```Date: Feb 4, 2013 6:33 AM
Author: William Hughes
Subject: Re: Matheology § 203

On Feb 4, 12:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 4 Feb., 11:19, William Hughes <wpihug...@gmail.com> wrote:>> > > Of course, every FIS is in a line.>> > True but irrelevant.  We can use induction to> > show that there is no natural number n, such> > that the nth line of L contains every FIS> > of 0.111....>> <snip> [For every n] there are> infinitely many lines remaining beyond line number n.This does not prevent us from using induction to show thatthere is no natural number n, suchthat the nth line of L contains every FISof 0.111....>>>> > The question is now>> > Can a potentially infinite list> > of potentially infinite 0/1> > sequences have the property that> > if s is a potentially infinite 0/1> > sequence, then there is a line, g, of L> > with the property that every> > initial segment of s is contained in g> > ?>> > Yes or No please>> No.So we have potentially infinite sets like |Nwhere you can sayIf L is a potentially infinite list ofnatural numbers then  can have the propertyIf n is a natural number then n is a line of Land potentially infinite sets likethe potentially infinite 0/1 sequenceswhere you cannot sayIf L is a potentially infinite listof potentially infinite 0/1 sequencesthen if s is a potentially infinitesequence then s is a line of L
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