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. All nodes are already used up. And, what is more important, also all combinations of nodes are used up.
