In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 29 Mrz., 19:40, Virgil <vir...@ligriv.com> wrote: > > In article > > <ce3c22f2-9116-4621-b3b4-e722fe51a...@a14g2000vbm.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 26 Mrz., 22:47, Virgil <vir...@ligriv.com> wrote: > > > > > > But a tree that contains paths for all binary rationals will contain a > > > > path for all limits of a sequences of binary rationals. > > > > > Does a sequence always contain its limit? > > > > Depends on the sequence, of course. but a sequence of paths in a > > Complete Infinite Binary Tree in which the nth path must share at least > > n nodes with each of its successors will always converge, though not > > neccessarily to a binary rational. > > A sequence of numbers may converge, but not necessarily to a limit > that is a term of the sequence.
Precisely my point!
> A sequence of paths may converge, but not necessarily to a limit that > is a term of the sequence.
So WM acknowledges that A sequence of binary rational paths can converge to a path that is not a binary rational.
> > In mathematics more precision is required.
Certainly more than WM is capable of producing,. > > > > > > > > > > In a COMPLETE INFINITE BINARY TREE, all paths are actually infinite > > -- > > This is again a simple statement of countermathematical belief
It is matter of simple definition.
The definition of a COMPLETE Infinite Binary Tree requires that no path in such a tree can terminate.
At least it does so everywhere outside of Wolkenmuekenheim, --