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.
We agree that any such m cannot be a constant natural number but must be a variable natural number.
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. 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.
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.