Date: Feb 4, 2013 4:30 PM
Author: Virgil
Subject: Re: WMytheology � 203
In article

<5a7f9508-96b5-4105-856b-2886b44b9d89@k4g2000yqn.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 3 Feb., 23:09, William Hughes <wpihug...@gmail.com> wrote:

> > 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

> > ?-

>

> Of course, every FIS is in a line. And every FIS contains all

> preceding FIS.

> This list

> 0.1

> 0.11

> 0.111

> ...

> contains every FIS of 0.111... as well in the (unchanged) diagonal as

> in a line. Obviously the diagonal cannot have more 1' than every line.

Any 'diagonal' for such a list necessarily contains more 1's that any

line, since for every line of length n it must contain as many positions

as the necessarily following line of length n + 1.

And not all of WM's wriggling can make things work otherwise!

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