```Date: Feb 14, 2013 5:15 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <5a4a908d-0b4d-4270-abc1-3a34e80dc0a2@c10g2000vby.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> 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.And beyond!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.--
```