https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus

måndag 31 juli 2023 kl. 11:18:09 UTC+2 skrev Eram semper recta:
> https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
The mean value theorem is not a trivial fact, nor an "unremarkable statement". It is the basis for most theorems in real analysis.

How do you know a such c exists? If you only allow for rational numbers, it's easy to construct a function that fails the mean value theorem.

On Monday, 31 July 2023 at 12:56:09 UTC-4, markus... wrote:
> måndag 31 juli 2023 kl. 11:18:09 UTC+2 skrev Eram semper recta:
> > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> The mean value theorem is not a trivial fact, nor an "unremarkable statement". It is the basis for most theorems in real analysis.
>
> How do you know a such c exists? If you only allow for rational numbers, it's easy to construct a function that fails the mean value theorem.

SHUT UP you ignorant little queer!

Eat my SHIT and DIE!!!!!

On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus

I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.

NONE of the stupid FUCKS who came before me where up to the task:

https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus

måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
>
> I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
>
> NONE of the stupid FUCKS who came before me where up to the task:
>
> https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
Your proof is invalid. The real mean value theorem requires real numbers.

On 7/31/2023 1:13 PM, Eram semper recta wrote:
> On Monday, 31 July 2023 at 12:56:09 UTC-4, markus... wrote:
>> måndag 31 juli 2023 kl. 11:18:09 UTC+2 skrev Eram semper recta:
>>> https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
>> The mean value theorem is not a trivial fact, nor an "unremarkable statement". It is the basis for most theorems in real analysis.
>>
>> How do you know a such c exists? If you only allow for rational numbers, it's easy to construct a function that fails the mean value theorem.
>
> SHUT UP you ignorant little queer!

Oh my. lol.

>
> Eat my SHIT and DIE!!!!!

Now this is going overboard.

On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> >
> > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> >
> > NONE of the stupid FUCKS who came before me where up to the task:
> >
> > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> Your proof is invalid.

You've said that about a lot of things and every time you have been wrong.

You're wrong here yet again.

> The real mean value theorem requires real numbers.

It doesn't have anything to do with an ill-formed object you think of as a "real number".

The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.

You're right - I don't understand the "limits" of your ignorance and stupidity.

tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > >
> > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > >
> > > NONE of the stupid FUCKS who came before me where up to the task:
> > >
> > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > Your proof is invalid.
> You've said that about a lot of things and every time you have been wrong..
>
> You're wrong here yet again.
> > The real mean value theorem requires real numbers.
> It doesn't have anything to do with an ill-formed object you think of as a "real number".
>
> The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
>
> You're right - I don't understand the "limits" of your ignorance and stupidity.
The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have

f'(c)=0-1=-1.

But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.

The mean value theorem requires a real number line.

On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > >
> > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > >
> > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > >
> > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > Your proof is invalid.
> > You've said that about a lot of things and every time you have been wrong.
> >
> > You're wrong here yet again.
> > > The real mean value theorem requires real numbers.
> > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> >
> > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> >
> > You're right - I don't understand the "limits" of your ignorance and stupidity.
> The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2.

Not a valid or coherent example because the mvt works only on ONE function, not multiple functions. Like I have often instructed you, the methods of calculus apply ONLY to SMOOTH curves.

The rest of your drivel is not even relevant. Try again, troll!

> It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
>
> f'(c)=0-1=-1.
>
> But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
>
> The mean value theorem requires a real number line.

tisdag 1 augusti 2023 kl. 14:20:30 UTC+2 skrev Eram semper recta:
> On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > >
> > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > >
> > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > >
> > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > Your proof is invalid.
> > > You've said that about a lot of things and every time you have been wrong.
> > >
> > > You're wrong here yet again.
> > > > The real mean value theorem requires real numbers.
> > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > >
> > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > >
> > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2.
> Not a valid or coherent example because the mvt works only on ONE function, not multiple functions. Like I have often instructed you, the methods of calculus apply ONLY to SMOOTH curves.
>
> The rest of your drivel is not even relevant. Try again, troll!
> > It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> >
> > f'(c)=0-1=-1.
> >
> > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> >
> > The mean value theorem requires a real number line.
No. You're wrong. As usual, you don't know basic facts. The function I gave its indeed a valid function, differentiable everywhere and even smooth. The derivate is zero. You are making up your own definition and mathematics when you are disproved. That's quite cranky.

But I forgot you didn't understand piecewise functions. If you really want to have a counterexample that's acceptable to you, how about a polynomial? Consider f(x)=x³ over [0, 1]. Then we have
f'(c)=f(1)-f(0)=1.

But 3c²=1 does not have a rational solution, so even simple polynomials don't have a mean value theorem without real numbers. Of course, the solution in the real numbers in the required interval [0, 1] is c=1/sqrt(3) and this is an irrational real number. I hope you enjoyed my lecture in elementary real analysis and learned something. 😊😊😊

Without real numbers, no MVT. 🤯

How cool is that! 🫡🙂

On Tuesday, 1 August 2023 at 17:34:32 UTC-4, markus...@gmail.com wrote:
> tisdag 1 augusti 2023 kl. 14:20:30 UTC+2 skrev Eram semper recta:
> > On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > >
> > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > >
> > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > >
> > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > Your proof is invalid.
> > > > You've said that about a lot of things and every time you have been wrong.
> > > >
> > > > You're wrong here yet again.
> > > > > The real mean value theorem requires real numbers.
> > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > >
> > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > >
> > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2.
> > Not a valid or coherent example because the mvt works only on ONE function, not multiple functions. Like I have often instructed you, the methods of calculus apply ONLY to SMOOTH curves.
> >
> > The rest of your drivel is not even relevant. Try again, troll!
> > > It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > >
> > > f'(c)=0-1=-1.
> > >
> > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > >
> > > The mean value theorem requires a real number line.
> No. You're <shit>
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onsdag 2 augusti 2023 kl. 00:39:02 UTC+2 skrev Eram semper recta:
> On Tuesday, 1 August 2023 at 17:34:32 UTC-4, markus...@gmail.com wrote:
> > tisdag 1 augusti 2023 kl. 14:20:30 UTC+2 skrev Eram semper recta:
> > > On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > > > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > >
> > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > >
> > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > >
> > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > Your proof is invalid.
> > > > > You've said that about a lot of things and every time you have been wrong.
> > > > >
> > > > > You're wrong here yet again.
> > > > > > The real mean value theorem requires real numbers.
> > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > >
> > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > >
> > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2.
> > > Not a valid or coherent example because the mvt works only on ONE function, not multiple functions. Like I have often instructed you, the methods of calculus apply ONLY to SMOOTH curves.
> > >
> > > The rest of your drivel is not even relevant. Try again, troll!
> > > > It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > >
> > > > f'(c)=0-1=-1.
> > > >
> > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > >
> > > > The mean value theorem requires a real number line.
> > No. You're <shit>
> 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Did you take a look at the counterexample proving ti wrong?

On Tuesday, 1 August 2023 at 18:42:22 UTC-4, markus...@gmail.com wrote:
> onsdag 2 augusti 2023 kl. 00:39:02 UTC+2 skrev Eram semper recta:
> > On Tuesday, 1 August 2023 at 17:34:32 UTC-4, markus...@gmail.com wrote:
> > > tisdag 1 augusti 2023 kl. 14:20:30 UTC+2 skrev Eram semper recta:
> > > > On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > > > > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > > > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > >
> > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > >
> > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > >
> > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > Your proof is invalid.
> > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > >
> > > > > > You're wrong here yet again.
> > > > > > > The real mean value theorem requires real numbers.
> > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > >
> > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > >
> > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2.
> > > > Not a valid or coherent example because the mvt works only on ONE function, not multiple functions. Like I have often instructed you, the methods of calculus apply ONLY to SMOOTH curves.
> > > >
> > > > The rest of your drivel is not even relevant. Try again, troll!
> > > > > It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > >
> > > > > f'(c)=0-1=-1.
> > > > >
> > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > >
> > > > > The mean value theorem requires a real number line.
> > > No. You're <shit>
> > 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> Did you take a look at the counterexample proving ti wrong?

torsdag 3 augusti 2023 kl. 13:14:03 UTC+2 skrev Eram semper recta:
> On Tuesday, 1 August 2023 at 18:42:22 UTC-4, markus...@gmail.com wrote:
> > onsdag 2 augusti 2023 kl. 00:39:02 UTC+2 skrev Eram semper recta:
> > > On Tuesday, 1 August 2023 at 17:34:32 UTC-4, markus...@gmail.com wrote:
> > > > tisdag 1 augusti 2023 kl. 14:20:30 UTC+2 skrev Eram semper recta:
> > > > > On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > > > > > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > > > > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > > > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > > >
> > > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > > >
> > > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > > >
> > > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > > Your proof is invalid.
> > > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > > >
> > > > > > > You're wrong here yet again.
> > > > > > > > The real mean value theorem requires real numbers.
> > > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > > >
> > > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > > >
> > > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2.
> > > > > Not a valid or coherent example because the mvt works only on ONE function, not multiple functions. Like I have often instructed you, the methods of calculus apply ONLY to SMOOTH curves.
> > > > >
> > > > > The rest of your drivel is not even relevant. Try again, troll!
> > > > > > It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > > >
> > > > > > f'(c)=0-1=-1.
> > > > > >
> > > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > > >
> > > > > > The mean value theorem requires a real number line.
> > > > No. You're <shit>
> > > 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> > Did you take a look at the counterexample proving ti wrong?
> See a psychiatrist soon.
I don't need to. But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.

On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > >
> > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > >
> > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > >
> > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > Your proof is invalid.
> > You've said that about a lot of things and every time you have been wrong.
> >
> > You're wrong here yet again.
> > > The real mean value theorem requires real numbers.
> > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> >
> > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> >
> > You're right - I don't understand the "limits" of your ignorance and stupidity.
> The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
>
> f'(c)=0-1=-1.
>
> But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
>
> The mean value theorem requires a real number line.

> See a psychiatrist soon.

You most definitely do need to see a psychiatrist. You are mentally ill.

> I don't need to.

> But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.

It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.

You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).

torsdag 3 augusti 2023 kl. 17:17:18 UTC+2 skrev Eram semper recta:
> On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > >
> > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > >
> > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > >
> > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > Your proof is invalid.
> > > You've said that about a lot of things and every time you have been wrong.
> > >
> > > You're wrong here yet again.
> > > > The real mean value theorem requires real numbers.
> > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > >
> > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > >
> > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> >
> > f'(c)=0-1=-1.
> >
> > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> >
> > The mean value theorem requires a real number line.
> > See a psychiatrist soon.
>
> You most definitely do need to see a psychiatrist. You are mentally ill.
> > I don't need to.
> > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
>
> It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
>
> You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
Then try it.

f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.

(b-a)f'(c)=f(b)-f(a)=1.

f'(c)=3c²=1.

This cannot be solved using rational numbers.

On Thursday, 3 August 2023 at 12:07:29 UTC-4, markus...@gmail.com wrote:
> torsdag 3 augusti 2023 kl. 17:17:18 UTC+2 skrev Eram semper recta:
> > On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > >
> > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > >
> > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > >
> > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > Your proof is invalid.
> > > > You've said that about a lot of things and every time you have been wrong.
> > > >
> > > > You're wrong here yet again.
> > > > > The real mean value theorem requires real numbers.
> > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > >
> > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > >
> > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > >
> > > f'(c)=0-1=-1.
> > >
> > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > >
> > > The mean value theorem requires a real number line.
> > > See a psychiatrist soon.
> >
> > You most definitely do need to see a psychiatrist. You are mentally ill..
> > > I don't need to.
> > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> >
> > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> >
> > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> Then try it.
>
> f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.

What?! f(b)=f(0)=0, not 1, you imbecile!

<scheißen>

torsdag 3 augusti 2023 kl. 21:03:50 UTC+2 skrev Eram semper recta:
> On Thursday, 3 August 2023 at 12:07:29 UTC-4, markus...@gmail.com wrote:
> > torsdag 3 augusti 2023 kl. 17:17:18 UTC+2 skrev Eram semper recta:
> > > On Tuesday, 1 August 2023 at 06:35:56 UTC-4, markus...@gmail.com wrote:
> > > > tisdag 1 augusti 2023 kl. 11:27:09 UTC+2 skrev Eram semper recta:
> > > > > On Monday, 31 July 2023 at 16:54:53 UTC-4, markus...@gmail.com wrote:
> > > > > > måndag 31 juli 2023 kl. 22:22:18 UTC+2 skrev Eram semper recta:
> > > > > > > On Monday, 31 July 2023 at 05:18:09 UTC-4, Eram semper recta wrote:
> > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > >
> > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > >
> > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > >
> > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > Your proof is invalid.
> > > > > You've said that about a lot of things and every time you have been wrong.
> > > > >
> > > > > You're wrong here yet again.
> > > > > > The real mean value theorem requires real numbers.
> > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > >
> > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > >
> > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > >
> > > > f'(c)=0-1=-1.
> > > >
> > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > >
> > > > The mean value theorem requires a real number line.
> > > > See a psychiatrist soon.
> > >
> > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > I don't need to.
> > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > >
> > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > >
> > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > Then try it.
> >
> > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> What?! f(b)=f(0)=0, not 1, you imbecile!
>
> <scheißen>
b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.

On Thursday, 3 August 2023 at 17:41:50 UTC-4, markus.
> > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > >
> > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > >
> > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > >
> > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > Your proof is invalid.
> > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > >
> > > > > > You're wrong here yet again.
> > > > > > > The real mean value theorem requires real numbers.
> > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > >
> > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > >
> > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > >
> > > > > f'(c)=0-1=-1.
> > > > >
> > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > >
> > > > > The mean value theorem requires a real number line.
> > > > > See a psychiatrist soon.
> > > >
> > > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > > I don't need to.
> > > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > > >
> > > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > > >
> > > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > > Then try it.
> > >
> > > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> > What?! f(b)=f(0)=0, not 1, you imbecile!
> >
> > <scheißen>
> b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.

It still is wrong, whether a typo or not. Incoherent gibberish out of your juvenile brain.

fredag 4 augusti 2023 kl. 00:44:53 UTC+2 skrev Eram semper recta:
> On Thursday, 3 August 2023 at 17:41:50 UTC-4, markus.
> > > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > > >
> > > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > > >
> > > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > > >
> > > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > > Your proof is invalid.
> > > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > > >
> > > > > > > You're wrong here yet again.
> > > > > > > > The real mean value theorem requires real numbers.
> > > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > > >
> > > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > > >
> > > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > > >
> > > > > > f'(c)=0-1=-1.
> > > > > >
> > > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > > >
> > > > > > The mean value theorem requires a real number line.
> > > > > > See a psychiatrist soon.
> > > > >
> > > > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > > > I don't need to.
> > > > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > > > >
> > > > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > > > >
> > > > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > > > Then try it.
> > > >
> > > > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> > > What?! f(b)=f(0)=0, not 1, you imbecile!
> > >
> > > <scheißen>
> > b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.
> It still is wrong, whether a typo or not. Incoherent gibberish out of your juvenile brain.
Can you solve f'(c)=3c²=1 without real numbers?

On Thursday, 3 August 2023 at 18:58:56 UTC-4, markus...
> > On Thursday, 3 August 2023 at 17:41:50 UTC-4, markus.
> > > > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > > > >
> > > > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > > > >
> > > > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > > > >
> > > > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > > > Your proof is invalid.
> > > > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > > > >
> > > > > > > > You're wrong here yet again.
> > > > > > > > > The real mean value theorem requires real numbers.
> > > > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > > > >
> > > > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > > > >
> > > > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > > > >
> > > > > > > f'(c)=0-1=-1.
> > > > > > >
> > > > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > > > >
> > > > > > > The mean value theorem requires a real number line.
> > > > > > > See a psychiatrist soon.
> > > > > >
> > > > > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > > > > I don't need to.
> > > > > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > > > > >
> > > > > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > > > > >
> > > > > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > > > > Then try it.
> > > > >
> > > > > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> > > > What?! f(b)=f(0)=0, not 1, you imbecile!
> > > >
> > > > <scheißen>
> > > b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.
> > It still is wrong, whether a typo or not. Incoherent gibberish out of your juvenile brain.
> Can you solve f'(c)=3c²=1 without real numbers?

Yes, idiot! It is the CONSTANT known as the square root of 1/3 and there is NO number that decribes its measure.

fredag 4 augusti 2023 kl. 13:27:35 UTC+2 skrev Eram semper recta:
> On Thursday, 3 August 2023 at 18:58:56 UTC-4, markus...
> > > On Thursday, 3 August 2023 at 17:41:50 UTC-4, markus.
> > > > > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > > > > >
> > > > > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > > > > >
> > > > > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > > > > >
> > > > > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > > > > Your proof is invalid.
> > > > > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > > > > >
> > > > > > > > > You're wrong here yet again.
> > > > > > > > > > The real mean value theorem requires real numbers.
> > > > > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > > > > >
> > > > > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > > > > >
> > > > > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > > > > >
> > > > > > > > f'(c)=0-1=-1.
> > > > > > > >
> > > > > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > > > > >
> > > > > > > > The mean value theorem requires a real number line.
> > > > > > > > See a psychiatrist soon.
> > > > > > >
> > > > > > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > > > > > I don't need to.
> > > > > > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > > > > > >
> > > > > > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > > > > > >
> > > > > > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > > > > > Then try it.
> > > > > >
> > > > > > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> > > > > What?! f(b)=f(0)=0, not 1, you imbecile!
> > > > >
> > > > > <scheißen>
> > > > b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.
> > > It still is wrong, whether a typo or not. Incoherent gibberish out of your juvenile brain.
> > Can you solve f'(c)=3c²=1 without real numbers?
> Yes, idiot! It is the CONSTANT known as the square root of 1/3 and there is NO number that decribes its measure.
The square root of 1/3 isn't rational. Thus the mean value theorem fails without real numbers.

On Friday, 4 August 2023 at 15:49:55 UTC-4, markus..wrote:
> fredag 4 augusti 2023 kl. 13:27:35 UTC+2 skrev Eram semper recta:
> > On Thursday, 3 August 2023 at 18:58:56 UTC-4, markus...
> > > > On Thursday, 3 August 2023 at 17:41:50 UTC-4, markus.
> > > > > > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > > > > > >
> > > > > > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > > > > > >
> > > > > > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > > > > > >
> > > > > > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > > > > > Your proof is invalid.
> > > > > > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > > > > > >
> > > > > > > > > > You're wrong here yet again.
> > > > > > > > > > > The real mean value theorem requires real numbers.
> > > > > > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > > > > > >
> > > > > > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > > > > > >
> > > > > > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > > > > > >
> > > > > > > > > f'(c)=0-1=-1.
> > > > > > > > >
> > > > > > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > > > > > >
> > > > > > > > > The mean value theorem requires a real number line.
> > > > > > > > > See a psychiatrist soon.
> > > > > > > >
> > > > > > > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > > > > > > I don't need to.
> > > > > > > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > > > > > > >
> > > > > > > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > > > > > > >
> > > > > > > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > > > > > > Then try it.
> > > > > > >
> > > > > > > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> > > > > > What?! f(b)=f(0)=0, not 1, you imbecile!
> > > > > >
> > > > > > <scheißen>
> > > > > b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.
> > > > It still is wrong, whether a typo or not. Incoherent gibberish out of your juvenile brain.
> > > Can you solve f'(c)=3c²=1 without real numbers?
> > Yes, idiot! It is the CONSTANT known as the square root of 1/3 and there is NO number that decribes its measure.
> The square root of 1/3 isn't rational.

And so? Stating the obvious incorrectly. There is no number that describes the measure of the constant root(3).

> Thus the mean value theorem fails without real numbers.

It doesn't because there is no such thing as "real number".

<END OF DISCUSSION>

fredag 4 augusti 2023 kl. 22:42:14 UTC+2 skrev Eram semper recta:
> On Friday, 4 August 2023 at 15:49:55 UTC-4, markus..wrote:
> > fredag 4 augusti 2023 kl. 13:27:35 UTC+2 skrev Eram semper recta:
> > > On Thursday, 3 August 2023 at 18:58:56 UTC-4, markus...
> > > > > On Thursday, 3 August 2023 at 17:41:50 UTC-4, markus.
> > > > > > > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > > > > > > >
> > > > > > > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > > > > > > >
> > > > > > > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > > > > > > >
> > > > > > > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > > > > > > Your proof is invalid.
> > > > > > > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > > > > > > >
> > > > > > > > > > > You're wrong here yet again.
> > > > > > > > > > > > The real mean value theorem requires real numbers.
> > > > > > > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > > > > > > >
> > > > > > > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > > > > > > >
> > > > > > > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > > > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > > > > > > >
> > > > > > > > > > f'(c)=0-1=-1.
> > > > > > > > > >
> > > > > > > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > > > > > > >
> > > > > > > > > > The mean value theorem requires a real number line.
> > > > > > > > > > See a psychiatrist soon.
> > > > > > > > >
> > > > > > > > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > > > > > > > I don't need to.
> > > > > > > > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > > > > > > > >
> > > > > > > > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > > > > > > > >
> > > > > > > > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > > > > > > > Then try it.
> > > > > > > >
> > > > > > > > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> > > > > > > What?! f(b)=f(0)=0, not 1, you imbecile!
> > > > > > >
> > > > > > > <scheißen>
> > > > > > b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.
> > > > > It still is wrong, whether a typo or not. Incoherent gibberish out of your juvenile brain.
> > > > Can you solve f'(c)=3c²=1 without real numbers?
> > > Yes, idiot! It is the CONSTANT known as the square root of 1/3 and there is NO number that decribes its measure.
> > The square root of 1/3 isn't rational.
> And so? Stating the obvious incorrectly. There is no number that describes the measure of the constant root(3).
> > Thus the mean value theorem fails without real numbers.
> It doesn't because there is no such thing as "real number".
>
> <END OF DISCUSSION>
If there is no such c, then the mean value theorem is false. The theorem states there is a such c.

On Friday, 4 August 2023 at 16:52:23 UTC-4, markus...
> > > > > > On Thursday, 3 August 2023 at 17:41:50 UTC-4, markus.
> > > > > > > > > > > > > > > https://www.academia.edu/45154026/Teaching_the_fundamental_theorem_of_calculus
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I was the FIRST HUMAN to fully understand the mean value theorem and to prove constructively.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > NONE of the stupid FUCKS who came before me where up to the task:
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
> > > > > > > > > > > > > Your proof is invalid.
> > > > > > > > > > > > You've said that about a lot of things and every time you have been wrong.
> > > > > > > > > > > >
> > > > > > > > > > > > You're wrong here yet again.
> > > > > > > > > > > > > The real mean value theorem requires real numbers..
> > > > > > > > > > > > It doesn't have anything to do with an ill-formed object you think of as a "real number".
> > > > > > > > > > > >
> > > > > > > > > > > > The mean value theorem is about a level magnitude (what you erroneously call an "arithmetic mean"). It's the reason calculus works at all.
> > > > > > > > > > > >
> > > > > > > > > > > > You're right - I don't understand the "limits" of your ignorance and stupidity.
> > > > > > > > > > > The mean value theorem doesn't work without real numbers. A very elementary counterexample is f(x)=0 if x²>2 and f(x)=1 if x²<2. It is continuous and differentiable everywhere on the rational number line with f'=0. If we consider [a, b]=[0, 2], we have a counterexample to the MVT (mean value theorem). From (b-a)f'(c)=f(b)-f(a) we have
> > > > > > > > > > >
> > > > > > > > > > > f'(c)=0-1=-1.
> > > > > > > > > > >
> > > > > > > > > > > But there is no such c. If we attempt to explicitly find c, we find that it doesn't exist.
> > > > > > > > > > >
> > > > > > > > > > > The mean value theorem requires a real number line.
> > > > > > > > > > > See a psychiatrist soon.
> > > > > > > > > >
> > > > > > > > > > You most definitely do need to see a psychiatrist. You are mentally ill.
> > > > > > > > > > > I don't need to.
> > > > > > > > > > > But you can consider f(x)=x³ over [0, 1] and see why the mean value theorem requires real numbers.
> > > > > > > > > >
> > > > > > > > > > It doesn't show at all what you claim. In fact, the mvt doesn't give a shit about anything but magnitudes.
> > > > > > > > > >
> > > > > > > > > > You obviously don't understand the mvt which is about a level magnitude (aka arithmetic mean in your bullshit mathematics).
> > > > > > > > > Then try it.
> > > > > > > > >
> > > > > > > > > f(x)=x³, a=0 and b=0. Then f'(x)=3x², f(b)=1, f(a)=0.
> > > > > > > > What?! f(b)=f(0)=0, not 1, you imbecile!
> > > > > > > >
> > > > > > > > <scheißen>
> > > > > > > b=0 was a typo. b=1, so f(b) is indeed one. You will get f'(c)=3c³=1, and this can't be solved with rational numbers only.
> > > > > > It still is wrong, whether a typo or not. Incoherent gibberish out of your juvenile brain.
> > > > > Can you solve f'(c)=3c²=1 without real numbers?
> > > > Yes, idiot! It is the CONSTANT known as the square root of 1/3 and there is NO number that decribes its measure.
> > > The square root of 1/3 isn't rational.
> > And so? Stating the obvious incorrectly. There is no number that describes the measure of the constant root(3).
> > > Thus the mean value theorem fails without real numbers.
> > It doesn't because there is no such thing as "real number".
> >
> > <END OF DISCUSSION>
> If there is no such c, then the mean value theorem is false. The theorem states there is a such c.

You'll have to tell me again what is your example. I stop after the first mistake I find and you get ignored.