Math Forum Discussions

Alan Smaill

Posts: 716
Registered: 1/29/05

Re: Cantor's first proof in DETAILS
Posted: Nov 29, 2012 10:35 AM

Plain Text

"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