```Date: Feb 13, 2013 2:54 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

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.>> 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.But according to your implicitely made assumption it should be truefor all n. The lines of the list, if written into one single line, L,yield: The potentially infinite sequences L and d are equal.123... = L112123...>> Your first claim is that there is a line l such that> d and l are equal as potentially infinite sequences.For every n this is true.>> Your other claim is that there is no line> l such that d and l are equal as potentially infinite> sequences.For every FIS of d there is a line. You cannot find a line for all FIS(because all FIS do not exist).>> You are asserting a contradiction.It is a contradiction only when confusing every and all.Regards, WM
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