In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 3 Mrz., 23:31, Virgil <vir...@ligriv.com> wrote: > > > > You claim that there are infinitely many lines necessary in the list > > > to contain all natural numbers. But for every of these claimed lines I > > > can prove that it is not required in that alleged set of lines that > > > contain all natural numbers. > > > > 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?
And since ANY infinite set of lines is sufficient, and some infinite set of lines is necessary, WM asks for what he knows need not exist.
> Or admit that no finite line is necessary to accomplish what you > believe, namely to be the first line of the set of finite lines that > contain all natural numbers.
I have no reason to merely admit what I have vigorously insisted upon, despite WM's denials. > > > > > > A fact that is trivially obviously from the requirement that every > > natural have a successor natural larger than it. > > No, the belief that an infinite set of finite lines can be finished is > trivially nonsense.
A great deal of non-WM mathematics is nonsense to those, like WM, who are incapable of comprehending it.
> Everybody not completely blinded by matheology can > obtain that from the fact that you claim that an infinite set of lines > is necessary, but you are not able to name only one of them
I did not say "AN infinite set, I said ANY infinite set, which clearly (at least to those not mired in WMytheology) means that no particular line is required.
So that WM is asking for something he should know (if he were at all competent as a mathematician) does not exist. --