Date: Jan 24, 2013 3:43 PM
Author: Virgil
Subject: Re: ZFC and God

In article 
<6dd94652-47c7-45c4-b02c-ed46c71cc1ba@4g2000yqv.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Jan., 12:36, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
> > > On 23 Jan., 19:04, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> >
> > >> > Understand the Binary Tree. After you will have understood it, you
> > >> > will understand, why it is important.

> >
> > >> No, let's first settle the point at hand.
> >
> > > I do it by means of tools that I choose without any censorship from
> > > your side.

> >
> > I'm not being unreasonable here.  You say ZF is inconsistent.  I want
> > to see whether you can indeed show that.
> >
> > So, I'd like to know what inconsistency you can show in ZF.  You have
> > already said (don't let me put words in your mouth!  Correct me if I'm
> > wrong) that you can show ZF proves
> >
> >   U_n {1,...,n} is not infinite.             (*)

>
> It is not actually infinite. The cardinality is not larger than every
> n.


Then there must be some n that it is not larger than.

Either
Em in |N (Card(U_n {1,...,n) = m)
or
Am in |N (Card(U_n {1,...,n) > m)

> >
> > Since we know it also proves the negation of (*), this would settle
> > your claim.
> >
> > Now, I'd just like to see the proof of (*).  Nothing else.  Just show
> > me that proof and we'll discuss it.

>
> Ok.
>
> 1) Certainly you agree that in ZF we have the set T of all terminating
> decimal fractions t_i of the reals in the unit interval, i.e., finite
> sequences of digits, indexed by the FISs {1,...,n}.
>
> 2) Certainly you agree that the set T is countable.
>
> 3) Certainly you agree that the set can be diagonalized.


If by that you mean that a non-terminating decimal can be found that is
unlisted, then yes. But, in fact, EVERY nonterminating decimal having
infinitely many nonzero digits will not be in your list.
>
> 4) Certainly you agree that, since all t_i = (t_i1, t_i2, ..., t_in)
> have only a finite, though not limnited, number n of digits, the
> diagonalization for every t_i yields a finite d_i =/= t_ii.
> (The i on the left hand side cannot be larger than the i on the right
> hand side. In other words, "the list" is a square. Up to every i it
> has same number of lines and columns. )
>
> So everything here happens among FISs. And d cannot be longer than
> every t_i.


That is equivalent to claiming that |N must be equal to one of its
finite initial segments, which, outside of WMytheology, is false.


> Nevertheless d_i differs from every t_ii. So we see that ZF
> proves the uncountability of a countable set.



Since WM's set is limited to ONLY terminating decimals and the diagonal
construction produces a necessarily non-terminating decimal, it does not
affect the countability of WM's set of terminating decimals, thus WM is
claiming an obvious falsehood. Again!! As Usual !!!

Which is SOP in WMytheology.
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