In article <d97be259-c60f-4c65-a49c-8efd08ddfabd@r34g2000vba.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 19 Jun., 19:37, William Hughes <wpihug...@hotmail.com> wrote: > > On Jun 19, 1:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 19 Jun., 17:56, William Hughes <wpihug...@hotmail.com> wrote: > > > > > > Your claim is that "no possibility exists to construct or to > > > > distinguish by one or many or infinitely many nodes > > > > of the tree another path." > > > > > > A: actually infinite paths exist, > > > > B: the infinite tree contains a path p that can be > > > > distinguished from every path of P. > > > > > > You agree > > > > > > A ==> B > > > > > > So if A is true then B is true > > > > and your claim is false. > > > > > > You want to show > > > > > > ~A [Follows from ( A ==> B, ~B) ==> ~A ] > > > > > > by proving ~B > > > > > > (Note that assuming ~A is circular) > > > > > > > > you have agreed that t can be distinguished from > > > > > > every element of P. > > > > > It does not matter whether I have agreed > > > > > > Outside of Wolkenmuekenheim it does. > > > > > > > it matters whether it is > > > > > true. > > > > > As you see from the tree, > > > > > > the subset of nodes t is in the tree > > > > <snip> > > > > > > And we agree that > > > > > > the subset of nodes t is not in > > > > a single element of the list P > > > > > if actual infinity axists. > > Otherwise your alleged "proof" is even more obviously wrong.
If actually infinite sets can exist, WM is wrong, and if they don't then all trees are finite and WM IS STILL WRONG. > > > > So you cannot prove ~B without making > > the assumption ~A which is what you are trying > > to prove. > > Wrong. ~B is proven by the impossibility to distinguish t from every > path of the binary tree and the fact that the tree does not contain > paths that are missing in P.
Neither of which claimed "facts" is true if any actually infinite sets exist, and the alleged tree and set P themselves do not exist at all if no actually infinite sets exist, so the issue would then be moot.
