In article <8eb0782b-60e7-4128-a03a-d1562cf4cd37@g16g2000vbf.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 13 Feb., 23:22, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 13, 9:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > <snip> > > > > > You cannot discern that two potentially infinity sequences are equal. > > > When will you understand that such a result requires completeness? > > > > Nope > > > > Two potentially infinite sequences x and y are > > equal iff for every natural number n, the > > nth FIS of x is equal to the nth FIS of y > > No concept of completeness is needed or used. > > Remember, there are only finite initial segments.
But infinitely many of them!
> The list contains every finite initial segment of d. > Do you agree?
Irrelevant
> Every finite initial segment is finite. > Do you agree?
Irrelevant
> For every finite initial segment induction holds. > Do you agree?
Irrelevant
> Every finite initial segment of d that is in line n is also in line n > +1. > Do you agree?
Irrelevant > > What do you conclude?
That for every finite line d is longer than that line, and thus not contained in in any line. > > Regards, WM --
