Re: How many different unit fractions are lessorequal than all unit fractions? (repleteness)

On 10/1/2024 2:02 PM, Ross Finlayson wrote:

On 10/01/2024 10:00 AM, Jim Burns wrote:

I hope this will help me understand you better.
Please accept or reject each claim and
-- this is important --
replace rejected claims with
what you _would_ accept.
>
⎛ ℝ, the complete ordered field, is
⎝ the consensus theory in 2024 of the continuum.
>
⎛ ℝ contains ℚ the rationals and
⎜ the least upper bound of
⎝ each bounded nonempty subset of ℚ and of ℝ
>
( The greatest lower bound of ⅟ℕ unit fractions is 0
>
⎛ A unit fraction is reciprocal to a natural>0
⎜
⎜ A set≠{} ⊆ ℕ naturals holds a minimum
⎜ A natural≠0 has a predecessor.natural.
⎜ A natural has a successor.natural.
⎜
⎜ The sum of two naturals is a natural
⎝ the product of two naturals is a natural.
>
⎛ There are no points in ℝ
⎜ between 0 and all the unit fractions
⎝ (which is what I mean here by 'infinitesimal').
>
Thank you in advance.

>
Here it's that "Eudoxus/Dedekind/Cauchy is
_insufficient_ to represent the character
of the real numbers".
>
Then, that there are line-reals and signal-reals
besides field-reals, has that of course there are
also models of line-reals and signal-reals in the
mathematics today, like Jordan measure and the ultrafilter,
and many extant examples where a simple deliberation
of continuity according to the definitions of
line-reals or signal-reals, results any contradictions
you might otherwise see as arriving their existence.
>
Then, besides noting how it's broken, then also
there's given a reasoning how it's repaired,
resulting "less insufficient", or at least making
it so that often found approaches in the applied,
and their success, make the standard linear curriculum,
unsuited.
>
Then, I think it's quite standard how I put it,
really very quite standard.

I hope this will help me understand you better.
Please accept or reject each claim and
-- this is important --
replace rejected claims with
what you _would_ accept.
⎛ ℝ, the complete ordered field, is
⎝ the consensus theory in 2024 of the continuum.
⎛ ℝ contains ℚ the rationals and
⎜ the least upper bound of
⎝ each bounded nonempty subset of ℚ and of ℝ
( The greatest lower bound of ⅟ℕ unit fractions is 0
⎛ A unit fraction is reciprocal to a natural>0
⎜
⎜ A set≠{} ⊆ ℕ naturals holds a minimum
⎜ A natural≠0 has a predecessor.natural.
⎜ A natural has a successor.natural.
⎜
⎜ The sum of two naturals is a natural
⎝ the product of two naturals is a natural.
⎛ There are no points in ℝ
⎜ between 0 and all the unit fractions
⎝ (which is what I mean here by 'infinitesimal').
Thank you in advance.