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