On 22 Mrz., 21:33, William Hughes <wpihug...@gmail.com> wrote: > On Mar 22, 7:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > <snip> > > > Line l_n and all its predecessors do not in any way influenturece (neither > > decrease nor increase) the union of all lines, namely |N. > > Yes, given any set of lines K, every element of K has > the property that it can be removed without changing > the union of all lines. Yes, the set of lines that > has this property is the complete set K.
No doubt. > > This is the result of your proof. > Given the premise is valid.
> No, this does not mean that one can do something > that does not leave any of the lines of K > and does not change the union of all lines.
That is clear because my proof rests upon the premise that actual infinity is a meaningful notion. I am glad that you have recognized that.
A ==> B & ~B implies ~A.
That is basic logic.
> You have not proved, > and cannot prove the contrary. > You can only state that it is obvious.
What contrary should I have proved or have intended to prove? I proven just what you said.
> I know you do not like this result
You are in error. I like just this very result.
> (it cannot > be true for finite sets)
Of course not. The premise is actual infinity. That is obviously not possible in finite sets.
> but it is something > you do not like, not a contradiction.