Re: The complete infinite binary tree has only countably many infinite paths.

On 28 Mrz., 09:27, "calvin.ost...@xxxxxxxxx" <calvin.ost...@xxxxxxxxx>
wrote:

Aaargh. The question I am asking is "what IS p(n) (as
a set of edges)?"

p(n) can be understood as a set of edges. It is the union of A and B.
A ist the set of all edges that belong to the intersection of all
paths (taken as sets of edges) that go through node number n.
B is the set of edges that are subsequent to node number n and always
turn left.

It is sufficient to consider only nodes that have value 1, i.e. only
nodes enumerated by an even number n. (When the first path 0.000... is
given.)

Example:

0
/ \
1 2
/ \ / \
3 4 5 6
/ \
.......13 14
....
p(6) contains
A) the edges 0-2, and 2-6, and
B) all edges that subsequently turn left. The first of them is 6-13.

 WM claims the  entire  tree
is a union of a countable set of paths.   That is
reaonable.  I am trying  to get  him  to formalize this.
So, we have T = union { p(i) : i in  Naturals }.

Dear Calvin,
there is no point of formalizing such an obvious truth as I have shown
by my three proofs in the initial posting. But I think that this
thread has yielded a lot of new insights for all parties. Perhaps you
will agree that when you first answered my FOM-contribution, you had
no clue what a multitude of facets the binary tree may hide, won't
you?

Regards, WM
.

Relevant Pages

  • Re: Unions
    ... response of "What planet are you posting from?" ... the most Elegant responses of the year. ... Gone are the days of a union protecting a marginal worker. ...
    (rec.crafts.metalworking)
  • Re: Unions
    ... response of "What planet are you posting from?" ... Gone are the days of a union protecting a marginal worker. ...
    (rec.crafts.metalworking)
  • Re: Zero tries
    ... Usually refers to a NZer talking about their national Rugby ... Union ... My posting makes Alvey jerk off? ... I've had some strange compliments, ...
    (rec.sport.rugby.union)
  • Re: plumbing: how tight should you have to crank a union
    ... surface with Rectorseal #5 for sealing effect. ... I had the same problem with a union on a steam heating system. ... After posting here, someone suggested Rectorseal #5 and I bought it and used it. ...
    (alt.home.repair)
  • Re: OT UNION BUSTING...
    ... The truth is without unions workers have no ... It may be your "truth" but it's not THE TRUTH. ... so I asked for a raise. ... The very existence of a union at a shop pretty much ...
    (rec.crafts.metalworking)
Quantcast