In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 27 Feb., 00:24, Virgil <vir...@ligriv.com> wrote: > > > > Is there any difficulty in summing or > > > multiplying two strings of two paths? > > > > What path is the sum of two paths? And does this "SUM' rule produce a > > commutative group? > > What is the appropriate field of scalars for the "group" of paths, and > > how does one find the product of a scalar and a path? > > > > What binary is the sum of two binaries, when the result must be a binary > > <= 1? > > The sum of two real numbers of the unit interval need not be a real > number of the unit interval.
Then the set of reals in the unit interval do not form a commutative group under addition and thus cannot be a linear space, and thus cannot be either the domain or codomain of any linear mapping.
> Nevertheless we have the same structure for reals, their > representation as binary strings, and paths of the Binary Tree.
WM claimed a linear mapping between the set of binomial sequences and the set of paths of a Complete Infinite Binary Tree.
Thus requires, among other things, that both sets have the structure of linear spaces, but neither of them do.
Thus we see again WM's amateurish sloppiness with mathematical terms.
> > And a final question: Do you really believe that your nit-picking will > remove the contradiction between set theory and the Binary Tree?
The only nit I m pick at is WM.
And what set theory contradicts the Complete Infinite Binary Tree?
Neither ZF nor NBG, which are well known axiomatic set theories, does.
WM has never presented us with the axiom system or any complete set of rules for his alleged set theory, so it exists only in his own private cloud of WMytheology.
The Complete Infinite Binary Tree is perfectly consistent with standard set theories , and WM cannot produce any axiom system or other complete description for any set theory in which the Complete Infinite Binary Tree is not consistent. --