in real numbers: unbounded
> > >                          (oo in extended reals)
> > >    limit of set of 1's:  not estimated

> >
> > > Set Theory
> > >    limit in real numbers: not estimated
> > >    limit of set of 1's: {}

> >
> > > Therefore he would have to confess now that there is a contradiction
> > > between set theory and analysis.

> >
> > To say that different definitions of "limit" can give different results
> > only confuses WM, not anyone else.

>
> The limit of a sequence is defined solely by the finite terms of the
> sequence.

It is also defined by the context of the sequence, which, among other
things, defines the allowable interpretations of those "finite terms".

A sequence of sets differs in essential ways from a sequence of reals so
that they necessarily will have different limits.

Thus WM's attempts to find a contradiction in such a difference is a
violation of common sense, as well as of mathematics.

> Mathematics is the art of finding this limit, not the art of
> inventing arbitrary limits.

Mathematics, before it can find a limit, must dfine what is expected of
that limit, and in sensible mathematics the limit of a sequence of real
numbers, if it exists, and the limit of a sequence of sets, if it also
exists, will never be the same thing.

And furthermore, the sequence of real number numerals that WM is harping
about does not exist as a real number numeral at all.
--

Date Subject Author
11/18/12 mueckenh@rz.fh-augsburg.de
11/18/12 Vurgil
11/18/12 William Hughes
11/18/12 Vurgil
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 William Hughes
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/20/12 mueckenh@rz.fh-augsburg.de
11/20/12 Virgil
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12
11/23/12 Virgil
11/24/12 mueckenh@rz.fh-augsburg.de
11/24/12 Virgil
11/23/12 Virgil
11/24/12 mueckenh@rz.fh-augsburg.de
11/24/12 Virgil
11/25/12 mueckenh@rz.fh-augsburg.de
11/25/12 Virgil
11/25/12 mueckenh@rz.fh-augsburg.de
11/25/12 Virgil
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/22/12 Virgil
11/22/12 Virgil
11/22/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/22/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/22/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/22/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/20/12 mueckenh@rz.fh-augsburg.de
11/20/12 Virgil
11/22/12 David Valdez