On 11 Apr., 20:52, William Hughes <wpihug...@gmail.com> wrote: > On Apr 11, 8:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 11 Apr., 19:19, William Hughes <wpihug...@gmail.com> wrote: > > > > > So you agree that B implies A. > > > > yep, but A does not imply C: P(d_1,d_2,d_3..) > > > That is your interpretation. > > One you agree with,
Not at all! It is completely unsensical to limit the number of removable lines to one.
> C: means that the collection has property > P. A: mean that every element of the collection has property > P. A does not imply C.
Since the collection is removed when every element is removed, and vice versa, there is not the least reason to distinguish A and C. We do not need to consider "the collection" at all. We habe every element and all elements, as you know both completely identical in logic. > > Now let P be (can remove the collection without changing > the union of the remaining lines). We have there is no > contradiction in saying A: for all n, the nth line can be removed.
As I said, that is tantamount with C. In order to see that, consider Cantor's A and B.