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.

--