On 4 Feb., 12:33, William Hughes <wpihug...@gmail.com> wrote:
> 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....
Of course. For every FIS in line n we can find a larger FIS. But there are not all. > > > > > 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
or if FIS(n) is finite, then it is a line of L > > and potentially infinite sets like > the potentially infinite 0/1 sequences
or the potentially infinite FISs (1, 2, ..., n) of |N
> 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
or if |N is potentiall infinite, then |N is a line of L.