On 23 Mrz., 23:36, William Hughes <wpihug...@gmail.com> wrote: > On Mar 23, 11:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 23 Mrz., 21:26, William hHughes <wpihug...@gmail.com> wrote: > > You claim that no finite line of the set changes the union. > > There is no single finite line such that the removal of this one line > changes the union.
This holds for every line and all its predecessors, i.e., for the whole potentially infinite set
1 1,2 1,2,3
> > > You claim that when every finite line which does not change the union, > > is deleted, then the union is changed. > > When every finite line with the property that when it alone is > removed then the union is not changed, is deleted, then the union > is changed.
That is an unconfirmed statement. And it is wrong, if every well- defined set of natural numbers has to have a least element. Do you accept this theorem? Do you agree that the definition "line of the list that does not change the union of all lines" is well defined? > > This is not equivalent to > > There is at least one line l, so that if l is removed the union > is changed.
See above. Do you reject this order-property of |N? Or do you think it is necessary to have an excemption for our special case?