On 1 Feb., 22:54, William Hughes <wpihug...@gmail.com> wrote: > Previous was too complicated
Then I will skip it. > > Can a potentially infinite list > of potentially infinite 0/1 > sequences have the property that > > if s it a potentially infinite 0/1 > sequence, then s is a line of L
You have to distinguish between every and all (in the usual sense) because a potentiall infinite list is not complete. Compare the potentially infinite set (or better say sequence) of natural numbers as the common example.
There is not a sequence of all natural numbers (because that would represent an actually infinite set). There is nothing but finite initial segments (1, ..., n). However there is no upper threshold m limiting n to n < m.
This potentially infinite sequence has the properties: 1) For every finite initial segment (1, ..., n) of the sequence we can find another n+1 (or 2n or 2^n or n^n) that is not in the initial segment. 2) For every n there is a finite initial segment containing n as well as (or 2n or 2^n or n^n). 3) There is no meaningful expression starting or ending or containg "for all finite initial segments of the sequence" or "for the whole sequence" but only "for every finite initial segment of the sequence" or "for every term of the sequence".