```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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