To solve quadratic equations without real roots of the type f(x)=x²+4x+5, mathematicians invented complex roots.
The idea, obviously, was not bad.
We then assumed an imaginary number, which we named i, such that i²=-1,
and this number would allow, not only to positiveize the discriminant, but
also to make the square root disappear.
All profit.
Except that it is not enough.
Why is it not enough? Because we do not explain what this i is, nor where
it really comes from.
We are content with a postulate, without seeing the horrible consequences
for all mathematical logic.
We say i²=-1, without understanding, without thinking, believing that it
is a very simple and harmless thing to handle explosives, and we handle
TNT so well that we affirm the following mathematical monstrosity: "If
i²=-1 then i²*i²=1.

This is one of the greatest mathematical crimes of the entire human
species, because ignorance of what i is has already led us to this.

We will then progress into the worst.

We can only progress into the worst.

When we are sick, we generally ask the doctor's opinion.

But when we are scientifically sick, and we believe such nonsense, we do
not ask the doctor's opinion, and it is the doctor who is judged crazy.

But the doctor, he still wants to explain himself, and to say WHY
i²*i²=-1 and not 1.

Basically, it was necessary to introduce the following notion, well more efficient than a simple i²=-1 which explains nothing, and explaining
nothing at all of its
mathematical being, becomes very dangerous to use unconsciously.

Basically, we must state: the number i is a complex which has the
particularity of being such that, for all x, i^x=-1.

Similarly for all x, 1^x=1, i^x=-1.

That is the basis, and that is what explains that i²=-1.

But now that we have understood who i is, the entire current mathematical
basis collapses, and, for example, i^4=-1 and NOT i^=1.

Similarly for "-1", we must respect the mathematical logic of the
imaginaries and not use the operations of the reals.

I give here, the correspondence table of the imaginaries, according to
their power and their sign. I hope you receive it well.


<http://nemoweb.net/jntp?Mhl_dvPLsa5T3I0u7LlBV0DezeM@jntp/Data.Media:1>

R.H.

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Le 15/02/2025 à 22:50, Alan Mackenzie a écrit :

Richard Hachel <[email protected]> wrote:

The ignorance is entirely yours. Mathematicians do "explain" what i is,
to anybody who's interested enough and intelligent enough to listen.
You might say i²=-1 without understanding (which seems fairly likely),
more educated people say it with full understanding.

Absolutely not.

Les mathématiciens n'expliquent rien du tout.

Ils partent de l'hypothèse i²=-1 ou de l'hypothèse x²+1=0.

Mais ils n'expliquent rien du tout.

MOI, j'explique. Le monde des imaginaires est tel que i^x=-1 quelque soit
x.

Il va de soi que si j'explique quelque chose, cela ne plait pas du tout.

C'est l'histoire de ma vie.

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Richard Hachel <[email protected]> wrote:

To solve quadratic equations without real roots of the type f(x)=x²+4x+5, mathematicians invented complex roots.
The idea, obviously, was not bad.
We then assumed an imaginary number, which we named i, such that i²=-1,
and this number would allow, not only to positiveize the discriminant, but also to make the square root disappear.
All profit.
Except that it is not enough.
Why is it not enough? Because we do not explain what this i is, nor where
it really comes from.
We are content with a postulate, without seeing the horrible consequences for all mathematical logic.
We say i²=-1, without understanding, without thinking, believing that it
is a very simple and harmless thing to handle explosives, and we handle
TNT so well that we affirm the following mathematical monstrosity: "If i²=-1 then i²*i²=1.

The ignorance is entirely yours. Mathematicians do "explain" what i is,
to anybody who's interested enough and intelligent enough to listen.
You might say i²=-1 without understanding (which seems fairly likely),
more educated people say it with full understanding.

This is one of the greatest mathematical crimes of the entire human
species, because ignorance of what i is has already led us to this.

You're a crank and a troll.

We will then progress into the worst.

We can only progress into the worst.

When we are sick, we generally ask the doctor's opinion.

But when we are scientifically sick, and we believe such nonsense, we do
not ask the doctor's opinion, and it is the doctor who is judged crazy.

But the doctor, he still wants to explain himself, and to say WHY
i²*i²=-1 and not 1.

i^4 = 1. NOT -1. If you want a number x such that x^4 = -1, then there
are four solutions, one of which is (1 + i)/SQRT(2).

Basically, it was necessary to introduce the following notion, well more efficient than a simple i²=-1 which explains nothing, and explaining nothing at all of its
mathematical being, becomes very dangerous to use unconsciously.

Why don't you just go away?

Basically, we must state: the number i is a complex which has the particularity of being such that, for all x, i^x=-1.

Similarly for all x, 1^x=1, i^x=-1.

You'd do far better actually to study some mathematics, then you would
see why what you're writing is just non-sensical.

That is the basis, and that is what explains that i²=-1.

But now that we have understood who i is, the entire current mathematical basis collapses, and, for example, i^4=-1 and NOT i^=1.

Similarly for "-1", we must respect the mathematical logic of the imaginaries and not use the operations of the reals.

I give here, the correspondence table of the imaginaries, according to
their power and their sign. I hope you receive it well.

[ .... ]

R.H.

--
Alan Mackenzie (Nuremberg, Germany).

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Le 15/02/2025 à 22:50, Alan Mackenzie a écrit :

Richard Hachel <[email protected]> wrote:

You're a crank and a troll.

Absolutely not.

i^4 = 1. NOT -1.

:))

If you want a number x such that x^4 = -1, then there
are four solutions, one of which is (1 + i)/SQRT(2).

x^4=-1 ---> (-i)^4=-1

Look here:

<http://nemoweb.net/jntp?92O42tWelD0-9rH-SLxG3UP-8fM@jntp/Data.Media:1>

Basically, it was necessary to introduce the following notion, well more
efficient than a simple i²=-1 which explains nothing, and explaining
nothing at all of its
mathematical being, becomes very dangerous to use unconsciously.

Why don't you just go away?

I mean that as a general rule, science and mathematics have very fair,
very precise, and very beautiful rules.
But not always.
I know of two cases where it would seem that science makes serious
blunders. I have already explained them, but it seems that many
do not think this "theologically" possible, because it is a matter of
faith.

To say that there are sometimes errors in things that are apparently
simple, is beyond imagination.

Basically, we must state: the number i is a complex which has the
particularity of being such that, for all x, i^x=-1.

Similarly for all x, 1^x=1, i^x=-1.

You'd do far better actually to study some mathematics, then you would
see why what you're writing is just non-sensical.

C'est le contraire qui est vrai, mais cela ne se passe jamais.

Il faudrait d'abord lire attentivement ce que j'écris, et tester si ce
que je dis est cohérent. Si cela a une logique interne. Si cela a une
logique interne, il faut approfondir la question, et se demander où je critique, et POURQUOI, je critique.

On ne le fait jamais.


R.H.

--- SoupGate-Win32 v1.05
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XPost: fr.sci.maths

Le 15/02/2025 à 22:56, Richard "Hachel" Lengrand a écrit :

Le 15/02/2025 à 22:50, Alan Mackenzie a écrit :

Richard Hachel <[email protected]> wrote:

The ignorance is entirely yours. Mathematicians do "explain" what i is,
to anybody who's interested enough and intelligent enough to listen.
You might say i²=-1 without understanding (which seems fairly likely),
more educated people say it with full understanding.

Absolutely not.

Les mathématiciens n'expliquent rien du tout.

Ils partent de l'hypothèse i²=-1 ou de l'hypothèse x²+1=0.

« hypothèse x^2+1 = 0 » ? ? ?!! Mais n'importe quoi, n'importe quoi...

Mais ils n'expliquent rien du tout.

MOI, j'explique. Le monde des imaginaires est tel que i^x=-1 quelque soit x.

Il va de soi que si j'explique quelque chose, cela ne plait pas du tout.

Ben oui, vu que tu ne racontes que des sottises infatuées noyé que tu es
dans ton égomanie.

Ce que tu "expliques" (c'est-à-dire prétend) est juste complètement
con, c'est pourquoi ça "plaît" assez peu :-) L'humanité entière n'est
pas liguée contre toi, Richard, t'es juste nul et bloqué dans cette
nullité par ton histrionisme égotique.

C'est l'histoire de ma vie.

L'histoire d'un naufrage dans la bêtise infatuée. Ouais. Génial.

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Richard Hachel <[email protected]> wrote:

Le 15/02/2025 à 22:50, Alan Mackenzie a écrit :

Richard Hachel <[email protected]> wrote:

The ignorance is entirely yours. Mathematicians do "explain" what i is,
to anybody who's interested enough and intelligent enough to listen.
You might say i²=-1 without understanding (which seems fairly likely),
more educated people say it with full understanding.

Absolutely not.

How would you know? You strike me as the sort of crank who refuses to
listen to experts.

Les mathématiciens n'expliquent rien du tout.

They did to me, and to many other pupils and students, and are doubtless
still doing so.

Ils partent de l'hypothèse i²=-1 ou de l'hypothèse x²+1=0.

There's a history of complex numbers going back several centuries.
There's more to it than that.

Mais ils n'expliquent rien du tout.

More likely, you're incapable of listening, or unwilling to listen to
the explanations.

MOI, j'explique. Le monde des imaginaires est tel que i^x=-1 quelque soit
x.

OK, let's assume that for the purposes of argument.
i^2 = -1, and i^3 = -1.
Then
(i^3 / i^2) = i, and
(i^3 / i^2) = (-1 / -1) = 1.
So i = 1.
But this contradicts i^2 = -1.

So your "system" is self contradictory.

Il va de soi que si j'explique quelque chose, cela ne plait pas du tout.

As said, what you're "explaining" is nonsense. (See above.)

C'est l'histoire de ma vie.

That I can believe.

R.H.

--
Alan Mackenzie (Nuremberg, Germany).

--- SoupGate-Win32 v1.05
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Le 16/02/2025 à 11:29, Alan Mackenzie a écrit :

MOI, j'explique. Le monde des imaginaires est tel que i^x=-1 quelque soit
x.

OK, let's assume that for the purposes of argument.
i^2 = -1, and i^3 = -1.

Yes.

And also, i^(1/2), i^5, i^0, i^-5, i^(-5/3), etc...etc...etc...

Always, i^x=-1.

In mirror effect, we have the same thing in the reals with 1. The unit 1 remains invariably 1 whatever the exponent we attribute to it. It is invariable. 1^x=1.

Then

Then what?

(i^3 / i^2) = i,

Yes.

and
(i^3 / i^2) = (-1 / -1) = 1.

No.

i^3/i^2=i

i=-1

So i = 1.

Absolutely not.

But this contradicts i^2 = -1.

No.

So your "system" is self contradictory.

Absolutely not.

You are making a conceptual error. You are multiplying imaginaries with
the laws of real numbers.
In real numbers 1*1=1.
In imaginary numbers i*i=i

It is quite counter-intuitive, I admit, but it is the truth of things, and sometimes you have to know how to question your preconceptions.
Let's take the example of the very young driver, who must learn to use the rearview mirror. He is initially surprised that the rear of the vehicle
turns to the right when he turns the steering wheel to the right. We have
the same thing with the first outing in a boat. The preconception is that
you have to force the right oar to turn right, but it is the opposite. The rower must force the left oar.

However, handling complex numbers is very simple if we get rid of a
ridiculous preconception that we use an imaginary mirror numbering while
using real mathematics.

Tableau d'Hachel

<http://nemoweb.net/jntp?GdmgdQ7A6Qp7r4f912_TcUKNB0U@jntp/Data.Media:1>

R.H.

--
<https://www.nemoweb.net/?DataID=GdmgdQ7A6Qp7r4f912_TcUKNB0U@jntp>

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