On Mar 12, 3:38 pm, Virgil <vir...@ligriv.com> wrote: > In article > <cef6abc9-a617-4649-9454-ca2d2e22a...@z3g2000vbg.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 10 Mrz., 19:36, "Peter Percival" <peterxperci...@hotmail.com> > > wrote: > > > Is there a theory of probability in which probabilities do not lie in the > > > real interval [0,1]? > > > Yes. > > >http://www.sciencedirect.com/science/article/pii/0370157386901109 > > >http://finden.nationallizenzen.de/Author/Home?author=M%C3%BCckenheim%.... > > > Regards, WM > > Not when using the standard definition of probability. > > *********************************************************************** > > WM has frequently claimed that a mapping from the set of all infinite > binary sequences to the set of paths of a CIBT is a linear mapping. > In order to show that such a mapping is a linear mapping, WM must first > show that the set of all binary sequences is a vector space and that the > set of paths of a CIBT is also a vector space, which he has not done and > apparently cannot do, and then show that his mapping satisfies the > linearity requirement that > f(ax + by) = af(x) + bf(y), > where a and b are arbitrary members of a field of scalars and x and y > are f(x) and f(y) are vectors in suitable linear spaces. > > By the way, WM, what are a, b, ax, by and ax+by when x and y are binary > sequences? > > If a = 1/3 and x is binary sequence, what is ax ? > and if f(x) is a path in a CIBT, what is af(x)? > > Until these and a few other issues are settled, WM will still have > failed to justify his claim of a LINEAR mapping from the set (but not > yet proved to be vector space) of binary sequences to the set (but not > yet proved to be vector space) of paths ln a CIBT. > > Just another of WM's many wild claims of what goes on in his WMytheology > that he cannot back up. > --
Well, identity from the real value of the expansion to the real value of the path is a continuous mapping, for the topology of the reals, as the Cantor space and CIBT are each R_[0,1] with dual representation of reals as expansions or paths.
Defining addition on the paths or expansions is simple enough with a convention for the representation. Obviously those sets aren't closed under that operation, or scalar multiplication that follows from the definition of multiplication of real numbers.
Notions of topologies or spaces, of the Cantor space and CIBT, may follow that aren't simply those of R_[0,1]. Look to union and for simplicity in binary. Make something, dammit.
A breadth-first ordering of the CIBT or BT sees the same results as a sweep of the Cantor space (not necessarily as with regards to Cantor dust) with EF: the antidiagonal argument doesn't apply. Similarly, countably many rays through ordinal points are dense in the paths of the CIBT, similarly to that the rationals are dense in the reals, and the irrationals are only their complement, in the reals, and the rational paths have terminating or repeating ends.