Re: New equation

Le 02/03/2025 à 18:54, Richard Hachel a écrit :

Le 02/03/2025 à 18:10, Python a écrit :

Le 02/03/2025 à 17:32, Richard Hachel a écrit :

Le 02/03/2025 à 06:06, Jim Burns a écrit :
 ⎜

(a+b𝑖)+(c+d𝑖) = (a+c)+(b+d)𝑖

  Yes.
 

(a+b𝑖)⋅(c+d𝑖) = (ac-bd)+(ad+bc)𝑖

  No.
  (a+b𝑖)⋅(c+d𝑖) = (ac+bd)+(ad+bc)𝑖
 >
 In all thing : (a+b𝑖)⋅(c+d𝑖) = (ac+bd)+(ad+bc)𝑖
 

 This is true in R(j) not in C.

  Non, c'est bon aussi dans C.   C'est (a+b𝑖)⋅(c+d𝑖) = (ac-bd)+𝑖(ad+bc) qui n'est plus bon.

This is the consequence of the definition of what is called C. Period. If you have another rule for the product of terms you are not talking about C but another algebraic structure such as R(j) or R(epsilon).
There is no way to reject a definition as long at it is consistent. And the definition of C is consistent. Definitions of other structures can be consistent too, see my yesterday post this cannot change what the definition of C is.
Seriously your stubborn stupidity, ignorance and hypocrisy is boring Richard.

 Il ne suffit pas de regarder les petits symboles sur le papier mais il faut se dire : à quoi correspondent les choses dont je me permets de parler? 

This is exactly what we do and what you don't do.