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

On 7/2/2024 9:49 PM, Ross Finlayson wrote:

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

[...]

>
With the least-upper-bound property for
reals in their _normal_ ordering and
reals in their _reverse_ ordering,
doesn't that sort of confound
just the usual partitioning scheme?

For each nonempty bounded.below set S of reals
there is nonempty bounded.above -1⋅ᴬS
with a least.upper.bound -1⋅σ
σ is the greatest.lower.bound of
nonempty bounded.below S
re: lub glb
You pays yer money and you takes yer choice.

That is to say,
isn't any real number defined both ways?
Aren't they, neighbors? No different?

No different. No problem.

Reading more from Hermann in that podcast, gets into
that mathematicians and physicists sort of need to
get together, and, mathematics _owes_ physics.

Even more obviously,
physics _owes_ mathematics, too.
There's enough owing to go around.
See also: shoulders of giants