On 3/24/2013 4:13 AM, WM wrote: > 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 >
Not when you fail to define your terms.
Crayon marks are not sets.
> 1 > > 1 > 1,2 > > 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? >>
Could you please illustrate what is meant by "well-defined" here?