|
|
Re: Matheology § 203
Posted:
Feb 3, 2013 5:09 PM
|
|
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
?
|
|
