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NNTP-Posting-Date: Sun, 29 Dec 2024 20:54:28 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 29 Dec 2024 12:54:32 -0800
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On 12/29/2024 12:34 PM, Jim Burns wrote:
> On 12/28/2024 10:54 PM, Ross Finlayson wrote:
>> On 12/28/2024 04:22 PM, Jim Burns wrote:
>>> On 12/28/2024 5:36 PM, Ross Finlayson wrote:
>
>>>> Then it's like
>>>> "no, it's distribution is non-standard,
>>>> not-a-real-function,
>>>> with real-analytical-character".
>>>
>>> Which is to say,
>>> "no, it isn't what it's described to be"
>>
>> You already accept
>
> No.
> You (RF) are greatly mistaken about
> my (JB's) position with regard to
> infinitely.many equal real.number steps
> from 0 to 1
>
> My position is and has been that they don't exist.
>
>> You already accept that the "natural/unit
>> equivalency function" has range with
>> _constant monotone strictly increasing_
>> has _constant_ differences, _constant_,
>> that as a cumulative function, for a
>> distribution, has that relating to
>> the naturals, as uniform.
>
> My position, expressed in different ways,
> is and has been that,
> for each positive real x,
> a finite integer n exists such that
> n⋅x > 1
>
> That conflicts with the existence of
> infinitely.many equal real.number steps
> from 0 to 1
>
>

Oh, you had that [0/d, 1/d, 2/d, ... oo/d]
was a thing, it's equi-partitioning at all,
you said "that's at most rationals",
so, now you have changed your mind
that "extent" and "density" were so?

The equi-partitioning is a very usual thing,
about things like Jordan measure for the
line-integral the line-elements of the
line-integral and the path-integral,
the equi-partitioning.

Anyways, yeah you already said "extent"
and "density" were so, about why the
natural/unit equivalency function is
a probabilistic distribution of the
natural integers at uniform random.



So, yeah, it conflicts with yourself,
yet, that's what you said.