```Date: Feb 13, 2013 3:48 AM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <1b2bb717-425f-488d-b50c-e442f20af58d@fe28g2000vbb.googlegroups.com>, WM <mueckenh@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.> >> > 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. 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.And inside Wolkenmuekenheim all lines are finite.> > 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.> >> > You are asserting a contradiction.> > It is a contradiction only when confusing every and all.The only way that some statement about a natural can fail to be true for all naturals is when there exists some natural for which it is false.--
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