```Date: Feb 4, 2013 7:05 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 4 Feb., 12:33, William Hughes <wpihug...@gmail.com> wrote:> This does not prevent us from using induction to show that> there is no natural number n, such> that the nth line of L contains every FIS> of 0.111....Of course. For every FIS in line n we can find a larger FIS. But thereare not all.>>> > > 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 |N> where you can say>> If L is a potentially infinite list of> natural numbers then  can have the property>> If n is a natural number then n is a line of Lor if FIS(n) is finite, then it is a line of L>> and potentially infinite sets like> the potentially infinite 0/1 sequencesor the potentially infinite FISs (1, 2, ..., n) of |N> where you cannot say>> If L is a potentially infinite list> of potentially infinite 0/1 sequences>> then if s is a potentially infinite> sequence then s is a line of Lor if |N is potentiall infinite, then |N is a line of L.Yes, infinity is never finished.Regards, WM
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