On 5 Apr., 12:08, William Hughes <wpihug...@gmail.com> wrote: > On Apr 5, 11:09 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 4 Apr., 23:08, William Hughes <wpihug...@gmail.com> wrote: > > > > Nope. Any single element can be removed. This does not > > > mean the collection of all elements can be removed. > > > You conceded that any finite set of lines could be removed. What is > > the set of lines that contains any finite set? Can it be finite? No. > correct > > So the set of lines that can be removed form an infinite set. > > More precisely. There is an infinite set of lines D > such that any finite subset of D can be removed.
What has to remain? > > This does not imply that D can be removed.
> It does however imply that there is no single element > of D that cannot be removed. That this does not > imply that D can be removed is a result that > you do not like, but it is not a contradiction.
It is simple mathological blathering to insist that |N contains only numbers that can be removed from |N but that not all natural numbers can be removed from |N.
It is a contradiction with mathematics, namely with the fact that every non-empty set of natural numbers has a smallest element.