On 10 Apr., 08:59, William Hughes <wpihug...@gmail.com> wrote: > On Apr 10, 7:52 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 9 Apr., 20:15, William Hughes <wpihug...@gmail.com> wrote: > > <snip> > > > > 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.
Numbers *are* their number. 10 positive naturals include the number 10. n tpositive naturals include the number n.
> Every single one of the things is finite.
The sequence of unions contains not more unions that the infinite union.
> No thing is infinite. Therefore no element of the > list is infinite.
Infinite in number means infinitely many finite unions means the same a an infinite union. Either both are infinite or both are not.
> > 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
By a single move. When applying induction, i.e., when n is removed, also n+1 is removed, every finite line is removed. Then no finite lines remain - only actually infinite lines remain.
> Thus, the fact that there is no line (along with > all its predecessors) that cannot be removed > is not a contradiction. > > Next argument.-
The old question that you heve refused to answer: The Binary Tree, when constructed by all its FISONs, does it contain more than all its FISONs?