serious-discussion

[foggy meadow]

I just want someone to help me with fractional calc.

[bronze pelican]

@deep mango can help with that

he can tell you about fractional laplacian and dynamics of waves

[foggy meadow]

Okay!

[deep mango]

No way

Im not going to talk about that

Ew

[foggy meadow]

aww, okay.

[deep mango]

Well what is your question about

I have erased it all from my head

[hexed tangle]

Fractional calc pushing back usually means the nonlocal piece isn’t built in yet, not that the idea is wrong.

[foggy meadow]

I have a type of transform that computes the derivative using sum of sign(x) functions. (this isn't that interesting). But I want it to also compute fractional derivatives g(n/m)/((n/m) + 1/m) is roughly the equation I used to compute this. There's some more happening, but I'm basically removing a power and it works.

[deep mango]

Hmm

[foggy meadow]

Yeah, I figure there is another way to go about doing a derivative with my thing. The modified mean value theorum it's based off of has it, but for what ever reason it doesn't want to work here.

[foggy meadow]

https://www.desmos.com/calculator/ybpjeljnxr

This is essentially my "sampler" in R, and it's just 1/x almost. Which seems to derive most functions including sin or e^{-x^2} or whatever I've tried. w is the sub sample count btw.

[fringe summit]

Bro is rediscovering distributions

[foggy meadow]

I know about distributions, but I'm deriving it from just sign which is interesting.

[hexed tangle]

the modified MVT expects things to behave nicely at a point but your operator looks at a whole window not just a single spot that’s why it doesn’t quite work it’s picking up slope in a nonlocal way

[runic tusk]

thats wayyyyy too advanced for me. god dayum

[timid bronze]

@deep mango Will we play today

[deep mango]

We can play soon, im eating lunch and will be free after

[timid bronze]

FINALLY UNC

It's about time

[deep mango]

@timid bronze ok.

what

[peak tide]

bruh

[bitter echo]

Lol

[silent junco]

i have no clue what youre saying but keep it sfw, please

[peak tide]

just noticed, same msg in #math-discussion fyi

ah you got it

[silent junco]

yeah thanks for letting me know anyway

[timid bronze]

Hi

Are you still available

Don’t get all pissy at me you goofy bird

[deep mango]

Yes

I just

@timid bronze SORRY I WAS READING THE INFINITY TRAIN REDDIT

[hexed tangle]

I might have found a solution, you can ping me if you wanna like know lol

[hexed tangle]

is blud still trying to play roblox

[timid bronze]

OK so do want to play

[deep mango]

Yes

[timid bronze]

Yes, and

[timid bronze]

Join obsidian

[last rose]

Behold, people of Discussion-2: I had hoped to share this glad tidings with you, ye most excellent souls———lo, I have come into possession of a new camera.

[old oak]

Looks like you've come into possession of a fairly old camera!

[wraith magnet]

I wish thee a most delightful experience capturing in flat form the happenings of our world! Should you be willing to graciously bestow to us some of your works aided with this newly-acquired camera, my elation would be guaranteed.

[last rose]

it's about 20+ years old

[last rose]

Thy goodwill is warmly received... As yet, I have not set this instrument to any earnest labour; nevertheless, in the meantime, thou mayest take some small pleasure in this humble capture of the bird and sunset.

[timid bronze]

@silent junco

Why are you defending ryc

HE LITERALLY CALLED YOU A LOSER

@silent junco @deep mango

☠️

[violet kiln]

hello everyone

[foggy meadow]

It looks at a single spot, it just also multiplies that single spot by that amount
(H1(a) - H2(b)) is the fuller operation.

Most operations take a single sample and do a subtraction ordeal.

[fathom swallow]

DisOneGuy

[foggy meadow]

Here you can see it uses a single sample of g(n/w) I just don't know how to get fractional working.

It's also weird this works in the limit at all, both integration and derivative are just a single sample operation.

[foggy meadow]

I also forgot 2 infront.

[silver basalt]

https://youtube.com/shorts/szAWFrI0pIw

[inner turtle]

The more I think about it… is it even possible for agi.. making a robot have a human brain. Hell I don’t think we figured out our brains either-

[hexed tangle]

Lil ally

[hexed tangle]

Awawawa

[bronze pelican]

Sybau

[hexed tangle]

[latent edge]

awawawa

[turbid sedge]

dance

[foggy meadow]

Yeah, idk how to get it to work.

[willow herald]

Awawawa

[sand yew]

Can anyone help me solve riemann hypothesis 🙏

Pls

[surreal sapphire]

try lis criterion

[twin meadow]

Hi chat

how's everything

[left tusk]

hi hii

[twin meadow]

How's everything

[left tusk]

pretty good, hbyy

[twin meadow]

me too^^

[left tusk]

yayy thats nice

[twin meadow]

yup

[dire siren]

Hey

[hexed tangle]

[odd tartan]

In which grade r u guys in?

[fresh comet]

@twin meadow welcome to the mathcord!

[twin meadow]

Hie^^ tysm

[viral oracle]

https://tenor.com/view/cat-hello-cat-peek-cat-door-cat-peek-door-gif-17361470248875227911

[turbid sedge]

Hi hana

[viral oracle]

hihi

[hexed tangle]

[viral oracle]

[hexed tangle]

hyd c:

[viral oracle]

dying as usual

[hexed tangle]

fair

[viral oracle]

hope you're better though

[hexed tangle]

usual research paper grind

but yeah i'm fine

[viral oracle]

all the best!

[hexed tangle]

💖 you too

[neat lintel]

# SAB QUIT? IMPORTANT: WE ARE NOT SAB QUIT!!

🙏** Hey everyone, I want to thank you all from the bottom of my heart.** We really did complete Steal a Brainrot. Unfortunately, you can tell that the game is slowly coming to an end and many people are gradually stopping watching. Starting tomorrow, I need to recover and will now focus on streaming only 1-2 times a day. Thank you for everything, and we thank Sab for the valuable time that will never come back. Thank you for everything.

Nevertheless, I promise you: We will continue to do our best and create an index every day ** to bring you joy. We will also only go live twice a day so that we can better focus on proper streams instead of short 30-minute streams.** @everyone 🙏

[viral oracle]

<@&268886789983436800> uh... not sure what this is but might wanna take a look

[wild lantern]

They are muted

[viral oracle]

ah

[wild lantern]

They left already though

[brave flare]

well its not a scam...

[turbid sedge]

Wyd

[turbid sedge]

https://tenor.com/view/funny-moderators-thanos-hubert-gif-11857701048565664572

[viral oracle]

curating book list

[turbid sedge]

Oh that's so peak

How long has it been so far

[viral oracle]

uh...

yes

[fallow iris]

is there a coding channel or smth

[hexed tangle]

no

[serene vault]

you can talk about coding in this channel or chill, but we don't exactly have a dedicated coding channel

[warm sable]

yo
can i just skip the fucking small talk and gain some friends
like u can trust me i'm a cool person likable blah blah blah

[torpid bay]

frac calc

[viral oracle]

has anyone heard of Loomis and Sternberg

[twin meadow]

Hi chat

how's everything

[fresh comet]

things are okay, how're you? c:

[viral oracle]

[fresh comet]

[hexed tangle]

yes

advanced calculus

[viral oracle]

I heard it's extremely difficult

[latent edge]

Does it talk about Galois descent?

[viral oracle]

let me see

no mentions

[latent edge]

then it's probably not difficult

[viral oracle]

as far as I can see

hm

[hexed tangle]

wrong reply lol

[hexed tangle]

nope

[hexed tangle]

it is

[viral oracle]

icic

[hexed tangle]

It comes out of the original Math 55 course at Harvard an accelerated course for well prepared and highly motivated first year undergraduates a good number of IMO and IPhO winners take it

[viral oracle]

[latent edge]

just saw the table of contents

sounds like a recipe for burnout

[hexed tangle]

cooked

[latent edge]

fr

[foggy meadow]

Yeah, I'm stuck with just the equation above and no fractional calc.

[dry copper]

To this day, I still have no clue how to interpret fractional calculus in the grand scheme of things other than, “oh cool, here’s how to take the 1/2-th derivative”

There’s applications in physics but that’s not my forte

[deep mango]

One more relevant context in which to think about it is in the context of fourier analysis

[dry copper]

Elaborate

[deep mango]

The derivative is the thing that takes your function's frequencies and scales each of them up proporitionally to the frequency. it amplifies the higher frequencies and damps the lower frequencies

(captures places where your function changes quickly and ignores places where it is changing very slowly)

the integral does the opposite. it damps high frequencies and captures low frequencies (averaging)

The higher the derivative, the more weight you assign to higher frequencies. when you do this, stuff like concavity, inflection, etc become more important than immediate change, since each subsequent derivative measures finer and finer scales of change than the last

Okay, what happens with a 1/2 derivative now?

on the fourier transform side, you're multiplying each of your oscillating parts by their frequency to the 1/2

So, you are still amplifying higher frequencies, but not nearly as much as you were before. you're paying more attention now to the function's original behavior. it's sort of a mix of the original function and its derivative

[hexed tangle]

frac calculus

[deep mango]

one way in which fractional derivatives come up in nature is through fractional damping

Usual damping happens either through your function (linear damping), its derivative (viscous damping), or its second derivative (heatlike dissipation). each of these gives you a different kind of behavior in your function that gets damped out. linear damping tries to regularize to a fixed reference position, viscous damping tries to regularize to a fixed reference speed, heatlike dissipation tries to smoothen out points of concavity and remove extrema

But from a wave perspective, damping says "this wave is gonna decrease in amplitude at this speed"

[silent junco]

is there a book that covers ts

[deep mango]

Okay, so for each frequency k, we can define a damping rate f(k). Who's to say every natural system has damping with f(k) = 1, f(k) = k, or f(k) = k^2? Those are the ones we had above, respectively. As an example, the waves on the surface of a pool of water do not damp like any of these. I think they damp like k^(1/2) if gravity is your main consideration and like k^(3/2) if surface tension is your main consideration, though I'm looking for a reference for this and not finding it so take it with a grain of salt

This guy has a bunch more examples where you have media or physical phenomena whose waves obey different power laws

https://arxiv.org/pdf/2305.07074

[deep mango]

Not really as far as i know, but it is part of harmonic analysis so you will see it pop up as you learn that

[silent junco]

oh okay thanks

[deep mango]

The most important fractional derivatives are the fractional laplacians which are defined using harmonic analysis tools

[silent junco]

i see

[charred sonnet]

((2x+3)^9(x-4)^24(x-6)^56(x²-9)^31)/((x+4)³²(x²-4)^9(x+6)^5(x-8)^94 ≥0 . Plzzz solve this for mee 🥺 🥺 🥺 🥺

[ocean harbor]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[worldly horizon]

They have a thread.

[foggy meadow]

magical stuff

[ocean harbor]

im busy

go help if u want

[zealous garden]

Wild

[foggy meadow]

@torpid bay Apprently it was really simple and I was over thinking it by a lot.

[plush idol]

https://open.spotify.com/album/77CZUF57sYqgtznUe3OikQ?si=QQ5r-iFXSGSHeDf0yprFJQ

this album is so fucking good

[foggy meadow]

It's simpler and more complex some how. Summed fractional derivatives are wacky. But my thing works better than just the raw Reimann sum. And it's a lot more like the integral, but still needs a correction term, (as always with this function). Probably just like a sign and a scale it seems.

Derivatives are also too finicky, ugh.

Yay, closeness.

In the limit it should converge pretty much, but still be shifted and the sign is off, which bugs me.

[wraith magnet]

@shadow steeple how did it go?

[shadow steeple]

Pretty good

[wraith magnet]

how much?

[shadow steeple]

7

[wraith magnet]

wahh

bro i wanna

{{.}}

i got 11

[shadow steeple]

Also ok bro

[wraith magnet]

11 can't go anywhere sia

oh yeah

did your computing help?

[shadow steeple]

Definitely

I don't think I'd be getting ts with bio bro💔

[wraith magnet]

lmaoo

[shadow steeple]

And somehow my humans decided to go from shit to not shit

[wraith magnet]

?

[shadow steeple]

Like it's my first time getting a 1 for humans

Before i would either sell for SS or history and get a 3 or something

[wraith magnet]

i choked so hard for SS lmao

haiz

i thought i would get a lot better for bio and physics

like in mock papers and prelims i was consistently getting 1

then somehow

THREE

fml

[shadow steeple]

Ggs

[wraith magnet]

how much did you get for your sciences?

[shadow steeple]

Chem was A2

Physics was A1

[wraith magnet]

wait you only have those two right?

[shadow steeple]

Yea

[wraith magnet]

what about maths?

[shadow steeple]

E Math A1

A Math A1

[wraith magnet]

lol nice

so only your chem pull you down?

[shadow steeple]

Oh I didn't use chem

It was the English

[wraith magnet]

ohhh

english A2??

[shadow steeple]

Yea

[wraith magnet]

that's surprising

[shadow steeple]

Tbh it's was either a A2 or B3 for me so

I was like straddling the fence during prelims I think

[wraith magnet]

haiz

i should have studied harder

[placid shadow]

@fresh comet hewos hewos 🩷

https://tenor.com/view/bunny-rabbit-bnuuy-bed-hyper-gif-25445957

[snow ice]

what is fisscussy two abt rn, discussion is only talking abt abstract algebra.

[fresh comet]

[hushed blaze]

bunny

[placid shadow]

Yayyy

[placid shadow]

https://tenor.com/view/eevee-valentine-love-kiss-pokemon-gif-453953983570110729

[ocean harbor]

https://tenor.com/view/cat-relax-vibes-rita-gif-25196274

[fringe summit]

There’s a book I know on hyposingular integrals, which covers the fractional derivatives of which ryc speaks but in the light of general integral kernel stuff

There’s that Leoni book on fractional Sobolev spaces

[torpid bay]

[fringe summit]

And I think there’s a CMS book on fractional calculus stuff but idt it is what you really want? Most of this stuff is gonna be secondary to general harmonic analysis or PDE stuff

[silent junco]

oh okay thanks sharp

[foggy meadow]

Sobolev space I have heard a lot about, and I know it's pretty cool. I don't know what it is exactly.

[fringe summit]

Yeah I don’t know much that’ll cover things in ways that are different to that

There may be a little bit in that CMS thing I discarded on some technical details between 1 sided derivatives on [0,\infty) type stuff or 2-sided on R or what have you in R^n

But that may be in the hyposingular book anyway

[foggy meadow]

So, are fractional derivatives generally not as interesting as normal derivatives?

[fringe summit]

I know some of that slight issue stuff I’ve seen Anatole in #advanced-analysis talk about, might be on Wikipedia

[fringe summit]

They show up in some heat equation or other pde stuff, just nowhere near as ubiquitous

Hence, not as interesting

[torpid bay]

iirc there's a few different ways to extend the derivative to fractional derivatives both in terms of the actual derivative used and what effect it has on let's say x^a for example, but also ye i haven't really needed it, maybe used it like once or twice

one frac deriv will give you a different answer for d^(1/2) x^a from another, tho from what ive seen skiming some stuff usually its in one of two camps

[foggy meadow]

What camps?

[long matrix]

ur evil

[fringe summit]

Yes

This is described in the hyposingular book I mentioned I believe

[foggy meadow]

Do you know any books on fractional calculus as a whole or articles?

[torpid bay]

I remember there was a specific function but i dont remember where it was where like one condition for a frac deriv was d^(a+b) = d^(a)d^(b), where as another one was d/dx^k (x^a)) = Gamma(1+a)x^(k-a)/Gamma(1+a-k) and those two quite reasonable conditions actually don't always agree or smthn

also, the non locality of fractinal derivatives

which can be useful or annyoign depending on the context

like, take x^1/2

ithink was one function where those two dont agree or smtgh

[placid shadow]

❤️

[foggy meadow]

How do they not agree?

[fringe summit]

Literally read the above

[torpid bay]

i think it took use of whenever gamma(1+k-a) = 1/0 or smthn

ill go check

[ocean harbor]

how are you doing?

[placid shadow]

im doing good thanks! hby

[torpid bay]

anotehr example would be that +c value

when d^(-1)

[foggy meadow]

Here the one in red is the Cauchy integral version, while the one in green is the function based one.

[ocean harbor]

suffering from group assignments but overall im fine

[foggy meadow]

My thing without gamma agrees more often with the Cauchy integral. Which is neat I guess.

[placid shadow]

glad ur doing fine! <33333

[foggy meadow]

I'm not sure if this is correct or not actually, but I'm trying.

[ocean harbor]

u too

[placid shadow]

ty

[torpid bay]

$\pdv[j]{x}\pdv[k]{x}(x^a)=\frac{\Gamma(1+a)}{\Gamma(1+a-k)}\frac{\Gamma(1+a-k)}{\Gamma(1+a-k-j)}x^{a-k-j}$

[fathom swallow]

Yeatte

[torpid bay]

taking a usual derivative of 1/x is fine, but suppose you take two half derivatives?, then that Gamma(1+a) can't be cancelled out by another 1/0 thing handelled carefully via limits, and so the intermediate step can't exists for any x

if you want to kind of make a path C where the d^k/dx^k exponent k takes, and then take a limit for that k, maybe you can recover something, but im not too familiar with if that would actually work

but without anything like that, the whole $\pdv[k]{x}\pdv[j]{x}=\pdv[k+j]{x}$ equality fails

[fathom swallow]

Yeatte

[foggy meadow]

Does this hold for fractional integrals too?

[torpid bay]

I think it would fail the same as well

not always guaranteed to fail, but nto guaranteed to converge for intermediate steps

so like just doing the reverse and taking two half integrals from x^-2 to -x^-1

and its quite easy to remove parts of a function after you're done and thinking you have d^0 when you have removed a whole polynomial's worth of data

[foggy meadow]

My function fails for x^{-1} anyway.

[torpid bay]

easy example is integral of f'(x)dx

the constant term is removed

and instead you get a +c which you just need to have known the original function to determine

so porlbmes there as well

all around its messy and needs careful handling whilst not something i really need for almost anything

tho one thing that is nice, usually we get

$\dv[k]{x}(e^{bx}) = b^ke^{bx}$

[fathom swallow]

Yeatte

[torpid bay]

prob some way to mess that up as well

lemme see if i can find where the reason behind it's nonlocality is

hm ill go with grunwald letnikov frac deriv then

its mah fav

[foggy meadow]

Yeah, the only reason I wanted it was to be able to describe more about my function. And hopefully describe more about calculus, it still is a useful endeavor for me. Otherwise I can just drop it and describe stuff still.

[torpid bay]

Have i shown you the grunwald letnikov derivative before>?

[foggy meadow]

no.

[torpid bay]

,,\lim_{h\to 0}{\frac{f(x+h)-f(x)}{h}} = \partial_xf(x) \ \lim_{h\to 0}{\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}} =\partial_x^2f(x)\ \lim_{h\to0}{\frac{f(x+3h)-3f(x+2h)+3f(x+h)-f(x)}{h^3}} = \partial_x^3f(x))

[foggy meadow]

Oh a partial fractional derivative?

[torpid bay]

yep

[foggy meadow]

Yeah, I sort of figured those would exist due to my function. I had notation for them too.

[fathom swallow]

Yeatte

[foggy meadow]

They're like a natural thing in it.

[torpid bay]

alternating binom coefficients is the way i like it

[foggy meadow]

Binomials is wild.

whoa.

I will have to play with it and see if it works out to something similar.

[torpid bay]

,,\lim_{h\to0}{\sum_{n=0}^{k}{\frac{f(x+(k-n)h)\binom{k}{n}(-1)^n}{h^k}}} = \partial_x^f(x)

[fringe summit]

Paley-Weiner

[fathom swallow]

Yeatte

[torpid bay]

now, we can set the k on the top to infinity, and when we do that it stays the same, and all terms but a finite amount have zero coefficients, but because each term gets closer to 0 then that stuff we care about only happens in a local setting

but if k = 1/2, then we have an infintie number of terms and we can always find some term that's as far away from x as we want

a little handwavy and a more general grunwald using specific bounds is better, but that's the argument i came up with

[foggy meadow]

~~I also just found the integration form for my function 🥳. ~~

[foggy meadow]

Interesting.

[torpid bay]

lemme see if i have the better upper bounds somewhere

it was something like $\abs{\frac{x+b_x}{h}}$

[fathom swallow]

Yeatte

[torpid bay]

where depending on an x, you have a specific constant b to off set it, tho if you have it constant, then you'll get issues with convergence near x = -b

[foggy meadow]

Yay, derivatives.

Well I can now apprently talk most about what I want to. Which will be neat.

Or cursed.

[torpid bay]

huh

for some reason i have the floor function in there as well

$\floor{\abs{\frac{x+b_x}{h}}}$

[fathom swallow]

Yeatte

[torpid bay]

one nice thing about the grunwald, is that it agrees with the sort of playing around that gets you e^d/dx f(x) = f(x+1)

take this for example

$\lim_{h\to0}{\frac{e^{h\partial_x}-1}{h} = \partial_x$

[fathom swallow]

Yeatte
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[torpid bay]

$\lim_{h\to0}{\frac{e^{h\partial_x}-1}{h} = \lim_{h\to0}{\frac{\triangle_{x,h}}{h}} = \partial_x$

[fathom swallow]

Yeatte
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[torpid bay]

tiangle being different operator with $\triangle_{x,h}f(x) = f(x+h)-f(x)$

[fathom swallow]

Yeatte

[torpid bay]

which quite naturally lends itself to

actually

first

assume we're always talking about x

so remove the x subacript

anyway, this lends itself nicely to $\lim_{h\to0}{\frac{\triangle_h^m}{h^m}} = \partial^m$

[fathom swallow]

Yeatte

[torpid bay]

as a possibe definition for tfrac calc

but instead if we define $E_{x,h}(f(x)) = f(x+h)$ and do it in terms of E, then

[fathom swallow]

Yeatte

[torpid bay]

$\lim_{h\to0}{\frac{(E_h-1)^m}{h^m}} = \partial^m$

[fathom swallow]

Yeatte

[torpid bay]

and expanding using binomial, we get the basic grunwald letnikov

so to me imo its the mos natural frac deriv

[foggy meadow]

Makes a lot of sense, I will have to try it when ever I work in R^{2} again with this.

[torpid bay]

I've already verified that it'll work with gamma and with the other condition sometimes, tho that was a wihle ago so maybe i should go back over that proof

oh yeah

i see the note i left here

[foggy meadow]

I just know my function should work naturally with partial derivatives.
So, having the fractional version will help my look over my work and see if it's correct in n-dimensions.

[torpid bay]

"*Not a complete proof"

[foggy meadow]

Half my stuff with this is like that right now, just me analytically being like "yep okay there we go."

[torpid bay]

i've always wondered about

$\int_{a}^{b}{\dv[k]{x}f(x)dk}$

[fathom swallow]

Yeatte

[torpid bay]

and the sorts of stuff that would do depending on the path

whther different paths were equivalent

[foggy meadow]

I feel like I have seen this.

[torpid bay]

but i never remembered to actually compute it

[foggy meadow]

You should try it out, and tell me how it goes!

[torpid bay]

I feel like it would either be intractible or just trivial with no inbetween

if the derivative's nice enough, then trivial, but if not converging in a lot of places then oof

[foggy meadow]

Maybe some of both depending on the function, but yeah no clue.

[torpid bay]

if nice enough, then i could probably do things like complex analysis path theorems where one path around a pole is different from that same path with an extra loop

at that point, the question really just because complex analysis and im not really sure if frac calc would really be a useful thing other than "another complex anal problem"

without anything really new to bring to the table

actually

take x^3

yeah

huh

i actually might need that one thing

hold on

$\partial_k \partial_x^k|^{k=0} = \omega_x$

[fathom swallow]

Yeatte

[torpid bay]

yeah

this rocks, euler mascheroni constant time!

$\omega(x^a)=-x^a\ln(x)+x^a\partial_a\ln(\Gamma(1+a))$

[fathom swallow]

Yeatte

[torpid bay]

$w(x)=-x\ln(x)-x(\gamma-1)$

[fathom swallow]

Yeatte

[torpid bay]

ig i can use this in the integral and get stuff

[foggy meadow]

I'm going to get a cheese burger I will be back in 30 or so.
Keep me updated.

[torpid bay]

huh

this is kinda cursed

$\partial_{a-k}\ln(\Gamma(1+a-k))$

[fathom swallow]

Yeatte

[torpid bay]

i mean, its the derivative at a-k, but i've never written one withan actual expression down below

[torpid bay]

hm

take a = 1/2

[turbid sedge]

What is happening

[torpid bay]

then look at the two paths, C1 = a circle for k centered at -1/2 with radius 1/2, and then C2 = a circle for k centered at -1 with radius 1, the first afaik doesn't have any poles on the boudry or the inside so should be fine, while the seocnd one has a pole at k = -3/2, which is inside the boudny, and using some theorems i dunno the name of, the closed path integral will be affected by the existence of this pole

and so therefore the two path's will make differeing integrals and so it matter along which path the derivative values are taken

[torpid bay]

some calculus

[turbid sedge]

Ah

[foggy meadow]

Okay I'm back

Turned into an hour ordeal.

[torpid bay]

,, \int_{C}{\partial_{C(k)}\partial^{C(k)}x(f(x))dk} \ = \int{C(k)}{\omega(\partial_x^{C(k)}(x^a))dk} \ = \int_{C(k)}{\omega(\frac{\Gamma(1+a)}{\Gamma(1+a-k)}x^{a-k})dk} \ = \int_{C(k)}{\frac{\Gamma(1+a)}{\Gamma(1+a-k)}(-x^{a-C(k)}\ln(x)+x^{a-C(k)}\partial_{a-C(k)}\ln(\Gamma(1+a-C(k))))dk}

[fathom swallow]

Yeatte

[torpid bay]

it's not quite as intimidating as it looks

i promise

[noble tinsel]

ew what that

[torpid bay]

it's stuff to prove that if you extend the idea of a derivative to fractional exponents, that the path that you take within that space to get from d/dx ^p to d/dx^q matters

,, \omega(f(x)) = \partial_k\partial^k_xf(x)|^{k=0} \ \omega(\partial_x^af(x)) = \partial_k\partial_x^kf(x)|^{k=a}

[fathom swallow]

Yeatte

[torpid bay]

as a footnoe to get from 1st to second line

[noble tinsel]

oh idk i fell asleep reading about geometric sequences

[torpid bay]

the last step afterwards is to just take note of any zeroes or poles of the function of k that our path C can possibly enclose, and in this case the function in terms of k only encounters that when x = 0 or when k = 3/2, 5/2, 7/2, ... .

but note:

[noble tinsel]

why do the scoliosis ds have subindices what is this notation for

[torpid bay]

it's for fractional calculus

[noble tinsel]

ooohhhhh

i haven't seen this notation before

[torpid bay]

in this case im writing partial with subcripts to notate $\pdv[k]{x}$ but shorter

[fathom swallow]

Yeatte

[torpid bay]

which partial/partial x really just d/dx in this case but for generality and coinveience im using partial

$\frac{1}{2\pi i}\int_{C}{g(C(z))\frac{1}{(z-a)^{n+1}}dz} = b_n: g(z) = \sum_{n=-infty}^{\infty}{b_n(z-a)^n}$

[fathom swallow]

Yeatte

[torpid bay]

so by such a closed integral in the complex plane, we can isolate the residue values of various zeros and poles, and because our integral expanded from before is exactly in this form, it actually is just a multipel of zeroes and poles of full d^k/dx^k for k in the complex plane acting on g(x), so because we know the only poles for the g(k) function are at 3/2, and this can take advantage of that, then it means through some more substituting one function f(k) = k h(k) and see that we have shifted from one non pole value to a pole's residue and thus have different values

and so the C1 path ends up finding the b_0 value, while the C2 path ends up finding the b_1 value, and these are not guaranteed to be equal, so differnt paths by which you move the k value for d^k/dx^k through the complex plane can lead you to different f(x) functions at the end of it even tho same start and end poitns

I'm fudgin the numbers with which b values are being chosen but eh

oh yeah

winding numbers

i kidna lost track whether its b_1 or b_-1 but i think its actually b_-1

anyway

ig that completes it

any question?

i kinda never needed to use laurent series before

nice to see it used for the other thing i might never need: frac calc

[foggy meadow]

What is Omega and what ultimately does this compute?

[torpid bay]

ah

$\omega = \frac{\ln(\partial^m)}{m}$

[fathom swallow]

Yeatte

[torpid bay]

that's how i originally defined it

[foggy meadow]

whats \Omega_{x}?

[torpid bay]

omega x is just omega with respect to x

like im writing partial without respect to anything sometimes

in that case just assume with respect to same variable like above

i haven't gone further along the exp line to do like ln(omega^m)/m to make something new, but its because i didnt think i would ever even use omega

going the otehr way wasn't too exciting

suppose we do $E_{x,k}f(x) = f(x+k)$

[fathom swallow]

Yeatte

[torpid bay]

in this case, i can move the k up top so we get $E_{x,k} = E_x^k$

[fathom swallow]

Yeatte

[torpid bay]

for like a repeated version of it

but for some operations, we can't do this

like $\triangle_{x,2} f(x) = f(x+2)-f(x)$

[fathom swallow]

Yeatte

[torpid bay]

but$\triangle_x^2 = f(x+2)-2f(x+1)+f(x)$

[fathom swallow]

Yeatte

[torpid bay]

[foggy meadow]

What does this all compute just the original integral??

[torpid bay]

for this, i just needed $\partial_k\partial_x^k(f(x)dx$

[fathom swallow]

Yeatte

[foggy meadow]

???

[torpid bay]

and because I can use omega for this as i conveniently already calculated omega for x^a for this already

so that i can take partial_x^p and move it to partial_x^q

put in term of k

$\int\partial_kg(k)dk = g(k)$

[fathom swallow]

Yeatte

[torpid bay]

where $g(k) = \partial_x^kf(x)$

[fathom swallow]

Yeatte

[torpid bay]

and then doing that along paths in the complex plane

for k complex

good?

[foggy meadow]

you can make k a complex number?

[torpid bay]

yep

works fine with gamma function definition

[foggy meadow]

So you're doing some fractional derivative of some path in C?

[torpid bay]

im doing the k'th fractional derivative, where the path that k is taking is in C

so like slowly moving d^1/dx^1 to d^(1+i)/dx^(1+i)

via this integral

i do this because the usual method is just sharp lines and otherwise this can be more general of an idea

different paths C result in a sense in different function results at the end of this path we choose

so i guess there's a 'principal branch' function

[foggy meadow]

So essentually a -> b where the f used to get a to b is different.

[torpid bay]

I don't think the b's would even be the same at that point

f(a) = b, f becomes g after some differentiation loop in C is taken, g(a) = c

[foggy meadow]

No like lets say d/dx -> d^{2}/d^{2}x, a here is d/dx and b is d^{2}/d^{2}x.

Then f is some sort of transformation moving a to b.

[torpid bay]

ye

[foggy meadow]

I'm wondering if switching to that other convex integral would fill in places where it can't find a fractional derivative.

[torpid bay]

e^kx works well, maybe put it interms of fourier?

[foggy meadow]

I tried this, but Fourier stuff broke quite a bit. e^{-x^2} is a good testing case for me. I forget how you made the other integral form. But it occurred to me it might make a type of Riemann surface almost, but with partial derivatives.

[torpid bay]

yep

100%, its essentially a function in terms of k, so complex stuff + riemann surface is good for it

we kinda dont need to care about x or f(x) other than its zeroes or roots for the sake of k

at this piont, i treat x as a secondary constant and k as the main variable

[foggy meadow]

That's wild, yeah I haven't messed with fractional derivatives, but it's neat to hear I'm close to understanding stuff .

[torpid bay]

there's one thing that might be connected to what the other guy from before was talking about

using fouier or laplace

lemme see if i can find it

$\partial_y^a\mathcal{L}{-y}{g(n)}=\mathcal{L}{-y}{n^ag(n)}$

[fathom swallow]

Yeatte

[torpid bay]

if you want another frac deriv contender

i haven't messed with this one whatsoever tho

I go sleep now

[long matrix]

i bore

[foggy meadow]

I just realized, due to this transform being an "all in one" the idea of a Fractional Inverse exists.

Which is odd.

I know a good use case for it too 🫤, why.

[foggy meadow]

This also means there's partial inverses, where it inverses, but only in respect to a single variable probably too. Bruh. This is sort of cursed this exists, but whatever.

[pseudo nest]

Greetings,
I’ve been trying to get into certain types of Minecraft modding (Modeling, animations, and shaders), from what I understood so far, I’ll need to learn vectors and matrices and the like.

I’ve honestly forgotten most of the math I’ve learnt, as my uni course (medschool) barely has any math.

I’m looking for suggestions of what I should learn and where to learn it (e.g., Books about this type of math)

I wasn’t sure this question was indeed the type to be posted in the help channels which is why I’m asking this here.

Thank you!

p.s. ping me if you reply, thanks!

[gritty heath]

Linear algebra is the way

[vast wraith]

@restive salmon my uni library has this book talking about the mathematics of knitting and some recipies for knitting mathematics

[restive salmon]

Yoooo thats really interesting
Ive only seen a vid about knots and mathematics ig knitting is just advanced knots of some sort with a pattern hmm it gotta he very interesting

[pseudo nest]

Thank you! Any books/resources you suggest?

[gritty heath]

More like braids than knots but yeah, interesting

[gritty heath]

There is a free resource called "linear algebra done wrong" by Sergei Treil, you can try that first

Its designed for honours students as a first linear algebra course

[pseudo nest]

Thank you, though I wonder if I’ll have some difficulties regarding the background knowledge needed.

But I’ll manage, thanks again

[gritty heath]

In my uni linear algebra is a first semester course

[restive salmon]

Yea actually braids is more accurate

[gritty heath]

So I assume there isn't much prerequisites

[vast wraith]

idk how they relate to knots probably in some way yeah. it’s very interesting that there’s lots of different styles of knitting, the way ive learned is apparently just called the norwegian knit, which differs from the continental style used in most of europe, and also from the english style; but in the end they all produce the same kinds of textures

i recall seing you mention you also want to learn, do you know someone who can teach you?

[old oak]

This is neat!

[restive salmon]

No i dont if i do get the equipment and all its gonna be me and youtube

[restive salmon]

Im soo sorry but the owls eyes in ur pfp creeps me out

[old oak]

Result!

[gritty heath]

Owldsider

[surreal sapphire]

even i learned multiple ways to knit

there are different tools for socks

to create round shapes

and multiple ways to do the stitches

[vast wraith]

i want to get to that eventually, the way my grandma does it is using five pins

[surreal sapphire]

in crocheting there is a technique to make flat shapes and one that creates round shapes

when you do the stitches uneven you can create a cone shape

as a child i made a hat for my cat

she was not impressed

[vast wraith]

mwahaha amazobg

[surreal sapphire]

that or there is also two needles connected by a plastic wire, that is a bit simpler

[vast wraith]

thats what im currently using to make a beanie

#discussion message

[surreal sapphire]

nice

so you are pro already

i just learned crocheting and knitting in school and then did a bit more

[vast wraith]

def not i have no idea what im doing

[surreal sapphire]

seems like nice book

[surreal sapphire]

are you doing chapter 2?

[vast wraith]

no im currently just trying to copy my grandma but ill def get around to ch 2 eventually mwahaha

[twin meadow]

Hai chat

how's everything going

[viral oracle]

[nova bane]

math equations are trees.

1+(2*3) is ```
f_add
d_1
f_mul
d_2
d_3

[round abyss]

binary operation moment

[zealous garden]

Abstract syntax tree moment

[loud whale]

If the Gelfond–Schneider proof works, I'm gonna go and say "Conjecture X is true' with my friend saying 'Conjecture X is false' and get the prizes for all of them

[old oak]

That's not an equation though

[zealous birch]

Is the study of geometries other than euclidian geometry basically pointless?
(hehe get it point-less?)

[zealous birch]

I don't if that is even code in any language

[oak condor]

Well well hello to all

[latent edge]

yeah so studying the earth is pointless

[small dust]

[old oak]

I mean, we've been studying it for years and what has it brought us

[old oak]

increasingly the policy of many governments, yes

[vast wraith]

inspired by this article i did a little reading about conformal geometry and the shape of the earth yesterday 😌 https://foreignpolicy.com/2025/02/14/trump-greenland-obsession-map-threats/

mercator projection, a view of the globe and the mollweide projection, respectively

mercator is conformal, but not area-preserving, mollweide is area-preservimg but not conformal

I love maps. And I always said, ‘Look at the size of this. It’s massive.’ That should be part of the United States.
— Trump

i would like to see someone try the presumably hopeless endavour of explaining the math to trump…

now this isnt really very related to the above but i was wondering how far the earth is from a sphere (because an ellipsoid is a better approximation) so i looked up the measurements (really just the ratio of the semi-axes) and made this very barebones demonstration 😌

[reef carbon]

@crystal dune what did you want to tell me

say it here

[crystal dune]

Just wanted to say a huge thank you to everyone here who helped me out with the math this semester. Your explanations, random late-night replies (AND patience lmao) honestly made a massive difference for me.

Because of your help, I managed to finish my first semester in Computer Science with a 3.97 GPA. That number still feels unreal, and a big chunk of the credit belongs to this server. I’m genuinely grateful for the time and effort you all put in. Thanks for being such a solid community 🖤

@reef carbon @fierce abyss @cloud rover

[reef carbon]

oh wow

congrats on that, that's pretty fucking impressive

[crystal dune]

Thank you 🥺

[fierce abyss]

Congratulation

[cloud rover]

A singular congratulation

Like, ONE clap lol

[crystal dune]

Looking forward to do multivariable calculus and linear algebra next semester guys

[old oak]

With one hand

[cloud rover]

ayo that... that's not a...

[foggy meadow]

@torpid bay Hey I have a question for you, if you're there.

[cloud rover]

!da2a

oh crap did they acc scrap that

(or maybe it doesn't work in discussion channels)

[timid bronze]

Is it just me or does phone waiting line music annoy everyone

I have been waiting for 10 million hours.

[vast wraith]

its horrible without exception

[old oak]

That's the point, it's supposed to weed out as many callers as possible

[timid bronze]

Crazy work

[jagged forge]

i switched from walgreens to cvs due to insurance change lately

i have NEVER experienced such bullshit from an automated phone line before

literally impossible to talk to a real human

[old oak]

Yeah, it sucks

[jagged forge]

my favorite is when they call you, you call back, and get an automated answering machine and it STILL won't let you talk to a human

[latent edge]

I vibe with the phone waiting music we are not the same

[vast wraith]

[old oak]

Music to self-react to

[small dust]

you forgot to thank me

[ocean harbor]

and me

[ebon pier]

Is there a discord server like this but for electronics?

[rugged socket]

Styropyro

[ocean harbor]

physics server

[ebon pier]

K

[ocean harbor]

please dont say that next time

I dont like it

[rugged socket]

W number theory

[zealous garden]

K?

If you don't like the letter K, what do you do when field theory?

[ocean harbor]

thats not what I meant

I just dont like in general because its rude

[zealous garden]

lucky you we're not in general, we're in #serious-discussion

https://tenor.com/view/big-brain-gif-27108854

[ocean harbor]

true

[cerulean oracle]

Try electrical engineering server

[ebon pier]

It’s usles
It has very little ppl so at that point i might as well ask in Reddit

[zealous garden]

then do that, it's more fruitful than asking here

maybe try physics

[old oak]

I wonder if there's a psyhics discord server

(I know it's spelled "psychics" but then the similarity to "physics" doesn't work as well)

[timid bronze]

What’s objectively the best time to wake up and sleep.

[ebon pier]

There were no proper ones so I created my own https://discord.gg/Ne9XzT5E

[timid bronze]

<@&268886789983436800>

[wild lantern]

See #old-network

I'm not gonna delete your link but please don't spam it.

[ebon pier]

I sent it only ones :/ also sry

[wild lantern]

Yeah I know. The ee server in #old-network has like 20k ppl apparently

I've never used it so idk if it'a very active but I doubt it's dead

[ebon pier]

That’s little

[ebon pier]

It is dead

[wild lantern]

Engineering is kinda niche

[ebon pier]

Also r u good at electronics

[wild lantern]

Not particularly

[ebon pier]

Can u just help me rq?

[plain island]

20k is significantly more than 1

[ebon pier]

Oh

[wild lantern]

You don't want me to try and help lmao

[ebon pier]

Well if u join it will be 2 😊

[ebon pier]

I do

[wild lantern]

Nah, I'm not really qualified for that.

[ebon pier]

Ok

[plucky raft]

.

[viral oracle]

[nocturne solar]

COMPUTAR

[ocean harbor]

i got biomedical electronics next year

gonna get cooked 🔥 🔥

@ebon pier whats your major

[blazing maple]

yo guys, is this a good major with a bright job outlook, and how can i get a job if i do this: https://degrees.apps.asu.edu/masters-phd/major/ASU00/ESMEDENMS/medical-engineering-ms

if u do reply to me, please ping me with the "@sherman" so i can search up the message and find it

cuz the chat fills up easily

[hollow granite]

Calc 3 or lin alg which is harder quick answer

[snow ice]

lin alg

[torpid bay]

ye?

[blazing maple]

i thought linear algebra was easy?

[snow ice]

for me at least, prolly cuz I was exposed to calc earliers than matrices

[hollow granite]

Interesting

[foggy meadow]

I got it answered, basically calc can't easily be viewed as a group. But maybe could be as a monoid due to there being an identity function for me. Like idk fully if this is what I should've gotten from it.

[blazing maple]

ahh i see, i mean im just saying it from what i saw from yt shorts, calc 3 is apparently calc 2 but in 3D

[torpid bay]

ye derivative doesn't have an inverse

[hollow granite]

Lin alg doesn’t look that bad on first viewing and I heard calc 3 is not that bad compared to calc 2 so I’m excited

[torpid bay]

the derivative and integral operators are linear, and you can put it into an operator space which i think ends up like a ring or smthn

i would have to double check

[foggy meadow]

Which is weird because integration "inverses it," but I guess it doesn't in actuality.

[blazing maple]

i also heard what u said, calc 2 was slightly harder than calc 3 apparently

either way, at some point, all calc are hard

[foggy meadow]

Again though, I have an Identity function which derivatives and integration stem from. So, I'm confused on what that implies.

[torpid bay]

because of linearity, linear algebra is absolutely a beast for calc ideas

[blazing maple]

im here having trouble understanding the app of der in calc 1, i have an exam in 2 weeks

ill just practice with infinite question software

[torpid bay]

it's just that not each operator has an inverse element given composition as the 'multiplication'

addition, subtraction, and multiplication work fine

in that sense

also scalars work perfectly fine in that space,

$\nexists p: p\partial_x = \partial_x p = 1$

p as an operator on a function

er how do i do not exist

[foggy meadow]

I don't know, because my function already doesn't work on every derivable or integrable function making it a subset of polynomials it works on.
Therefore I don't know if the subset it works on makes integration an inverse of derivation.
But I will assume not for most functions. And by identity I mean a transform that take f and gives back f, which I lable e. e[f(x)] = f(x).

[fathom swallow]

Yeatte

[torpid bay]

i would say polynomials are the worst behaved given if you want invertability of derivative

e^kx is best

[foggy meadow]

🤷‍♂️ that makes sense.

[torpid bay]

ye

$1 \cdot f = f$

[fathom swallow]

Yeatte

[foggy meadow]

Yeah, which is technically correct, but mine isn't just a multiplication.
It's a transform.

So it's a summation, which leaves it the same.

[torpid bay]

what transform is it?

integral type?

[foggy meadow]

Yeah, but the integral wont show up correctly on Desmos .

I worked it out on paper, and it works fine, and the Riemann sum too.

[torpid bay]

[foggy meadow]

Again the neutral transform (the errors are on all the functions).

The errors are just visual in nature, they go away in the integral. Like the previous sign(x) transforms.

basically it's 1*f(x), but in sum form, which you modify to get calculus and some other inverse junk we we did.

[torpid bay]

i wanna see

[foggy meadow]

https://www.desmos.com/calculator/fdduxr4zei

[fathom swallow]

DisOneGuy

[foggy meadow]

figuring out mu took forever and it's still not fully correct. The Reimann sum works so much better for all of this stuff.

Basically I have to prove that some how and it will be most of the basis for me talking about this set of functions.

[torpid bay]

hm

is h(x) always going to be zero or is this just a special case?

oh

[foggy meadow]

It's a special case, it's used when doing a derivative or integration and makes where the function intersects y to be 0.

[torpid bay]

i think i see what's going on

[foggy meadow]

It's super simple.

[storm sage]

DisOneGuy, what's the thing you're trying to accomplish here?

[torpid bay]

all that H1 H2 is essentially a delta function, like kronecker delta

[foggy meadow]

I'm researching a function currently!

[foggy meadow]

Yeah, basically, but in the limit.

[storm sage]

Where did you get the function from 🧐

[foggy meadow]

My head, and then yeatte and me, then my head again.

[storm sage]

But I mean what's your goal with the function lol

Or thing that you find cool about it

[foggy meadow]

It gives "inverses," derivatives and integration. Including partial, fractional, etc. And it seems to give me calculus in stuff with whatever field I've tried.

Basically I do a sum of "buildings" which are made by sign(x) functions. These buildings stack to make "cities".

I just sum these and I get an approximation to my original function unchanged.
Then I just do a Reimann sum squeezing them to get the continuous version.

[torpid bay]

and because we are choosing f(x) such that f(x+a) approx f(x) for small a, then the approximation of that delta-like function where for a bunch of values and with shortening width, means that the sum is always within some error bound for each specific delta-like's width, and because that width gets smaller, therefore the error bound gets smaller for every single point within that width. And because that width you made it tie in exactly with the terms you sum, theres no overlap and each j(x) ill call it will always gets closer and closer to f(x).

[storm sage]

Oh okay so the main idea is that you're trying to approximate a function with a step function?

[torpid bay]

yeah that should be the outline for the proof then

alternatively, use e^-x^2 for brownie points with me

[foggy meadow]

This works worse for inversing functions in the long run. And just doing other stuff.

[foggy meadow]

No by a square function basically.

[storm sage]

:? what's the difference

[foggy meadow]

A square v.s. steps.

One is just a square basically, and that square can be broken down even further.

Allowing for some other special stuff to happen.

The difference between them is one can be represented by a sign transform and the other a floor transform. To turn the sign into a floor it would take an extra sum.

[storm sage]

Is the difference just the vertical lines

[foggy meadow]

Yeah, but from the square's view it's an extra sum of difference.

and from the sign's view it's an extra subtraction and sum.

[torpid bay]

the thing is, with the resulting integral if you take terms -> infty, then the resulting delta-like thingy will necessarily turn into dirac delta inside an integral

[storm sage]

But aren't the vertical lines just artifacts of the grapher

[foggy meadow]

Yep!

[foggy meadow]

In this case I'm taking buildings and stacking them.

each one it's it's own square function.

[storm sage]

I'm still just confused what the difference between square and step function is in your eyes, what's the definition?

[foggy meadow]

And a step function becomes this:

[torpid bay]

the purpose of having that square function that is zero everywhere except within a certain bound k, where it is 1, is to be able to build many more things much more easily with just this 'square function' instead of using the step function that can easily be built out of said squares

~~then again you defined it using step, so im not sure how much extra work it would be to still use step the whole way ~~

[foggy meadow]

I also don't technically use squares in all my transforms.

[foggy meadow]

A lot more from what I tried in the past. They become more like weird Fourier transforms.

[storm sage]

Wait but I thought you said that you were approximating the function using sums of squares, isn't that a step function?

Now I'm more confused 😭

[torpid bay]

the function being chosen to approximate happens to be the step function

but in the sum from before, it used the square function to approximate uh... x^3 or smthn

[foggy meadow]

https://en.wikipedia.org/wiki/Rectangular_function

I'm using sign to make a Rectangular function in this case.

[storm sage]

Wait but you can still use a step function to approximate x^3, the steps will just be of different sizes

Are we maybe just using different definitions of step function

[foggy meadow]

n...not really?

[storm sage]

I agree you can add up rectangular functions to make a step function

[torpid bay]

its def possible ye

[foggy meadow]

Yeah, but I don't use rectangular functions the whole time for what this can do.

[storm sage]

Oh so it's not about rectangular functions

[foggy meadow]

Not as a whole, it's specifically about sign transforms.

Or jusst this function shape in general. (idk how to put it).

[storm sage]

What's a sign transform

[foggy meadow]

Here's what the inverse transform looks like btw:
https://www.desmos.com/calculator/abaisy2wks

[torpid bay]

big x smol, small x big?

[foggy meadow]

https://en.wikipedia.org/wiki/Sign_function

[storm sage]

I know what the sign function is

[foggy meadow]

Also to integrate you just use sign(x) only and basically half it with the measure included.

[storm sage]

I'm asking what you mean by sign transform

[foggy meadow]

A sign transform is a sum of sign(x) functions in this case.

[storm sage]

Okay wait I'm going crazy, is that not just a step function

[foggy meadow]

No because I end up multiplying them by a g(x).

So there's an input g(x) and it returns g(x) in the limit with in a given area.

Idk the step function honestly.

It looks similar, but idk 🤷‍♂️

[silent junco]

cant you approximate any riemann integrable function with step functions arbitrarily well

[storm sage]

A step function's not a specific function, it just refers to any function which is piecewise constant

So its graph looks like a bunch of horizontal line segments

[foggy meadow]

Yeah probably related.

[storm sage]

Yeah, if by approximate you mean that when you integrate f - approx f, it goes to 0

[silent junco]

yes

[foggy meadow]

https://www.desmos.com/calculator/pvhxkba01q

Okay idk.

[silent junco]

of course it wont be uniform in general

but pointwise it should work

[storm sage]

huh

[foggy meadow]

I mean there it is working for both in some range and added constant.
But okay.

[storm sage]

not pointwise, you need to calculate an integral to get the error for that to work

are you thinking of continuous functions rays

not integrable

[silent junco]

i mean even with continuous functions im starting to doubt this approximation

[storm sage]

for sure any continuous function on a compact interval can be approximated uniformly w a step function

[silent junco]

consider like sin(1/x) on [-k, k]\{0}. its continuous

[foggy meadow]

Yeah it can't do every function, which I've said. ()

[storm sage]

not on a compact interval tho

[silent junco]

yeah i sent that message as soon as you sent yours

on a compact interval its fine

[storm sage]

ah

yeah I think uniform continuity is what's appropriate

[silent junco]

yeah

[foggy meadow]

Yeah and yeatte found another stipulation a while ago with the inverse thing.
1/x fails for example.
It must be increasing for the most part.

[silent junco]

well 1/x fails but i dont think thats because its decreasing

[storm sage]

wait disoneguy can you elaborate

I get you're trying to approximate functions with step functions, but what's the inverse thing you're talking about

[foggy meadow]

https://www.desmos.com/calculator/abaisy2wks

[foggy meadow]

you basically modify h1 and h2 a little and swap f and g. Then bam "inverse."

Ofc with in bounds.

It was originally derived from that.

[silent junco]

well what are you trying to accomplish

approximating the inverse?

[storm sage]

Wait I have no idea what you mean, what are f g h1 and h2

[foggy meadow]

@storm sage ^ this should give a bit of an idea.

[foggy meadow]

I stumbled across this function. I didn't really have a goal parse, more so just to explore and catalogue what I find with the rules given.

But I have always loved sums of floor, ceil, mod, and sign.

[storm sage]

I have no idea what I'm looking at .-.

what are you trying to find the inverse of

[foggy meadow]

Just type something in for f(x).

[torpid bay]

I'm still lookin at da integral

[foggy meadow]

It could be wrong, but it's what I've figured out so far.

[foggy meadow]

Is D confusing you?

[silent junco]

yeah i think riemann integrable with compact support is necessary and sufficient for your thing to work

[torpid bay]

I don't see a D

o.o

[foggy meadow]

Probably, which how do I write that then?

[storm sage]

Wait what thing and work how

[silent junco]

wdym

[storm sage]

I still haven't figured out what they're trying to do

[foggy meadow]

Like how do I set "this works on the set of functions which are riemann integrable with compact support"

[storm sage]

Huh, is it supposed to be showing the inverse of x^2? Because the graph isn't the square root function

[foggy meadow]

aww I got the scale factor wrong.

Forgot a 2.

[foggy meadow]

https://www.desmos.com/calculator/abaisy2wks

[silent junco]

if $f$ is riemann integrable with compact support, then we have that there exists a sequence of step functions $g_n$ such that $\int \vert f - g_n\vert\to 0$ or something along those lines

[fathom swallow]

rays

[foggy meadow]

Two comes up a lot for whatever reason.

[storm sage]

Okay yea now it works cool

[foggy meadow]

try changing f to (x - 1)!

[storm sage]

Oh, yeah I said that a while back didn't I

[silent junco]

oh i didnt notice lol. i thought you said it only for continuous functions

[foggy meadow]

Everyone is so confused in here including me about how you guys put stuff.

[torpid bay]

i was racking my brain trying to see the difference between ur 2 integrals, then i realized you said you changed the H1,H2's

[storm sage]

the pointwise approximation only works for unif. cts functions

[foggy meadow]

Those mainly change, and I try to keep them finite only using sign, floor, and ceil. But mostly sign. The floor and ceil allow me to do derivation. Sadly I needed it there. There could be a way to do it with just sign, but Idk what that is yet. I think I could work it out and it seems very likely it exists, as I've gotten really close before.

[silent junco]

oh okay i see. yeah youre right

[foggy meadow]

So, what exactly does this mean?

[silent junco]

if you want $\vert f(x) - g_n(x)\vert \to 0$ for every $x$ where $g_n$ is a sequence of step functions, $f$ must be uniformly continuous

[fathom swallow]

rays

[foggy meadow]

Yeah, I'm probably not doing anything really new, but interesting to me for sure. There's like a game to it.

[storm sage]

Oh I wasn't commenting on what you were doing

I was answering rays

[foggy meadow]

I was just saying in general, because forever ago you asked what I was doing.

That's mostly what I'm doing though.

[storm sage]

that's really neat!

[foggy meadow]

Even for differentiation it's just changing H1 and H2 in R. Once you have that you can do it multiple times on different axis in R^{n} and it will give you differentiation. If you want a derivative on a specific axis, then you just set all the other axis to zero and then integrate like it's a 1d. I'm pretty sure that's a partial, but idk.

The complex plain it works similar, but I want to work it out more. Because something changes fundamentally about the neutral transform even.

[torpid bay]

I remember having a certain function that worked well, but anything complex went to 0

so the effective domain was a striahgt line only in the reals

[foggy meadow]

oof.

[foggy meadow]

For me it works in the complex, but it's in half steps for derivation and integration it seems. Same for the neutral transform.

So I have to square my input function to get it back out unsquared.

Which lets me know Calculus on C is different than on R probably.

[torpid bay]

the step functions and such are a bit definition specific regarding C

I remember there was a discussion about modulo with like 4 other people regarding compelx numbers

like 2 months ago

[foggy meadow]

Well, if you keep the building idea in mind it starts to click what you're trying to make.

[torpid bay]

more and more minecraft mods with tinier miniblocks

yep

[foggy meadow]

That or a ditch, which is just a flipped building.

[foggy meadow]

Yeah so either way you have to go inside and do a series of sign(x) for the real and imaginary. Then it works out when you treat it like that, because it makes a building.

Rather than how sign(z) is normally defined.

And then inverses on C just start to work and converge naturally.

Same for the neutral in such.

I have yet to try Q.

[foggy meadow]

Also even though this is a meme. I was drawing these out on the circle to make circular harmonics. But it's a good example of a building on S^{1}.

[torpid bay]

[short acorn]

,ti disoneguy

[fathom swallow]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[short acorn]

,ti

[fathom swallow]

The current time for coolempire93 is 12:00 AM (EST) on Sat, 17/01/2026.

[past wedge]

adoes anyone know a lil about data managment ⁠ #help-8

[hasty yarrow]

would you rather get cancer every time you eat a mcchicken or get a mcchicken every time you get cancer

[worldly horizon]

cancer every time i eat a mcchicken. if i submit myself to eating mcdonalds garbage i can submit myself to cancer, i deserve it

[sudden patrol]

wot is dis adomination😭🙏

yall prob in university or something and im stuck in sec 4 lol

[lofty forge]

Won't this work in Topology

[twin meadow]

Hi chat

how's everything going

eveything Hurts T-T

[spring vortex]

you......fine?

[magic python]

Hopefully everything gets better for you, you deserve happiness.

[twin meadow]

yea i don't know what even i deserve 🥀

whatever i want it never wanted me

[magic python]

Happiness, joy, pleasure, and fulfillment

[twin meadow]

even if does so

it leaves when i am slightly attached to it

AND IT SUCKS

[magic python]

That's the worst feeling 3:

[twin meadow]

indeed

[magic python]

Hopefully it can get better girl

[twin meadow]

yea hope so 🥀

[viral oracle]

[fresh comet]

https://tenor.com/view/don't-worry-hug-it-will-be-ok-gif-18038177795981558039

I hope things get better for you soon 🤍

[unreal meadow]

Did that bear just get asian with a hug?

Thats crazy, can someone hug me please? I need some better brain than this one man

[fresh comet]

https://tenor.com/view/kristigocouple2024-gif-11331379229047422940

[twin meadow]

aww thankyouuu sm you so kind

[twin meadow]

yep🍿🍩🍟🌻💌

[willow hearth]

nice name

[mild bane]

I got an exam can anyone help, someone who knows maths and computer science

[fresh comet]

thank you! welcome to the mathcord too!!

[willow hearth]

tried to get help in math but i got into a religional discussion 🙂

[viral oracle]

[fresh comet]

we don’t really do one on one tutoring in this server, I’m afraid

that said if you’ve got a specific question, you can ask it in a help channel (see #❓how-to-get-help), and wait for somebody to answer

note that we don’t permit academic dishonesty here, so I hope you’re not asking for help with an actual exam

[unreal meadow]

I dont know math, but i do know Matt maybe he can be helpfull for you?

[crude lark]

Gang i need help in smthing anyone know evan chen? If you do what should I do after functional eqns this is my alternate and I don't have access to one where I'm in the office discord for the program so pls help .

[latent edge]

where lmao

[willow hearth]

here

[rose ridge]

[latent edge]

@timid bronze

Day ruined

[timid bronze]

Why are their feet so visible

[noble tinsel]

are these supposed to be labubus

[neat lintel]

I had exactly the same thought, I'm devastated that people were paid to make a stuffed animal like this

Plz work to change the world not to make feet on our plush..

[latent edge]

I saw a girl getting super exciting over something so I was curious what it was

[timid bronze]

Bro was thinking it was some Galois theory book

[latent edge]

No I was thinking it's something interesting but I was just super disappointed

My sis was begging me to buy the stupid doll

brainrot ass doll

[latent edge]

It's so over

[deep mango]

How is that what you noticed

[snow ice]

I'm still wondering why ally removed her carrd from her profile

[zealous garden]

tfw you have 9 mutual servers with deltoid

@latent edge

[brave flare]

wow

i got 2

and one of them is hpysics

[hollow ginkgo]

Same

[hollow ginkgo]

Different

[zealous garden]

I got 5 with mecejide

I have 4 with you matroid

I'm in like every math server but sheafification

That's cus I got kicked out of sheafification for not reading enough Shilov

[brave flare]

that guy has a server?

wowzwer

probably lots of cat nerds

[neat lintel]

guys do u think it’s possible to study for a math exam in 5 days

[latent edge]

I am not in sheafification

[hollow ginkgo]

I am in several math servers without you

[snow ice]

yes

[zealous garden]

Fix that

[zealous garden]

Yes indeed

[hollow ginkgo]

How?

[zealous garden]

Invite me obviously

[neat lintel]

I’m lowk js gonna spam past paper questions

[brave flare]

i am in 1 math server

i suppose it is not hard to figure out which that is

[latent edge]

oh i dont have matroid as a friend lol

yey now i can view servers lmao

[zealous garden]

Wow

[timid bronze]

Because it's right in front of my face?

[timid bronze]

Bored of it

It needs a revamp but I'm not going to change it rn

[snow ice]

i see...

fair

[civic canopy]

Don't study

[ocean harbor]

yes its possible

[bronze pelican]

[true zinc]

I'm sorry what

how'd you get kicked out for not reading enough of a specific textbook

unless this was a reading group or something

[zealous garden]

The sheafification server basically demands that you are making steady enough progress on one of the books on their list, although I think they might make exceptions if you can satisfy whatever ker's standard is in some other way

I wouldn't necessarily say reading group

[true zinc]

Oh wtf

fuck that shit

[zealous garden]

https://sheafification.com/the-fast-track/

[latent edge]

lol wtf lmao

[true zinc]

Oh I've sen this before, wtf, like actually wtf, what about people who want to do number theory, or combi, or like..anything that's not diff geo or physics, who is this even intended for, cracked whizkids? Like even then this seems annoying at BEST to work through

[latent edge]

that's not fun at all lol

disappointed

[timid bronze]

At the same time, idk if I like having a carrd