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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: WM's WMatheology § 074
Posted: Jul 17, 2012 3:43 PM

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.
>
>
>

> > > 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.
>
> > Do you believe that the indexed digits of the sequence
> > 1
> > 11
> > 111
> > 1111
> > ...
> > converge to the empty set?

>
> 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?

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.

Regards, WM

Date Subject Author
7/13/12 mueckenh@rz.fh-augsburg.de
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