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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