In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 14 Feb., 22:02, Virgil <vir...@ligriv.com> wrote: > > In article > > <8eb0782b-60e7-4128-a03a-d1562cf4c...@g16g2000vbf.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@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! > > Do you miss one of them in all lines of the list? Or is each one in > infinitely many lines? So you can choose one of these infinitely many > lines in order to get FIS(n) of d. > > > > > The list contains every finite initial segment of d. > > > Do you agree? > > > > Irrelevant > > In fact, it is irrelevant whether you agree.
Until you provide the list and the d it is irrelevant whether anyone agrees. > > > > > Every finite initial segment is finite. > > > Do you agree? > > > > Irrelevant > > Please note, I did not ask you. > > > > > > > > What do you conclude? > > > > That for every finite line d is longer than that line > > You think that d in actually infinite.
All I said was that it is longer than any finite line.
If you claim otherwise you are claiming it to be no longer than some finite line, which makes it also a finite line.
> It is not. It stretches from > d_1 to the d_n of your choice.
If it is not longer than some finite line of one's choice, then, since it is already a line, it is a finite line.
> And exactly the same is in infinitely > many lines. Of course you can choose whatever n you like (because that > is the meaning of potentially infinite: you can choose whatever n you > like).
And d must be longer than any n one chooses, or that one CAN choose, as otherwise it is finite. --