Re: Equation complexe

Le 26/02/2025 à 19:16, Richard Hachel a écrit :

Le 26/02/2025 à 18:11, Moebius a écrit :

Am 26.02.2025 um 11:30 schrieb Barry Schwarz:

On Wed, 26 Feb 25 00:11:36 +0000, Richard Hachel <r.hachel@tiscali.fr>
wrote:

 

i is an imaginary unit such that, for all x, i^x=-1.

 Fascinating! So i = i^1 = -1 in your "system"?

  Absolutely.
  Je ne me contente pas d'écrire i²=-1 mais pour tout x, i^x=-1.
  Nous sommes en train d'utiliser une unité imaginaire et nous devons l'utiliser correctement jusqu'à bout, et pas seulement si x=2. 

"imaginary" does not mean that you can accept contradiction this is not a fairy tale.
Using such a word when it comes to complex numbers is an history relief because they were first used, centuries ago, without proper definition. Mathematician just noticed that "it works" but stayed doubtful before a proper consistent definition was coined up.
The word "imaginary" could have been dropped out at that time. There is no problem in preserving it as long as we know it has since then a proper meaning (completely different to the usual sense). Moreover in math it is common (contrary to physics) to use common words with different meanings than the usual one (matrix, ring, field, etc.)
Mathematicians are NOT supposed to take care of stupid hypocrite kooks of your kind. You don't matter Lengrand.