```Date: Feb 15, 2013 5:58 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 15, 10:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 15 Feb., 00:44, William Hughes <wpihug...@gmail.com> wrote:>> > > > Two potentially infinite sequences x and y are> > > > equal iff for every natural number n, the> > > > nth FIS of x is equal to the nth FIS of y>> > So we note that it makes perfect sense to ask> > if potentially infinite sequences x and y are equal,>> and to answer that they can be equal if they are actually infinite.> But this answer does not make sense.> You cannot prove equality without having an end, a q.e.d..A very strange statement.  Anyway there is no reason toclaim equality.  Let us define the term coFISTwo potentially infinite sequences x and y are said to becoFIS iff for every natural number n, thenth FIS of x is equal to the nth FIS of y.We note that it makes perfect sense to askif potentially infinite sequences x and y are coFIS,we have cases where they are not coFIS and caseswhere they are coFIS..  We also note that noconcept of completed is needed, so coFIS canbe demonstrated by induction. In particular, youdo not need a last element to prove that x and yare coFIS.So WMs statements arethere is a line l such that d and lare coFISthere is no line l such that d and lare coFIS
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