
Re: ran(EF) contains ~EF(n)
Posted:
Apr 30, 2013 10:46 PM


On Apr 30, 7:28 pm, William Elliot <ma...@panix.com> wrote: > On Tue, 30 Apr 2013, Ross A. Finlayson wrote: > > Basically this EF is the limit of a function. > > Basically this all is nonsense without a clear and precise definition > of EF (electromagnetic frequency?) instead of hand waving woo woo voodoo. > > > > > > > > > Notarealfunction, 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: (dn)/d > > > As there exists dn 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]. >
It has an established definition.
http://groups.google.com/groups/search?safe=off&q=EF+definition+author%3AFinlayson&btnG=Search&sitesearch=
Pretty much the same definition is used throughout.
Regards,
Ross Finlayson

