Date: Nov 27, 2012 11:04 AM Author: ross.finlayson@gmail.com Subject: Re: Cantor's first proof in DETAILS 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:

>

>

>

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>

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>

>

>

> > 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, at least the university affirms that I

think mathematically, unless they are regularly giving unmerited B.S.

degrees, which they don't. This is the regular modern undergraduate

curriculum with topology, algebra, real analysis, dynamical methods,

numerical methods, formal methods, and etcetera (National Merit

Finalist, Putnam). In computer programming I'm familiar with Java

since 1.0 and work Java and C++ at large, well-known corporations, for

bread, from chips and boards to the cloud, and have actually read

Knuth's TaoCP.

If you continue reading that thread from 1999 you'll find that it is

described what were termed "general" and "valid" EF being EF(n,d) and

EF(n).

http://groups.google.com/group/sci.math/msg/6c66dd07999bf4cf

Then, apparently I've spent almost fifteen years working up from that.

http://groups.google.com/group/sci.math/msg/dcaec5f3fd9d74c0

http://groups.google.com/groups/search?as_q=Dirac&as_epq=Equivalency+Function

http://groups.google.com/groups/search?as_q=Heaviside&as_epq=Equivalency+Function

http://groups.google.com/groups/search?as_q=Cantor&as_epq=Equivalency+Function

http://groups.google.com/groups/search?as_q=Finlayson&as_epq=Equivalency+Function

It matters not my opinion on EF as a function: for the mathematical

Platonist, the numbers have their own features, and we know that

standard, modern mathematics does not encompass them all, as Goedel

told us of its incompleteness.

So, and I agree that it's unlikely that a simple individual would put

forward mathematical progess, that's the only way it's ever been,

humble giants for Atlas.

So warm regards, my friends, and have a great day, as you would.

Regards,

Ross Finlayson