Re: Does the number of nines increase?

On 07/01/2024 04:42 PM, Ross Finlayson wrote:

On 06/30/2024 09:22 PM, Jim Burns wrote:

On 6/30/2024 11:32 PM, Ross Finlayson wrote:

On 06/30/2024 06:38 PM, Jim Burns wrote:

On 6/30/2024 5:05 PM, Ross Finlayson wrote:

>

Well, iota-values are defined and
satisfy making for the IVT
which results the FTC's,
Fundamental Theorems of Calculus.

>
If I use the usual definitions for
the limit of a sequence of sets
for your iota.values,
they do not satisfy the Intermediate Value Theorem.
>
I understand your iota.values to be the limit
n/d: 0≤n≤d: d → ∞
>
For n/d: 0≤n≤d  I read {0/d,1/d,...,d/d}
>
For lim[d → ∞] I read ⋂[0<dᵢ<∞] ⋃[dᵢ<d<∞]
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Is that what you mean? You (RF) don't say.
>
⋂[0<dᵢ<∞] ⋃[dᵢ<d<∞] {0/d,1/d,...,d/d}
does not satisfy the Intermediate Value Theorem.

>

Yes it does, the iota-values result that they do
make for the IVT,

>
Tell me what you are talking about.
>
I understand your iota.values to be the limit
n/d: 0≤n≤d: d → ∞
>
For n/d: 0≤n≤d  I read {0/d,1/d,...,d/d}
>
For lim[d → ∞] I read ⋂[0<dᵢ<∞] ⋃[dᵢ<d<∞]
>
Is that what you mean? You (RF) don't say.
>
⋂[0<dᵢ<∞] ⋃[dᵢ<d<∞] {0/d,1/d,...,d/d}
does not satisfy the Intermediate Value Theorem.
>
>

>
There must be satisfied "extent density completeness
measure" to satisfy the IVT, though one may aver that
"extent density completeness" would suffice.
>
So, iota-values or ran(EF) of the natural/unit equivalency function,
or sweep, has "extent density completeness measure",
thus the IVT follows.
>
It's sort of irrelevant what I intend as I don't see
value in nominalist fictionalism, what it is is what it is,
what it is.
>
It's not really any of the initial approximations,
this limit, this infinite limit, this continuum limit.
>
It's an _infinite_ limit.
>
>
In some places the only known non-standard function
with real analytical character is the Dirac delta,
the unit impulse function. Anywhere besides at zero:
its value is zero. It's not so that it's all the
things that go to it, it's where it goes.
>
Unless you'd care to see that most all the modern structure
of analysis in infinite series and function theory is, "wrong",
it's only so in the _infinite_ case, and it is so.
>
>
>
>

I'm not a nominalist fictionalist, yet
there's a theory where it's an axiom, it is so.