Date: Feb 14, 2013 4:02 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots
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

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