In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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.
It is true that no one of 1 or 2 or 3 is neccessary to make the sum of them positive, so by WM's argument, none of them are necessary, and 0 is positive. > > > > 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.
But I do not claimed that any line is neccessary.
My claim is that any infinite set of lines is sufficient, and that no finite set of lines is sufficient.
So if WM wishes to prove me wrong, he must disprove either (1) that any infinite set of lines is sufficient or (2) that no finite set of lines is sufficient.
Neither of which he has done or can do. > > > > > > > > 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?
I do not see anything by WM that qualifies as a proof of anythng relevant to my claim that any infinite set of lines is sufficient, and that no finite set of lines is sufficient. > > > 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.
Anyone who would believe that is as ditzy as WM. > > > > > 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.
There is no PARTICULAR set which is necessary, as one can come up with two or more pairwise disjoint sets all of which are sufficient.
For example, take the residue classes modulo any prime and intersect them with |N. Each of the resulting pair-wise disjoint sets of naturals is sufficient, sowing that WM is totally wrong, again, as usual.
So that WM's continual references to some illusory necessary set or necessary member just shows his total incompetence as a mathematician. --