On Nov 22, 1:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 22 Nov., 13:58, William Hughes <wpihug...@gmail.com> wrote: >
WM: There are infinitely many lines. So we have infinitely many unions of WM: a finite initial segment and its predecessors. But infinitely many WM: unions are not an infinite union?
WH: No, of course not.
WM: How then can that be in the first line?
> > > Because, if you take each element from the first line, you are forming > > a union, > > In fact??? is that the way we have to conclude? > If writing in one line, I take the union? If writing, with greates > precision, the same in a new line, I don_t take the union?
In Wolkenmuekenheim "the same in a new line" means "write each S_k on a different line". Strange place Wolkenmuekenheim
If you take each element from a different line, then you form a union as well, but not a union from one line.
The infinite union is not the infinite sequence of finite unions, nor is it an element of the infinite sequence of finite unions, but it is "in" the infinite sequence of finite unions in the sense that you can get it by taking the last element of each finite union.