Re: How? ? ?

Le 02/04/2025 à 15:31, Richard Hachel a écrit :

Le 02/04/2025 à 15:21, Python 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

 It is a quite elegant way to show that sqrt(i) + sqrt(-i) = +/- sqrt(2)
(only keep "+" if you're interested only by the principal values of sqrt).
 Why does it bother you ?
 As an exercise you can also show that sqrt(i) - sqrt(-i) = +/- i*sqrt(2)

 In my case, that's  sqrt(i) + sqrt(-i) = 0
 and sqrt(i) - sqrt(-i) = 2i.
 But everyone understands that I don't count the same way.

Yes, we know. It your "system" i^x = -1 for all x, so i is -1 and i^2 =/= (-1)^2 = 1. Your "system" is definitely inconsistent : it can "prove" anything (including 8 = 0 as I've shown you on fr.sci.maths).