```Date: Feb 13, 2013 4:20 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <47d84a88-950f-4091-8dcb-13cdaa3b2e62@z4g2000vbz.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> 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.--
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