In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> Or what is your explanation of the fact that the Binary > Tree constructed by all finite initial segments of all paths cannot > be > distinguished from the Binary Tree that in addition contains all > infinite paths?
Since enough finite initial segments (an actual infinity of them) are necessary to get all of the actual infinity of nodes necessary for an actually Complete Infinite Binary Tree, that many of finite initial segments also are enough to produce all the nodes needed by those uncountably many complete paths.
Note that any actually infinite set of nodes must necessarily have uncountably many infinite subsets and paths are just infinite sets of nodes. --