On 5 Apr., 21:03, William Hughes <wpihug...@gmail.com> wrote: > On Apr 5, 6:04 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 5 Apr., 12:08, William Hughes <wpihug...@gmail.com> wrote: > > <snip> > > > > There is an infinite set of lines D > > > such that any finite subset of D can be removed. > > > What has to remain? > > This depends on the finite subset removed. > If the finite set removed is E then > D\E has to remain.
Is E restricted to an upper threshold? If not, how do you prove its finiteness?
> Note that whatever > subset E is chosen the number of lines > in D\E is infinite (but of course we > do not know which lines are in D\E).
Can you prove for at least one fixed line that it cannot be removed? If not, why do you think that some (even infinitely many) lines must remain? Don't you feel a bit ridiculous, when you again and again claim infinitely many natural numbers none of which you can name? > > However, D cannot be removed without > changing the union of the remaining lines.
That is true if D is nothing but the union of the lines. But in that case we can prove that every rational-complete Cantor-list contains infinitely many anti-diagonals, because for all n in |N, there are infinitely many FISs d_1, ..., d_n in the list. - And more than all FIS of the anti-diagonal is not available as anti-diagonal.