On 30 Okt., 23:33, SPQR <S...@roman.gov> wrote: > In article > <9c125891-8f06-4977-9447-fa2d31e5a...@h24g2000yqm.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 30 Okt., 16:30, William Hughes <wpihug...@gmail.com> wrote: > > > On Oct 30, 11:40 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 30 Okt., 15:27, William Hughes <wpihug...@gmail.com> wrote: > > > > > > Nope. being infinite is a property of the string, not a point > > > > > in the string. (E.g. for strings indexed by the natural numbers, > > > > > a string is infinite iff it does not have a largest index). > > > > > There are lots of ways to be sure the string being investigated > > > > > is infinite. > > > > > You will see the failure of this wrong assumption if you try to find > > > > out (discern?) whether the following Binary Tree contains infinite > > > > paths: > > > > > 0 > > > > /\ > > > > 0 1 > > > > ... > > > > [If the usual assumption is made that any time there is a 0 in the > > > tree there > > > is one branch to a 0 and one branch to a 1] > > > > Let P, a set of nodes, have the following properties. > > > > P contains the root 0 > > > If P contains a node 0 on level n, it contains the node > > > 0 on level n+1. > > > > Then P is an infinite path, (0,0,0,...) > > > > Any tree that contains every node needed to define all finite paths > > > also contains every node needed to define all infinite paths. > > > But does it contain an infinite path? > > Since such a tree must contain a child of every node in order to define > all possible finite paths, it cannot contain any path having a terminal > node with no children. > > > > > Two questions: > > > 1) It is impossible to take the union over all finite trees with n > > levels? > > If you mean binary trees and unions of node sets, it is possible, at > least as a union of suitably chosen isomorphic images of their node sets! > > The result will be the node set of a complete n-leveled binary tree > with 2^(n-1) paths, each of n nodes- Zitierten Text ausblenden -
Would it be possible to discern the complete and the incomplete tree (that without any infinite path) by the set of nodes alone?
