```Date: Feb 13, 2013 9:27 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

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.>>>> > > 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 oflegth 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.Regards, WM
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