Le 02/04/2025 à 14:32, Richard Hachel a écrit :

How can mathematicians come up with such absurdities?

https://www.youtube.com/watch?v=XZriBHTNPw0

No mathematician would write \sqrt{i} because the symbol "\sqrt" designs
the positive square root of a real number, which does not make sense in
\C since it is not an ordered set and the word "positive" is a nonsense
in \C.

Anyway, "i" has 2 square roots : ±(1+i)/\sqrt{2}
and "-i" too : ±(1-i)/\sqrt{2}
Thus, the mathematically wrong expression "\sqrt{i}+\sqrt{-i}" is non
univoque and could be any of these 4 values :

±\sqrt{2}, ±i\sqrt{2}

You're welcome

--
F.J.

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Le 02/04/2025 à 15:05, Richard Hachel a écrit :

Le 02/04/2025 à 14:49, efji a écrit :

Le 02/04/2025 à 14:32, Richard Hachel a écrit :

How can mathematicians come up with such absurdities?

https://www.youtube.com/watch?v=XZriBHTNPw0

No mathematician would write \sqrt{i} because the symbol "\sqrt"
designs the positive square root of a real number, which does not make
sense in \C since it is not an ordered set and the word "positive" is
a nonsense in \C.

Anyway, "i" has 2 square roots : ±(1+i)/\sqrt{2}
and "-i" too : ±(1-i)/\sqrt{2}
Thus, the mathematically wrong expression "\sqrt{i}+\sqrt{-i}" is non
univoque and could be any of these 4 values :

±\sqrt{2}, ±i\sqrt{2}

You're welcome

Four possible values?

To think that Python gave us a nervous breakdown when I explained that a function could have multiple roots, which was actually true.

But here, we're falling into the opposite madness.

We add two numbers, and we find four answers, which is stupid, to say
the least.

We don't add two numbers since \sqrt{i} is not a number because this
notation is a nonsense ! Can you read carefully what I wrote ???

No, no, the correct answer is simply √i+√(-i)=0.

Please, once for all, save us from your shitty delirium, dumbass.



--
F.J.

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Le 02/04/2025 à 15:37, Python a écrit :

Le 02/04/2025 à 14:49, efji a écrit :

Le 02/04/2025 à 14:32, Richard Hachel a écrit :

How can mathematicians come up with such absurdities?

https://www.youtube.com/watch?v=XZriBHTNPw0

No mathematician would write \sqrt{i} because the symbol "\sqrt"
designs the positive square root of a real number, which does not make
sense in \C since it is not an ordered set and the word "positive" is
a nonsense in \C.

Not really, see https://en.wikipedia.org/wiki/Principal_value#Square_root

OK, it is a definition, but actually, in practice, no one takes the risk
to use \sqrt{z} for z\in\C in a development since it could be
misleading. And there is almost no interest to use it.

--
F.J.

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Op 02/04/2025 om 15:14 schreef efji:

Le 02/04/2025 à 15:05, Richard Hachel a écrit :

Le 02/04/2025 à 14:49, efji a écrit :

Le 02/04/2025 à 14:32, Richard Hachel a écrit :

How can mathematicians come up with such absurdities?

https://www.youtube.com/watch?v=XZriBHTNPw0

No mathematician would write \sqrt{i} because the symbol "\sqrt"
designs the positive square root of a real number, which does not
make sense in \C since it is not an ordered set and the word
"positive" is a nonsense in \C.

Anyway, "i" has 2 square roots : ±(1+i)/\sqrt{2}
and "-i" too : ±(1-i)/\sqrt{2}
Thus, the mathematically wrong expression "\sqrt{i}+\sqrt{-i}" is non
univoque and could be any of these 4 values :

±\sqrt{2}, ±i\sqrt{2}

You're welcome

Four possible values?

To think that Python gave us a nervous breakdown when I explained that
a function could have multiple roots, which was actually true.

But here, we're falling into the opposite madness.

We add two numbers, and we find four answers, which is stupid, to say
the least.

We don't add two numbers since \sqrt{i} is not a number because this
notation is a nonsense ! Can you read carefully what I wrote ???

It seems to work just fine in wolfram alpha (desmos in complex mode
gives the same answer).

https://www.wolframalpha.com/input?i=sqrt%28i%29

https://www.desmos.com/calculator/ztfet88jmu

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Le 02/04/2025 à 16:24, sobriquet a écrit :

Op 02/04/2025 om 15:14 schreef efji:

We don't add two numbers since \sqrt{i} is not a number because this
notation is a nonsense ! Can you read carefully what I wrote ???

It seems to work just fine in wolfram alpha (desmos in complex mode
gives the same answer).

https://www.wolframalpha.com/input?i=sqrt%28i%29

https://www.desmos.com/calculator/ztfet88jmu

The fact that online tools give an answer is not a proof.
These tools are made to give an answer to almost everything. I bet you
could not find any research paper using this notation. Same as \sqrt{-1}
which is never used.

--
F.J.

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Le 02/04/2025 à 21:53, Chris M. Thomasson a écrit :

On 4/2/2025 5:49 AM, efji wrote:

Le 02/04/2025 à 14:32, Richard Hachel a écrit :

How can mathematicians come up with such absurdities?

https://www.youtube.com/watch?v=XZriBHTNPw0

No mathematician would write \sqrt{i} because the symbol "\sqrt"
designs the positive square root of a real number, which does not make
sense in \C since it is not an ordered set and the word "positive" is
a nonsense in \C.

Anyway, "i" has 2 square roots : ±(1+i)/\sqrt{2}
and "-i" too : ±(1-i)/\sqrt{2}
Thus, the mathematically wrong expression "\sqrt{i}+\sqrt{-i}" is non
univoque and could be any of these 4 values :

±\sqrt{2}, ±i\sqrt{2}

You're welcome

sqrt(0+1i) has two roots:

[0] = sqrt(0+1i)
[1] = -sqrt(0+1i)

any of them raised to the the 2'nd power equals 0+1i.

wow, the dumb Hachel has got a dumb cousin :)


--
F.J.

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Am 02.04.2025 um 16:30 schrieb Python:

Le 02/04/2025 à 14:32, Richard Hachel a écrit :

How can mathematicians come up with such absurdities?

https://www.youtube.com/watch?v=XZriBHTNPw0

Il n'y a rien d'absurde. Le raisonnement est un peu rapide, certes, à un moment (à 8mn 15s) quand il dit "it is obvious that you can factorize by
+/- 1/sqrt(2)" en réalité en faisant cela l'auteur de la vidéo fait en sorte que c'est la même branche de la fonction sqrt qui est prise en
compte pour les deux racines, et du coup le résultat final est correct
(il y a deux valeurs possibles).

Le maniement de fonction telles que sqrt est délicat dans C, et même
dans R ! 4 a déjà deux "racines" 2 et -2 ! On sélectionne la valeur positive dans R comme "valeur principale" tandis que dans C le critère
est d'avoir l'argument dans ]-pi, pi]

voir : https://fr.wikipedia.org/wiki/ D%C3%A9termination_d%27une_fonction_multivalu%C3%A9e#Racine_carr%C3%A9e_complexe

https://en.wikipedia.org/wiki/Principal_value#Square_root

C'est pour cela que dans le cas des nombres complexes on évite
d'utiliser sqrt comme une fonction mono-valuée et on parle de racines
(au pluriel) n-èmes et on sait qu'il y en a toujours exactement n.

What did you say?

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Am 02.04.2025 um 22:11 schrieb efji:

wow, the dumb Hachel has got a dumb cousin :)

Keep cool, Chris M. Thomasson is a programmer who is sometimes quite
stubborn [...], but he's not a crank [I'd say].

He seems to lack a thorough mathematical education thought and it shows.

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