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

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