Date: Feb 14, 2013 6:53 PM
Subject: Re: Matheology � 222 Back to the roots
William Hughes <email@example.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
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