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.

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