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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