On 1 Apr., 17:05, William Hughes <wpihug...@gmail.com> wrote: > On Mar 27, 8:55 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > Matheology § 233 > > > The set of all termination decimals is a subset of Q. If the set of > > all terminating decimals of the unit interval is arranged as set of > > all terminating paths of the decimal tree, > > It is, of course, impossible to write this out > (there number of terminating decimals is infinite). > But it is possible to construct the Binary Tree according to this method.
> > unavoidably all irrationals > > are written as infinite paths too. But we know that it is impossible > > to write the path of even one single irrational number, let alone of > > several or infinitely many or uncountably many. > > Correct, it is impossible.
It is impossible to write them out. Yes. But they are constructed like the finita paths. It is impossible to prohibit infinite paths (of rationals and of irrationals) to be constructed when the complete set of nodes of the Binary Tree is constructed by means of all finite paths. Therefore it is impossible to distinguish infinite paths by nodes other than be naming infinite sets of nodes. Alas there are only countably many names available.