On Feb 4, 12:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 4 Feb., 11:19, William Hughes <wpihug...@gmail.com> wrote: > > > > Of course, every FIS is in a line. > > > True but irrelevant. We can use induction to > > show that there is no natural number n, such > > that the nth line of L contains every FIS > > of 0.111.... > > <snip> [For every n] there are > infinitely many lines remaining beyond line number n.
This does not prevent us from using induction to show that there is no natural number n, such that the nth line of L contains every FIS of 0.111.... > > > > > 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 > > ? > > > Yes or No please > > No.
So we have potentially infinite sets like |N where you can say
If L is a potentially infinite list of natural numbers then can have the property
If n is a natural number then n is a line of L
and potentially infinite sets like the potentially infinite 0/1 sequences where you cannot say
If L is a potentially infinite list of potentially infinite 0/1 sequences
then if s is a potentially infinite sequence then s is a line of L