In article <email@example.com>, 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 > > 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. --