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

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 William Elliot Posts: 2,637 Registered: 1/8/12
Re: ran(EF) contains ~EF(n)
Posted: Apr 30, 2013 10:28 PM

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.

> 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
>