Re: Does the number of nines increase? (axiomatizing completeness)

On 7/2/2024 8:47 PM, Ross Finlayson wrote:

On 07/02/2024 05:06 PM, Jim Burns wrote:

On 7/2/2024 4:32 PM, Ross Finlayson wrote:

Anyways,
this putative countable domain

>
Do you refer to  n/d: 0≤n≤d: d → ∞  ?

Do you refer to  n/d: 0≤n≤d: d → ∞  ?

via its construction as
a range of continuum limit of functions
isn't contradicted by the anti-diagonal and so on,
nor by being a Cartesian function,
as a model of a unit line segment of
the linear continuum.

>
continuum limit
greatest.lower.bound of inter.point distances is 0
>
continuum
for each split, either
its foresplit holds a last  or
its hindsplit holds a first

>
Isn't that, ..., contiguum?

| In mathematical physics and mathematics,
| the continuum limit or scaling limit of a lattice model
| characterizes its behaviour in the limit
| as the lattice spacing goes to zero.
[1]
| [...]
| If [A,B] is a cut of C,
| then either A has a last element or B has a first element.
| [...]
[2]
[1]
https://en.wikipedia.org/wiki/Continuum_limit
[2]
https://en.wikipedia.org/wiki/Continuum_(set_theory)