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 your claim is false.
You want to show
~A [Follows from ( A ==> B, ~B) ==> ~A ]
by proving ~B
(Note that assuming ~A is circular)
<snip>
WM: What unadded subset, than can be WM: (a part of) a path, is created when WM: what path is added?
<snip>
> > as previously noted, > > to create a path requires creating an infinite subset. > > To create a path requires to add that path. >
Nope I give a counterexample.
> > > > To do this [create a path] we > > need to add a subset of paths. > > > E.g. The subset of paths added is > > > 1000... > > 11000... > > 111000... > > ... > > > The subset of nodes that is now in the tree is > > > t={1,11,111, ...} > > > Note that t is not an element of P, so the subset > > t is never added to the tree. >
Which is the first statement you disagree with
all nodes of t are in the tree t is in the tree all nodes of t are in P t is not an element of P
Note: if all the nodes of a path h are in the tree then h is in the tree, however, if all the nodes of h are in P, h may or may not be an element of P.
