On 24 Mrz., 11:02, William Hughes <wpihug...@gmail.com> wrote: > On Mar 24, 10:23 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 23 Mrz., 23:58, William Hughes <wpihug...@gmail.com> wrote: > > > WH: this does not mean that one can do something > > > WH: that does not leave any of the lines of K > > > WH: and does not change the union of all lines. > > > This does not mean that one can really do so > > It does, however, mean that you have not shown > that one can or cannot.
The proof shows that one can remove all finite lines of the set. If you believe that the set of all finite lines is something else, I will not object. But if we remove all finite lines of the set, then no finite line remains.
This holds because induction holds for all finite lines, which in ordinary logic of set theory is the same as every finite line including all its predecessors.
So this has been proved in case the actual infinite set |N is existing and containing more than every finite line of the list.