On 2/3/2013 3:58 PM, WM 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. What finite > initial segment (FIS) of 0.111... is missing? Up to every line there > is some FIS missing, but every FIS is with certainty in some trailing > line. And with FIS(n) all smaller FISs are present. > >> Is there a sensible way of saying >> s is a line of L ? > > There is no sensible way of saying that 0.111... is more than every > FIS. And every FIS is in a line.
Do you mean "is in some line"?
As in "there exists a line containing a given FIS"