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Topic: Cantor's first proof in DETAILS
Replies: 85   Last Post: Dec 10, 2012 7:23 AM

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 2,715 Registered: 2/15/09
Re: Cantor's first proof in DETAILS
Posted: Nov 30, 2012 11:39 AM

On Nov 30, 8:16 am, FredJeffries <fredjeffr...@gmail.com> wrote:
> On Nov 26, 9:19 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>
> wrote:
>
>
>
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>
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>

> > On Nov 26, 12:03 pm, Virgil <vir...@ligriv.com> wrote:
>
> > > In article
> > >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>
> > > > On Nov 25, 11:22 pm, Virgil <vir...@ligriv.com> wrote:
> > > > > In article
> > > > > <be566287-1de6-426b-a9d8-420bb9279...@n2g2000pbp.googlegroups.com>,
> > > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>
> > > > > > EF is simple and it's defined simply as a function, not-a-real-
> > > > > > function, standardly modeled by real functions. Dirac's delta and
> > > > > > Heaviside's are as so defined, as functions, not-real-functions,
> > > > > > standardly modeled by real functions. And, the definition of function
> > > > > > itself, here is modern and reflects over time the development of the
> > > > > > definition of what is a mathematical function. Then, in actually
> > > > > > extending the definition of what are the real numbers, in A theory, it
> > > > > > is directly defined, and applied.

>
> > > > > > There are hundreds of essays on it here.
>
> > > > > Then give a reference to some of them, preferably by someone other than
> > > > > yourself.

>
> > > > > In particular we need a mathematically satisfactorily definition of your
> > > > > alleged EF, again preferably by someone other than yourself, which will
> > > > > take it out of the realm of mythology.
> > > > > --

>
> > > > I wrote all that.
>
> > > Did you?
>
> > > I certainly do not ever recall seeing your alleged EF adequately
> > > presented, and see now no references to where one might see it
> > > presented, whether adequately or not.

>
> > > And if you still will not provide a reference to it, a url, or something
> > > through which anyone can access it to see it for him or her self, it is
> > > as if no such thing ever existed.

>
> > > Which in the absence of any evidence to the contrary, I will continue to
> > > assume.
> > > --

>
> >http://mathforum.org/kb/search!execute.jspa?forumID=13&objID=f13&forc...
> > at least hundreds of results

>
> >http://mathforum.org/kb/message.jspa?messageID=7888348"Cantor-
> > Finlayson theory"

>
> > "Equivalency Function"

>
> > the first mention

>
> > Do you know the old saw about "assume"?
>
> > My friends, or as I would so address you, the definition of EF is
> > written in some few lines:  constantly monotonically increasing from
> > zero through one.

>
> You've had this function for 13 years now and you STILL can't
> calculate the area of a triangle with it.

Fred Jeffries who I respect: I'd like to think that's in the context
of modeling Dirac's delta with triangles or radial basis functions,
but what's important to describe of EF as plotted is this: removing
all the space between the integers and plotting the elements in the
range it would look like f(x) = x from zero to one, half a square and
a triangle, but the F-Sigma Lebesgue integral of EF evaluates to one
not one half, now that's the surprise.

EF: CDF: of the uniform distribution of the natural integers.

Regards,

Ross Finlayson

Date Subject Author
11/25/12 ross.finlayson@gmail.com
11/25/12 Virgil
11/25/12 ross.finlayson@gmail.com
11/25/12 Graham Cooper
11/25/12 ross.finlayson@gmail.com
11/25/12 Virgil
11/25/12 ross.finlayson@gmail.com
11/26/12 Virgil
11/26/12 ross.finlayson@gmail.com
11/26/12 Virgil
11/26/12 ross.finlayson@gmail.com
11/26/12 Virgil
11/27/12 ross.finlayson@gmail.com
11/27/12 Virgil
11/27/12 ross.finlayson@gmail.com
11/27/12 Virgil
11/27/12 ross.finlayson@gmail.com
11/28/12 Virgil
11/28/12 ross.finlayson@gmail.com
11/28/12 Virgil
11/28/12 ross.finlayson@gmail.com
11/28/12 Virgil
11/29/12 ross.finlayson@gmail.com
11/29/12 Virgil
11/29/12 ross.finlayson@gmail.com
11/30/12 Virgil
11/30/12 FredJeffries@gmail.com
11/30/12 ross.finlayson@gmail.com
11/30/12 FredJeffries@gmail.com
11/30/12 ross.finlayson@gmail.com
12/1/12 Virgil
11/30/12 ross.finlayson@gmail.com
12/1/12 Virgil
12/1/12 ross.finlayson@gmail.com
12/1/12 Virgil
12/1/12 FredJeffries@gmail.com
12/1/12 ross.finlayson@gmail.com
12/1/12 Virgil
12/2/12 ross.finlayson@gmail.com
12/2/12 Virgil
12/2/12 ross.finlayson@gmail.com
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12/3/12 ross.finlayson@gmail.com
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12/3/12 Virgil
12/3/12 ross.finlayson@gmail.com
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12/5/12 ross.finlayson@gmail.com
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12/9/12 Virgil
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12/10/12 Virgil
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12/4/12 Virgil
12/5/12 ross.finlayson@gmail.com
12/5/12 Virgil
11/30/12 Virgil
11/25/12 Graham Cooper
11/25/12 Virgil
11/25/12 ross.finlayson@gmail.com
11/25/12 Virgil