On Mar 16, 1:16 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 16 Mrz., 12:26, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Mar 16, 10:30 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 15 Mrz., 23:27, William Hughes <wpihug...@gmail.com> wrote: > > > > > On Mar 15, 8:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > Let's first prove that already two cannot be necessary by the fact > > > > > that two always can be replaced by one of them without changing the > > > > > contents. > > > > > This is true but the fact that the two lines are > > > > necessary has nothing to do with their contents. Two lines > > > > cannot be replaced by one of them without changing the number > > > > of lines. > > > > Why should line-numbers be changed? Perhaps we are misunderstanding > > > each other. > > > I said "number of lines" not "line-numbers". > > If you replace two lines by one of them, you do > > not change the contents, but you do change the number > > of lines. Since the number of lines is important > > and the contents are not, you cannot replace > > two lines with one line. > > Ok, I understand. Anyhow, if the number of lines is not empty, then > there must remain at least one line as a necessary line.
Not a particular line. This is similar to the case where any set of lines with an unfindable last line has at least one "necessary" findable line. This line has a line number in the original list but we can choose the "necessary" findable line to have any line number we want. The fact that more than one findable line is "necessary" does not mean there must be a set of line numbers which is nonempty and has a least element.