Date: Jan 14, 2013 5:09 PM
Subject: Re: Matheology � 191
WM <email@example.com> wrote:
> On 13 Jan., 23:44, Virgil <vir...@ligriv.com> wrote:
> > > 0.
> > > 0.0
> > > 0.1
> > > 0.00
> > > 0.01
> > > 0.10
> > > 0.11
> > > ...
> > Since every path of a Complete Infinite Binary Tree must have infintely
> > many nodes (or, equivalently, infinitely many branchings), your list of
> > finite objects contains none of them
> Which node of what path is missing?
It is sets of nodes and sets of paths which are missing, not merely
individual nodes or paths. And which paths are be missing cannot be
determined without a list of those paths which are included.
On does not have set of nodes being a complete path in a Complete
Infinite Binary Tree until the root node is in the set and for each node
in the set one and only one of its child nodes is also in the set.
Thus only infinite sets of nodes can represent (complete) paths in a
Complete Infinite Binary Tree. Any finite set of nodes in a Complete
Infinite Binary Tree either does not all lie in any one path or all lies
in uncountably many paths, as many as in the whole tree.