On 3/30/2013 8:34 AM, WM wrote: > On 29 Mrz., 19:40, Virgil <vir...@ligriv.com> wrote: >> >> In a COMPLETE INFINITE BINARY TREE, all paths are actually infinite, so >> the issue does not arise.. >> -- > > This is again a simple statement of countermathematical belief and as > such without value in mathematics.
The definition of a compete infinite binary tree requires each and every node to have two child nodes, which means no non-empty path can ever have last node, which means each path must have more than any finite number of nodes.
Which. outside of peculiar places like Wolkenmuekenheim, means each path has an actual infinitely of nodes, as many nodes as here are naturals.
WM is perfectly within his rights to deny that any such Complete Infinite Binary Tree exist within the borders of his Wolkenmuekenheim, but he does not have the power to determine what is to be allowed elsewhere.
In true mathematics, one can require for oneself any axioms one likes, but one cannot impose one's own axioms on anyone unwilling to accept them, except possibly one's own students, liked WM does. --