Basically this all is nonsense without a clear and precise definition of EF (electromagnetic frequency?) instead of hand waving woo woo voodoo.
> Not-a-real-function, it's modeled by real functions and in fact very > simply n/d. Then, the properties of its range have that: it is > symmetric about some midpoint in its range 1/2, for f^-1(1/2), defined > for even d. Just as ran(f) starts from .000... and increases in > constant monotone, in reverse it starts with .111... (or for example in > decimal, .999...) and decreases. Then, as there is a less than finite > difference between elements of the range for consecutive elements of the > domain by their natural ordering, there is in the range an element that > starts with .1, .11, .111, ..., and each finite initial segment of > integers as expansion. This is from seeing that the elements of ran(f) > are the same elements of ran(REF) for REF the "reverse" equivalency > function. > > EF: n/d > REF: (d-n)/d > > As there exists d-n for each n and d, there exists here ~EF(n) = > REF(n) constructively, and each element in ran(EF) is in ran(REF). > > Then, here, constructively: ~EF(n) e ran(EF), quod erat > demonstrandum. > > There are replete properties of this function and its range that its > range is R_[0,1]. > > Regards, > > Ross Finlayson >