The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 2,720
Registered: 2/15/09
Re: ran(EF) contains ~EF(n)
Posted: Apr 30, 2013 10:46 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Apr 30, 7:28 pm, William Elliot <> 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.

> > 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.

Pretty much the same definition is used throughout.


Ross Finlayson

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.