On 24 Mrz., 20:39, Virgil <vir...@ligriv.com> wrote:
> But if David had left out the world "all", and said merely > "In fact, Aleph_0 lines are required > (necessary sufficient) to contain all of the naturals." > then David would have been correct, since EVERY set of aleph_0 lines is > sufficient but no set of less than aleph_0 lines is sufficient.
We know your statements of faith. But where do you get aleph_0 lines without using lines of the infinite set of aleph_0 lines that, as provable in mathematics, are not sufficient? And why would you apply lines of a provably insufficient set in an asserted sufficient set - other than for cheating, I mean?