In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> And if I append to every finite path every infinite tail that has a > finite definition like 0.? What will you choose then??? > Nevertheles I will have used only countably many paths yet.
That you have only used countably many does not mean that there are not many more than you have used.
And is has been shown many times, and beyond WM's ability to falsify, that the number of paths in a Complete Infinite Binary Tree is beyond counting (that is, there is not, and cannot be, any mapping from |N to the set of paths that uses us every path. --