Date: Jan 24, 2013 3:57 PM
Author: Virgil
Subject: Re: ZFC and God

In article 
<b54a6889-70b6-49c6-851a-56303d5be1da@d12g2000yqe.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Jan., 13:36, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
>
> > Well, what you present below is *not* a proof of (*).
>
> That is wrong. You have no reason to believe that your definition of
> proof is correct or the only one.


We have lots of reason to beeive that anything WM presents as a proof
that is not copied from soemone more competent, is incorrect.

Some of those reasons are the obvious flaws in logic that WM is know for.
>
> >
> >   Clearly, for all j, d(j) != t_j(j) and hence d != t_j for any j in
> >   N.
> >
> > Is this what you mean up 'til now?

>
> Yes.
>

> >
> > > 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. )

> >
> > No idea what you mean by the parenthetical remark.

>
> You will have have recognized that here the diagonal argument is
> applied. It is obvious that up to every line = column the list is a
> square.


Not at all. there is no reason why line n, for any n > 1, must be of
length >= n.

In decimal notation, one could start with 10 lines of length 1 followed
by 90 lines of length 2, followed by 900 lines of length 3, etc., and
never repeat a number.


> >
> > I do agree that d_i is defined for every i in N.  In particular, (d_i)
> > is an infinite sequence of digits.  Is this what you're claiming, too?
> > You've lost me.  I don't know what you mean when you say, "everything
> > here happens among FISs."  And I'm also puzzled by the meaning of the
> > next sentence.

>
> Every t_i is finite. Hence, in a square, if the width is finite, also
> the length must be finite.


But a "diagonal" need not be, and will not be finite.
> >
> > Here are some obvious things.
> >
> >   d(j) is defined for every j in N.
> >   d(j) != 0 and d(j) != 9 for any j in N.
> >
> >   Hence the number d does not have a terminating decimal
> >   representation.

>
> Neither the set of t_i does have a largest element. Nevertheless there
> is no t_i of actually infinite length.

> >
> > This looks like I do *not* agree with your claim that "d cannot be
> > longer than every t_i".

>
> A sequence of squares will never result in a square such that all
> sides are finite but the diagonal d is infinite. The overlap of d and
> t_i cannot be larger than t_i.
>
> In particular, what would be changed in the length of d if we admitted
> also non-terminating t_i (of infinite length)?


The diagonal is already required to be infinitely long, so its length
need not change.
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