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 there

are 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 L

or if FIS(n) is finite, then it is a line of L

>

> and potentially infinite sets like

> the potentially infinite 0/1 sequences

or 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 L

or if |N is potentiall infinite, then |N is a line of L.

Yes, infinity is never finished.

Regards, WM