In article <fc4f3bf2-083d-4cbf-9437-5cfbaea67d03@c10g2000vbt.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> 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.
I have no idea what WM means by saying that the mapping between the set of binary strings and the set of paths of a Complete Infinite Binary Tree is "linear". There is certainly no meaning of "linear" in English mathematics that is appropriate. > > > > 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
Not outside WMytheology
> - at least in case someone accepts > Hessenberg's trick as part of mathematics.
To which Hessenberg, Karl or Gerard or some other one, does WM refer?
And to what alleged "tricks"?
And accepting any of the tricks of real matheticians like the Hessenbergs sure beats accepting any of WM's tricks in being any part of real mathematics. --
