```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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