On 8 Apr., 23:30, William Hughes <wpihug...@gmail.com> wrote: > On Apr 8, 7:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > <snip> > > > 1) Why do you think that the union of FISONs of paths is not a > > supremum? > > I don't.
You answered on: Does the same sequence understood as FISONs of paths contain the path 1/9?
You answered on: Is the union of these FISONs 1/9?
> > 2) Is there a difference between an infinite sequence of finite unions > > of elements and an infinite union of the same elements? > > No. [but note the fact that every element of the sequence > has property P does not mean the sequence has property P]
In 0.1 0.11 0.111 ... an infinite union is *in* the sequence and an infinite union is not in the sequence.
> Let D be the collection of all finite lines. > > Do you agree with > > If you remove the collection of all finite > lines from D there is nothing left.
You have not yet answered my question which is necessary for me to know, in order what your collection is. Since every line is a finite union the collection contains infinite unions (i.e., more than every finite number of unions). Does this mean that there are properties changed? In contrast the union of all lines is assumed to be 1/9. There obviously properties are changed.
Therefore I need to know whether you think that an infinite sequence of finite unions is property-changing like an infinite union or not? And if not: why not?
My answer to your question: If not, then removing every line of the collection means nothing remains.
But then my question remains: Why do you think that an infinite sequence of finite unions has other P-changing properties than an infinite union?