Date: Nov 29, 2012 10:35 AM
Author: Alan Smaill
Subject: Re: Cantor's first proof in DETAILS

"Ross A. Finlayson" <ross.finlayson@gmail.com> writes:

> On Nov 28, 4:58 pm, Marshall <marshall.spi...@gmail.com> wrote:

>> On Monday, November 26, 2012 11:33:02 PM UTC-8, Virgil wrote:

>>

>> > 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"

>>

>> Um, so EF is a restriction of division?

>>

>> The domain of x depends on the value of d. I don't recall having seen

>> that sort of thing before, but I guess I do know what that means.

>> But I can't figure out what the domain of d is. It sorta looks like the

>> domain of d depends on what d is, but what the heck would that mean?

>>

>> And it's just a name, but what about EF has anything to do with

>> equivalency?

>>

>> Marshall

>

> Mr. Spight, it's about the equivalency or equipollency or equipotency

> of infinite sets.

> EF(n) = n/d, d->oo, n->d.

>

> Properties include:

> EF(0) = 0

> EF(d) = 1

> EF(n) < EF(n+1)

> The domain of the function is of those natural integers 0 <= n <= d.

>

> It's very simple this. Then, not a real function, it's standardly

> modeled by real functions:

> EF(n,d) = n/d, d E N, n->d

> with each having those same properties.

>

> Then, the co-image is R[0,1] as is the range.

Is this a version of the natural density of a subset of the natural

numbers?

http://en.wikipedia.org/wiki/Natural_density

> Regards,

>

> Ross Finlayson

--

Alan Smaill