Date: Jan 13, 2013 5:44 PM
Subject: Re: Matheology � 191
WM <firstname.lastname@example.org> wrote:
> > The definition of a set being countable is that there is a surjection
> > from |N to that set.
> > Thus in order to PROVE a set is countable one must show a surjection
> > from |N to that set, which is just a listing, possibly with repetitions,
> > of that sets members.
> > But any listing of the paths of a Complete Infinite Binary Tree (as
> > infinite binary sequences) proves itself incomplete.
> > Thus the set of paths cannot be made to fit the "countable" definition.
> Above you see the enumeration of the set
> Regards, WM
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