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 ?