Re: Cantor and the binary tree

In article <MPG.1d0fd70a2aca34399896a7@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> In article <ITSnetNOTcom#virgil-7F6FBB.13541107062005
> @comcast.dca.giganews.com>, ITSnetNOTcom#virgil@xxxxxxxxxxx says...
> > In article <1118166450.883263.12840@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > mueckenh@xxxxxxxxxxxxxxxxx wrote:
> >
> > > Virgil wrote:
> > > > In article <1118049962.009645.111100@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > > mueckenh@xxxxxxxxxxxxxxxxx wrote:
> > > >
> > > > > Daniel W. Johnson wrote:
> > > > > > <mueckenh@xxxxxxxxxxxxxxxxx> wrote:
> > > > > >
> > > > > > > You have shown that set theory is inconsistent. Congratulations.
> > > > > >
> > > > > > No.
> > > > > >
> > > > > > He has shown that the combination of set theory with your
> > > > > > assertions is
> > > > > > inconsistent.
> > > > >
> > > > > The basic element of the binary tree is the branching where a path is
> > > > > separated.
> > > > > /
> > > > > B
> > > > > /\
> > > > > If set theory cannot describe this fact then it is useless.
> > > >
> > > > And if this path separation cannot do contour integration is it equally
> > > > useless? Set theory is not obligated to analyse binary trees.
> > >
> > > Does it forbid my way of analysing the tree?
> >
> > Only logic is needed to do that. In a maximal binary tree, every maximal
> > path can only be "separated" from ALL other paths by the set of ALL
> > nodes that it passes through (except for the root node which is common
> > to all) so the set of paths associates with a set of infinite subsets of
> > the set of nodes.
> >
> And yet, one can say each node in the tree is identified by the infinite
> set of unique paths which pass through it, so by that logic, there are
> infinitely many more nodes than paths. That chain of thought doesn't
> work.

Actually, any node is uniquely identified by any pair of paths which
split at that node, so on that argument the number of nodes cannot
exceed half the number of paths.
.

Relevant Pages

  • Re: Cantor Confusion
    ... And as 10^-k is never zero, that sum is never an irrational number. ... The infinite binary tree contains this limit. ... Therefore we can calculate the union of all ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... In a maximal binary tree, ... one can say each node in the tree is identified by the infinite ... paths as emanate from the root node. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... tree), one has both the right and duty to make him state his meaning. ... with infinitely many nodes, a path must consist of an infinite sequence ... is a set containing a single path bundle. ...
    (sci.math)
  • Re: Binary Tree and Pairs of Nodes
    ... was an infinite countable set of nodes" and "iff infinite sets could ... entire infinite complete binary tree. ... This shows that there is no set of all reals. ...
    (sci.logic)
  • Re: Cantor Confusion
    ... Apparently you do not understand the working of limits. ... > the infinite series there is an edge passed in full. ... You should know that you can *not* reverse absolutely converging series. ... Care to give a *proof* that the tree ...
    (sci.math)
Quantcast