Date: Jan 24, 2013 8:02 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

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.

>
>   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.
>
> 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.
>
> 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)?

Regards, WM