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Topic: WMytheology � 259
Replies: 2   Last Post: May 2, 2013 5:44 PM

 Virgil Posts: 8,833 Registered: 1/6/11
Re: WMytheology � 259
Posted: May 2, 2013 5:44 PM

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

> On 2 Mai, 11:29, Zeit Geist <tucsond...@me.com> wrote:
>

> > The mistake is that you use different constructions and expect to
> > get the same structure as a result.  Just because all the
> > constructions use the natural numbers does not mean that
> > end result is the same.

>
> There are three sequences leading to "lists".

Actually only one of WM's methodology leads to any list of all the
elements.

>
> I produce three identical seqeunces.

If they were really identical then you would have proved 3 = 1.

> 1
> 2,1
> 3,2 1
> ...
>
> Proving that |N is not in the first column when it is not in a line.

Where is you alleged proof of that obvious falsehood?

WM's claimed proof that are actually proofs are as rare as hen's teeth.

>
> > But, I don't need to because ZFC gives me a big mouth.
>
> Here we are discussing whether ZFC is self contradictory.

Which would have to be established within ZF itself, which puts it well
beyond WM's capabilities to analyse.

>
> There are many convergent sequences in mathematics, not only
> irrational numbers. But in every case the limit depends merely on the
> finite terms.

It actually depends on infinitely many mostly finite terms.

> It has never been heared of in mathematics, that two
> identical sequences have different limits.

But it has often been heard that different sequences have the same
limits.
.
>
> Your assumption that there is a set |N with more elements than every
> natural number can count, has been contradicted.

No it has not!
And certainly not by anyone as mathematically incompetent as WM.

WM quite regularly declares valid arguments to be invalid and invalid
arguments, usually his own, to be valid, so he is no valid judge of
validity.

> To put it in the wise
> words of Euclid: For every set of natural numbers I can show the
> existence of a natural number not contained in that set.

Remarkable that Euclid should have written that in English.

But back in his day, they had no grasp or how infinities work, so did
not allow themselves to consider them. By Archimedes time, things had
improved a bit.
>
>

> >  Or maybe it will occur to me when
> > you prove the existence of your j,k,m,n that you keep mentioning.

>
> Take the negation.

That negation actually proves out as true, since the set of naturals
and the set of fisons, which WM represents below as s_j = {1,2,..,k},
are obviously and trivially order isomorphic, which disproves WM's claim
that
exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.

For that to be true would require
(m <= j) & (k < m) & (j < n) & (n <= k)
or m <= j < n <= k < m
which may work in Wolkenmuekenheim but not elsewhere.

Note that while WM keeps claiming that result, m < m, he has yet to
offer anything like a proof of it, or even any evidence that he has not
just made it up .
--