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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