Date: Feb 12, 2013 5:01 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<a6904dcf-201a-4340-89fa-3db6bc11de8d@w4g2000vbk.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.


Not if d starts out as 111...

> There are never two or more lines required to contain anything that is
> in the list.


WRONG! SEE ABOVE!
> >
> > > 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"?


We do not understand "potentially infinite" to have any sensible meaning
other than "actually infinite".

One adequate definition of actually infinite would be
"a non-empty set is infinite if it can be ordered so as
NOT to have a largest member"
>.
>.

.

> Just that is obviously realized in above list. Every FIS of d is a
> line and every FIS of a line is a FIS of d.


l1 = 0
l2 = 10
l3 = 110
and so on with line ln = being n-1 "1"'s followed by "0".

And let d = 111... with no 0 in it ever.

Then no FIS of d is any line
and at least one FIS of any line is NOT a FIS of d.

Thus WM is TOTALLY! WRONG!! AGAIN!!! AS USUAL!!!!




> Everything of d that is in the list is in one line. This line cannot
> be addressed.

Then it does not exist.
>
> > 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.


Since only actual infiniteness can exist in a well constructed set
theory, of course.
--