On 12 Jan., 23:21, Virgil <vir...@ligriv.com> wrote: > In article > <c971e75b-20e3-4761-b39a-aab5a20a6...@d10g2000yqe.googlegroups.com>, > > > > > > 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 possible. 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.