In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 26 Feb., 22:54, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 26, 6:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 26 Feb., 13:11, William Hughes <wpihug...@gmail.com> wrote:> On Feb > > > 26, 12:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > We both agree > > > > > > There does not exist an m > > > > such that the mth line > > > > of L is coFIS with the diagonal > > > > (here we interpret "There does > > > > not exist" to mean "we cannot find"). > > > > > > So we agree any such m must be an > > > > unfindable natural number. > > > > > It is a variable that can take any natural number. > > > > OK, so we have constant natural numbers > > and variable natural numbers. > > No. We have a "limit" (not an infinite limit however) of the list and > of the FIS of the d (which both are the same) that assumes a natural > number which however cannot be known.
But if it is the limit, even if unknowable, it can not have any successor, which makes it NOT a natural number. > > > > We agree that any such m cannot be > > a constant natural number but must > > be a variable natural number. > > The "limit" is a variable, yes.
The "limit" must without any sucsessor, thus NAN (not a natural). > > > > Now, in standard terminology (where there > > is no such thing as a variable > > natural number) we have > > a natural number valued function of time > > (or of the number of FISs of d that "actually > > exist", an increasing function of time) > > m(t). It is trivial to see that there > > is an m(t) such that the "actually existing" > > line with index m(t), contains all > > "actually existing" FISs of d. > > Exactly! > > > However, calling m(t) "the index of the line > > that contains every FIS of d" > > strains language beyond the breaking point. > > > > > > Similarly, it follows by definition > > of "actually existing", that > > there is a time varying function max(t), > > such that at any time max(t) is the maximum > > of the "actually existing" natural numbers. > > However, calling the function max(t) > > the largest element of the potentially > > infinite set |N, is silly. > > Wo does that?
WM does that!
> Note, there is no "set |N" in potential infinity.
If one can distinguish natural numbers from things which are not natural numbers WHY is there no set of all natural numbers in WMYTHEOLOGY?
Note that there is such a set everywhere else!
> The > "set |N" is an actual, i.e., completed infinity. But this assumption > is contradicted (see below).
Not outside of WMYTHEOLOGY ! > > > > Now no one can stop you using whatever > > terminology you want. However, do not > > expect that you can use idiotic terminology > > without being considered an idiot. > > But one can use such arguing without being considered as such? > Remember: Your point of view requires, what you often have emphasized: > There are all FIS of d in the list, but there is no line containing > them. This implies that they are distributed among several lines and > contradicts the plain fact, according to which the list is > constructed.
Your LIST of lines is constructed so that there is no line containing all the elements in all the lines, but in any decent form of set theory, the union of the lines (considered as the union of the set of their sets of elements) must exist, and that union, appropriately ordered, is d.
Thus WMytheology cannot exist in the presence of any decent set theory. > > Do you have any explanation for that point of view?
Yes! WM's point of view is corrupt and self-contradictory, and thus of no mathematical value whatsoever. > > Regards, WM --