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From: efji <efji@efi.efji>
Newsgroups: sci.math
Subject: Re: New way of dealing with complex numbers
Date: Sun, 9 Mar 2025 00:26:21 +0100
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Le 08/03/2025 à 23:55, Moebius a écrit :
> Am 08.03.2025 um 23:47 schrieb Moebius:
>> Am 08.03.2025 um 14:32 schrieb efji:
>>> Le 08/03/2025 à 14:18, Richard Hachel a écrit :
>>
>>> Associativity is MANDATORY to be able to write something like i^4 = 
>>> i*i*i*i.
>>>
>>> For a non associative operator, i^4 means NOTHING.
>>
>> Oh, i^(n+1) just might mean (i^n) * i (with n e IN).
>>
>> [And i^0 = 1.]
>>
>> Then: i^4 = ((i*i)*i)*i.
>>
>> [Hint: recursive definition:
>>   x^0 = 1
>>   x^(n+1) = x^n * x   (for all n e IN)]
> 
>      x^0 = 1
>      x^(n+1) = (x^n) * x   (for all n e IN)]
> 
> ... if you like.

I don't like.
What if * is not commutative ?

(x^n) * x =/= x * (x^n)


-- 
F.J.