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. --
