Re: How? ? ?

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.
No, no, the correct answer is simply √i+√(-i)=0.
We still need to correctly define i.
i is i²=-1, of course. But that doesn't define i. Only the square of i.
And a hasty conclusion like (i²)²=(-1)²=1 was one of the worst mathematical disasters in human history.
We manipulate an imaginary with the rules of a real without paying attention to even the concepts and signs.
R.H.