On Apr 10, 7:52 am, WM <mueck...@rz.fh-augsburg.de> wrote: > On 9 Apr., 20:15, William Hughes <wpihug...@gmail.com> wrote:
> > No line is an infinite > > sequence of finite unions. > > But if the list contains infinitely many (more than any finite number > of) FISONs, then it contains infinitely many (more than any finite > number of) unions, doesn't it? >
Yes, things that are elements are infinite in number. Every single one of the things is finite. No thing is infinite. Therefore no element of the list is infinite.
> > So now we have: > > > D is the collection of all finite > > lines. > > If you remove the collection of all finite > > lines from D > > i.e., if you remove, according to induction, with FIS n also FIS n+1 > > > nothing is left > > If you remove any one line (and all its predecessors) > > every natural number is left. > > > This is exactly what you keep saying > > is a contradiction.- > > Not at all!
Good. Then we are agreed that it makes perfect sense to say that any one line (and all its predecessors) can be removed, but the collection of all lines cannot be removed.
Thus, the fact that there is no line (along with all its predecessors) that cannot be removed is not a contradiction.