On 17 Apr., 21:33, Virgil <vir...@ligriv.com> wrote:
> > Is there any number of A that is not in at least one line? > > The set A in not "in" any one line so the set A is not in B.
I did not ask about the set A, because it will turn out that there is no such set, if one is willing to accept that nothing of the set remains, after all its elements have been removed. > > > So we have an identity. There is no actually infinite line in B, so > > there is no actually infinite sequence A. > > At least not as a term of B.
So it is. But it is trivially true that every element of A together with all its predecessors is in a line.
The argument is similar to: (A < B & B < C) ==> (A < C), well-known and often applied in mathematics.