In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 20 Mrz., 21:21, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 20, 9:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 20 Mrz., 21:01, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Mar 20, 8:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 20 Mrz., 20:40, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > On Mar 20, 4:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > I show that every line, that is not the last line, is not needed. > > > > > > > > Nope. You show that it is not necessary for its contents. > > > > > > This is not the same as not needed. > > > > > > > Agreed: > > > > > I show that every line, that is not the last line, is not needed to > > > > > remain in the list in order to have its contents in the list. > > > > > Agreed? > > > > > > Nope. It may be needed for something else whose contents are > > > > needed (in this case the tail of the list) to exist. > > > > > Please name a line that is needed for the tail of the list to exist. > > > (You do agree that every set of lines has a first element?) > > > > We need an infinite number of lines. > > Choose lines 3,4,6,7,8... > > Then line 3, being one of the needed set chosen is needed. > > Note, that we do not have to choose line 3, so line > > 3 is not necessary. > > Then choose a line that is necessary.
Why must any particular line be necessary?
In a real vector space is there ever any one particular vector necessary for a basis of that space?
> If you say you need an infinite set of lines, then there must be a > first one that is needed.
Since the set of even-numbered lines is sufficient and the set of odd numbered lines is also sufficient and these two sets of lines are disjoint, what MISleads WM to claim that some particular first line is necessary? Other than his overall incompeence?
> Remember: A line is needed if its absence > changes the set of numbers of the list. You state that a set of lines > all of which are needed does exist.
On the contrary, what we have repeatedly said, and proved, is that the infiniteness of a set of lines/FISONs is both necessary and sufficient.
That WM is incapable of learning that marks im s even more incompetent att mathematics that previously known. > > > > Compare to choosing a basis for |R^2. Two vectors > > are needed. However, there is no necessary vector.- > > That is the difference between an enumerated set and a not-enumerated > set.
There are finite vector spaces of several dimensions which can be as thoroughly ennumerated as the set of naturals, so WMs unnatural arguments again fail! --