Date: Feb 3, 2013 5:09 PM
Author: William Hughes
Subject: Re: Matheology § 203
On Feb 3, 10:58 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote:

>

>

>

>

>

>

>

>

>

> > > > We can say "every line has the property that it

> > > > does not contain every initial segment of s"

> > > > There is no need to use the concept "all".

>

> > > Yes, and this is the only sensible way to treat infinity.

>

> > So now we have a way of saying

>

> > s is not a line of L

>

> > e.g. 0.111... is not a line of

>

> > 0.1000...

> > 0.11000...

> > 0.111000....

> > ...

>

> > because every line, l(n), has the property that

> > l(n) does not contain every initial

> > segment of 0.111...

>

> But that does not exclude s from being in the list.

It certainly excludes 0.111... from being a single line

of the list.

So 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

?