serious-discussion

[neat lintel]

if you were thrown in jail for that it would be close to a police state

even this server is

[surreal sapphire]

feel free to stop using this server if you dont like the rules lol

[neat lintel]

möder is also illigl

[neat lintel]

lol

You are right

my comment was unnecessary

I shouldve deleted it

but itll be forgotten

so I dont have to

it wont go in the textbooks

[ancient flame]

lmao wtf is wrong with people

[sterile hare]

lol

[nova scarab]

@sonic grove I'm curious to see your solution
This was mine, I tried it out on a few numbers (not just ones that are solved by removing the last number, so it does work but I don't know if I communicated it properly). I just don't know if there is an algebraic solution

##### unknown values are #
 #### +
52713

5#### Try out a 5, there is potential to carry a 1, this number will be 5 or 4
 #### +
52713

5####
 5### If anything but the first number were to be deleted this will be a 5, however something + 5 = 2 and it can't carry over because it will make the ten thousands 6, so it must be a 4
52713

4####
 4### Now it is something + 4 = 12
52713

48###
 48## It's easiest to assume the last digit has been removed, until it doesn't work then move to the left. now it's something + 8 = 7, but it can't be, so 8 is incorrect, decrement it
52713

47###
 47## Something + 7 = 17, which meeans we want a 9 where the next column carries a 1
52713

479##
 479# Something + 9 = 11
52713

4792#
 4792 Something + 2 = 3
52713

47921
 4792
52713

[sick burrow]

barges in
says they can't ask their question because they have to go to class
refuses to elaborate
leaves

[ivory sundial]

today (√-1)2^3Σπ and it tastes good

[toxic schooner]

nice

[stray kite]

I can't reply to this message, i have to go to class

[ancient flame]

I can't reply to this message, i have to go to class

[long matrix]

I can't reply to this message, i have to go to class

[alpine kindle]

I can't go to class, i have to reply to this message

[toxic schooner]

[neat lintel]

BROOOO

Why are you guys saying it better than I have?

I have been in school until like 16:00

dude

[ancient flame]

I'm on spring break

[neat lintel]

I wish I was too

[bright hill]

but spring hasn't begun yet

• gmod is in the northern hemisphere doxxxxxed

[ancient flame]

bruh

lmao

[umbral oxide]

Being on the spring break is the same as being in school just because of the amount of sheer work that has been assigned to you

[neat lintel]

ikr

that is one of the perks of not living in that country anymore

[dire mulch]

I am forcing my self to be extremely lazy this spring break. This semester had been annoying and difficult so far.

[ancient flame]

my teachers don't give me much work over break

and yeah don't overwork yourself

[pearl moth]

is it spring break time already?

it's not even spring yet

that's not for like another week

[vast surge]

I do spring break next week

[neat lintel]

Our Break is on rn

It started on 5 march after the exams

And ends on 20th april

[alpine kindle]

gm

[neat lintel]

Its 12:42 in my timezone

So good afternoon

No

gm

tis 8:19

in my timezone

[ocean terrace]

Guys did anyone take IGCSE before???

I filled in my date of birth wrongly!!!

my exam is after2 days, anyone know what should i do?

[brave hollow]

have you contacted the admins there?

[tacit herald]

SAME

[pearl moth]

contact the administrators of the examination

you'll need to have it corrected before they issue any certificate because a birthday mismatch will make the certificate putatively invalid

[flint island]

Felt.
I'm worried I can't tho

First term I'll be on grades and I'm worried my classes are gonna be rough :(

[neat lintel]

Wish I could take IIT JEE someday even if I couldn't afford to pass lol

[late valley]

is sweden a good country for something like quantum information science research? or stuff related to quantum computing, more in research side

they don't have huge funding (afaik from limited googling), but have made some headlines

[modern geyser]

goodday people

[fair mural]

good day

[modern geyser]

linear algebruh done wrong

ik that the point of linear algebruh done right is that it teaches det at the very end

whats the thing with done wrong

[empty stratus]

that's racist

[modern geyser]

howdy CV

[empty stratus]

Hello.

[modern geyser]

also whats racist?

[empty stratus]

Forcing determinants to wait at the back of the textbook.

[modern geyser]

i see lmao

my TA told me that it was a good book though

[fair mural]

@modern geyser https://www.math.brown.edu/streil/papers/LADW/LADW-2014-09.pdf

third page

[modern geyser]

i even have it downloaded (OH NO!)

[fair mural]

will explain why it’s “done wrong”

well

it’s a free book

available for free on the internet

[modern geyser]

nah i have done right downloaded for free

also CV what timezone ar eyou

i feel like i only talk to you at like 1 am lol

[fair mural]

what time is it for you?

[modern geyser]

,ti

[fathom swallow]

The current time for Brontochad is 06:41 PM (PDT) on Thu, 17/03/2022.

[modern geyser]

,ti @empty stratus

[fathom swallow]

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

[fair mural]

wait where do you live

[modern geyser]

rip

washington

[fair mural]

expected

you’re 3 hours behind me

[empty stratus]

Pacific Standard Time.

[modern geyser]

same as me?

[empty stratus]

Yes

[modern geyser]

i se

i only ask because i saw something called PST that was like 8 hours in front

confuesd me

[fair mural]

guess you two just stay up all night then

[modern geyser]

yeah lmao

he finished his dissertation a little bit ago

[fair mural]

i’m almost done with chapter 2 in ladw

[modern geyser]

so maybe he was grinding the dissertation late at night

so CV are you Dr. CV now?

[fair mural]

wouldn’t surprise me

[modern geyser]

he told me a lot about it

its pretty much generalizing the collatz conjecture + thinking about it in a way that is useful

[empty stratus]

I suppose, but I don't technically get my PhD until I graduate in may.

[modern geyser]

[fair mural]

early congratulations

[modern geyser]

early congrats indeed

[empty stratus]

I've basically shown that you can approach Collatz and a wide range of similar dynamical systems in terms of spectral theory

In other words, eigenvalue problems.

[modern geyser]

have you made new theorems

[fair mural]

oh that sounds cool

[empty stratus]

Yes.

[modern geyser]

like when you go to terrance tao's wikipedia page you see all his new theoremes

[empty stratus]

I submitted by dissertation yesterday.

[modern geyser]

CV has the CV theorem #1 2 and 3!!!

[empty stratus]

It was 443 pages long.

[modern geyser]

443!?

[empty stratus]

Yes.

[modern geyser]

how long is your book

[empty stratus]

My novel?

[modern geyser]

yeah

[empty stratus]

Right now, it's about 430k words long.

[modern geyser]

[empty stratus]

which is like 1200 pages.

[modern geyser]

jeez

[fair mural]

cv seems to be very interesting

[modern geyser]

he is very interesting

[empty stratus]

It's not finished, though.

[modern geyser]

how many pages do you think it willbe?

[empty stratus]

Yes, this is one of my specialties.

[modern geyser]

1400?

[ancient flame]

what's it about

[empty stratus]

Basically.

[modern geyser]

this right

or is the novel different from the dissertation

[empty stratus]

This is what my dissertation is about.

[ancient flame]

oh god

[empty stratus]

The novel is different.

[ancient flame]

pain

oh no this guy ends all his sentences in periods too

laaaaame

[modern geyser]

nah but hes professional

Senku Just Likes Talking Like This. (no hate to senku)

[empty stratus]

The novel is about a world-ending fungal pandemic that kills 99.99% of the population and turns the remaining 0.01% into magical fungal lindwurms.

[modern geyser]

lmao

[ancient flame]

all hate to senku

[empty stratus]

It's a hospital medical drama, told from the perspective of a neuropsychiatrist who is turning into one of the wyrms.

[ancient flame]

oh damn

[modern geyser]

wait that's actually what the book is about?

that's dope then

[empty stratus]

Among other things.

[modern geyser]

i saw magical fungal lindwurms and i thought i was being trolled

[ancient flame]

among us?

[modern geyser]

i read this book that sounds simliar

it was called "The insanity conspiracy: in a world gone insane, who can you trust"?

[empty stratus]

Other highlights include:

hallucinogenic MMORPG realities created and sustained by pure mental power, therapy sessions inside the memories of the ghosts of the recent dead; a time-traveling samurai dealing with future shock; an old hag recently awoken from a 60-year coma who wants to watch the world burn (and who might have the power to do so); an aging graphic novelist idolized by my MC; multiple realities; and a mysterious, memoryless entity in the form of a forlorn little girl who holds the secret to some sort of cosmic power—possibly the only hope to save the world from the darkness before all is lost.

[empty stratus]

I don't troll.

[modern geyser]

i see

[fair mural]

every outrageous sounding thing cv says is facts

[modern geyser]

"an old hag recently awoken from a 60-year coma" LMAO

that sounds very interesting

[empty stratus]

There is also a pangolin-dragon.

[modern geyser]

a dragon???

[empty stratus]

Yes.

[modern geyser]

when is this book going to come out

i wanna preorder it

[fair mural]

that actually seems very fitting

[modern geyser]

also was that paragraph the back-cover paragraph

[empty stratus]

The reference image:

[modern geyser]

claws on the wings?

[empty stratus]

I'm going to try to get back to writing it starting this weekend.

I hope to have it through-written by the end of the summer.

[fair mural]

is this art by you or did you just find it?

[empty stratus]

Google found it.

[modern geyser]

then you gotta get editing + published

[empty stratus]

I'm going to release it as a web serial.

[modern geyser]

i see i see

ive heard of web novels but not web serials

[empty stratus]

And then, after that, release it in self-published form, hopefully with some extra content as an incentive.

[modern geyser]

i will assume its like web novel but american

DLC CONTENT!

[empty stratus]

Hopefully something involving Super Gerbil World.

[modern geyser]

this?

(it was the first picture that came up when i searched "super gerbil world"

[empty stratus]

Anyhow, again, here's the first 141 pages:

https://docs.google.com/document/d/1UHkBKRuWwjrkP-xyF7k4OFkWYapmwsQsoAqYWyZuQJE/edit?usp=sharing

[empty stratus]

No.

At one point in the story, discussion of video game RPGs becomes relevant.

And Genneth (the main character) mentions that he is a big fan of the award-winning RPG Super Gerbil World.

I should also mention that the story takes place in a fictional world.

[modern geyser]

or wait fantasy lmao

@fair mural what genre would this be

so u made a game within your book story?

[fair mural]

idk

[empty stratus]

It's really unclassifiable.

[modern geyser]

inception

[empty stratus]

Actually, this also happens.

There's a good deal of adventuring inside of people's consciousnesses in this story.

[modern geyser]

[empty stratus]

I like to think of it as being an epic fantasy that just so happens to take place in a hospital in a retrofuturistic setting.

[modern geyser]

that sounds awesome

[empty stratus]

(That is, a futuristic version of 1940s-1950s USA)

[modern geyser]

what aspects of the 1940s and 50s does it keep?

[empty stratus]

It's hard to explain. It's not a copy of the 40s or 50s, per se, but rather more of a futuristic version thereof.

Like maybe half of the way to the technological level of the Jetsons.

[modern geyser]

i see

[empty stratus]

They have mag-lev cars.

Videophones.

The retrofuturism is mostly a matter of aesthetics.

[modern geyser]

videophones? like facetime?

[empty stratus]

Yes.

[modern geyser]

sounds very cool

flying cars?

i think that's what mag-lev means

[empty stratus]

It means magnetic levitation.

Not flying, but hovering.

While still keeping relatively close to the ground.

[modern geyser]

ilke the deluxo but without flying

[empty stratus]

They also have a kind of flying vehicle—an "aerostat".

It's like a combination of a plane and a helicopter.

[modern geyser]

GTA has something like this

[empty stratus]

Anyhow, like everything else I write, the story ends up going cosmic.

Because I love cosmic fantasy.

[modern geyser]

this thing but it can transfer between a plane & helicopter

yeah cosmic fantasy sounds like a super dope genre

[empty stratus]

The story's prologue is basically a preview to the reader of the tone and style toward which the story is headed.

It slowly becomes more and more fantastical over time.

[modern geyser]

fantastical or comsoS?

[empty stratus]

Both.

[modern geyser]

i see very cool

so do they like fly throguh space in a spaceship?

cuz its futuristic

[empty stratus]

No. There are no stars in the sky over the story-world.

[modern geyser]

no stars in outer space?

so like only planets or is the MC's planet the only one in existence

[empty stratus]

As far as they're concerned, the only things beyond the atmosphere are their sun and moon.

That's it.

[modern geyser]

i see

[empty stratus]

This.

[modern geyser]

any particular reason why you deleted all other planets from existence?

[empty stratus]

Yes.

It's important to the story.

I can spoil it for you now, our you can read and find out on your own.

[modern geyser]

i (partially) see

no i want to read it and see for myself cuz it sounds important

[empty stratus]

Everything is important. xD

[modern geyser]

True

anyways this book sounds awesome

also i was wondering if you posted your dissertation anywhere so in a few (or many many) years when i can understand it i want to read it

[empty stratus]

https://cdn.discordapp.com/attachments/952714093872185354/953051470343864350/PhD_Dissertation_Defense_Presentation_Document.pdf

Here's the summary document I prepared of it.

It distills the 443 pages into about 36 pages' worth of content.

It is accessible to undergraduates, provided that they know what a p-adic number is.

[modern geyser]

443 to 36 pages???

that's some major skill right there

[empty stratus]

My theory basically emerged out of a length computation and analysis of a function I constructed in association to the Collatz map.

My dissertation covers the background material, as well as covering all of the general cases in great detail.

[modern geyser]

all of the general cases

[sharp pumice]

I'm having trouble being able to focus on my career work. I'm a highschool senior admitted to a university for computer engineering. Whenever I start working on this, whether it be software development, reading, or hardware engineering, I keep thinking I should be studying for my calculus AP exam and whatnot. Then i get guilty and cant work. Does anyone have any recommendations to get around this?

[empty stratus]

Study for AP exams first as a "condition" for allowing yourself to to the computer engineering stuff.

[sharp pumice]

I tried that but i always find more to study :/

Studying is like a plague

Everytime i think i figure it all out i find something else i dont know how to do

And boom there goes the rest of my day

[empty stratus]

Yep.

[fair mural]

me with every next section of a book

[cobalt star]

allocate a certain task or tasks related to ap calc to complete every week, then when you complete it you can do computer engineering

make like a timeline of when you'll cover each part of the course etc

if you haven't

[modern geyser]

^ that's actually a great idea. set goals for yourself, complete them, then you have a sense of completion + a break

[neat lintel]

It is only good if you pull through with yourself

it is pointless if you keep getting distracted

this is why I founded NATO

so that everyone can at least make some progress on their work

even when you are not actually working

properly

in the head

[neat lintel]

Hello

[cobalt star]

hi

whats up

[sharp pumice]

I feel like this may be a bait, but what is your NATO?

[neat lintel]

olol

it is a homework alliance

lol

[sharp pumice]

[neat lintel]

would you want to join?

[sterile hare]

all that writing just for "we do ur work for u"

[fair mural]

<@&268886789983436800>

[pale orchid]

thanks

[devout nacelle]

Thanks

Dammit

[fair mural]

who did it

[pale orchid]

i rokabe'd manan

[fair mural]

oof

[pale orchid]

[devout nacelle]

[pale orchid]

i recommend you try the "Suggest A Laptop" discord server

you'll get good input there

[inner finch]

lol

[viral mango]

Is it just me or is any textbook higher than differential equations allergic to geometric intuition

[rapid ginkgo]

Just you

[viral mango]

Like is part of the skill of getting into higher math being able to translate these abstract proofs into meaningful pictures in your head

Okay I guess I've just gotten unlucky then

[charred mortar]

Wdym by higher than differential equations

[viral mango]

Intro to real analysis, abstract algebra, set theory, etc

Undergrad math major stuff

[charred mortar]

Well those three topics you listed are pretty algebra heavy I guess

But there certainly exist geometric perspectives for those things too

[viral mango]

I feel like every book I've read has lacked any sort of "this is what this means if you were to draw this out"

I spend 20 minutes staring at a proof not getting it at all, and then I go to YouTube and some guy sketches a diagram and it's like "oh this is so obvious"

[charred mortar]

For analysis I mostly used R2 and R3 as a base to draw examples and form some intuition

But you do need to be careful, because intuition sometimes breaks down

[torn willow]

It's funny

Low level math is "visual" . Low uni math is "algebraic" . After that it becomes more visual again

[deep mango]

Pugh's real analysis, needham visual complex analysis, guillemin and pollack differential topology, etc etc

Yes, there are books that dodge it, but there are also lots of books that embrace it

[viral mango]

Thanks for these, c:

[proper anvil]

I know that it differs between universities but what would be best 1-2 math electives for someone doing a statistics major?

Here are the options.

1. "Vector Calculus and Differential Equations"
2. "Linear and Abstract Algebra"
3. "Discrete Mathematics and Graph Theory"
4. "Analysis"
5. "Number Theory and Cryptography"

[terse flax]

discrete and anal

[echo glacier]

can someone take a quick look at my proof and make sure its ok?

i know the values but i dont really understand how to write up epsilon delta proofs

because it doesnt make sense where you get values from

[stray marsh]

#proofs-and-logic ?

[neat frost]

No

#calculus

[stray marsh]

right, missed the epsilon delta part

[umbral oxide]

Oh no

[median zinc]

Vector and Linear. Even for stats.
Random variables form some vector space (and they have even more structure than this) - you're expected to know what this means

As for why Differential equations - while you may not exactly see DEs unless you do SDEs or the like, you will still see diff/inte in statistics. I'd say you'd want to be good at solving diff/inte which generic DE courses should typically train

Analysis will be immediately useful if you do further statistics.
Discrete/Number theory seem like applications of statistics, but not the 'I have experiment, we can apply this kind' For cryptography it is somewhat obvious, but for discrete, it's immediately useful in terms bettering your math. Use of statistics with graph theory generally implies advanced models (at least, to me Random Graphs are advanced)

[fading hull]

lin alg

take lin alg

[leaden torrent]

i am very surprised that #1, 2, & 4 on that list are only electives for a stat major

1 and 4 are required for any advanced stats and lin alg is just everywhere

[stray kite]

question

if a questions states something like

"There are x people in a country on Sunday, and there are y people on Wednesday. If the rate of growth of the population is proportional to the number of people in the country, how many people will there be on Friday"

i can consider sunday x(t=0), do i consider wednesday x(t=3) or x(t=4)?
i feel dumb because idk which makes more sense to take

[waxen lily]

x(t=3)

Wednesday is 3 days after sunday

however the time from the start of sunday to the end of wednesday is 4 days

[weak sand]

"I'm not going to vote, my favourite is going to win anyway!"
"What if everyone else thinks the same way?"
"Then everyone else is going to vote, but I will not, one man can't make a difference!"
"What if everyone else thinks the same way?"
"Then no one will vote, so maybe I should go vote anyway? But everyone else could think the same way, so they are going to vote, but I will not, one man can't make a difference!"
"What if everyone else thinks the same way?"
"Then no one will vote, so maybe I should go vote anyway? But everyone else could think the same way, so they are going to vote, but I will not, one man can't make a difference!"...
and so on.
So, should you vote or not?

[torn willow]

Your mistake is assuming humans are logical

[deep mango]

I always vote when I can, and the one time I missed the voting window by like 30 minutes I saw the status of the vote 12 or so hours later and the person I was going to vote for was behind by 5 votes.
As they counted more it turned out fine and he overtook and went ahead by a good margin. But it was really terrifying for an hour or so.

This is not to say that this anecdote answers your question, but it certainly means I'm not going to stop voting.

You can also regret voting, but if you're liable to doing so I'd say you might want to reevaluate where your votes are going. Lol

I like when I get to say shit

[weak sand]

what if they were?

[modest rune]

I do think this is probably untrue

realistically speaking

No I am saying it's 0

not tiny.

Your vote literally could never have made a difference, mathematically

[deep mango]

But that's conditioned on the result of the vote

Well

Ok, yeah, it definitely depends on what voting pool you occupy

[long matrix]

theres a small chance it makes a difference

[modest rune]

I think that the illusion that voting makes more of a difference than it does is a bad narrative to push

i still vote

[long matrix]

this is also game theory thing

everyone or no one, etc

[deep mango]

Yeah

[weak sand]

small chance is still possible

[deep mango]

Yeah

I think the choice changes based on where you are

And also like

Is obviously contingent on other people making the choice they usually make

[modest rune]

On disproportionately small voting pools there’s a chance

[long matrix]

It also doesnt have to be everyone choosing on their own

[modest rune]

But this would like

Just never happen on say the scale of a US national election

[long matrix]

If a group of you collectively decide that has more impact

[modest rune]

Groups and individuals are shockingly different yes

[deep mango]

local elections could easily lead to this, and those are the ones people don't feel much pressure to vote in

[modest rune]

Arguably convincing other people to vote is a more important thing than voting yourself

[long matrix]

dont do the work, get other ppl to

[modest rune]

But yeah I always get annoyed by voting efforts

For say a presidential election

That tell people their vote could individually make a difference

Just seems manipulative

Maybe it’s okay to lie if the net effect is positive tho

I’m no kantian

[deep mango]

I kind of dont mind lying about this to make sure that their vote doesnt individually make a difference though

[modest rune]

Yeah

But for example I feel a decent amount of sympathy to anyone who like

Sees a 2hr voting line or something

And decides against it

[deep mango]

(or that the vote of someone who cares a lot more DOES make a difference, when they have a pretty reasonable chance of being totally unhinged)

Yes absolutely

[modest rune]

Realistically that 2hrs is a bigger net impact on you than your vote is on the entire population lol

[deep mango]

Like, voting where I've been has always taken like 15 minutes. So I definitely cannot understand that experience

[umbral oxide]

I quit voting

I realized too that individual voting doesn't amount to anything because the probability of being a decisive voter is less than one percent

It's akin to playing a lottery imo

[limber thunder]

voting isn't about individuals being decisive but about large, organized groups of people

if you want to be "decisive" then campaign for a party

[deep mango]

Yeah you can do more productive things than voting definitely

(but will you? some people will, many will not)

[long matrix]

if you enter the lottery you should vote

Wonder if that will convince anyone

[umbral oxide]

I meant that your probability of being a decisive voter is very low

So I compared it to a lottery

[worn garnet]

Intrestring question hows graduate admissions for new programs compared to established ones ?

Saw this: https://gsas.harvard.edu/programs-of-study/all/quantum-science-and-engineering

[sick burrow]

what is the name of the thing you get when you cut a sphere by a plane

[turbid epoch]

circle

[sick burrow]

right but in 3d

like the actual piece of the sphere, not the intersection

It's shocking how little geometry terminology I know

[turbid epoch]

idk if theres a special name for that

if you cut a sphere in half, you get a hemisphere and that's all the sphere slicing terminology I know.

and need

[sick burrow]

I envy you

[odd narwhal]

Cross section?

Or wait, you mean the like hemisphere parts leftover?

[static loom]

spherical cap

[tender grotto]

for fermats last theorem, is there anything for when n < 0?

or is it only proven for n > 2

[surreal sapphire]

multiply $a^n + b^n = c^n$ with $(abc)^{-n}$ to get $(bc)^{-n} + (ac)^{-n} = (ab)^{-n}$

[fathom swallow]

Lochverstärker

[tender grotto]

ah so u can get every negative case converted into a positive case then

ok thx

[ancient flame]

is there a proof of why $\dv{f(x)}{x} = \dv{}{x} f(x)$ or is that defined to be equal?

[fathom swallow]

guh mode

[fair mural]

it’s defined that way

[ancient flame]

alright ty

[long matrix]

equivalent notation

~~these are all fractions ~~

[modern geyser]

The doge doesn’t get stricken through

[alpine kindle]

https://en.m.wikipedia.org/wiki/Differential_(mathematics)

[long matrix]

[deep mango]

[alpine kindle]

I don't understand what the article's talking about but

sounds cool

[modern geyser]

Fractional calculus

Is pretty cool (or is it?)

[idle summit]

[edgy hill]

Its not correct, is it?

Cause my teacher told me d/dx is a operator and not the fraction

Correct me if I am wrong

[empty stratus]

Yes, but it is also horrible.

[empty stratus]

It is technically just two different ways of writing the same thing—the derivative of f—but each has its use.

df/dx is Leibniz notation. This is particularly useful in engineering and physics. There, ∆f / ∆x would denote the ratio of a small, but discrete, change in the value of f to the associated small change in the value of x. For example, average velocity over a time interval of length ∆t is given by ∆x / ∆t, where ∆x is the change in position over the interval. Because of the interdependence of x and t, as ∆t becomes small, ∆x will become small in a comparable way, enough so that after taking limits and arriving at the infinitesimal ratio dx / dt, the result is well-defined at every time t, where is then equal to the derivative of position with respect to time, otherwise known as velocity.

On the other hand, (d/dx)(f) is operator notation. This notation emphasizes the fact that differentiation is a linear operator on spaces of functions.

This is particularly useful when studying differential equations, because it allows for perspective from linear algebra and functional analysis to be brought in to analyze the situation.

[idle summit]

technically this is not wrong if we are talking about non-standard analysis

[empty stratus]

Physics is a kind of non-standard analysis. xD

[idle summit]

But still we can think of differentiable forms

[alpine kindle]

*usually

you can define it so it is one

[idle summit]

i'm a physicist 🤷‍♂️

[ancient flame]

oh wow I got an essay response

thanks so much

[empty stratus]

Nice.

[empty stratus]

No, just two paragraphs. My essays are multiple paragraphs long.

Still, you're welcome. 🙂

[ancient flame]

I was kidding lol

[empty stratus]

This is one of my essay responses:

#dynamical-systems message

[ancient flame]

PAIN.

[empty stratus]

?

[fair mural]

good response cv

dedication

[empty stratus]

Thank you.

But I consider that an ordinary response. xD

I like being comprehensive, and comprehensible.

[alpine kindle]

what actually is a derivative tho

[empty stratus]

Depends on your point of view.

[alpine kindle]

hm

what points of view are there

because it's first introduction is as a rate of change

is there more to it than that

[empty stratus]

Bill Thurston wrote a famous essay where he discusses, among other things, different conceptions of the derivative.

https://arxiv.org/pdf/math/9404236.pdf

[cobalt star]

oo interesting essay

[cobalt star]

hm i got introduced to it as the tangent line at a point

[idle summit]

I don't even try to read 👍 👍

[alpine kindle]

what does that last one even mean

[empty stratus]

No clue.

[alpine kindle]

lmao

[odd narwhal]

Normalise introducing the derivative as the unique best linear approximation at a point

That way you don't condition students to think about it one way then have to beat it out of them in calc 3

[surreal sapphire]

is this actually good though?

for single var you rarely use it i think

[odd narwhal]

I think you should show both approaches

[surreal sapphire]

i think it should be an early theorem, so that you can recall it later

[odd narwhal]

But introducong this concept early rather than late helps students internalise it

So we don't have to tell them that the definition of the derivative they learned is wrong because it doesn't generalise

And the real definition is this other thinf

[alpine kindle]

what is the "real" definition

[odd narwhal]

The differentoal of f at x is a linear transformation D_xf such that
f(x+h)-f(x)=D_xf(h)+o(||h||)

[surreal sapphire]

this was a theorem in my analysis class, but we rarely (if ever) used it

[odd narwhal]

For single var it's not very helpful but showing it early would help students not to think of the derivative strictly as a number

[surreal sapphire]

until we had to define it in higher dimensions

[deep mango]

i think it's important to give both perspectives of "instantaneous speed" and "best linear approximation" and to clearly explain why these are the same thing

[frosty basalt]

Ayeeeee wsp guys

[odd narwhal]

Yes, that's exactly my take

[empty stratus]

What about fractional derivatives and derivatives in Sobolev space?

Or weak derivatives?

[alpine kindle]

thinking of derivative as a number?

[deep mango]

what about derivations on a bimodule shin? what about those?

[odd narwhal]

The derivative of a single variable function at a point is a number

[deep mango]

[velvet dagger]

I mean that's a bit more like... how to put it... Still "fundamentally" your ordinary derivative as a linear approximation is what's up

[empty stratus]

My position is that the interpretations given of derivatives depend on the level of knowledge attained by audience.

[dense belfry]

That's everyone's position

[alpine kindle]

what does the o mean

[velvet dagger]

It's just that when you define a Sobolev space, turns out smooth functions aren't closed under Sobolev norm so you need to take additional limits

[empty stratus]

In that viewpoint, more general definitions of the derivative are important not just because they tell us what the derivative is, but because they give us a way to apply and integrate knowledge from other subjects.

[velvet dagger]

And these additional limits are weak derivatives

ANd then when you characterize by Fourier transform and all you can get shit like fractional

[empty stratus]

And let's not forget the Radon-Nikodym derivative.

[velvet dagger]

But the "actual" derivative is the linear map one and the other notions are outgrowths

[empty stratus]

You could just as easily argue that linearity is a property of the derivative that needs to be proven. 😉

[velvet dagger]

You could and you'd be wrong

[odd narwhal]

It means some function (we don't care which) g such that the limit of g/||h|| is 0 as h goes to 0

Basically some function that goes to zero faster than the norm of h does

[alpine kindle]

oh

[odd narwhal]

Signifying the rate at which the error decreases as we approach x

[alpine kindle]

ok

[empty stratus]

Tell that to my introductory real analysis students. xD

[dense belfry]

[deep mango]

lebesgue differentiation theorem

[velvet dagger]

Like I definitely sound flippant when I say that but I do actually believe that the fundamental idea is the linearity

[empty stratus]

Of course.

[velvet dagger]

The other stuff are emergent phenomena

[empty stratus]

That's certainly the most unifying property of the derivative's many different incarnations.

[deep mango]

complexvariable is definitely right

[alpine kindle]

is it normal notation to divide functions by values
is it just like
scalar multiplication

[deep mango]

if you're defining the derivative by linearity, you're not really defining it in a way which makes it clear how to compute it imo

well

unless you do scuffed stuff

[dense belfry]

I mean then you do the jacobian

And show it satisfies the property

[odd narwhal]

Yes it's just scalar multiplication by the inverse

[alpine kindle]

ah

[deep mango]

hmm

[odd narwhal]

Actually

[velvet dagger]

ryc: Complexvariable is suggesting the even more general ideas of fractional derivatives, weak derivatives, and so on

So I don't see how that's a case in favor of computation

[alpine kindle]

function spaces are just vector spaces ig

[odd narwhal]

Maybe it should be the norm of o(||h||)

I forgor

[velvet dagger]

But also I am fairly certain that partial derivatives fall out easily once you ask about linear maps evaluated on a basis

[deep mango]

ah, so what you want to hear is "derivatives are polynomial fourier multipliers"

[odd narwhal]

Yea it should be the norm my bad

[alpine kindle]

so you have the norm both inside and outside?

[fathom swallow]

ShiN

[odd narwhal]

That b was supposed to be an n

[deep mango]

R^b?!?!?

[odd narwhal]

I'm not weird

[deep mango]

oh

lmao

[odd narwhal]

The norm.on the inside isn't an argument of a function

[alpine kindle]

oh

[odd narwhal]

It's just a shorthand for "this function follows this limiting behaviour"

[rapid ginkgo]

I'll add another definition - just take a commutator with a matrix

to Thurstons

[odd narwhal]

In fact technically o(||h||) is a set of functions which satisfy this

[empty stratus]

What about the Fréchet derivative?

That might occur in an infinite-dimensional space.

[dense belfry]

I mean if g(||h||) is going to 0 it doesn't matter

If you norm it or not

[rapid ginkgo]

It is cool, but I was just appealing to basic lie theory really

[empty stratus]

In which case, matrix multiplication is going to be potentially undefined / divergent.

[dense belfry]

[rapid ginkgo]

the lie product is a derivative

[odd narwhal]

It matters for the rate of decay compared to norm.of h emma

[rapid ginkgo]

(literally)

[velvet dagger]

I mean my take here is this. Obv in calc for science/engineering, you first care about rate of change. You show in math that this is identical to linear approximations, and in higher dimensions linearity is the way you want to think about things. Then when the time comes, you say ah take this or that property of the derivative, this allows you to get some extensions that are useful to do things. For example, we can do integration by parts and see that limits of smooth functions under Sobolev norms are precisely those which satisfy "an integration by parts"

[odd narwhal]

You can't really measure this without taking norm of g

[velvet dagger]

In another setting you see that when you take Fourier transforms, differentiating is multiplying by polynomials

[dense belfry]

Oh I see

Makes sense

[odd narwhal]

Point being that it goes to 0 faster than h does

[deep mango]

yes, this is right

[empty stratus]

Isn't the dirac delta not the limit of a smooth function under Sobolev norm?

[velvet dagger]

Smooth functions are dense in Sobolev spaces

[deep mango]

dirac delta is not in sobolev space

sobolev spaces are compete

[empty stratus]

Nor is its derivative.

[rapid ginkgo]

actual trivial math btw

[deep mango]

so no, it's not

[empty stratus]

As I thought.

[velvet dagger]

And then distributional derivative is even further, for now I'm talking weak derivative

[deep mango]

weak derivative and distributional derivative are synonymous

[empty stratus]

This.

[deep mango]

the norm you use to complete tells you what kinds of functions you want, everything is always in terms of integration by parts but the completion is nicer (satisfies more properties) if your norm forces things to be "more like" differentiable functions

[velvet dagger]

I've mostly seen weak derivative refer to Sobolev spaces in particular

[rapid ginkgo]

but its there for interesting reasons

[velvet dagger]

And then distributional when you're dealing with distributions

[empty stratus]

Yes, but in practice, "weak derivatives" means "distributional derivative".

[deep mango]

i do not think this is standard notation

[empty stratus]

Technically, it's passing through a minor abuse of terminology where we identify a function in sobolev space with the distribution it induces via integration against itself.

[velvet dagger]

Well, not in the practice I've seen. I guess it's a matter of whose notation is more common then lmfao

[empty stratus]

Then there's the arithmetic derivative.

[alpine kindle]

if the general derivative at a point in a vector space evaluates to a linear map, can you define the directional derivative as a specific element of the column space of that map

[empty stratus]

And derivations.

[rapid ginkgo]

Btw still in analysis land

[empty stratus]

Yes, but in the part that has a non-trivial intersection with algebra.

[odd narwhal]

Directional.derivatives are usually only defined for maps into R (maybe C too idk)

[empty stratus]

There's also the issue of whether or not we include finite differences in the mix.

Oh, and let's not forget non-Newtonian derivatives!

Like the multiplicative derivative.

[odd narwhal]

Why sully ryc

[deep mango]

I shouldn't sully before verifying this but it's very fishy to me

why can't i pop the directional derivatives of each component into a vector

[odd narwhal]

I mean you could define itnin every component

[deep mango]

isn't that a thing

[odd narwhal]

Idk how meaningful that would be

[velvet dagger]

I imagine the key word in Shin's statement is "usually"

[odd narwhal]

It's not something i've really seen at least

[deep mango]

this is literally just "multiply the differential by a tangent vector"

[empty stratus]

Directional derivatives can potentially be defined for any map f:V —> V where V is a vector space over a metrically complete valued field.

[deep mango]

so idk what this "it's not something i've seen" means

it's what you always do

[odd narwhal]

Sure, but usually it's just dot product with the gradient. I haven't seen any use case for directional derivative for maps not into R

[alpine kindle]

what actually is a directional derivative
I'm not sure if i understand it properly

[odd narwhal]

Granted J haven't looked far

[empty stratus]

You can also go for the case f:V—>W, where W is a vector space over a metrically complete valued field extension K of the metrically complete valued field F associated with V.

[rapid ginkgo]

No, you basically just do it anyway. Physicists like to say that that you can just write del_mu in front of anything and then just add a term ro make it make sense in coordinates. Mathematicians just say "go ahead, do it anyway, but make sure it respects orthogonality and leibniz rule"

[velvet dagger]

Alison: derivative evaluated at a tangent vector

[deep mango]

if i have f : M to N, do people every write Vf for f_* V, or do they only write Vf for f : M to R?

i don't know

[empty stratus]

In single variable calculus, there are exactly two directions you can take a limit in: to the right, or to the left.

[rapid ginkgo]

A lot of math amounts to "do things anyway"

[deep mango]

how fast are you changing in the direction v

[empty stratus]

When working with functions defined on spaces of dimension ≥2, you then have infinitely many directions to choose when approaching things in the limit.

[rapid ginkgo]

Just do it anyway

point being

[deep mango]

(it's wacky and unintuitive that this is linear, which is why i took umbridge with assuming the derivative to be a linear map)

[alpine kindle]

with respect to this definition i mean

[velvet dagger]

D_xf(v) is the directional derivative of f at x in the direction v

[empty stratus]

It's what you get when you apply D_xf to a given vector

[alpine kindle]

oh

[empty stratus]

What Sloths said.

[alpine kindle]

wait

[velvet dagger]

Waiting

[odd narwhal]

Umbrage

[deep mango]

good night shin

[empty stratus]

Thank you.

[rapid ginkgo]

I highly recommend this

[odd narwhal]

Good morning ryc

[deep mango]

you're right

thank you

[rapid ginkgo]

makes life more fun

makes math more fun

[alpine kindle]

so are you just applying the linear map derivative to a specific vector called the direction

[velvet dagger]

Yeah

[neat lintel]

heron's formula is the most OP formula for triangles

[fathom swallow]

Several Sloths

[rapid ginkgo]

Follow papa grothendieck

[alpine kindle]

so for R that's just multiplying by a scalar so it doesn't matter?

[rapid ginkgo]

dont let your memes be dreams

[velvet dagger]

Which connects with the intuition ryc is saying

Of how much f changes in the direction v

[rapid ginkgo]

[odd narwhal]

Except this also works for non differentiable functions sometimes

[deep mango]

y^2/(x^2 + y^4)

or something

[odd narwhal]

Ah yes, the only example in calc 3 ever

[fathom swallow]

Several Sloths

[alpine kindle]

so could you potentially take derivatives over function spaces

[velvet dagger]

There's something called the Frechet derivative

[deep mango]

yes! there are two kinds

(two common kinds)

[velvet dagger]

Which pretty much transplants the idea of the derivative into Banach spaces

[alpine kindle]

oh that's useful

[deep mango]

frechet derivative = the best linear approximation one

gateaux derivative = the directional derivatives one

[rapid ginkgo]

Now I dont recommend taking life advice from Grothendieck

[velvet dagger]

Prob more general spaces but idk the deets of how hard you can squeeze things since they haven't come up much

[deep mango]

they are not equivalent in infinite dimensions!

[alpine kindle]

oh

[deep mango]

i think frechet implies gateaux though

[alpine kindle]

how are they not equivalent

[rapid ginkgo]

but sometimes its okay

[velvet dagger]

Inverse and implicit function theorem still hold in infinite dimensions

[empty stratus]

Infinite dimensional spaces be crazy.

[velvet dagger]

Alison: I imagine the proof that functions with C^1 partial derivatives are differentiable will be something like

[deep mango]

idk you can be gateaux differentiable (all directional derivatives exist) but fail terribly to be frechet differentiable

[velvet dagger]

You take an estimate along each thing and bound by epsilon/C

[odd narwhal]

They are not equivalent in finite dimensions either!

[deep mango]

worse than the stupid "failures" in finite dimensions

thanks shin

[velvet dagger]

ShiN I think ryc is making the stronger claim that even "C^1 Gateaux differentiable" doesn't imply Frechet

[odd narwhal]

My comment was delayed by bad internet

[deep mango]

yes

well

no

i wasn't making any claim

[velvet dagger]

Wait what

Oh

[deep mango]

because i didn't know what claim to make

[odd narwhal]

Well isn't that true in finite dimensions either

[deep mango]

thank you for providing the claim daminark

[odd narwhal]

The prototypical example

[alpine kindle]

so you can evaluate all of the directional derivatives, but not package them all nicely into a linear transformation?

[velvet dagger]

C^1 partial derivatives => differentiable in finite dimensions

[odd narwhal]

Oh right

[deep mango]

ugh just exxclude tthat dumbass eample

[odd narwhal]

True

I forgor

[velvet dagger]

So I'm guessing that if there's any meaningful divergence between the two notions it has to be the claim that C^1 gateaux doesn't imply Frechet

[deep mango]

yeah the thing becomes unbounded or something

[velvet dagger]

Hence why I autofilled/guessed what I was fairly certain ryc was alluding to

[deep mango]

frechet looks for a bounded derivative (as it should)

[alpine kindle]

is it just that it's not linear

that being the issue

[deep mango]

i think it's still linear but im not sure

[odd narwhal]

But this is only true if the function is continuous at the point

xy/x^2+y^2 with 0 at 0 is still a counterexample I think

[deep mango]

every function is continuous

[alpine kindle]

what's a bounded derivative?

[velvet dagger]

Hmm

Partial in x is \frac{y(x^2 + y^2) - 2x^2y}{(x^2 + y^2)^2}

Which isn't continuous (or defined) at 0

I think

[odd narwhal]

It's 0 at 0

Take the limit

Since you set the function to be.0 at 0

Otherwise this doesn't work

[rapid ginkgo]

the difference between physicists and mathematicians I suppose

[deep mango]

in infinite dimensions, there is something called "boundedness" for linear transformations. it's equivalent to continuity. boundedness is super important for doing anything and unbounded maps are a complete mess.

[alpine kindle]

oh

[odd narwhal]

Wait ok right, it's not C^1 then

[deep mango]

so frechet derivatives should be bounded

[odd narwhal]

Well, the partial derivatives aren't continuous

So ig you're right dami

[deep mango]

(this makes sense, if your function is continuously differentiable of course you want the best linear approximations to it to be continuous too)

[velvet dagger]

Yeah

I'm pretty sure that if the partial derivatives are continuous

Then the function is continuous and in fact differentiable

Spivak Calc on Manifolds agrees with me

[deep mango]

it's time to forget about CoM

forever

[odd narwhal]

You're right Dani

Dami

[velvet dagger]

You don't like that book?

[deep mango]

no just the subject

[velvet dagger]

lmfao

[odd narwhal]

Ryc had secondhand ptsd from my course this semester

[deep mango]

oh please

my exam also went shit

[velvet dagger]

How bad was your course?

[odd narwhal]

I bitched about it a bunch on ivory dami

[alpine kindle]

so if you collect the gateaux derivatives on all the bases, you'd still get a linear map?

[odd narwhal]

The staff was the biggest problem

[deep mango]

i think so!

i haven't seen a proof though

[odd narwhal]

I don't wanna get into it now, it's done

[alpine kindle]

oh so frechet derivatives are just a stricter type of derivative

[deep mango]

yes

[alpine kindle]

that do nicer things

[deep mango]

(or gateaux is a weaker kind, depending on your perspective)

and the latter perspective is the more accurate one in practice

[odd narwhal]

One could argue frechet is the correct notion

[deep mango]

yes

gateaux but not frechet causes big problems

you see the distinction pretty clearly in calculus of variations

when you want to find critical points of infinite dimensional functions

so the questions "is the differential 0" and "are all the directional derivatives 0" sometimes have different answers

and you only really have access to the latter if you want to use calc of vars techniques

[alpine kindle]

thanks everyone

[velvet dagger]

Lol I remember we had this convo ryc

Where I thought calc of variations was gonna use frechet haha

[cold needle]

i might take calc of variations next semester

[velvet dagger]

I feel like I should learn calc of variations eventually

I heard it's good shit

All I really know is that Euler-Lagrange equations are a thing because if you have a minimum then the derivative (I guess Gateaux?) is 0

[odd narwhal]

Don't you use weak derivatives in CoV?

[deep mango]

umm

you use weak convergence

[odd narwhal]

Something something minimising the action

Wait no

There's like

[deep mango]

and weak convergence gives you weak solutions

[odd narwhal]

Variational derivative

[deep mango]

which are solutions to equations with weak derivatives

but this is kind of

a coincidence

not really but

[odd narwhal]

Wait is variational derivative just a special case of directional derivative

[deep mango]

idk what a variational derivative is

i think it's a gateaux derivative

[odd narwhal]

Seems like it from the definition

[deep mango]

nice

is that the one where you do a lowercase delta

but it's a normal delta and not partial

[odd narwhal]

Yes

Pretty sure it is

Well it's like

When you integrate the variational derivative of a functional against a smooth function you recover the gateaux derivative in the direction of that function

Formally it seems like you define it to be a certain radon Nikodym derivative

Through riesz markov

[deep mango]

Yes

That sounds right

[odd narwhal]

CoV sounds cool

[deep mango]

Cool

Yes its very nice as is all functional analysis

[odd narwhal]

We'll see about that

[deep mango]

The sooner you go to sleep the sooner we'll see

[odd narwhal]

Tomorrow is ant

And logic

[deep mango]

Yikes

Nvm stay up

[odd narwhal]

Lmao

[velvet dagger]

What do you like for cov ryc?

[deep mango]

Oh idk a book

I learned a bunch from evans and from various courses that have done it in a few different styles

Ch 8 of evans is perfectly good for the pdes perspective

[neat lintel]

did someone say "weak convergence"?

how weak is the convergence

[deep mango]

[empty stratus]

Weak enough to not guarantee convergence in norm.

[velvet dagger]

I guess you could say

It doesn't lift enough to guarantee convergence in norm

[tender grotto]

can someone explain parameterization and how to use it for animations and stuff? i dont need anything complex just something to get started

is it possible to generate an equation that would make a certain shape with parameterization?

[torn willow]

So let's say you want to model a circle

x^2+y^2=1

The normal way of getting y from x is a tad bit messy

So what you could do instead is let
y= sin t and x=cos t

Where t is a new variable

Now everything is constructed wrt t

This is easy and convenient to code

Well
$y(t)=\frac{2t}{t^2+1}
x(t)=\frac{t^2-1}{t^2+1}$

[fathom swallow]

Drink Drake

[torn willow]

is a more convenient parameterisation

[rapid ginkgo]

It has a few numerical issues

1. It isnt uniform like the usual parameterization via the the trig functions/e^ix.

2. You have to formally program in an exception for the "point at infinity"

[torn willow]

What point at infinity

Wait,Are you considering t over C?

[rapid ginkgo]

This parameterization doesnt cover all of S^1 without it.

it leaves out one point

or if you have an upper bound on the size of t allowed - a cut out interval

[rapid ginkgo]

(1,0)

[torn willow]

mb

[rapid ginkgo]

I am no numerical analyst ofc, but this parameterization is good for algebraic reasons

its a useful technique for solving some integrals and it also solves the equation x^2+y^2=1 in rationals

[rapid ginkgo]

if you use wolfram to check this, try plugging in integer values into this

you will have points accumulating towards (1,0)

[tender grotto]

yeah when i use desmos, it only does a half circle, but doesnt reach that point

[rapid ginkgo]

you can allow negative t to make it the almost full circle

[tender grotto]

oh lol that makes more sense yea now it works

[rapid ginkgo]

All of this would be easier with a blackboard

online sucks

but go ahead use desmos

[tender grotto]

hm, i have been messing around with trig functions with the parameterization

weird stuff happens

tho im trying to figure out how to make it grow diagonally

[torn willow]

You want a slanted ellipse?

[rapid ginkgo]

but anyway, this has bad properties except for algebraic ones

But then again any parameterization is just bad somehow by default, this is mild

dimension 2 and up is where things get bad

[tender grotto]

no, i want something like (sin(t), ln(t^t)) or whatever is similar but t is constantly growing so it keeps on expanding so basically the blue line but slanted

[rapid ginkgo]

btw it has nothing to do with S^1 specifically

this kind of mapping from R^n to S^n exists in all dimensions

[tender grotto]

so if i understand parameterization, its basically plotting out the points of an equation between a certain range infinitely?

[torn willow]

You convert the given equations to a easily plottable form and then plot the points in the domain (which depends on parameterisation)

[tender grotto]

ok, but how would you parameterise the equations

[torn willow]

Try
(1/√2 sin t + 1/√2 t ln t , 1/√2 t lnt - 1/√2 Sin t)

Should tilt by 45°

[tender grotto]

yea it does

tysm

[torn willow]

If you have (f(t),g(t)) ,(f(t) cos x+g(t) sin x, g(t) cos x - f(t) sin x) will be the curve tilted by angle x

https://en.m.wikipedia.org/wiki/Rotation_of_axes

For explanation,See Derivation part

That's one more convenient thing with parameterisation. You can rotate or stretch a curve easily

[ancient flame]

we do this a lot in physics

[torn willow]

Well,Yea I can imagine Classical mechanics having tons and tons of rotations and translations

[surreal sapphire]

should section headings be serif or sans-serif 🤔

vs

[torn willow]

First one feels better

[devout nacelle]

I don't like Sans Serif ngl

The only minus with Amann-Escher

[surreal sapphire]

i ask because koma-script provides replacements for the standard latex documentclasses and changes serif to sans-serif section headings

while the body text still is serif

such an odd change

fonts in general seem to move towards sans-serif (i think word uses calibri now by default)

[devout nacelle]

Word has had Calibri default for as long as I can remember

[surreal sapphire]

i remember times new roman

[long matrix]

Comic sans

[leaden torrent]

beleren is the only good font

[surreal sapphire]

i am switching my standard latex font and it triggered this existential crisis

[neat lintel]

comic sans

[alpine kindle]

is there a field of study which studies solutions to equations like cos(xy) = cos(x)+cos(y)

because the graphs look crazy

is that a part of algebraic geometry

[surreal sapphire]

no

algebraic geometry only studies polynomials

[alpine kindle]

ah

[last elbow]

you could try using a power series to expand it

then youd get an infinite polynomial

[alpine kindle]

then is there a field of study that would deal with this

[last elbow]

im not sure if algebraic geometry studies infinite polynomials...

maybe it does though

[surreal sapphire]

it doesnt

you dont have a notion of convergence in general fields (or rings...)

[last elbow]

right

[surreal sapphire]

i also cant answer this, probably something complex analysis

[last elbow]

but wait

why cant you have a (albeit weird) notion of convergence in polynomial space

[surreal sapphire]

pretty sure you run into issues

like the only valuation on finite fields is the trivial one

there is probably ways to do stuff like this but then you need to find replacements for sin and cos inside your new fields

[last elbow]

then what feild studyies which power series converge?

complex ana?

[surreal sapphire]

complex analysis

[last elbow]

yup

ok

so you can do it with in the feild of the complex numbers

[surreal sapphire]

you can do analysis in e.g. local fields but i dont think you can define sin and cos (?)

[last elbow]

but you need an entire feild of study to do so

[surreal sapphire]

i.e. the powerseries wont converge there

[last elbow]

the power series for sin and cos converge

[surreal sapphire]

with standard absolute value, yes

but then you are working in R or C

[alpine kindle]

which fields do sin and cos converge in

is it just subfields of C

[static loom]

as power series with rational coefficients they converge in p-adic fields as well

they have a somewhat small radius of convergence though

[alpine kindle]

oh

[last elbow]

huh

ok

[static loom]

well one problem you'd run into is how to homogenize an infinite polynomial

[devout nacelle]

Boomerstärker

Maybe this could be a language-default thing too

[winter hinge]

Does anyone know what's the criteria for getting the active role ? I just got it and now I'm curious about my stats, but #bots gives the score and I don't know how to get a meaningful stat out of it

[neat lintel]

I wonder, how much time should one spent with math topics

Algebra II - Precalc - Calc BC levels

Like a chapter logarithms, how long would it take? Or a chapter limits?

[surreal sapphire]

it's intentionally not public knowledge

you should spend as much time as you need to understand it

[neat lintel]

Like spending one day on a chapter is enough? If you do enough practice?

Or do I need to repeat a lot of days?

[surreal sapphire]

this varies widely per chapter and per person

[neat lintel]

Sometimes I don't get a topic, and spent couple days on it

but sometimes I figure it out instantly, do couple practice and then move on

[surreal sapphire]

ye, thats fine

[neat lintel]

but not sure if I should revise a couple time?

or can I just move on

[surreal sapphire]

you will need some repetition because you are human, but lots of those topics should build on the previous

i think it should be enough to revise when you forgot something but need it

[neat lintel]

Alright, so just keep progressing?

[surreal sapphire]

or before exams

ye, as long as you are being honest with yourself and no lack of knowledge stops your progress, you can just keep going

[neat lintel]

Aight cool

[winter hinge]

If you find yourself often needing to go back to a certain topic because you lack knowledge, that's when you know you are no longer good enough at it. That's when you actually go back and study more in depth. For instance I went back to trig when I found myself often not knowing useful formulas when computing integrals

[neat lintel]

ha

rq

[ancient flame]

it always trips me up for some reason when I see the word revise to mean review

I usually associate the word revise with edit lmao

idk it's weird

[long matrix]

americans are weird i agree

imagine using the word review to mean revise

[ancient flame]

lmao

bruh

[long matrix]

ill stick to revising for exams and writing book reviews, thank you very much

[ancient flame]

WHAT

bruh

makes no sense

you're using two words for the same thing

[long matrix]

@sleek wing ^ look at this poor creature which cannot use the English language properly

[ancient flame]

bruhhhhh

[deep mango]

yeah that restaurant was shit. i left them a 2 star revise

[devout nacelle]

I mean, it's supposed to be a 2 star rating, not review either.

You'd usually say "the restaurant was shit, I left them a bad review"

In the context of revise/review above, I've grown up with the former so it feels more natural to me, but what gmod said also makes sense.

[deep mango]

Correction: You'd usually say that.

I would say "2 star review"

The rating is the part of the review where I assign a score. The review is the whole thing (score + explanation)

A 2 star review is a review where the rating is 2 stars.

[inner finch]

shutup

[deep mango]

lol is your name still blushysullyforemoteforrycformod?

[long matrix]

abuse of notation I see.

[bronze pelican]

U should feel guilty

RguiltYC

[open aspen]

does anyone have a good energetic playlist they listen to while doing homework/studying? Lofi and similar make me sleepy

[late valley]

i dont have a playlist solely for studying but i do listen to hip hop/rap

kendrick, 2pac, nas, a tribe called quest, MF Doom