```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 naturalnumbers? http://en.wikipedia.org/wiki/Natural_density> Regards,>> Ross Finlayson-- Alan Smaill
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