```Date: Feb 23, 2013 11:21 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 22 Feb., 23:23, Virgil <vir...@ligriv.com> wrote:> > Here is a summary of the argument concerning the Binary Tree:>> > 1) The set of all real numbers of the unit interval is (said to be)> > uncountable.> > 2) An uncountable set has (infinitely many) more elements than a> > countable set.> > 3) Every real number has at least one unique representation as an> > infinite binary string (some rationals have even two representations> > but that's peanuts).> > 4) In many cases the string cannot be defined by a finite word.> > 5) Without loss of information the first bits of two strings, if> > equal, need not be written twice.> > 6) Application of this rule leads to the Binary Tree.> > 7) The binary strings of the unit interval are isomorphic to the paths> > of the Binary Tree.>> If WM means they are of equal cardinality or biject with each other ,> true, but to establish an isomorphism, as WM is claiming, one must> specify the structure that is being preserved by the bijection, which WM> has NOT done.The mapping is bijective and linear.> > 8) It is not possible to distinguish more than countably many paths by> > their nodes.>> The set of paths of a CIBT is easily bijected with the set of all> subsets of |N (the path generates the set of naturals corresponding to> the levels at which that path branches left rather than right) which> allows us easily to distinguish any path from any other by the diffences> in their corresponding sets of naturals.This shows a contradiction - at least in case someone acceptsHessenberg's trick as part of mathematics.Regards, WM
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