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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: New equation
Date: Fri, 28 Feb 2025 10:33:14 -0800
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On 2/28/2025 9:50 AM, Ross Finlayson wrote:
> On 02/27/2025 11:49 PM, Chris M. Thomasson wrote:
>> On 2/27/2025 8:51 PM, Ross Finlayson wrote:
>>> On 02/27/2025 01:46 AM, efji wrote:
>>>> Le 27/02/2025 à 05:19, Ross Finlayson a écrit :
>>>>
>>>>>
>>>>> Division in complex numbers is opinionated, not unique.
>>>>
>>>> :)
>>>> Hachel has a brother !
>>>>
>>>>>
>>>>> So, the natural products and alll their combinations
>>>>> don't necessarily arrive at "staying in the system".
>>>>
>>>> wow
>>>>
>>>>>
>>>>> Furthermore, in things like Fourier-style analysis,
>>>>> which often enough employ numerical methods a.k.a.
>>>>> approximations here the small-angle approximation
>>>>> in their derivations, _always have a non-zero error_.
>>>>
>>>> big time BS :)
>>>>
>>>>>
>>>>> Then, something like the "identity dimension", sees
>>>>> instead of going _out_ in the numbers, where complex
>>>>> numbers and their iterative products may neatly model
>>>>> reflections and rotations, instead go _in_ the numbers,
>>>>> making for the envelope of the linear fractional equation,
>>>>> Clairaut's and d'Alembert's equations, and otherwise
>>>>> with regards to _integral_ analysis vis-a-vis the
>>>>> _differential_ analysis.
>>>>
>>>> Nonsense ala Hachel
>>>>
>>>>>
>>>>> These each have things the other can't implement,
>>>>> yet somehow they're part of one thing.
>>>>>
>>>>> It's called completions since mathematics is replete.
>>>>
>>>> A BS-philosophical version of Hachel. Let's park them together.
>>>>
>>>
>>> Division in complex numbers most surely is
>>> non-unique, whatever troll you are from
>>> whatever troll rock you crawled out from under.
>>>
>>>
>>> Furthermore, if you don't know usual derivations
>>> of Fourier-style analysis and for example about
>>> that the small-angle approximation is a linearisation
>>> and is an approximation and is after a numerical method,
>>> you do _not_ know.
>>>
>>> Then about integral analysis and this sort of
>>> "original analysis" and about the identity line
>>> being the envelope of these very usual integral
>>> equations, it certainly is so.
>>>
>>>
>>> So, crawl back under your troll rock, troll worm.
>>>
>>>
>>> I discovered a new equation one time, it's another
>>> expression for factorial, sort of like Stirling's,
>>> upon which some quite usual criteria for convergence die.
>>>
>>>
>>
>> How would you implement the following algorithms using your special
>> systems?
>>
>> http://www.paulbourke.net/fractals/septagon/
>>
>> http://www.paulbourke.net/fractals/multijulia/
>>
>> http://www.paulbourke.net/fractals/logspiral/
>>
>> http://www.paulbourke.net/fractals/triangle/
>>
>> http://www.paulbourke.net/fractals/fractionalpowers/
>>
>> http://www.paulbourke.net/fractals/cubicjulia/
>>
>> ect... ?
> 
> Why, they're just actual features of "the system",
> they're objects of mathematics, having all their relations,
> in structures, a structuralist, constructivist account.

If Richard Hachel has a new way to do things, then I am interested in 
how his system would work with my work. It might be very interesting 
indeed. Well, to me at least! :^)

> 
> You can start looking at it as about inversions,
> integral equations and their plane curves vis-a-vis
> differential equations and their solutions, since
> the usual curriculum sort of abandoned integral equations,
> since many differential systems are easily tossed to
> a common solver, yet, the differintegro and integrodiffer
> systems are quite a natural model of equilibria.
> 
> Inversions:  and completions.
> 
>