Does my new way of dealing with complex numbers bring an advantage or is
it stupid? The goal is to find something more coherent (it already is),
but above all more useful.

I recall the idea: the imaginary number i is a unit such that it is
invariant whatever its power. For all x, we have i^x=-1.

This was already the case with the real unit n=1. For all x, 1^x=1.

In this sense, not only is i²=-1 true, i^(1/2)=-1, but also i^4=-1,
i^5689=-1, i^(-3/2)=-1.

Second, the real or complex roots of quadratic equations are:

<http://nemoweb.net/jntp?kRgli3QEdimCvJ9569p9c9pq7Kc@jntp/Data.Media:1>

Exemple : Roots of f(x)=x²+4x+5 ---> x'=i, x"=-5i

Finally, the complex roots of a function are the real roots of the
function in point symmetry $(0,y), and vice versa.

R.H.

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Le 07/03/2025 à 12:50, Alan Mackenzie a écrit :

Richard Hachel <r.hachel@tiscali.fr> wrote:

Does my new way of dealing with complex numbers bring an advantage or is
it stupid?

It's stupid. Your "complex numbers" are not complex numbers. They're something else altogether. The term "complex number" has a meaning in mathematics, science, engineering, etc., and you are being deliberately ignorant of that meaning.

The goal is to find something more coherent (it already is), but above
all more useful.

You have failed at that goal.

I recall the idea: the imaginary number i is a unit such that it is
invariant whatever its power. For all x, we have i^x=-1.

That is just ignorance. It's not even clear what you mean by the above.
Your ^ operator clearly has nothing to do with multiplicative powers.

This was already the case with the real unit n=1. For all x, 1^x=1.

And for all x apart from 0, x^0 = 1. That includes i^0 = 1.

In this sense, not only is i²=-1 true, i^(1/2)=-1, but also i^4=-1,
i^5689=-1, i^(-3/2)=-1.

That isn't sense, it's nonsense.

Second, the real or complex roots of quadratic equations are:

They are well understood by virtually everybody but you, and have been
for many centuries.

[ .... ]

Exemple : Roots of f(x)=x²+4x+5 ---> x'=i, x"=-5i

Wrong.

Finally, the complex roots of a function are the real roots of the
function in point symmetry $(0,y), and vice versa.

That's meaningless gibberish.

R.H.

I see you didn't understand anything.

But it doesn't matter.

For those who are more open-minded and less stupid than Alan:

I'm not saying that mathematicians treat things like that. I'm saying that
I treat things like that.
Everyone does what they want.

Nothing prevents mathematicians from proposing their ideas, nothing
prevents me from proposing mine (validated in logic by AI).
Mathematicians pose i²=-1 and sqrt(i)=-1.

NOTHING prevents me from proposing a different law, encompassing these two truths to bring them to i^x=-1 whatever x.

I affirm this as a new and universal law.

I am told that I am wrong, and that i^4=1.

I answer that they are wrong, and that they misunderstood me.

I tell them that if i^x=-1 (new global theory) then i^4=-1 and so on.

They start telling me again: "No, no, i^4=1".

This kind of knee-jerk response is stupid.

R.H.

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Le 07/03/2025 à 13:04, Richard Hachel a écrit :
..

Nothing prevents mathematicians from proposing their ideas, nothing prevents me
from proposing mine (validated in logic by AI).

AI "validates" also that cows lay eggs.

Mathematicians pose i²=-1 and sqrt(i)=-1.

They don't "pose" i^2 = -1 they *define* C and i in such a way that i^2 =
-1.

They certainly don't pretend that sqrt(i) = -1 ! Where did you get this
from ?

sqrt(i) is (1 + i)/sqrt(2) (for the principal value of sqrt).

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Am 07.03.2025 um 12:50 schrieb Alan Mackenzie:

Richard Hachel <r.hachel@tiscali.fr> wrote:

I recall the idea: the imaginary number i is a unit such that it is
invariant whatever its power. For all x, we have i^x = -1.

Then i = (I guess) = i^1 = -1, one might think.

But then i^2 = (I guess) = i*i = (-1)*(-1) = 1, one might think.

So we get a contradiction, since 1 =/= -1.

This was already the case with the real unit n=1. For all x, 1^x=1.

And for all x apart from 0, x^0 = 1. That includes i^0 = 1.

So again a contradiction (since 1 =/= -1).

So a rather bad "idea" by Hachel.

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Richard Hachel <r.hachel@tiscali.fr> wrote:

Does my new way of dealing with complex numbers bring an advantage or is
it stupid?

It's stupid. Your "complex numbers" are not complex numbers. They're something else altogether. The term "complex number" has a meaning in mathematics, science, engineering, etc., and you are being deliberately ignorant of that meaning.

The goal is to find something more coherent (it already is), but above
all more useful.

You have failed at that goal.

I recall the idea: the imaginary number i is a unit such that it is invariant whatever its power. For all x, we have i^x=-1.

That is just ignorance. It's not even clear what you mean by the above.
Your ^ operator clearly has nothing to do with multiplicative powers.

This was already the case with the real unit n=1. For all x, 1^x=1.

And for all x apart from 0, x^0 = 1. That includes i^0 = 1.

In this sense, not only is i²=-1 true, i^(1/2)=-1, but also i^4=-1, i^5689=-1, i^(-3/2)=-1.

That isn't sense, it's nonsense.

Second, the real or complex roots of quadratic equations are:

They are well understood by virtually everybody but you, and have been
for many centuries.

[ .... ]

Exemple : Roots of f(x)=x²+4x+5 ---> x'=i, x"=-5i

Wrong.

Finally, the complex roots of a function are the real roots of the
function in point symmetry $(0,y), and vice versa.

That's meaningless gibberish.

R.H.

--
Alan Mackenzie (Nuremberg, Germany).

--- SoupGate-Win32 v1.05
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Richard Hachel <r.hachel@tiscali.fr> wrote:

Le 07/03/2025 à 12:50, Alan Mackenzie a écrit :

Richard Hachel <r.hachel@tiscali.fr> wrote:

Does my new way of dealing with complex numbers bring an advantage or is >>> it stupid?

It's stupid. Your "complex numbers" are not complex numbers. They're
something else altogether. The term "complex number" has a meaning in
mathematics, science, engineering, etc., and you are being deliberately
ignorant of that meaning.

The goal is to find something more coherent (it already is), but above
all more useful.

You have failed at that goal.

I recall the idea: the imaginary number i is a unit such that it is
invariant whatever its power. For all x, we have i^x=-1.

That is just ignorance. It's not even clear what you mean by the above.
Your ^ operator clearly has nothing to do with multiplicative powers.

This was already the case with the real unit n=1. For all x, 1^x=1.

And for all x apart from 0, x^0 = 1. That includes i^0 = 1.

In this sense, not only is i²=-1 true, i^(1/2)=-1, but also i^4=-1,
i^5689=-1, i^(-3/2)=-1.

That isn't sense, it's nonsense.

Second, the real or complex roots of quadratic equations are:

They are well understood by virtually everybody but you, and have been
for many centuries.

[ .... ]

Exemple : Roots of f(x)=x²+4x+5 ---> x'=i, x"=-5i

Wrong.

Finally, the complex roots of a function are the real roots of the
function in point symmetry $(0,y), and vice versa.

That's meaningless gibberish.

R.H.

I see you didn't understand anything.

But it doesn't matter.

For those who are more open-minded and less stupid than Alan:

Is that all you've got? Ad hominem attacks?

I'm not saying that mathematicians treat things like that. I'm saying that
I treat things like that.
Everyone does what they want.

You're implicitly suggesting that these things are arbitrary, and that
your worthless suggestions are the equal of many centuries' development
of complex numbers by mathematicians, scientists and engineers. They're
not.

Nothing prevents mathematicians from proposing their ideas, nothing
prevents me from proposing mine (validated in logic by AI).
Mathematicians pose i²=-1 and sqrt(i)=-1.

Again, your ideas are objectively worthless.

NOTHING prevents me from proposing a different law, encompassing these two truths to bring them to i^x=-1 whatever x.

If you're going to do that, then stop lying by calling your "system"
complex numbers.

I affirm this as a new and universal law.

You're not in a position to affirm any such "law".

I am told that I am wrong, and that i^4=1.

That is indeed the case, yes.

I answer that they are wrong, and that they misunderstood me.

I understand you very well. You are a troll and a crank, devoid of basic education in maths.

I tell them that if i^x=-1 (new global theory) then i^4=-1 and so on.

i^x=-1 leads immediately to contradictions, as you have been told several
times already, hence is nonsense.

They start telling me again: "No, no, i^4=1".

This kind of knee-jerk response is stupid.

No, it is the affirmation of sense over nonsense.

R.H.

--
Alan Mackenzie (Nuremberg, Germany).

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Le 07/03/2025 à 13:04, Richard Hachel a écrit :

I'm not saying that mathematicians treat things like that. I'm saying
that I treat things like that.
Everyone does what they want.

Nothing prevents mathematicians from proposing their ideas, nothing
prevents me from proposing mine (validated in logic by AI).
Mathematicians pose i²=-1 and sqrt(i)=-1.

NOTHING prevents me from proposing a different law, encompassing these
two truths to bring them to i^x=-1 whatever x.

I affirm this as a new and universal law.

The real question is : Is he truly that stupid, or is he history's
greatest troll?

Up to now, I think he is the most stupid, pretentious, arrogant,
conceited and haughty I've ever met. But I may be wrong.

--
F.J.

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Le 07/03/2025 à 13:12, Python a écrit :

Le 07/03/2025 à 13:04, Richard Hachel a écrit :
...

Nothing prevents mathematicians from proposing their ideas, nothing prevents me
from proposing mine (validated in logic by AI).

AI "validates" also that cows lay eggs.

Mathematicians pose i²=-1 and sqrt(i)=-1.

They don't "pose" i^2 = -1 they *define* C and i in such a way that i^2 = -1.

They certainly don't pretend that sqrt(i) = -1 ! Where did you get this from ?

sqrt(i) is (1 + i)/sqrt(2) (for the principal value of sqrt).

I obviously understand what you're saying.

What I blame you for is unconditionally following what you've learned (I'm
not saying everything is wrong, I'm not a conspiracy theorist), and never questioning a system of thought that may have flaws.

For traditional mathematicians, it's true.

For me, it's false.

Everyone sees noon at their door.

R.H.

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Le 07/03/2025 à 14:23, Alan Mackenzie a écrit :

Richard Hachel <r.hachel@tiscali.fr> wrote:

Exemple : Roots of f(x)=x²+4x+5 ---> x'=i, x"=-5i

Wrong.

It's false for you, it's true for me.

It all depends on the point of view, and how we conceive of complex roots
and the idea we have of the imaginary i.

Finally, the complex roots of a function are the real roots of the
function in point symmetry $(0,y), and vice versa.

That's meaningless gibberish.

On the contrary, it is very clear, mathematically coherent, and very
elegant as a development.

For those who are more open-minded and less stupid than Alan:

Is that all you've got? Ad hominem attacks?

Not realy.

You are a troll and a crank, devoid of basic education in maths.

Ad hominem attack.

R.H.

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On 3/7/2025 11:40 AM, efji wrote:

Le 07/03/2025 à 13:04, Richard Hachel a écrit :

I'm not saying that mathematicians treat things like that.
I'm saying that I treat things like that.
Everyone does what they want.

𝑖 = (-​🐎​✨​🌈​🐦)¹ᐟ²

Nothing prevents mathematicians from proposing their ideas,
nothing prevents me from proposing mine
(validated in logic by AI).

💩→💻→💩

Mathematicians pose i²=-1 and sqrt(i)=-1.

NOTHING prevents me from proposing a different law,
encompassing these two truths
to bring them to i^x=-1 whatever x.

I affirm this as a new and universal law.

The real question is :
Is he truly that stupid, or
is he history's greatest troll?

Up to now, I think he is the most
stupid, pretentious, arrogant, conceited and haughty
I've ever met. But I may be wrong.

"He wears a mask, and his face grows to fit it."
-- George Orwell, "Shooting an Elephant" (1936)

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Le 07/03/2025 à 13:04, Richard Hachel a écrit :

Nothing prevents mathematicians from proposing their ideas, nothing
prevents me from proposing mine.

Yeah, you might propose your "ideas" in a mental hospital, for example.

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Le 07/03/2025 à 21:50, "Chris M. Thomasson" a écrit :

On 3/7/2025 4:04 AM, Richard Hachel wrote:

Le 07/03/2025 à 12:50, Alan Mackenzie a écrit :

Okay. Well. Let's start small. Use your new way to implement the
Mandelbrot set and/or any Julia set. Plot the sucker! Then show us the resulting plot...

Thank you for your answer.

You raise the problem of Benoit Mandelbrot's fractals. I could not answer
that, because I do not know the subject at all.
I just know that it is a mathematical representation that presents a
similar structure at all scales. A bit like Russian dolls.
I look on the internet, where it is written that these fractals start from complex numbers of the nature of Z = a + bi.
It is obviously very interesting, but I do not see the difficulty with
what I said about complex numbers.
Have you yourself made a fractal using complex numbers? Can you give me
the equation? It would be very surprising if with my principles, we did
not arrive at anything at all.

Best regards.

R.H.

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Le 07/03/2025 à 21:50, "Chris M. Thomasson" a écrit :
..

Okay. Well. Let's start small. Use your new way to implement the
Mandelbrot set and/or any Julia set. Plot the sucker! Then show us the resulting plot...

There is no way to compute Mandelbrot or Julia type of set on an
inconsistent "structure" as the one Richard proposes.

By the way, there is a demo on Wolfram's site displaying what happens with Complex numbers, duals and split-complex numbers :

https://demonstrations.wolfram.com/IteratedMapsUsingComplexDualAndSplitComplexNumbers/

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Le 08/03/2025 à 12:08, Python a écrit :

Le 07/03/2025 à 21:50, "Chris M. Thomasson" a écrit :
..

Okay. Well. Let's start small. Use your new way to implement the
Mandelbrot set and/or any Julia set. Plot the sucker! Then show us the
resulting plot...

There is no way to compute Mandelbrot or Julia type of set on an
inconsistent "structure" as the one Richard proposes.

By the way, there is a demo on Wolfram's site displaying what happens
with Complex numbers, duals and split-complex numbers :

https://demonstrations.wolfram.com/ IteratedMapsUsingComplexDualAndSplitComplexNumbers/

Great :)
So the poor structure R(j) accidentally "found" by Hachel leads to a
poor square when you iterates.
By poor structure I mean only the split-complex structure where j^2=1,
and of course not the total delirium he is now stuck on (i^x=-1 forall x).

Pathetic idiot...

--
F.J.

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Le 07/03/2025 à 19:00, Richard Hachel a écrit :

Le 07/03/2025 à 13:12, Python a écrit :

Le 07/03/2025 à 13:04, Richard Hachel a écrit :
...

Nothing prevents mathematicians from proposing their ideas, nothing prevents me
from proposing mine (validated in logic by AI).

AI "validates" also that cows lay eggs.

Mathematicians pose i²=-1 and sqrt(i)=-1.

They don't "pose" i^2 = -1 they *define* C and i in such a way that i^2 = -1.

They certainly don't pretend that sqrt(i) = -1 ! Where did you get this from ?

sqrt(i) is (1 + i)/sqrt(2) (for the principal value of sqrt).

I obviously understand what you're saying.

What I blame you for is unconditionally following what you've learned (I'm not
saying everything is wrong, I'm not a conspiracy theorist), and never questioning
a system of thought that may have flaws.

For traditional mathematicians, it's true.

For me, it's false.

What you claimed above is "Mathematicians pose i²=-1 and sqrt(i)=-1." was
not about your "system" (which does not even exists as it is
inconsistant), you wrote that some "mathematicians" would have "posed"
that sqrt(i) = -1. This is factually WRONG.

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Le 08/03/2025 à 13:20, Python a écrit :

Le 07/03/2025 à 19:00, Richard Hachel a écrit :

Mathematicians pose i²=-1 and sqrt(i)=-1.

What you claimed above is "Mathematicians pose i²=-1 and sqrt(i)=-1." was not
about your "system" (which does not even exists as it is inconsistant), you wrote
that some "mathematicians" would have "posed" that sqrt(i) = -1. This is factually
WRONG.

To me, it's not wrong.

i²=-1, sqrt(i)=-1, i^5347=-1, i°=-1.

i^x=-1.

To me, is a new definition. More general, more beautiful, more universal,
more true.

R.H.

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Le 07/03/2025 à 19:00, Richard Hachel a écrit :

Le 07/03/2025 à 13:12, Python a écrit :

Le 07/03/2025 à 13:04, Richard Hachel a écrit :
...

Nothing prevents mathematicians from proposing their ideas, nothing prevents me
from proposing mine (validated in logic by AI).

AI "validates" also that cows lay eggs.

Mathematicians pose i²=-1 and sqrt(i)=-1.

They don't "pose" i^2 = -1 they *define* C and i in such a way that i^2 = -1.

They certainly don't pretend that sqrt(i) = -1 ! Where did you get this from ?

sqrt(i) is (1 + i)/sqrt(2) (for the principal value of sqrt).

I obviously understand what you're saying.

This is very unlikely.

What I blame you for is unconditionally following what you've learned (I'm not
saying everything is wrong, I'm not a conspiracy theorist), and never questioning
a system of thought that may have flaws.

This is not how learning math works. I don't "unconditionally" follow
anything, I started by understanding what it is about, how C is defined,
what properties this set has when it comes to mathematical operations and
I did so, as a student, by writing down proofs by myself.

You are the one following unconditionally any idea that came through your
(very silly) mind and stubbornly refuse to consider *proofs* that your
"system" is inconsistent, even when these proofs are trivial. Moreover you
have this completely delusional claim that several centuries of research
and discussions between mathematicians, that end up in a rigorous
definition of complex numbers and zillions of applications is wrong
without taking time to seriously study it.

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Le 08/03/2025 à 12:47, efji a écrit :

Le 08/03/2025 à 12:08, Python a écrit :

the total delirium he is now stuck on (i^x=-1 for all x).

Pathetic idiot...

To me, i is that imaginary unit with a mathematical property such that
i^x=-1.

i=-1
i²=-1
i².i=-1
i².i²=-1

i^(1/2)=-1
i^57=-1
i^(-8697)=-1

R.H.

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Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Le 08/03/2025 à 12:47, efji a écrit :

Le 08/03/2025 à 12:08, Python a écrit :

the total delirium he is now stuck on (i^x=-1 for all x).

Pathetic idiot...

To me, i is that imaginary unit with a mathematical property such that i^x=-1.

i=-1
i²=-1
i².i=-1
i².i²=-1

Again, learn once for all what "associativity" means!

Associativity is MANDATORY to be able to write something like i^4 = i*i*i*i. For a non associative operator, i^4 means NOTHING.
For an associative operator,
i^4 = i*i*i*i = (i*i)*(i*i) = i*i^3 = (i^2)*i*i etc.

Then, if you assume i^2=-1 you MUST have i^4 = (i^2)^2 = (-1)^2 = 1

End of the story, and then you shut the fuck up forever on the subject.
Thanks


--
F.J.

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Le 08/03/2025 à 14:07, Richard Hachel a écrit :

Le 08/03/2025 à 13:20, Python a écrit :

Le 07/03/2025 à 19:00, Richard Hachel a écrit :

Mathematicians pose i²=-1 and sqrt(i)=-1.

What you claimed above is "Mathematicians pose i²=-1 and sqrt(i)=-1." was not
about your "system" (which does not even exists as it is inconsistant), you wrote
that some "mathematicians" would have "posed" that sqrt(i) = -1. This is factually
WRONG.

To me, it's not wrong.

Do you even read what you wrote ? You wrote that "mathematicians" "poses" sqrt(i) = -1, it was not a claim about your inconsistent system but a
claim about the "standard" complex numbers system. And, as such, it is
WRONG, factually WRONG.

i²=-1, sqrt(i)=-1, i^5347=-1, i°=-1.

i^x=-1.

To me, is a new definition. More general, more beautiful, more universal, more
true.

Because of your pathological egotism you fail to notice that this is
trivially inconsistent.

i^x = -1 leads to direct contradiction in a lot of ways:

if i^1 = i = -1 THEN i^2 = 1 =/= -1 : contradiction!

if i^2 = -1 THEN i^4 = (i^2)^2 = (-1)^2 = 1 =/= -1 : contradiction again!

Math is not a fairy tale. You cannot assume a inconsistent property.

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Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Le 08/03/2025 à 12:47, efji a écrit :

Le 08/03/2025 à 12:08, Python a écrit :

the total delirium he is now stuck on (i^x=-1 for all x).

Pathetic idiot...

To me, i is that imaginary unit with a mathematical property such that i^x=-1.

i=-1
i²=-1
i².i=-1
i².i²=-1

This is completely inconsistent.

This contradict an elementary logical property of equality which is that
if a is in the domain of a function f, then a = b implies f(a) = f(b)
[pick f:x->x^2, a = i, b = -1] You cannot do any reasoning in a system
that contradict this.

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Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject.

In your dreams. :))

R.H.

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Le 08/03/2025 à 17:34, Richard Hachel a écrit :

Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject.

In your dreams. :))

Being proven wrong never prevents an imbecile to continue spouting
nonsense.

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Le 08/03/2025 à 14:32, efji a écrit :

Again, learn once for all what "associativity" means!

Associativity is MANDATORY to be able to write something like i^4 = i*i*i*i. For a non associative operator, i^4 means NOTHING.
For an associative operator,
i^4 = i*i*i*i = (i*i)*(i*i) = i*i^3 = (i^2)*i*i etc.

Then, if you assume i^2=-1 you MUST have i^4 = (i^2)^2 = (-1)^2 = 1

End of the story, and then you shut the fuck up forever on the subject. Thanks

F.J.

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Le 08/03/2025 à 18:27, Richard Hachel a écrit :

i^x=-1.

As showed several times, this is a complete nonsense for x integer, but
let's play, since usualy "x" designs a real number.

Dear Dr Hachel, how do you define the following quantities, for a given

0 and x real number ?

a^x ?
(-a)^x ?

--
F.J.

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Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Le 08/03/2025 à 17:52, Python a écrit :

Le 08/03/2025 à 17:34, Richard Hachel a écrit :

Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject. >>>

In your dreams. :))

Being proven wrong never prevents an imbecile to continue spouting nonsense.

i^x=-1.

Q.E.D.

Such an object is trivially inconsistent i.e. does not exist.

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Le 08/03/2025 à 17:52, Python a écrit :

Le 08/03/2025 à 17:34, Richard Hachel a écrit :

Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject.

In your dreams. :))

Being proven wrong never prevents an imbecile to continue spouting nonsense.

i^x=-1.

R.H.

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Le 08/03/2025 à 18:38, efji a écrit :

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

i^x=-1.

As showed several times, this is a complete nonsense for x integer, but
let's play, since usualy "x" designs a real number.

Dear Dr Hachel, how do you define the following quantities, for a given

0 and x real number ?

a^x ?
(-a)^x ?

Dear Professor Efji.

I don't feel like answering you.

If you want to know something ask on usenet, on social networks, or to artificial intelligence.

You will have answers.

You just have to type:

"how do you define the following quantities, for a given a>0 and x real
number ? a^x ? (-a)^x ?"

R.H.

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Le 08/03/2025 à 18:39, Python a écrit :

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Le 08/03/2025 à 17:52, Python a écrit :

Le 08/03/2025 à 17:34, Richard Hachel a écrit :

Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject. >>>>

In your dreams. :))

Being proven wrong never prevents an imbecile to continue spouting nonsense.

i^x=-1.

Q.E.D.

Such an object is trivially inconsistent i.e. does not exist.

sqrt(-5) does not more exist

R.H.

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Le 08/03/2025 à 18:47, Richard Hachel a écrit :

Le 08/03/2025 à 18:39, Python a écrit :

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Le 08/03/2025 à 17:52, Python a écrit :

Le 08/03/2025 à 17:34, Richard Hachel a écrit :

Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject. >>>>>

In your dreams. :))

Being proven wrong never prevents an imbecile to continue spouting nonsense.

i^x=-1.

Q.E.D.

Such an object is trivially inconsistent i.e. does not exist.

sqrt(-5) does not more exist

It does. Not in R though. In C, it is i*sqrt(5) where i is rigorously
defined as I've shown you.

The point is that the existence of x such as x^2 = -5 does not lead to a contradiction like your ‘i’ does.

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Le 08/03/2025 à 18:52, Python a écrit :

Le 08/03/2025 à 18:47, Richard Hachel a écrit :

Le 08/03/2025 à 18:39, Python a écrit :

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Le 08/03/2025 à 17:52, Python a écrit :

Le 08/03/2025 à 17:34, Richard Hachel a écrit :

Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject. >>>>>>

In your dreams. :))

Being proven wrong never prevents an imbecile to continue spouting nonsense.

i^x=-1.

Q.E.D.

Such an object is trivially inconsistent i.e. does not exist.

sqrt(-5) does not more exist

It does. Not in R though. In C, it is i*sqrt(5) where i is rigorously defined as
I've shown you.

The point is that the existence of x such as x^2 = -5 does not lead to a contradiction like your ‘i’ does.

Ben si, au départ, c'est une contradiction.

C'est autant une contradiction que la théorie de la relativité
d'Einstein "Cent auteurs contre Einstein".

Et cela reste une contradiction si l'on n'explique pas pourquoi on
pratique comme cela.

Toutes ces contradictions, finalement, on une cause très simple. On voit
que quelque chose est possible,
que quelque chose est faisable.

Mais par une immense arrogance, doublée d'une incroyable incapacité, on n'explique pas pourquoi.

Pourquoi i^2=-1? On ne sait pas pourquoi, alors on le dit, et on est
content quand même.

Pourquoi Stella revient âgée de 18 ans alors que son frère en a 30, on l'explique très mal, surtout si on analyse le problème en deux tronçons différents. Mais ça fait rien, on est content.

On a sa petite équation T'=T/sqrt(1=v²/c²), on est content, on se prend
pour Einstein.

On a sa petite équation i²=-1, on est content : on se prend pour Gauss.

R.H.

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Le 08/03/2025 à 20:06, Richard Hachel a écrit :

Le 08/03/2025 à 18:52, Python a écrit :

Le 08/03/2025 à 18:47, Richard Hachel a écrit :

Le 08/03/2025 à 18:39, Python a écrit :

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Le 08/03/2025 à 17:52, Python a écrit :

Le 08/03/2025 à 17:34, Richard Hachel a écrit :

Le 08/03/2025 à 14:32, efji a écrit :

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

End of the story, and then you shut the fuck up forever on the subject.

In your dreams. :))

Being proven wrong never prevents an imbecile to continue spouting nonsense.

i^x=-1.

Q.E.D.

Such an object is trivially inconsistent i.e. does not exist.

sqrt(-5) does not more exist

It does. Not in R though. In C, it is i*sqrt(5) where i is rigorously defined as
I've shown you.

The point is that the existence of x such as x^2 = -5 does not lead to a
contradiction like your ‘i’ does.

Ben si, au départ, c'est une contradiction.

C'est autant une contradiction que la théorie de la relativité d'Einstein "Cent auteurs contre Einstein".

Et cela reste une contradiction si l'on n'explique pas pourquoi on pratique comme cela.

Toutes ces contradictions, finalement, on une cause très simple. On voit que quelque chose est possible,
que quelque chose est faisable.

Mais par une immense arrogance, doublée d'une incroyable incapacité, on n'explique pas pourquoi.

Pourquoi i^2=-1? On ne sait pas pourquoi, alors on le dit, et on est content quand même.

Pourquoi Stella revient âgée de 18 ans alors que son frère en a 30, on l'explique très mal, surtout si on analyse le problème en deux tronçons différents. Mais ça fait rien, on est content.

On a sa petite équation T'=T/sqrt(1=v²/c²), on est content, on se prend pour
Einstein.

On a sa petite équation i²=-1, on est content : on se prend pour Gauss.

R.H.

How come, Richard, that you cannot grasp that it is rude to post in French
in an English speaking group? You have no respect for the audience.

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Am 08.03.2025 um 18:39 schrieb Python:

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Being proven wrong never prevents an imbecile to continue spouting
nonsense.

Mückenheim comes to mind.

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Am 08.03.2025 um 14:16 schrieb Python:

Do you even read what you wrote? You wrote that "mathematicians"
"poses" sqrt(i) = -1, it was not a claim about your inconsistent system
but a claim about the "standard" complex numbers system. And, as such,
it is WRONG, factually WRONG.

See /delusion/:

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

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Le 08/03/2025 à 23:34, Moebius a écrit :

Am 08.03.2025 um 18:39 schrieb Python:

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Being proven wrong never prevents an imbecile to continue spouting
nonsense.

Mückenheim comes to mind.

Sure. But far worse. While Hachel/Lengrand is an old retired M.D. spitting nonsense in the void, Wolfang Mückenheim is actually "teaching" his
nonsense in a German school.

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Am 08.03.2025 um 23:38 schrieb Python:

Le 08/03/2025 à 23:34, Moebius a écrit :

Am 08.03.2025 um 18:39 schrieb Python:

Le 08/03/2025 à 18:27, Richard Hachel a écrit :

Being proven wrong never prevents an imbecile to continue spouting
nonsense.

Mückenheim comes to mind.

Sure. But far worse. While Hachel/Lengrand is an old retired M.D.
spitting nonsense in the void, Wolfang Mückenheim is actually "teaching"
his nonsense in a German school.

Agree. :-/

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Am 08.03.2025 um 14:32 schrieb efji:

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Associativity is MANDATORY to be able to write something like i^4 = i*i*i*i.

For a non associative operator, i^4 means NOTHING.

Oh, i^(n+1) just might mean (i^n) * i (with n e IN).

[And i^0 = 1.]

Then: i^4 = ((i*i)*i)*i.

[Hint: recursive definition:
x^0 = 1
x^(n+1) = x^n * x (for all n e IN)]

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Am 08.03.2025 um 23:47 schrieb Moebius:

Am 08.03.2025 um 14:32 schrieb efji:

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Associativity is MANDATORY to be able to write something like i^4 =
i*i*i*i.

For a non associative operator, i^4 means NOTHING.

Oh, i^(n+1) just might mean (i^n) * i (with n e IN).

[And i^0 = 1.]

Then: i^4 = ((i*i)*i)*i.

[Hint: recursive definition:
 x^0 = 1
 x^(n+1) = x^n * x   (for all n e IN)]

x^0 = 1
x^(n+1) = (x^n) * x (for all n e IN)]

... if you like.

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Am 09.03.2025 um 00:26 schrieb efji:

Le 08/03/2025 à 23:55, Moebius a écrit :

Am 08.03.2025 um 23:47 schrieb Moebius:

Am 08.03.2025 um 14:32 schrieb efji:

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Associativity is MANDATORY to be able to write something like i^4 =
i*i*i*i.

For a non associative operator, i^4 means NOTHING.

Oh, i^(n+1) just might mean (i^n) * i (with n e IN).

[And i^0 = 1.]

Then: i^4 = ((i*i)*i)*i.

[Hint: recursive definition:
  x^0 = 1
  x^(n+1) = x^n * x   (for all n e IN)]

     x^0 = 1
     x^(n+1) = (x^n) * x   (for all n e IN)]

... if you like.

I don't like.
What if * is not commutative ?

(x^n) * x =/= x * (x^n)

Might be the case, yes. So what? :-P

But -hint- you talked about *associativity*, not about *commutativity*. :-)

Trying to use crank strategies?

.
.
.

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Le 08/03/2025 à 23:55, Moebius a écrit :

Am 08.03.2025 um 23:47 schrieb Moebius:

Am 08.03.2025 um 14:32 schrieb efji:

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Associativity is MANDATORY to be able to write something like i^4 =
i*i*i*i.

For a non associative operator, i^4 means NOTHING.

Oh, i^(n+1) just might mean (i^n) * i (with n e IN).

[And i^0 = 1.]

Then: i^4 = ((i*i)*i)*i.

[Hint: recursive definition:
  x^0 = 1
  x^(n+1) = x^n * x   (for all n e IN)]

    x^0 = 1
    x^(n+1) = (x^n) * x   (for all n e IN)]

... if you like.

I don't like.
What if * is not commutative ?

(x^n) * x =/= x * (x^n)


--
F.J.

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Le 09/03/2025 à 00:31, Moebius a écrit :

Am 09.03.2025 um 00:26 schrieb efji:

Le 08/03/2025 à 23:55, Moebius a écrit :

Am 08.03.2025 um 23:47 schrieb Moebius:

Am 08.03.2025 um 14:32 schrieb efji:

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Associativity is MANDATORY to be able to write something like i^4 =
i*i*i*i.

For a non associative operator, i^4 means NOTHING.

Oh, i^(n+1) just might mean (i^n) * i (with n e IN).

[And i^0 = 1.]

Then: i^4 = ((i*i)*i)*i.

[Hint: recursive definition:
  x^0 = 1
  x^(n+1) = x^n * x   (for all n e IN)]

     x^0 = 1
     x^(n+1) = (x^n) * x   (for all n e IN)]

... if you like.

I don't like.
What if * is not commutative ?

(x^n) * x =/= x * (x^n)

Might be the case, yes. So what? :-P

But -hint- you talked about *associativity*, not about *commutativity*. :-)

I just pointed out the fact that the notation x^n is never used in the
case of non associative operators because it is ambiguous without
further definition. Think about the vector product in R^3 for example,
which is not associative, and not commutative too. Nobody would write
x^3 for (x \wedge x)\wedge x.

In the case of Hachel's delirium, the product is obviously associative,
thus i^2 = -1 and i^4 = -1 makes no sense.

And of course, even with your recursive definition, it makes no sense.

Trying to use crank strategies?

fighting fire with fire :)


--
F.J.

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Am 09.03.2025 um 00:43 schrieb efji:

Le 09/03/2025 à 00:31, Moebius a écrit :

Am 09.03.2025 um 00:26 schrieb efji:

Le 08/03/2025 à 23:55, Moebius a écrit :

Am 08.03.2025 um 23:47 schrieb Moebius:

Am 08.03.2025 um 14:32 schrieb efji:

Le 08/03/2025 à 14:18, Richard Hachel a écrit :

Associativity is MANDATORY to be able to write something like i^4
= i*i*i*i.

For a non associative operator, i^4 means NOTHING.

Oh, i^(n+1) just might mean (i^n) * i (with n e IN).

[And i^0 = 1.]

Then: i^4 = ((i*i)*i)*i.

[Hint: recursive definition:
  x^0 = 1
  x^(n+1) = x^n * x   (for all n e IN)]

     x^0 = 1
     x^(n+1) = (x^n) * x   (for all n e IN)]

... if you like.

I don't like.
What if * is not commutative ?

(x^n) * x =/= x * (x^n)

Might be the case, yes. So what? :-P

But -hint- you talked about *associativity*, not about
*commutativity*. :-)

I just pointed out the fact that the notation x^n is never used in the
case of non associative operators because it is ambiguous without
further definition. Think about the vector product in R^3 for example,
which is not associative, and not commutative too. Nobody would write
x^3 for (x \wedge x)\wedge x.

In the case of Hachel's delirium, the product is obviously associative,
thus i^2 = -1 and i^4 = -1 makes no sense.

And of course, even with your recursive definition, it makes no sense.

Trying to use crank strategies?

fighting fire with fire :)

:-P

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Le 09/03/2025 à 00:43, efji a écrit :

I just pointed out the fact that the notation x^n is never used in the
case of non associative operators because it is ambiguous without
further definition. Think about the vector product in R^3 for example,
which is not associative, and not commutative too. Nobody would write
x^3 for (x \wedge x)\wedge x.

In the case of Hachel's delirium, the product is obviously associative,
thus i^2 = -1 and i^4 = -1 makes no sense.

And of course, even with your recursive definition, it makes no sense.

Why would it not make sense?
When zero was introduced into mathematics, perhaps some people said, it's absurd, since zero is nothing.
When negative numbers were introduced, perhaps some people thought the
idea was stupid, and that in a field you couldn't have a herd of minus
three sheep, or in a basket, minus three apples to go and sell them on the market in Baghdad.
The first relativistic physicists thought that relative time was absurd,
and that a second was worth a second for everyone, in short that it was impossible for Stella to be 18 years old, and Terrence 30 years old.
Newton wondered what all the abstract manipulations based on the imaginary could be for, and how we could use them in a concrete way in our universe.

Here, we have a much more precise definition than what we have been taught
for several centuries. We simply pose:
i is this imaginary unit such that it can never be made positive by any
power. Similarly for 1, which is constant and similar to itself whatever
its exponent, we have, for any exponent x: i^x=-1.

If this is an imaginary concept why not imagine it?

Is it less extravagant, in a mathematical thought, to say that i²=-1 than
to say that i^x=-1?

If the natural law wants an imaginary to have its own law when we join
positive or negative signs to it, how would this make no sense?

R.H.

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Le 09/03/2025 à 05:27, "Chris M. Thomasson" a écrit :

On 3/8/2025 4:11 PM, Richard Hachel wrote:

Le 09/03/2025 à 00:43, efji a écrit :

The imaginary component is a real thing.

<http://nemoweb.net/jntp?S85leDWYck_uzsT1ud850Y7JSSw@jntp/Data.Media:1>


R.H.

--
Ce message a été posté avec Nemo : <https://www.nemoweb.net/?DataID=S85leDWYck_uzsT1ud850Y7JSSw@jntp>

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Le 09/03/2025 à 01:11, Richard Hachel a écrit :

Le 09/03/2025 à 00:43, efji a écrit :

I just pointed out the fact that the notation x^n is never used in the
case of non associative operators because it is ambiguous without
further definition. Think about the vector product in R^3 for example,
which is not associative, and not commutative too. Nobody would write
x^3 for (x \wedge x)\wedge x.

In the case of Hachel's delirium, the product is obviously associative,
thus i^2 = -1 and i^4 = -1 makes no sense.

And of course, even with your recursive definition, it makes no sense.

Why would it not make sense?
When zero was introduced into mathematics, perhaps some people said, it's absurd, since zero is nothing.

True in the sense that it took quite a long time for zero to be considered
as a number as any other.

When negative numbers were introduced, perhaps some people thought the idea was
stupid, and that in a field you couldn't have a herd of minus three sheep, or in a
basket, minus three apples to go and sell them on the market in Baghdad.

True in the sense that negative numbers were at first treated as
"fictitious" quantities, just like square roots of negative quantities a
few years (not that much !) later.

What matters is that *now* (for more than one century) zéro, natural and relative integers, fractions, reals, complex numbers, etc. have rock-solid definitions.

If this is an imaginary concept why not imagine it?

You've been explained 1000 times that the word "imaginary" when it comes
to complex numbers is a historical remnant of the fact they had no
rigorous definitions when they first were considered (to solve degree 3 polynomial equations with real coefficient).

The word "imaginary" stays but not as its usual meaning.

Is it less extravagant, in a mathematical thought, to say that i²=-1 than to say that i^x=-1?

It is. Considering that exists i such as i^2 = -1 leads to no
contradiction. This is what puzzled mathematicians and was addressed three centuries later with a lot of debates amongst them.

Considering that exists i such as for all x i^x = -1 leads to immediate contradictions. As you've been shown.

If the natural law wants an imaginary to have its own law when we join positive
or negative signs to it, how would this make no sense?

In maths, "no sense" is a synonymous with "inconstant". Your proposal (i^x
= -1) is inconsistent.

You proposal contradicts this simple property of equality:

if a is in the domain of a function f, then a = b implies f(a) = f(b)

[pick a = i, b = -1, f:x->x^2 or a = i^2, b = -1 and the same f]

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Am 09.03.2025 um 19:40 schrieb Python:

In maths, "no sense" is a synonymous with "inconstant".

"inconsistent" :-P

Your proposal (i^x = -1) is inconsistent.

Yeah, it's nonsense. :-)

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Le 09/03/2025 à 20:16, Moebius a écrit :

Am 09.03.2025 um 19:40 schrieb Python:

In maths, "no sense" is a synonymous with "inconstant".

"inconsistent" :-P

Your proposal (i^x = -1) is inconsistent.

Yeah, it's nonsense. :-)

Absolutely not.

Dr. Richard Hachel (triple Nobel Prize winner and future Fields) has
imagined a new mathematical tool full of promise if we study it and use it well.

He poses a general law using a purely imaginary unit, such that i is a
negative invariant, whatever the power we propose to it, and always
remaining equal to itself. That is to say i^x=-1.

We have the same thing with 1 in reality.

Now, we have the same thing, in mirror, in the imaginary.

Simply, we must handle this i with care because already, in reality,
children and students make many sign errors.

This notion makes things even worse if we use it badly.

It's not a nonsense.

R.H.

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