On 15 Mrz., 13:56, William Hughes <wpihug...@gmail.com> wrote: > On Mar 14, 10:31 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 14 Mrz., 08:39, William Hughes <wpihug...@gmail.com> wrote: > > > > On Mar 13, 11:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 13 Mrz., 22:41, William Hughes <wpihug...@gmail.com> wrote: > > > > > > 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? > > > > > Remove all lines. > > > > Can any numbers remain in the list? No. > > > > Therefore at least one line must remain in the list. > > > > > We do not know which it is, but it is more than no line. > > > > In other words, it is necessary, that one line remains. > > > > However, it is not necessary that any one particular > > > line remain. So while it is necessary that the set > > > J contain one line, there is no particular line l that is > > > necessary. > > > Correct. But I have not claimed that there are particular lines. > > Then it is a mistake to call particular line necessary > e.g. to say "There is a necessary line".-
I don't say that there is a necessary line. It is necessary, that there remains a line or two. In detail:
In potential infinity it is necessary that at least one line has to remain undeleted in order to contain all natural numbers that are in the list.
In actual infinity it is necessary that at least two lines have to remain undeleted in order to contain all natural numbers of |N.
No special line is necessary. But we know that two or more lines can never do a better job than one. So whatever lines may remain, the assertion is falsified.
I have explained this in Matheology § 224. Please switch to that thread if you have to say more, because this one would be very uncomfortable to load for readers with slow internet connection.