On 17 Apr., 21:41, Virgil <vir...@ligriv.com> wrote:
> > A rhetorical question. Even Virgil knows that the answer is "no". > > Is there a line containing EVERY member of A?
Yes, of course. Name an element of A that is not in a line together with all its predecessors. You will fail. So every element you can name, is in a line of B. And in A there are only elements that you can name.
> Is there for every line a member of A not in that line?
Of course. Potential infinity has this property: For every even number there is a larger odd number, and for every odd number, there is a larger even number. That's the reason that we cannot find a FISON of A that is larger than every line of B and vice versa.
If A was actually infinite, then it should be larger than all lines of B. This could only be proven by an element of A that is not in B. But it cannot be proven. It can at most be believed. But here we do mathematics.