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....
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 ?
