In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 8 Jun., 22:18, Virgil <virg...@nowhere.com> wrote: > > > I prefer to call what is left after removing the head of a path, its > > tail. > > No objection. X is a tail. > > > > > There are infinitely many nodes mapped on every X, > > > > And uncountably many X through every node. > > Let us choose one of them and map it one that node. For the others we > will find other nodes, below that one chosen. Then we have one tail > mapped on one node, and therefore, one path mapped on one node. This > procedure uses up a countable number of paths as it exhausts the set > of nodes. Therefore there is no possibility to construct any further > tail.
There is no need to construct what are already there.
> All nodes are already used up.
From every node issue at least two tails (actually uncountably many tails in every maximal infinite binary tree), and your method only involves one of them, so is incomplete.
> And, what is more important, also > all combinations of nodes are used up.
Then paths must not be what WM calls "combinations of nodes" as not all paths are "used up".