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Topic: Matheology § 074
Replies: 114   Last Post: Jul 22, 2012 4:15 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: WM's WMatheology � 074
Posted: Jul 17, 2012 6:38 PM

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

> On 16 Jul., 23:10, Virgil <vir...@ligriv.com> wrote:
>

> > > > And {} is provably that common value.
> >
> > > In mathematics, the components (digits) of a diverging sequence of
> > > real numbers diverge also.

> >
> > But in mathematics (which despite WM's delusions DOES contain numerous
> > set theories) the vase proble resolves into finding the limit of a
> > sequence of SETS, not a sequence of real numbers.

>
> I prove that the limit of a seqeunce of sets of numbers cannot be
> empty if the mathematics of the reals which are formed by these
> numbers is correct.

You claim all sorts of proofs which any competent mathematician can
debunk.

And what we have is not merely a sequence of sets of numbers, but a
sequence of sets of numbered balls, for which we have no need of any
real numbers other than the natural numbers, and which "form" no numbers
other than natural numbers.

In any case, any such alleged proof is so far only notable for its
absence.
> >
> >
> >

> > > > When one looks for a limit value to a sequence of sets, one must use an
> > > > appropriate method for sequences of sets, which WM does not do.

> >
> > > In mathematics we have
> > > a_n --> oo <==> set of digits of a_n does not vanish.

> >
> > But a_n is NOT the set of numbered balls in the vase at any time, so is
> > irrelevant to the vase problem.

>
> The digits left and right of the decimal point are identical to the
> sets of numbered balls in the vase and removed from the vase,
> respectively.

A (finite) sequence of digits is NOT identical to a set of naturals, and
no handwaving by WMatheologists will make it become identical.
> >
> > > Do you believe that the indexed digits of the sequence
> > > 1
> > > 11
> > > 111
> > > 1111
> > > ...
> > > converge to the empty set?

How is that relevant to finding the limit of a sequence of sets?
> >
> > Unless all, or at least all but finitely many of them, are sets, the
> > sequence of them cannot converge to a set at all,

>
> The indices of the digits are sets of natural numbers:
> 1
> 2, 1
> 3, 2, 1
> 4, 3, 2, 1
> ...
>
> Should set theory yield here the limit empty set?

No one claims that the set of place values used in naming naturals (in
decimal or other place value notations) is not infinite.
>
> Same holds for the indices of the digits before the decimal point of
>
> 01
> 0.1
> 010.1
> 01.01
> 0101.01
> 010.101
> ...
>
> On the other hand, the indices of all digits are
>
> 2 , 1
> 4, 3 . 2, 1
> 6, 5, 4 . 3, 2, 1
>
> The left sets converge to the empty set.
>
> This proves a contradiction in set theory.

It only proves a contradiction (one of many) in WM's WMatheology, but
has no effect on standard mathematics.
--

Date Subject Author
7/13/12 mueckenh@rz.fh-augsburg.de
7/13/12 MoeBlee
7/13/12 Virgil
7/14/12 dilettante
7/14/12 LudovicoVan
7/14/12 dilettante
7/14/12 mueckenh@rz.fh-augsburg.de
7/14/12 LudovicoVan
7/14/12 Virgil
7/14/12 dilettante
7/14/12 mueckenh@rz.fh-augsburg.de
7/14/12 dilettante
7/14/12 LudovicoVan
7/14/12 Virgil
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 LudovicoVan
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 LudovicoVan
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 Virgil
7/15/12 LudovicoVan
7/15/12 Virgil
7/15/12 Virgil
7/15/12 Virgil
7/15/12 Virgil
7/15/12 Virgil
7/14/12 Virgil
7/14/12 dilettante
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 dilettante
7/15/12 Frederick Williams
7/15/12 dilettante
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 Virgil
7/15/12 mueckenh@rz.fh-augsburg.de
7/15/12 dilettante
7/16/12 mueckenh@rz.fh-augsburg.de
7/16/12 LudovicoVan
7/16/12 mueckenh@rz.fh-augsburg.de
7/16/12 LudovicoVan
7/17/12 mueckenh@rz.fh-augsburg.de
7/17/12 Virgil
7/16/12 Virgil
7/16/12 Virgil
7/16/12 mueckenh@rz.fh-augsburg.de
7/16/12 Virgil
7/16/12 LudovicoVan
7/16/12 Virgil
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7/16/12 Virgil
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7/17/12 William Hughes
7/18/12 mueckenh@rz.fh-augsburg.de
7/18/12 LudovicoVan
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7/19/12 Virgil
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7/19/12 YBM
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7/19/12 FredJeffries@gmail.com
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7/20/12 mueckenh@rz.fh-augsburg.de
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7/21/12 mueckenh@rz.fh-augsburg.de
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7/22/12 mueckenh@rz.fh-augsburg.de
7/22/12 Virgil
7/20/12 Marshall
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7/21/12 mueckenh@rz.fh-augsburg.de
7/15/12 Virgil
7/15/12 Virgil
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