Re: Does the number of nines increase?

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<∞]
>
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.