On 26 Mrz., 21:51, Virgil <vir...@ligriv.com> wrote: > In article > <520f68df-9a86-4e5f-bd69-d92294e2d...@y4g2000yqa.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 26 Mrz., 03:10, "Ross A. Finlayson" <ross.finlay...@gmail.com> > > wrote: > > > > Two different paths, finite or infinite, have at least one node not in > > > common. > > > If the path of 1/pi is not in the Binary Tree, it is impossible to > > find that path in the Binary Tree > > It is obviously impossible to find any path in a tree when that path is > not in that tree.
So it is, but in matheology that is not obvious. Therefore I emphasized it.
> > notwithstanding the fact that for > > every rational approximation q of 1/pi, there is a better one q' (with > > a node belonging to 1/pi but not to q). The result remains that q' is > > not 1/pi. > > If no binary sequence for 1/pi exists in WM's Complete Infinite Binary > Tree, there must be a first node at which the infinite binary sequence > for 1/pi from every path of length n in the tree.
Wrong. There is no first node in the path of 1/pi that identifies 1/ pi. None of the nodes does so. Therefore there cannot be that first node that is missing if the path of 1/pi is missing. > > I.e., there must be a first binary digit at which the binary > representataion of 1/pi differs from every binary sequence.
In fact, if 1/pi could be identified by a path of its own, that node or bit should exist. But provably it does not. > > And thus there must be a finite binary approximation of 1/pi which does > not appear in WM's tree. > > Contradiction
Nonsense. Read the above.
> WEven though there are only countably many nodes, there are UNcountably > many sets of nodes, and paths are SETS of nodes.
And every real has its own path and its own first node that distinguishes it from every other? (That is the nonsense yuo wrote above.) How should uncountably many paths exist with only countably many different nodes? > > So countability of the set of nodes does not imply countability of the > set of paths, but tends to contradict it.
Yeah, you contradict a lot in this posting, mainly everything you say.