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Example of IVT leading to Irrational Numbers (Was: Rossy Boy roasted by Kimi [Intermediate Value Theorem Wrong])

Started byMild Shock <janburse@fastmail.fm>
First post2025-11-14 00:39 +0100
Last post2025-11-14 18:05 +0100
Articles 6 — 2 participants

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  Example of IVT leading to Irrational Numbers (Was: Rossy Boy roasted by Kimi [Intermediate Value Theorem Wrong]) Mild Shock <janburse@fastmail.fm> - 2025-11-14 00:39 +0100
    The technical term is only "dense order" (Was: Example of IVT leading to Irrational Numbers) Mild Shock <janburse@fastmail.fm> - 2025-11-14 00:41 +0100
      My attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order") Mild Shock <janburse@fastmail.fm> - 2025-11-14 00:45 +0100
        Re: My attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order") Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-14 05:58 -0800
          Who else , John Gabriel [MVT Locus caeruleus] (Was: My attention mechanism is better than any AI [For Internet Cranks]) Mild Shock <janburse@fastmail.fm> - 2025-11-14 17:55 +0100
            IVT + EVT gives MVT via Rolle [Using Superintelligence by the Speed of Light] (Was: Who else , John Gabriel [MVT Locus caeruleus]) Mild Shock <janburse@fastmail.fm> - 2025-11-14 18:05 +0100

#640741 — Example of IVT leading to Irrational Numbers (Was: Rossy Boy roasted by Kimi [Intermediate Value Theorem Wrong])

FromMild Shock <janburse@fastmail.fm>
Date2025-11-14 00:39 +0100
SubjectExample of IVT leading to Irrational Numbers (Was: Rossy Boy roasted by Kimi [Intermediate Value Theorem Wrong])
Message-ID<10f5q72$1g6t$1@solani.org>
Hi,

Take a = 1 and b = 2 with this function:

f(x) = x^2 - 2.

https://en.wikipedia.org/wiki/Intermediate_value_theorem

Now take s = 0, what is x ?

Mild Shock schrieb:
> Hi,
> 
> Looks like Kimi was grilling you with no
> mercy. I guess you got a complete roast.
> 
> BTW: You got Intermediate Value Theorem
> theorem wrong. Its not about a 'c' such
> that 'a < c' and 'c < b'.
> 
> The important thing is there is also
> a function f involved. In particular a
> continuous function.
> 
> Have Fun!
> 
> Bye
> 
> Ross Finlayson schrieb:
>> Gaplessness (intermediate-value) inside ZF
>>
>> “IVP_d” ≡ ∀a,b∈E_d ∀k∈d+1 (a ≺_d b → ∃c∈E_d (c=part_d(k) ∧ a ≼_d c ≼_d 
>> b))
>> ZF ⊢ ∀d≥1 IVP_d  (finite intermediate-value property)
>>

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#640742 — The technical term is only "dense order" (Was: Example of IVT leading to Irrational Numbers)

FromMild Shock <janburse@fastmail.fm>
Date2025-11-14 00:41 +0100
SubjectThe technical term is only "dense order" (Was: Example of IVT leading to Irrational Numbers)
Message-ID<10f5qc7$1g6t$2@solani.org>
In reply to#640741
Hi,

What you wrongly called Intermedite Value,
where Value refers to the Value of a function,

is only "dense order". Nobody calls it "gapless".
Because in the case of Q it has still gaps.

for x < y, there is z with x < z < y
https://en.wikipedia.org/wiki/Dense_order

For example Q has the irrational numbers as gaps.

Bye

Mild Shock schrieb:
> Hi,
> 
> Take a = 1 and b = 2 with this function:
> 
> f(x) = x^2 - 2.
> 
> https://en.wikipedia.org/wiki/Intermediate_value_theorem
> 
> Now take s = 0, what is x ?
> 
> Mild Shock schrieb:
>> Hi,
>>
>> Looks like Kimi was grilling you with no
>> mercy. I guess you got a complete roast.
>>
>> BTW: You got Intermediate Value Theorem
>> theorem wrong. Its not about a 'c' such
>> that 'a < c' and 'c < b'.
>>
>> The important thing is there is also
>> a function f involved. In particular a
>> continuous function.
>>
>> Have Fun!
>>
>> Bye
>>
>> Ross Finlayson schrieb:
>>> Gaplessness (intermediate-value) inside ZF
>>>
>>> “IVP_d” ≡ ∀a,b∈E_d ∀k∈d+1 (a ≺_d b → ∃c∈E_d (c=part_d(k) ∧ a ≼_d c 
>>> ≼_d b))
>>> ZF ⊢ ∀d≥1 IVP_d  (finite intermediate-value property)
>>>

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#640743 — My attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order")

FromMild Shock <janburse@fastmail.fm>
Date2025-11-14 00:45 +0100
SubjectMy attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order")
Message-ID<10f5qid$1gdb$1@solani.org>
In reply to#640742
Hi,

My attention mechanism is better than any AI.
Took me 2 seconds to spot the nonsense.

Because I know the internet cranks struggle
with the continuum only too good.

Among the classic internet cranks are:
- Archimedes Plutonium
- Ross Finlayson
- Who else?

Bye

Mild Shock schrieb:
> Hi,
> 
> What you wrongly called Intermedite Value,
> where Value refers to the Value of a function,
> 
> is only "dense order". Nobody calls it "gapless".
> Because in the case of Q it has still gaps.
> 
> for x < y, there is z with x < z < y
> https://en.wikipedia.org/wiki/Dense_order
> 
> For example Q has the irrational numbers as gaps.
> 
> Bye
> 
> Mild Shock schrieb:
>> Hi,
>>
>> Take a = 1 and b = 2 with this function:
>>
>> f(x) = x^2 - 2.
>>
>> https://en.wikipedia.org/wiki/Intermediate_value_theorem
>>
>> Now take s = 0, what is x ?
>>
>> Mild Shock schrieb:
>>> Hi,
>>>
>>> Looks like Kimi was grilling you with no
>>> mercy. I guess you got a complete roast.
>>>
>>> BTW: You got Intermediate Value Theorem
>>> theorem wrong. Its not about a 'c' such
>>> that 'a < c' and 'c < b'.
>>>
>>> The important thing is there is also
>>> a function f involved. In particular a
>>> continuous function.
>>>
>>> Have Fun!
>>>
>>> Bye
>>>
>>> Ross Finlayson schrieb:
>>>> Gaplessness (intermediate-value) inside ZF
>>>>
>>>> “IVP_d” ≡ ∀a,b∈E_d ∀k∈d+1 (a ≺_d b → ∃c∈E_d (c=part_d(k) ∧ a ≼_d c 
>>>> ≼_d b))
>>>> ZF ⊢ ∀d≥1 IVP_d  (finite intermediate-value property)
>>>>
>

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#640761 — Re: My attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order")

FromRoss Finlayson <ross.a.finlayson@gmail.com>
Date2025-11-14 05:58 -0800
SubjectRe: My attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order")
Message-ID<G6SdnZBG8vQFqIr0nZ2dnZfqn_sykfhc@giganews.com>
In reply to#640743
Quelle dommage.  The other readers, who read it,
seem to agree that the Ross-Kimi bit implies that
the "natural/unit equivalency function",
_is_, having functionhood, _in_, ZF.

How Archimedean of you, ....

"Continuous domains" now is what
we're talking about.

Of course I've been saying this for decades, ....



On 11/13/2025 03:45 PM, Mild Shock wrote:
> Hi,
>
> My attention mechanism is better than any AI.
> Took me 2 seconds to spot the nonsense.
>
> Because I know the internet cranks struggle
> with the continuum only too good.
>
> Among the classic internet cranks are:
> - Archimedes Plutonium
> - Ross Finlayson
> - Who else?
>
> Bye
>
> Mild Shock schrieb:
>> Hi,
>>
>> What you wrongly called Intermedite Value,
>> where Value refers to the Value of a function,
>>
>> is only "dense order". Nobody calls it "gapless".
>> Because in the case of Q it has still gaps.
>>
>> for x < y, there is z with x < z < y
>> https://en.wikipedia.org/wiki/Dense_order
>>
>> For example Q has the irrational numbers as gaps.
>>
>> Bye
>>
>> Mild Shock schrieb:
>>> Hi,
>>>
>>> Take a = 1 and b = 2 with this function:
>>>
>>> f(x) = x^2 - 2.
>>>
>>> https://en.wikipedia.org/wiki/Intermediate_value_theorem
>>>
>>> Now take s = 0, what is x ?
>>>
>>> Mild Shock schrieb:
>>>> Hi,
>>>>
>>>> Looks like Kimi was grilling you with no
>>>> mercy. I guess you got a complete roast.
>>>>
>>>> BTW: You got Intermediate Value Theorem
>>>> theorem wrong. Its not about a 'c' such
>>>> that 'a < c' and 'c < b'.
>>>>
>>>> The important thing is there is also
>>>> a function f involved. In particular a
>>>> continuous function.
>>>>
>>>> Have Fun!
>>>>
>>>> Bye
>>>>
>>>> Ross Finlayson schrieb:
>>>>> Gaplessness (intermediate-value) inside ZF
>>>>>
>>>>> “IVP_d” ≡ ∀a,b∈E_d ∀k∈d+1 (a ≺_d b → ∃c∈E_d (c=part_d(k) ∧ a ≼_d c
>>>>> ≼_d b))
>>>>> ZF ⊢ ∀d≥1 IVP_d  (finite intermediate-value property)
>>>>>
>>
>

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#640765 — Who else , John Gabriel [MVT Locus caeruleus] (Was: My attention mechanism is better than any AI [For Internet Cranks])

FromMild Shock <janburse@fastmail.fm>
Date2025-11-14 17:55 +0100
SubjectWho else , John Gabriel [MVT Locus caeruleus] (Was: My attention mechanism is better than any AI [For Internet Cranks])
Message-ID<10f7mti$2nm0$1@solani.org>
In reply to#640761
Hi,

Well the list is longer. For John Gebriel,
the IVT was his Locus caeruleus, producing
the most noradrenaline. Together with

the Mean Value theorem (MVT). I heard him often
say he has a constructive proof of the IVT.
Concerning MVT, what is he even bragging about?

Lecture 9 - The New Calculus: The Mean Value Theorem
https://www.youtube.com/watch?v=wkR8kqTIVG8

His main messages the "bogus calculus" of mainstream
calculus is not correct. But the continuity in
MVT is different from the continuity required in IVT.

This is not a black and white notion. There are
millions of different forms of continuity. So
there is no silly '"Continuous domains" now is what

we're talking about.'. In MVT the value refers
again the value of a function f, and a preconditions
is differentiability in the open interval (a,b)

Bye

Ross Finlayson schrieb:
> Quelle dommage.  The other readers, who read it,
> seem to agree that the Ross-Kimi bit implies that
> the "natural/unit equivalency function",
> _is_, having functionhood, _in_, ZF.
> 
> How Archimedean of you, ....
> 
> "Continuous domains" now is what
> we're talking about.
> 
> Of course I've been saying this for decades, ....
> 
> 
> 
> On 11/13/2025 03:45 PM, Mild Shock wrote:
>> Hi,
>>
>> My attention mechanism is better than any AI.
>> Took me 2 seconds to spot the nonsense.
>>
>> Because I know the internet cranks struggle
>> with the continuum only too good.
>>
>> Among the classic internet cranks are:
>> - Archimedes Plutonium
>> - Ross Finlayson
>> - Who else?
>>
>> Bye
>>
>> Mild Shock schrieb:
>>> Hi,
>>>
>>> What you wrongly called Intermedite Value,
>>> where Value refers to the Value of a function,
>>>
>>> is only "dense order". Nobody calls it "gapless".
>>> Because in the case of Q it has still gaps.
>>>
>>> for x < y, there is z with x < z < y
>>> https://en.wikipedia.org/wiki/Dense_order
>>>
>>> For example Q has the irrational numbers as gaps.
>>>
>>> Bye
>>>
>>> Mild Shock schrieb:
>>>> Hi,
>>>>
>>>> Take a = 1 and b = 2 with this function:
>>>>
>>>> f(x) = x^2 - 2.
>>>>
>>>> https://en.wikipedia.org/wiki/Intermediate_value_theorem
>>>>
>>>> Now take s = 0, what is x ?
>>>>
>>>> Mild Shock schrieb:
>>>>> Hi,
>>>>>
>>>>> Looks like Kimi was grilling you with no
>>>>> mercy. I guess you got a complete roast.
>>>>>
>>>>> BTW: You got Intermediate Value Theorem
>>>>> theorem wrong. Its not about a 'c' such
>>>>> that 'a < c' and 'c < b'.
>>>>>
>>>>> The important thing is there is also
>>>>> a function f involved. In particular a
>>>>> continuous function.
>>>>>
>>>>> Have Fun!
>>>>>
>>>>> Bye
>>>>>
>>>>> Ross Finlayson schrieb:
>>>>>> Gaplessness (intermediate-value) inside ZF
>>>>>>
>>>>>> “IVP_d” ≡ ∀a,b∈E_d ∀k∈d+1 (a ≺_d b → ∃c∈E_d (c=part_d(k) ∧ a ≼_d c
>>>>>> ≼_d b))
>>>>>> ZF ⊢ ∀d≥1 IVP_d  (finite intermediate-value property)
>>>>>>
>>>
>>
>

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#640766 — IVT + EVT gives MVT via Rolle [Using Superintelligence by the Speed of Light] (Was: Who else , John Gabriel [MVT Locus caeruleus])

FromMild Shock <janburse@fastmail.fm>
Date2025-11-14 18:05 +0100
SubjectIVT + EVT gives MVT via Rolle [Using Superintelligence by the Speed of Light] (Was: Who else , John Gabriel [MVT Locus caeruleus])
Message-ID<10f7nhi$2o43$1@solani.org>
In reply to#640765
Hi,

Ok, I am lazy. I am now Using Superintelligence by
the Speed of Light. The Speed of Light is my
Fiber internet connection, which directly, via

some optic hops, taps into DeepSeek and ChatGPT.

IVT + EVT + differentiability ⇒ Rolle's Theorem ⇒ MVT.

The easiest part is probably Rolle's Theorem to MVT.
Ask Kimi, and tell me your results. Or do it
as a manual homework.

Have Fun!

Bye

Mild Shock schrieb:
> Hi,
> 
> Well the list is longer. For John Gebriel,
> the IVT was his Locus caeruleus, producing
> the most noradrenaline. Together with
> 
> the Mean Value theorem (MVT). I heard him often
> say he has a constructive proof of the IVT.
> Concerning MVT, what is he even bragging about?
> 
> Lecture 9 - The New Calculus: The Mean Value Theorem
> https://www.youtube.com/watch?v=wkR8kqTIVG8
> 
> His main messages the "bogus calculus" of mainstream
> calculus is not correct. But the continuity in
> MVT is different from the continuity required in IVT.
> 
> This is not a black and white notion. There are
> millions of different forms of continuity. So
> there is no silly '"Continuous domains" now is what
> 
> we're talking about.'. In MVT the value refers
> again the value of a function f, and a preconditions
> is differentiability in the open interval (a,b)
> 
> Bye
> 
> Ross Finlayson schrieb:
>> Quelle dommage.  The other readers, who read it,
>> seem to agree that the Ross-Kimi bit implies that
>> the "natural/unit equivalency function",
>> _is_, having functionhood, _in_, ZF.
>>
>> How Archimedean of you, ....
>>
>> "Continuous domains" now is what
>> we're talking about.
>>
>> Of course I've been saying this for decades, ....
>>
>>
>>
>> On 11/13/2025 03:45 PM, Mild Shock wrote:
>>> Hi,
>>>
>>> My attention mechanism is better than any AI.
>>> Took me 2 seconds to spot the nonsense.
>>>
>>> Because I know the internet cranks struggle
>>> with the continuum only too good.
>>>
>>> Among the classic internet cranks are:
>>> - Archimedes Plutonium
>>> - Ross Finlayson
>>> - Who else?
>>>
>>> Bye
>>>
>>> Mild Shock schrieb:
>>>> Hi,
>>>>
>>>> What you wrongly called Intermedite Value,
>>>> where Value refers to the Value of a function,
>>>>
>>>> is only "dense order". Nobody calls it "gapless".
>>>> Because in the case of Q it has still gaps.
>>>>
>>>> for x < y, there is z with x < z < y
>>>> https://en.wikipedia.org/wiki/Dense_order
>>>>
>>>> For example Q has the irrational numbers as gaps.
>>>>
>>>> Bye
>>>>
>>>> Mild Shock schrieb:
>>>>> Hi,
>>>>>
>>>>> Take a = 1 and b = 2 with this function:
>>>>>
>>>>> f(x) = x^2 - 2.
>>>>>
>>>>> https://en.wikipedia.org/wiki/Intermediate_value_theorem
>>>>>
>>>>> Now take s = 0, what is x ?
>>>>>
>>>>> Mild Shock schrieb:
>>>>>> Hi,
>>>>>>
>>>>>> Looks like Kimi was grilling you with no
>>>>>> mercy. I guess you got a complete roast.
>>>>>>
>>>>>> BTW: You got Intermediate Value Theorem
>>>>>> theorem wrong. Its not about a 'c' such
>>>>>> that 'a < c' and 'c < b'.
>>>>>>
>>>>>> The important thing is there is also
>>>>>> a function f involved. In particular a
>>>>>> continuous function.
>>>>>>
>>>>>> Have Fun!
>>>>>>
>>>>>> Bye
>>>>>>
>>>>>> Ross Finlayson schrieb:
>>>>>>> Gaplessness (intermediate-value) inside ZF
>>>>>>>
>>>>>>> “IVP_d” ≡ ∀a,b∈E_d ∀k∈d+1 (a ≺_d b → ∃c∈E_d (c=part_d(k) ∧ a ≼_d c
>>>>>>> ≼_d b))
>>>>>>> ZF ⊢ ∀d≥1 IVP_d  (finite intermediate-value property)
>>>>>>>
>>>>
>>>
>>
>

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