In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 1 Feb., 16:18, William Hughes <wpihug...@gmail.com> wrote: > > Let a potentially infinite list, L, > > of potentially infinite 0/1 sequences > > have the property that every > > (in the sense of "all from 1 to n") > > potentially infinite 0/1 sequence > > is a line of L > > I just gave an example. Do you agree? Or do you think of something > else? > > > > Let s be a potentially infinite > > 0/1 sequence. > > > > Does this imply that there is > > a natural number m, such that s > > is the mth line of L > > ? > > Would you please notice that "all" in the sense of "from 1 to n" > simply means "all lines that are in the list". Of course they are in > the list. Not more and not less. Why the heck should some other, > external line that is not in the list, be in the list?
But is the last line in the list? NOTE that a set with a first line and for each line a successor line different from all its predecessors is necessarily ACTUALLY infinite. > > Hint: You try to ask for a 0/1 sequence of the set of all possible 0/1 > sequences. My answer is: There is no set of all possible 0/1 > sequences. Therefore your question is meaningless in potential > infinity.
But still meaningful in standard mathematics, in which a set is either actually infinite or actually finite, but never so neurotic as to be unable to tell which. --