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.