On 13 Dez., 11:42, Zuhair <zaljo...@gmail.com> wrote: > On Dec 13, 9:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:> > Ah I see, so you are imposing another condition on the definition of a > > > path, > > > No, that is *the* definition of a path in a Binary Tree. > > Actually it is not. There is no need at all to stipulate that a path > must begin by 0. It is a fixed > definition.
MY Binary Tree contains the paths of real numbers of the unit interval. Of course a path starts at the root node, And as you wanted to contradict MY argument concerning the set of real numbers, other paths would be completely meaningless. You have made a mistake but don't want to confess it. That's all. > > I already showed you that the number of paths in a second degree > binary tree (or third degree if you want to adop the empty path) IS > larger than the total number of nodes. And what I mean by paths those > that can start with 1 or with 0, but with the condition that it must > be unidirectional. And showed it clearly and I've illustrated each > path. You have 9 paths (inclusive of the empty path) and only 7 nodes.
Are you are too dishonest, to confess your error? Or do you really not understand, that your pieces of paths are irrelevant?
> > No. I proved that the number of infinite paths is countable by > > constructing all nodes of the Binbary Tree by a countable set of > > infinite paths. > > This only means that you can have a bijective function from a > countable subset of infinite paths of the binary tree to the set of > all nodes, which everyone already know that this is possible, because > we all agree that the total number of nodes of the infinite binary > tree is countable.
There is a bijective function between N and all finite words. All distinct paths are defined by finite words. Infinite words and infinite paths cannot be distinguished as I proved by this complete infinite Binary Tree:
0 0 1 ...
What kind of paths did I use to construct it?
> What would be a proof is if you manage to define an injection from the > set of ALL infinite paths of the binary tree to the set of all nodes > of the binary tree. > > If you managed to do that, the next question is: > > where is that proof? please show us
I will it show it to you for all the paths that I used to construct the above tree and, in addition, for all the paths that you can identify as beeing missing there.