Re: i²=-1

Richard Hachel <r.hachel@tiscali.fr> wrote:

Le 15/02/2025 à 22:50, Alan Mackenzie a écrit :

Richard Hachel <r.hachel@tiscali.fr> wrote:

The ignorance is entirely yours.  Mathematicians do "explain" what i is,
to anybody who's interested enough and intelligent enough to listen.
You might say i²=-1 without understanding (which seems fairly likely),
more educated people say it with full understanding.

Absolutely not.

How would you know?  You strike me as the sort of crank who refuses to
listen to experts.

Les mathématiciens n'expliquent rien du tout.

They did to me, and to many other pupils and students, and are doubtless
still doing so.

Ils partent de l'hypothèse i²=-1 ou de l'hypothèse x²+1=0.

There's a history of complex numbers going back several centuries.
There's more to it than that.

Mais ils n'expliquent rien du tout.

More likely, you're incapable of listening, or unwilling to listen to
the explanations.

MOI, j'explique. Le monde des imaginaires est tel que i^x=-1 quelque soit
x.

OK, let's assume that for the purposes of argument.
  i^2 = -1, and i^3 = -1.
Then
  (i^3 / i^2) = i, and
  (i^3 / i^2) = (-1 / -1) = 1.
So i = 1.
But this contradicts i^2 = -1.

So your "system" is self contradictory.

Il va de soi que si j'explique quelque chose, cela ne plait pas du tout..

As said, what you're "explaining" is nonsense.  (See above.)

C'est l'histoire de ma vie.

That I can believe.

R.H.

--
Alan Mackenzie (Nuremberg, Germany).