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

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

On 07/02/2024 05:07 AM, Jim Burns wrote:

[...]

>
Anyways,
this putative countable domain

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