On 5 Mrz., 01:20, Virgil <vir...@ligriv.com> wrote: > In article > <81241eb4-af0d-46d8-922b-6bf1651b0...@hq4g2000vbb.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 4 Mrz., 22:31, Virgil <vir...@ligriv.com> wrote: > > > > > > ANY infinite set of lines will suffice to contain all naturals, but no > > > > > finite set of lines will suffice. > > > > > Name the first finite line that is necessary. > > > > Why should there be any one line necessary to the union of all of them > > > when every line is only a subset of another line? > > > Exactly. Why should there infinitely many be necessary, if none is > > necessary! > > Who says none are necessary? only WM!
I prove for every n that line n is not necessary. You should be able to understand this proof. > > What those who are less confused than WM say is that a set of such lines > being infinite is both necessary and sufficient to include every FIS. >
Neither nor. Proof, line n is not necessary, because line n+1 contains all FIS of line n. This holds for every n that you may claim necessary. > > > > > And since ANY infinite set of lines is sufficient, and some infinite set > > > of lines is necessary, > > > That should be proved and not only be asserted. > > Why bother with proofs when WM never proves but only asserts?
Can you understand the above proof?
> WM often claims to prove, but no one reading his claimed proofs believes > it.
No matheologian may state that he understand, because he has to be afraid to be called a crank and to be expelled from the community of believers. > > > Name at least three lines of the asserted infinitely many. > > ANY three lines, as part of an infinite set of lines, will work.
No, the lines 1, 2, and 3 do not belong to a necessary set.