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! > > 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. Name at least three lines of the asserted infinitely many.
> WM asks for what he knows need not exist.
If a bigmouth shouts "infinity", then he should be able to show at least one element. And if he can't, he is a shown bigmouth.