Date: Feb 13, 2013 9:27 AM
Subject: Re: Matheology § 222 Back to the roots
On 13 Feb., 09:48, Virgil <vir...@ligriv.com> wrote:
> In article
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 12 Feb., 20:40, William Hughes <wpihug...@gmail.com> wrote:
> > > > What do you understand by being equal "as potentially infinite
> > > > sequences"?
> > > two potentially infinite sequences x and y are
> > > equal iff every FIS of x is a FIS of y and
> > > every FIS of y is a FIS of x.
> > Every means: up to every natural number.
> Which includes being up to all natural numbers.
No. After all there is nothing after all natural numbers.
> > > You can use induction to show that two potentially
> > > infinite sequences are equal (you only need
> > > "every" not "all").
> > Up to every n there is a line l identical to d.
> Only in Wolkenmuekenheim.
For which n is this line lacking?
> Since for every line of length n, d is of length at least n+1, at least
> everywhere else besides Wolkenmuekenheim, WMs claim does not hold true
> outside it.
For every line of lenght n there is a line of length n^n^n, so d of
legth n+1 has no problems with accomodation.
> And inside Wolkenmuekenheim all lines are finite.
Do you know of an infinite line? A line inexed by omega, for instance?
> > For every FIS of d there is a line. You cannot find a line for all FIS
> > (because all FIS do not exist).
> But for each finite line l,there is FIS of d longer than l.
Again for each FIS of d there is a longer l.