Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively)

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.