Date: Jan 13, 2013 4:23 AM
Subject: Re: Matheology § 191
On 12 Jan., 23:21, Virgil <vir...@ligriv.com> wrote:
> In article
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 12 Jan., 12:45, Zuhair <zaljo...@gmail.com> wrote:
> > > On Jan 12, 11:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > Matheology § 191
> > > > The complete infinite Binary Tree can be constructed by first
> > > > constructing all aleph_0 finite paths and then appending to each path
> > > > all aleph_0 finiteley definable tails from 000... to 111...
> > > No it cannot be constructed in that manner, simply because it would no
> > > longer be a BINARY tree.
> > No? What node or path would be there that is not a node or path of the
> > Binary Tree? This is again an assertion of yours that has no
> > justification, like many you have postes most recently, unfortunately.
> Your claim that there are only aleph_0 possible tails is falsified by
> the Cantor diagonal argument:
> Any listing of those tails as binary sequences allows the anti-diagonal
> constriction of a tail not listed. and if you cannot list them, you have
> no proof that they are only countable in number.
A listing of all finite initial segments of all possible tails is
Cantor's diagonal argument leads to an anti-diagonal that differs from
every finite initial segment by a finite initial segment which is a
self-contradiction since all possible finite initial segments that
possibly could differ are already there.