Date: Nov 27, 2012 11:52 PM Author: ross.finlayson@gmail.com Subject: Re: Cantor's first proof in DETAILS On Nov 27, 11:34 am, Virgil <vir...@ligriv.com> wrote:

> In article

> <ff6de177-a8db-461e-9048-b054aae71...@ah9g2000pbd.googlegroups.com>,

> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>

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> > On Nov 26, 11:33 pm, Virgil <vir...@ligriv.com> wrote:

> > > In article

> > > <b144a62b-11a5-4397-9c0d-ecd39e274...@6g2000pbh.googlegroups.com>,

> > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>

> > > > On Nov 26, 12:03 pm, Virgil <vir...@ligriv.com> wrote:

> > > > > In article

> > > > > <ba2d403e-154a-46d2-9fc9-6e5ae92ed...@vy11g2000pbb.googlegroups.com>,

> > > > > "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...

> > > > rch=true&q=%22Equivalency+Function%22

> > > > at least hundreds of results

>

> > > Not one of which posts contains an original definition of what the

> > > alleged "equivalency function" actually is, only a lot of crap by Ross

> > > about how it is the greatest things since sliced bread.

>

> > >http://groups.google.com/group/sci.math/msg/ccb0941dc3421afd

>

> > > I find a citation from r 9/22/99 In which Ross states, what may well be

> > > Ross' original "definition" of his alleged "Equivalency Function" which

> > > as any mathematician can plainly see is not a function at all, and is

> > > only equivalent to nonsense::

>

> > > " Consider the function

> > > f(x, d)= x/d

> > > for x and d in N. The domain of x is N from zero to d and the domain of

> > > d is N as d goes to

> > > infinity, d being greater than or equal to one.

> > > I term this the Equivalency Function, and note it EF(x,d), also EF(x),

> > > assuming d goes to

> > > infinity."

>

> > >http://groups.google.com/group/sci.math/msg/af29323d694cf89e1999-

> > > "Equivalency Function"

>

> > > > 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.

>

> > > Anyone who would call that mess a function, when it is either two

> > > separate functions or infinitely many depending on which part of the

> > > "definition" one is reading, is no mathematician.

>

> > > Ant the only thing it demonstrates is Ross' total inability to think

> > > mathematically.

>

> > > I do not find any area of mathematics which would not be improved by its

> > > total absence.

>

> > I have a mathematics degree

>

> I have three of them, so what?

>

> Your EF is, at least as so far presented, of no mathematical interest or

> impotance whatsoever.

> --

As a function, it has particular results in the framework of results

on uncountability of the reals, different than any other. And, it's

simply and standardly modeled by real functions.

That includes your quaint take on it.

That concludes your quaint take on it.

Then plain friends or whoever, well then it is with warm regards and a

general lack of affrontery to note that: for someone with a

continuing interest in mathematics, EF is great.

Now we'd all be interested in application of transfinite cardinals,

and we'd all like to know how the universe and everything is itself

and its own collection of all its subsets, then as to what particular

foundation (or, lack thereof) establishes mathematically that it is.

The twain don't meet.

Regards,

Ross Finlayson