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Topic: ran(EF) contains ~EF(n)
Replies: 9   Last Post: May 1, 2013 10:16 AM

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
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.
>
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> > 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].

>

It has an established definition.