In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 26 Mrz., 00:18, Virgil <vir...@ligriv.com> wrote: > > In article > > <ad404888-6726-4aa3-b421-fcc887b93...@7g2000yqy.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > So the set of all rational numbers always contains all irrational > > > numbers? Or only some? Or is that a speciality of the Binary Tree? > > > > It is a speciality of a complete binary tree. > > > > It is something that would be fairly obvious to any competent > > mathematician, which is, no doubt, why it is not obvious to WM. > > -- > > I let this stand as it is.
I should have said a Complete INFINITE Binary Tree.
There is no Complete INFINITE Binary Tree which can represent all binary rationals in the interval [0,1] by paths without also having a path for every limit of a convergent sequence of such binary rationals.
As any competent mathematician can easily verify for himself. --