On 8 Apr., 12:18, William Hughes <wpihug...@gmail.com> wrote: > On Apr 8, 12:10 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 8 Apr., 10:31, William Hughes <wpihug...@gmail.com> wrote: > > > > On Apr 8, 9:48 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 7 Apr., 23:25, William Hughes <wpihug...@gmail.com> wrote: > > > > > Note that any line plus its predecessors is a finite set. > > > > > So, there is no contradiction in saying that you can > > > > > remove any one line (plus its predecessors) but you cannot > > > > > remove the collection of all lines > > > > Is there a contradiction, Yes or No > > Please answer the question
You can remove a finite set of lines without removing the infinite set. That is obvious. But why should it not be possible to remove all finite lines? That set is well defined. And then something remains, if you are right in saying that an infinite union is more than an infinite sequence of finite unions.
> > > A side-question: Why then can the anti-diagonal of a list of finite > > lines be an infinite line? > > The number of elements in the anti-diagonal of a list of finite > lines is the supremum of the line lengths, not the maximum.
Why do you think that the union of FISONs of paths is not a supremum?
> > The infinite union is already built into the construction principle of > > the sequence: Every line l_n is the union of all lines l_1 to l_n. Why > > do you think there would be a difference when the infinite union is > > explicitly mentioned? > > Because the fact that for every finite union P > is true, says nothing about whether P is true > for an infinite union.-
Why do you think that an infinite sequence of finite unions is not an infinite union?