On 20 Mrz., 20:02, Virgil <vir...@ligriv.com> wrote: > In article > <52fc6409-ea7d-4704-9782-6ba192770...@z3g2000vbg.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 20 Mrz., 14:00, William Hughes <wpihug...@gmail.com> wrote: > > > On Mar 20, 1:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > <snip> > > > > > > So your proof that any two lines can be replaced > > > > > by one line without changing the contents is irrelevant. > > > > > Since contents can only exist in lines, and since every line is > > > > superset to all its predecessors, the proof is correct. > > > > The proof is irrelevant (it is, however, correct) > > > Nice to hear. Not that I had any doubt, but it is nice to hear that > > you have no doubt too. > > > > since showing that lines are not needed for their > > > contents does not show that the lines are not needed. > > > The lines were invented by myself solely for this purpose. > > Then the invention was futile for your purpose was not achieved, as at > least infinitely many of those lines are necessary and have been proved > to be.
Does every infinite set contain at least two elements? Does every two-element-set of enumerated elements contain a first element?
If you agree, name the first element of your infinite set. If you don't agree, please disappear out of sci.logic. > > > > > The first question is: > > Is the first line necessary to have the number 1 in the list. > > > Formulated somewhat more "mathematically": > > Is the union of all lines different from the union of all lines except > > the first one. > > Theorem: Every finite union of lines omits some naturals and every > infinite union of lines includes all naturals
and probably also all quaternions and all race-horses, because infinity is very powerful. It destroys ever sober thought and every reasonable idea.