In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 11 Jun., 13:00, William Hughes <wpihug...@hotmail.com> wrote: > > > > Because paths cannot be distinguished without nodes. > > > > Proves nothing. We know that a countable > > number of elements can distinguish an uncountable > > number of subsets. A countable number of nodes can > > distinguish an uncountable number of paths. > > No that is provably wrong.
It may be considered wrong in WM's mythic world of MathUnrealism, but is not wrong in ZF, which WM s unable to show self-contradictory though it is easily show to contradict WM's mathUnrealism.
> All nodes are used up by a countable number > of paths, e.g., all paths ending in a tail of zeros.
But not all paths. And using the same set of nodes, one can easily add infinitely more paths. One can even add countably many more paths endlessly.
> Therefore no > possibility exists to construct or to distinguish by one or many or > infinitely many nodes of the tree another path.
Except that I can do what WM claims cannot be done merely by reversing all the 0's and 1's of every path to get as many new paths using only the same node set.
> All combinations of > nodes that are possible in the tree have already been occupied.
Except that there is an easy way to get as many new and supposedly impossible paths as WM already has by merely switching all 0's with 1's.
WM really make an ass of himself when he makes claims so easily and obviously falsifiable