Date: Feb 12, 2013 5:01 PM
Subject: Re: Matheology � 222 Back to the roots
WM <firstname.lastname@example.org> 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
> 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.
> > 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
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
> You seem again to fall back into actual infinity.
Since only actual infiniteness can exist in a well constructed set
theory, of course.