Date: Feb 14, 2013 6:53 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<edc41700-d86f-4db5-8928-62768ed77a36@z9g2000vbx.googlegroups.com>,
William Hughes <wpihughes@gmail.com> wrote:

> On Feb 14, 8:26 am, 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

> >
>
> So we note that it makes perfect sense to ask
> if potentially infinite sequences x and y are equal,
> we have cases where they are not equal and cases
> where they are equal. We also note that no
> concept of completed is needed, so equality can
> be demonstrated by induction.
>
> So WMs statements are
>
> there is a line l such that d and l
> are equal as potentially infinite sequences.
>
> there is no line l such that d and l
> are equal as potentially infinite
> sequences.


Thus WM accepts
'P and not P' but rejects 'Tertium Non Datur'.
>
>
>
>
>
>

> > And just this criterion is satisfied for the system
> >
> > 1
> > 12
> > 123
> > ...
> >
> > For every n all FISs of d are identical with all FISs of line n.


For every n there is an (n+1)st fison of d not identical to any FIS of
line n.
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