In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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?
Which infinite sets of lines does WM claim are provably not sufficient?
What WM claims is provable in mathematics is far to often not provable outside Wolkenmuekenheim, and in this instance is definitely not provable outside Wolkenmuekenheim.
THEOREM: To have a subset of the infinite set of lines(FISONs) whose union is |N, it is both necessary and sufficient that that subset of lines also be infinite.
This theorem is valid everywhere outside of Wolkenmuekenheim. Its validity inside Wolkenmuekenheim is unknowable to those not already self-imprisoned, in it.
> And why would you apply > lines of a provably insufficient set in an asserted sufficient set - > other than for cheating, I mean? > I should very much like to see WM try to "prove" outside of Wolkenmuekenheim, that any infinite subset of the set of all lines(FISONS) does not union to give all of |N. --