In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 25 Mrz., 00:49, Virgil <vir...@ligriv.com> wrote: > > In article > > <39dd320b-1f56-4cf7-bb03-f0f634420...@l5g2000yqe.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> 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? > > All FISONs are not sufficient, because forall F in the set of FISONs: > There are infinitely many natural numbers not covered by F and all its > predecessors and all its followers.
Partly false,at least everywhere outside of Wolkenmuekenheim!
While a FISON and all its predecessors are not sufficient, any one FISON together with all its followers, or even any infinite set of follower covers all naturals, at least everywhere outside of 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. > > Nonsense. All FISONs cannot be sufficient, since no FISON is > necessary.
So that WM seems to be claiming that more than what is necessary cannot be sufficient. Such is the inverted logic corrupting Wolkenmuekenheim. > > Corollary: To catch a unicorn it is both necessary and sufficient to > ask an infinity of horses to help.
Outside of Wolkenmuekenheim, it is rumored that one pure virgin is enough, but that would be impossible to test inside Wolkenmuekenheim, --