In article <f6d08279-d0cf-499f-8dc2-ebf332d4c877@a36g2000yqc.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 16 Jun., 13:41, William Hughes <wpihug...@hotmail.com> wrote: > > On Jun 16, 6:52 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 16 Jun., 12:38, William Hughes <wpihug...@hotmail.com> wrote: > > > > > > On Jun 15, 4:44 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 15 Jun., 22:04, 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." > > > > You have repeatedly noted > > > > WM: If actually infinite paths exist, > > WM: then there is a path p that can be > > WM: distinguished from every path of P. > > A ==> B > > > > You also claim > > > > WM: There is no path p that can > > WM: be distinguished from every path of P.
Since that does not, and cannot, happen in ZF nor anywhere else outside WM's silly world, it is of no mathematical consequence. >
> > This is not my claim but the proven impossibility to distinguish p > from every element of P.
Except that everyone but WM can do it.
> > > > > > > Every path of the tree is from P. I explicitly forbid every other path > > > > > to enter my tree.
Maximal infinite binary trees are not yours to command, and yours, not being among them, are irrelevant. > > > > > > Nope. You cannot forbid every other path to enter the > > > > tree. You add nodes to the tree. > > > > > I add infinite paths. > > > > Which consist of subsets of nodes. > > When you add subsets of nodes to the tree you create > > other subsets nodes in the tree that you did not add. > > That is a bare lie.
It is true even for finite sets: Given P = {{a,b}, {a,c}}, there are subsets of Union(P) that are not members of P. More of them than there are members of P.
> I add the paths p_n , that have a tail of zeros beginning at node n, > one by one, in the following order: > > 0 > -, 1 > -, 2, -, 3 > -, 4, ... > > What unadded subset is created when what path is added?
All sorts of set which are not paths are added with each new node. But the new paths do not all appear until after WM's additions are completed. > > Remember: A union of sets contains only elements that are contained in > at least one of the united sets.
Which means that for any given fison, the union of all fisons also contains at least one element not in that given fison.
> I add singlets {p_n}.
Since none of them is infinite, no set of them contains, as a subset, any paths at all but the union of the set of all of them contains all paths as subsets.
> > Why do you believe that we should stick to mathematics and logic in > that case, if we believe in magic creation of paths in case of the > tree?
WM may believe in such magic, but those of us who pay attention to definitions and logic only see such sight of hand trickery in WM's arguments, not in the actual meanings of actual definitions or in the implications of actual logic.
