On Mar 13, 5:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote:
> > 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. However, this does *not* imply that there are two numbers that are not in a single line. Nor does it imply that there is a necessary line in K. Note that a sufficient set does not imply a necessary line even in potential infinity. There is no line that is needed to make L have an unfindable last line.