Re: New equation

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.
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.