Date: Feb 13, 2013 4:20 PM
Subject: Re: Matheology � 222 Back to the roots
WM <firstname.lastname@example.org> wrote:
> On 13 Feb., 09:48, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <1b2bb717-425f-488d-b50c-e442f20af...@fe28g2000vbb.googlegroups.com>,
> > 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.
No on implied there were. But if not all, name an exception!
> > > > 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?
The n's for which the nth line of the list is not a FIS of d depends on
the list and the d, so
Show me your list and I will show you a 'd' such that
NO line of the list is a FIS of 'd'.
> > 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.
But not any l longer than d, or even as long, if each l is finite.
The point is that for any listing of binary sequences, finite or
infinite, one can define a diagonal which is not listed.
And no matter how loudly WM screams that it is not so, it remains so.