Date: Feb 12, 2013 2:26 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 12 Feb., 19:41, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 12, 6:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > > Your claim is that there is a line of the list that contains
> > > every FIS of d (there is no mention of all)


Obviously the list

1
12
123
...

contains every FIS of d in lines.
There are never two or more lines required to contain anything that is
in the list.
>
> > But you seem to interpret some completeness into "every".
> > Remember, beyond *every* FIS there are infinitely many FISs.,

>
> I am using your claim including the fact that beyond
> *every* FIS there are infinitely many FISs.


Fine.
>
> I simply note that if line l contains every FIS of d, then
> d and line l are equal as potentially infinite sequences.


The list is a potetially infinite sequence of lines.
A line is finite.
>
> Your first claim is that there is a line l such that
> d and l are equal as potentially infinite sequences.


What do you understand by being equal "as potetially infinite
sequences"?

I said that every FISs of d is in some line of the list. However we
cannot fix the number since there is no last line that could contain a
last FIS (which also does not exist) of d.
>
> Your other claim is that there is no line
> l such that d and l are equal as potentially infinite
> sequences.


All we can prove is: For every n in N: FIS(1) to FIS(n) of d are in
line n.
Everything of d that is in the list is in one line. This line cannot
be addressed. It is not fixed since there is no last step in infinity.

> You are asserting a contradiction.

You must say what you mean by being equal "as potentially infinite
sequences".

You seem again to fall back into actual infinity.

Regards, WM