On Mar 13, 6:33 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 13 Mrz., 17:59, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Mar 13, 5:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote: > > > <snip> > > > > > If you wish to contest this, use my words not > > > > yours (e.g. I have never said "The list contains more > > > > numbers than fit into a single line", I have said > > > > "There is no line in the list which contains every > > > > number in the list".) > > > > Correct. The list has more numbers than a single line has. Since every > > > number that is in the list, must be in at least one line, this implies > > > that the numbers are in more than one line. > > > To be precise, a set of lines, say K, that contains all the numbers > > contains at least two lines. > > In actual infinity, this is not avoidable. > We note: At least two lines belong to the set that contains all > numbers. We call these lines necessary lines.
Why, when they are clearly not necessary?
Let J be a set of the lines of L with no findable last line. At least two lines belong to J. Are any lines of J necessary?