On 25 Mrz., 20:50, Virgil <vir...@ligriv.com> wrote:
> > > 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!
So, if there are infinitely many FISONs, then one or more of them are infinite, or two or more together reach into the infinite that is larger than every single FISON. You should proclaim your due faith from the pulpit. > > 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.
It seems, your brain must be very cloudy (in German wolkig) to believe and to herald such nonsense. > > > > > > 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.
No. Alas, I see that all elements that you name can be proved to be not necessary, so you name only unnecessary elements, believing that infinitely many will do what none of them does. You must really have lost touch with rational thinking to argue in that manner.