In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 9 Apr., 12:21, William Hughes <wpihug...@gmail.com> wrote: > > On Apr 9, 11:39 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > <snip> > > unsnip
> > You said that the list > 1 > 1, 2 > 1, 2, 3 > ... > does not contain a line |N, but this list contains an infinite > sequence of finite unions.
Your list contains an strictly increasing infinite sequence of finite sets, making a strictly increasing sequence, which, therefore, cannot contain its limit, if any. > > Why is the result of infinitely many unions different from the result > of an infinite union?
Those infinitely many finite unions only produce the same strictly increasing sequence of sets which sequence cannot contain that infinite union which is its limit because: A strictly increasing infinite sequence cannot contain its limit, if any, as a member. At least outside of Wolkenmuekenheim. > > > > > > > > > > > > Do you agree with. > > > > > > If you remove a finite collection of lines > > > > from D then something remains. > > > > > Yes. > > > > Do you agree with > > > > If you remove any one finite collection > > of lines from D then what > > remains contains every natural number. > > Any one? Does this include the line n+1 if I remove line n? > Then it depends on your answers.
Does WM not know what the word "finite" means any longer? It is quite possible to remove a finite set from D = |N without removing the successor of any element removed, and it is necessary that in removing a non-empty finite set from D = |N, that one remove at least one member without removing its successor.
But WM already know that this is the case everywhere outside of his personal cave, Wolkenmuekenheim. --