Virgil
Posts:
4,482
Registered:
1/6/11
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Re: WMytheology � 203
Posted:
Feb 4, 2013 4:30 PM
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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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