The h Bar

ACuriousMind

00:01

@heather We usually don't manually delete stuff like that. Since it's closed and downvoted, the roomba (automatic deletion routine) will get to it at some point.

0celóñe7

So take derivatives, use a bit of common sense, then integrate and use the comparison principle

This doesn't seem like a calculus 1 exercise though

heather

@ACuriousMind oh, okay.

Anonymous

@0celóñe7 That's what I'm doing

Anonymous

@0celóñe7 Yeah, it's more of high school type problem

Anonymous

Sort of revision classes we're having

0celóñe7

00:03

@Blue it's calculus 2 level...

Anonymous

@0celóñe7 Heh?

Anonymous

I dunno...this is a JEE type problem

0celóñe7

Shouldn't you be doing limits?

Anonymous

@0celóñe7 I am

Anonymous

Real Analysis + Differential Calculus + Vector Calculus....all side by side

Anonymous

00:05

(In our uni)

Anonymous

This problem was a part of Differential Calculus

heather

you just said JEE to 0celo

prepare for the end of the world

Anonymous

Don't worry. I hate JEE too

Anonymous

I just like the problems sometimes

Anonymous

They are usually challenging.

DanielSank

00:08

Haha, wow, I got +18 rep from reversal of serial downvoting on Math.

Anonymous

But as far as the system is concerned...it's crap

Anonymous

I agree with 0celo on that :P

heather

@DanielSank wow

DanielSank

+34 on physics

Then shortly after I got a bit more for a user being removed.

Looks like a bad guy got caught. Nice.

@Blue Should do linear algebra and multivariable differential calculus together, IMHO.

...because derivatives of multivariable functions are linear operators.

Anonymous

@DanielSank I am learning LA at home

Anonymous

00:09

We have it next semester

Anonymous

Balarka is teaching me :P

Anonymous

Mainly....so that I can understand QM properly

0celóñe7

Properly?

@Blue I will teach you the math you need for that

Anonymous

@0celóñe7 That's debatable

Anonymous

:P

Anonymous

00:11

@0celóñe7 Uh....wouldn't you say something like "blah blah blah" ....now prove linear algebra? :'D

0celóñe7

@Blue Linear algebra is trivial, I wouldn't insult your intelligence by asking you to do busy work

We will learn Functional Analysis

I don't like capitalizing the names of subjects but Functional Analysis deserves it

Anonymous

Functional Analysis sounds cool. But not now :P Lemme finish this semester first. I'm overloaded with subjects to study on my to-do list

Anonymous

Maybe sometime around January next year

dmckee

@heather It's not really a candidate for moderator intervention: it's on track to be vacuumed in due course, so it doesn't require special handling.

heather

@dmckee yeah, I forgot about the vacuuming - ACM reminded me. thank you though =)

@DanielSank how are you (aside from being restored your rep)?

0celóñe7

00:35

@Blue Will you have had courses on general topology and Measure Theory?

DanielSank

@heather crummy

I'm sick and losing my hearing.

heather

@DanielSank i'm sorry

here, have a virtual chocolate chip cookie

made fresh tonight

0celóñe7

what is this cookie meme about

heather

it's not a meme, we actually have cookies in the house

0celóñe7

@heather proof?

DanielSank

00:50

The proof is in the cookie.

heather

i'm not taking a photo, i'm too lazy

DanielSank

@heather P = NP?

says who?

That sounds like something you just made up.

0celóñe7

Why should P ~= NP

heather

yesterday, by heather

A Solution of the P versus NP Problem

yesterday, by Mithrandir24601

@heather Yeah... He's super legit...

Norbert Blum

0celóñe7

that seems like algebra at first, but it has inequalities. Computer science = analysis?

DanielSank

00:52

Yeah but who knows if it's right?

heather

::shrugs:: just pointing it out because it's a fairly reputable researcher

DanielSank

@0celóñe7 Massive amounts of evidence.

heather

i'm by no means saying it's right

DanielSank

Also, the paper concludes P not equal to NP.

0celóñe7

@DanielSank then why is it a debate?

DanielSank

00:53

The star board has it wrong.

@0celóñe7 We want a proof.

0celóñe7

@DanielSank We?

DanielSank

Oh by the way, @BernardoMeurer now lives in Santa Barbara. We're taking over hbar.

2

heather

@DanielSank yeah...i'm not seeing anything to the contrary on the starboard though

0celóñe7

Since when do physicists want proofs

DanielSank

Yes, me and my mouse.

heather

00:54

@Bernardo congrats on making the move!

dmckee

@DanielSank When they're talking about math, obviously.

DanielSank

@heather Perhaps I'm confused. There's a starred comment by you saying NP = P.

dmckee

And most of computer science is math.

heather

oh, lol

DanielSank

@dmckee ...or when they are computer scientists.

heather

00:55

@DanielSank that was a joke, I was saying NP in the context of no problem, and then to convey it did a =P sarcastic face, with the bonus that it looked like P = NP

dmckee

Well, they sure aren't grammarians. Or at least not decent typists.

DanielSank

@heather ah

@dmckee har hardee har har

heather

@DanielSank though i hadn't noticed the latter effect.

DanielSank

That is quite a coincidence.

heather

which is why i'm cracking up laughing right now =)

dmckee

00:56

Have you seen what my typo rate looks like. It's embarrassing except that it's been that way to long I've become inured to the humiliation.

DanielSank

heheheh

@dmckee eh, you're fine.

heheh, I should have said "you're fine".

dammit

I mean "your fine"

wow, I can't write a typo when I want one.

dmckee

My line you were responding too said "When their talking..." before I fixed it.

@DanielSank ::chuckles::

Nice.

DanielSank

Why did someone link "Frontier Psychiatrist"?

That is a weird song.

Oh it was John.

I withdraw the question.

heather

well, i'm off, good night =)

DanielSank

good night

@JohnRennie <3

0celóñe7

01:02

@heather ok, what do you want to learn

DanielSank

@JohnRennie if you like Frontier Psychiatrist, there's a nonzero chance that you may enjoy this

Ra Ra RasPutin animation 720 1080 HD Version @slocband @paceaudio

►

0celóñe7

4

Q: Continuity of the Fourier transform of a measure

If $\mu$ is a complex finite Borel measure on a separable real Hilbert space $H$ then $$x \mapsto \hat \mu (x) = \int \limits _H \Bbb e ^{\Bbb i \langle x, y \rangle } \Bbb d \mu _{(y)}$$ is continuous. This slightly reminds me of showing that the convolution of a function in $L^p$ and anoth...

$\Bbb e,\Bbb i,\Bbb d$

what horror

DanielSank

Calmate

Prathyush Poduval

03:26

@0celóñe7 Ping me too if youre gonna teach him. I'm interested to learn to learn it too

GPhys

04:29

finished 5th 13 hour day at university in a row

gotta ship to CERN Friday Q__Q

vzn

04:40

@GPhys congratulations! great topic for an AMA, wink ;)

@0celóñe7 eg crypto security is based (currently indirectly) on P≠NP. that includes online commerce/ banking etc. military also heavily reliant on crypto. cybercurrency economy alone now estimated $100B. etc. more here vzn1.wordpress.com/category/p-vs-np

@DanielSank holy cow playing hooky or just summer break? some kind of big story there for sure o_O

vzn

05:00

question for the audience: has anyone noticed the uncanny similarity between QM formalism for a set of particles and waves emanating from a set of classical harmonic oscillators? am wanting to write this up lately but need some help of a hardcore physicist... this ties in with a lot of the discussion in here about QM interpretations... does anyone want to plunge into terra incognita and advance the frontiers of knowledge? any takers? :)

John Rennie

@Phase Have a look at Are vacuum fluctuations really happening all the time?

Sir Cumference

06:49

@Kaumudi.H How's college? :)

Anonymous

07:03

@GPhys Wow. :)

Slereah

07:13

Hey

DanielSank

07:40

@vzn "Big story" = he moved here for college.

@vzn I have a post on the main site about this.

Anonymous

@DanielSank Which college? UC Santa Barbara?

DanielSank

Santa Barbara City College (SBCC).

He'll transfer to a UC later.

Anonymous

@BernardoMeurer Great news :) How's the new college? :)

Anonymous

@DanielSank Oh, nice

Anonymous

Good for him. He said that he didn't like his previous college.

Anonymous

07:43

Meanwhile here I'm bunking my English class and reading QP for dummies =P

Anonymous

08:10

Hi @BalarkaSen! Exam over?

Balarka Sen

yeah

tomorrow's chemistry

Anonymous

Nice. How was it? :)

Balarka Sen

dumpster fire lol

Anonymous

@BalarkaSen Good luck =P I know you don't like chem much :'D

Balarka Sen

the exam was apparently rather nonstandard

Sir Cumference

08:11

@BalarkaSen How's your new college?

Balarka Sen

I am not in college yet

Anonymous

Balarka is in school, dude

Sir Cumference

Wow...

I thought you were Bernardo...

I can't work at 4:12am...

Balarka Sen

#needeyeglasses

Anonymous

@BalarkaSen Ah, sounds bad. Don't worry

Anonymous

08:13

Anyhow, I need to set out for college again in 30 mins

Anonymous

I'm bunking classes

Sir Cumference

@Blue In the U.S. we can use "school" to refer to "college", though usually not

Anonymous

@SirCumference Not the other way round I hope ?

Sir Cumference

@Blue :P

Anonymous

:)

CooperCape

08:14

in the uk college is still technically school...

Anonymous

I was shocked once when somebody mentioned that MIT is a school

Anonymous

lol

CooperCape

becuase college isn't university here. go us.

DanielSank

Uh... graduate school.

Balarka Sen

@Blue Nah I don't really care. The average of the class is going to be pretty low in any case.

Sir Cumference

08:16

@CooperCape People say "I'm in college" but no one says "I'm in university"

Anonymous

Hehe. "average" is what matters :'D

Sir Cumference

Ugh this makes 25 hours without sleep ;-;

Anonymous

Nothing better than failing together :P

Anonymous

@SirCumference Go to bed!

Sir Cumference

@Blue I can't

Anonymous

08:17

Or sleep on your chair

Anonymous

y?

Sir Cumference

@Blue Can't sleep :P

Anonymous

You've got Balarka's disease I think

Anonymous

:'D

Sir Cumference

@Blue "Balarka's disease"?

Anonymous

08:19

I find @BalarkaSen awake everynight till 4am-5am in the maths chat

Anonymous

@SirCumference

Balarka Sen

@Blue Some people just like to watch the world fail at physics.

But yeah I'm pretty sure I'm going to be close to the higher fraction of numbers

Anonymous

@BalarkaSen True. Nothing could make our physics teacher happier than making us fail :P

Anonymous

Okay....gotta rush to college

Anonymous

Tata

Balarka Sen

08:23

See ya

Prathyush Poduval

@Blue no attendance rule?? :P

Anonymous

@PrathyushPoduval 60 % I think

Anonymous

Our HOD told us not to attend classes which we don't like and use time more productively :P He's a great guy

Anonymous

I'm on the way :D

Balarka Sen

Sounds like a great HoD

Prathyush Poduval

08:50

@Blue then you enjoy as much as you can:P

Sid

Wow.. we have much stricter rules here

Prathyush Poduval

@Sid How much stricter?

Sid

For example, our Physics course is a 3 credit course. If I am absent in >6 classes, I get a grade back. (That is, if I get an A, they will turn it into a B).

If I am absent in >12 classes, that is a straight F.

Slereah

How is substraction defined on $\mathbb{Z}_n$

What is $0 - 2$ on $\mathbb{Z_3}$

Prathyush Poduval

@Sid now thats too strict

Sid

09:00

@PrathyushPoduval told you. Of course, having friends for proxy attendance also helps. :P

Prathyush Poduval

Ha Ha yeah :P

ACuriousMind

@Slereah All the operations on $\mathbb{Z}_n$ work by doing the corresponding operation in $\mathbb{Z}$ and then applying "mod n" to the result.

Slereah

@ACuriousMind I know, but I'm trying to implement it in C

And C has some odd behaviours when you do mod to negative numbers

I'm not sure what $-2 \% 2$ is supposed to be "for real"

ACuriousMind

Well, $-2 \mod n$ is equivalent to $n-2$.

Prathyush Poduval

@Slereah You can implement it manually right?

calculate the quotient after dividing by 3

Slereah

09:03

sure, but that is unfortunate

mod operations are done at the CPU level so they're very fast

Implementing them by hand would be quite sad

Prathyush Poduval

What kind of wierd behaviour are you talking bout?

Anonymous

@Sid Actually as a result of the freedom we get some people go astray. You can see two extremities - super nerds and drug addicts :'D

ACuriousMind

@Slereah Just add a sufficiently large multiple of $n$ to the negatives to make them positive, then.

Slereah

$-5 \% 3$ is $-2$, apparently

ACuriousMind

Which is correct

Slereah

09:05

Hm

Prathyush Poduval

@Slereah add 3 to it

ACuriousMind

@Blue Super addicts and drug nerds would be a more interesting setting.

Slereah

But -2 isn't part of $\Bbb Z_3$, is it?

Since it is just $\{ 0, 1, 2 \}$

Prathyush Poduval

@Slereah Computer doesn't know that i thinkk

ACuriousMind

@Slereah Well, it's equal to $3-2 = 1$ in it.

Slereah

09:06

Yeah so I need to do More Things

Prathyush Poduval

Its just calculating the remainder

ACuriousMind

Don't forget: The "elements" of $\mathbb{Z}_n$ are really equivalence classes, and both $1$ and $-2$ belong to the equivalence class we abbreviate by writing $1$.

Slereah

Sure but this is in the computer

I need to represent them

Ideally the same for all elements

Prathyush Poduval

@Blue They're there everywhere (Maybe cause i know only the colleges with lots of freedom :P)

ACuriousMind

@Slereah Sure, so if taking mod of a negative number always produces the largest (smallest?) negative number with the same mod, then the fix seems to be to simply add $n$ to the result of taking the mod of a negative number,.

Slereah

09:09

Alright, thx

Though this is mostly for safety, really, I don't think I'm gonna use a lot of substractions in Zq

Slereah

10:26

Criminals can be smooth, but can they be analytic

" −10 User was removed"

UNBAN THAT MAN

user147690

This is a test.

ACuriousMind

@Slereah That's not a ban, that's a deletion, which may well have been voluntary :P

@AlexClark A test for what?

Balarka Sen

10:41

For a test.

0celóñe7

10:54

@ACuriousMind to see if he has been shadow banned

ACuriousMind

There is no shadow-banning on SE, you'll be very much aware if you get banned, as you should know :P

0celóñe7

@ACuriousMind what are you insinuating

ACuriousMind

@0celóñe7 Hm? Not "insinuating" anything, I'm straightforwardly referring to the fact that you have been banned in the past and therefore know that banned users get notified about their bans, hence there not being "shadow bans".

user228700

11:10

Hello, everyone! :-) Can anybody confirm that the follow diagram is, in fact, that of a poker:

user228700

0celóñe7

@ACuriousMind @Mithrandir24601 @Slereah GOT EPISODE 6 LEAKED IN ENTIRETY

ACuriousMind

@Kaumudi.H That doesn't look like a poker to me. As far as I know a poker is a iron with a hook at the end used to rake coals or burning wood.

It does look like something you could poke someone with, though

user228700

Ah, hmm. This is the definition given in the same manual:

user228700

0celóñe7

11:13

@JaimeGallego your country is an absolute failure

user228700

I'm confirming because our teacher told us that not all diagrams in the manual are correct and I have no way to know if that is, indeed, an effing poker.

user228700

(Gah, I'm majoring in CSE. I shouldn't need to spend hours drawing these diagrams so meticulously)

ACuriousMind

Well...the diagrams does look like what the definition describes, doesn't it?

So maybe "poker" here is indeed the correct technical term for that tool

user228700

Yup, it does but so do all the other diagrams.

user228700

Hmm :-/ Alright, thank you :-)

ACuriousMind

11:16

What kind of manual is this and why do you need to worry about whether or not that thing is a poker?

user228700

@ACuriousMind It's the Electrical lab manual and I must worry about this stuff because a teacher will grade me on my drawings.

ACuriousMind

@Kaumudi.H Wait, all the diagrams look like what the definitions describe but you know that some of the diagrams are "wrong"? In what sense are they wrong?

user228700

Lol, yes, precisely. I don't know how, really; some have been updated in subtle ways, it would seem.

0celóñe7

@Kaumudi.H pics of your drawings?

user228700

@0celóñe7 Haven't started yet :-P I'll post a few after I'm done.

user228700

11:18

The poker is the first one on the list, so...

ACuriousMind

@Kaumudi.H wat

Sounds like you should ask your teacher what exactly he meant by "not correct", I think

user228700

Yeah.

user228700

Well, she said exactly that; some of them have changed over the years since the manual was published.

ACuriousMind

Ohhh, so the manual may depict an older version of the tool which is not what you'll be using?

user228700

Exactly.

ACuriousMind

11:20

(Also, why do you need to draw the tools? I've never needed to make anything but very stylized drawings)

AccidentalFourierTransform

0

Q: i know what is the buoyancy force acting on a soli body body but what is the buoyant force when the body is hollow

A empty cylinderical bucket when forced with its open end first into the water untill its lower end is below the surface then what will be the buoyant force acting on it?

fluid-statics

> force acting on a soli body body

user228700

...to be completely correct, however, we will not be using most of these tools in the first place -_- GAH.

ACuriousMind

@Kaumudi.H Drawing them sounds like a horribly boring waste of time, then :P

user228700

@ACuriousMind Yeah, tell that to the university :-(

user228700

@ACuriousMind MY POINT EXACTLY, you see!

user228700

11:21

Anyway, OK, don't mind me as I slip into drawing purgatory for awhile. I'll keep coming back to ask more questions :-P

AccidentalFourierTransform

good luck with that

and remember, green is not a creative colour

user228700

x'D (Y)!

Sid

Why would you want to color your drawings?

Heh, I would rather pay my friend to do my diagrams than do them myself

AccidentalFourierTransform

now let's all agree to never be creative again

user228700

Incidentally, I decided to switch to calculus for a bit and have a quick question (ah, back to this :'-). What is meant by a closed-form expression? My textbook says that it is one in which the number of terms doesn't vary but Wikipedia says something apparently different to this:

user228700

11:32

> "A mathematical expression that can be evaluated in a finite number of operations."

user228700

Huh?

ACuriousMind

I'm with Wikipedia: A closed-form expression is one into which you can plug in numbers for the variables and get a result.

For instance, a polynomial is a closed-form expression, an infinite series is not.

AccidentalFourierTransform

there is no unique definition of closed-form

anything can be closed if you use a lax enough definition

ACuriousMind

True enough

AccidentalFourierTransform

in essence, it means that the expression contains polynomials, trig functions, exponentials and logarithms

and nothing else

ACuriousMind

11:34

But it depends on the definition of "operation", then, I think most would agree with the Wikipedia definition, even if they interpret it differently

0celóñe7

Is sin(x) closed form?

AccidentalFourierTransform

not unevaluated intergrals, not infinite series

user228700

Hmm...

AccidentalFourierTransform

yeah, if sin(x) can be evaluated in with finite number of operations, then so can erf(x), etc

user228700

Tell me this. Is $S_n=a+ar+ar^2+ ... +ar^n$ a closed form?

user228700

11:36

My textbook says that it isn't and that the following is:

AccidentalFourierTransform

that includes a series, so it may not be considered closed form

Sid

@AccidentalFourierTransform But.. it's not infinite

AccidentalFourierTransform

otoh, $a\frac{1-r^n}{1-r}$ is its closed form expression

0celóñe7

Bessel functions are defined exactly like sine/cosine. Are they closed form?

They certainly make us queasy

user228700

@AccidentalFourierTransform Yup, that is what I was typing.

user228700

11:38

I don't understand the clear distinction though.

AccidentalFourierTransform

IIRC there is a theorem due to Lagrange (?) about when integrals can be evaluated in closed form, and the definition of closed form in this context includes what I said: composition of rational, trig and exp functions, and their inverses

Sid

...but that's exactly what that series is. You are telling that, before evaluating that, it's not a closed form expression and after applying the formula, it is?

AccidentalFourierTransform

yeah, if a formula includes unevaluated integrals, or unevaluated series, it is typically not considered a closed form expression

the series one may be considered closed form, depending on context

there is not a unique definition

user228700

And what do you mean by unevaluated?

AccidentalFourierTransform

$\int \mathrm e^x\,\mathrm dx$ is unevaluated

$\mathrm e^x+C$ is evaluated

they are the same thing

but the first one includes a $\int$ sign

so the integral is unevaluated

not every integral can be evaluated, e.g. $\int\mathrm e^{-x^2}\,\mathrm dx$

so we say that such an integral doesnt have a closed form solution

user228700

11:41

@AccidentalFourierTransform So do you mean to say expressions with a bunch of operators in it?

AccidentalFourierTransform

it depends on what you mean by "operators"

user228700

(Excuse the dumbness)

user228700

@AccidentalFourierTransform :-( What would count as an operator?

Sid

@AccidentalFourierTransform Do you mean, integrals that can't be evaluated or those that we are too lazy to evaluate?

user228700

@Sid x'D

0celóñe7

11:43

@Sid integrals that we don't know how to evaluate

AccidentalFourierTransform

Liouville's theorem (differential algebra)

In mathematics, Liouville's theorem, originally formulated by Joseph Liouville in 1833 to 1841, places an important restriction on antiderivatives that can be expressed as elementary functions. The antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions. A standard example of such a function is e − x 2 , {\displaystyle e^{-x^{2}},} whose antiderivative is (with...

there you go

Liouville≠Lagrange

user228700

...but I don't care about integrals.

0celóñe7

Leave then

Balarka Sen

what is going on

0celóñe7

Integrals are the most important thing in mathematics

user228700

11:44

@0celóñe7 But I do need to understand what it basically means.

Balarka Sen

what is le question

excuse my french

AccidentalFourierTransform

Closed-form expression

In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations. It may contain constants, variables, certain "well-known" operations (e.g., + − × ÷), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit. The set of operations and functions admitted in a closed-form expression may vary with author and context. Problems are said to be tractable if they can be solved in terms of a closed-form expression. == Example: roots of polynomials == The solutions of any...

see the table there ^

user228700

@BalarkaSen Le question is "What is a closed form expression?"

AccidentalFourierTransform

actually, that table is wrong

0celóñe7

A form a is closed if da=0

AccidentalFourierTransform

11:45

it says that gamma, bessel, etc are not closed-form expressions

wtf

Balarka Sen

@Kaumudi.H Usually an adjective applied to antiderivatives/indefinite integral of various functions. Basically whatever that has an antiderivative you can express in terms of functions you know.

A good waste of time is to convince yourself $\int \sin(x)/x \, dx$ has no closed form.

(You can't find the antiderivative of $\sin(x)/x$ in terms of trigonometric, algebraic, logarithmic and exponential and various other functions you know)

AccidentalFourierTransform

the relevant example was $\sum ar^i=a\frac{1-r^n}{1-r}$, the r.h.s. being a closed form expression for the l.h.s.

user228700

^

0celóñe7

@BalarkaSen how is that proof supposed to go

AccidentalFourierTransform

Liouville's theorem

Sid

11:47

@0celóñe7 Since when did Physicists begin to ask proof? :P

user228700

And I don't understand it yet, despite all the talk about integrals.

Balarka Sen

@0celóñe7 i have no flipping clue

@Kaumudi.H I would consider the sum to be a closed form as long as it's finite.

AccidentalFourierTransform

rule of thumb: if an expression contains any of $\sum,\prod,\int,\lim,\frac{\mathrm d}{\mathrm dx}$, it is not a closed-form expression

Balarka Sen

But honestly, closed form is really an adjective for antiderivatives of functions

user228700

@AccidentalFourierTransform I was just about to say "I understand it now" in response to Balarka but your message made me literally say "Wtf".

0celóñe7

11:50

@Sid since when am I a physicist

Why would you insult me

AccidentalFourierTransform

@Kaumudi.H yeah, as I said, sums may or may not be considered closed-form expressions

but from your example before, I believe you are not expected to consider them closed form

user228700

Nope, I am not.

Balarka Sen

What is considered as a closed form or not varies textbook to textbook. There's really no standard definition.

user228700

OK, I have a vague idea of this now and think I can proceed. THANK YOU ALL! :-)

The Raiders of Las Vegas

@0celóñe7 What?

AccidentalFourierTransform

11:52

👍👍

0celóñe7

What is pi if not a limit

The Raiders of Las Vegas

A ratio.

Balarka Sen

It is a limit, but I am sure there are ten million ways to define it.

AccidentalFourierTransform

$\arccos(-1)$ pls

Balarka Sen

arccos is a limit bruh

it's series

AccidentalFourierTransform

11:55

no its not bruh

its the inverse of an integral

Balarka Sen

an integral is a limit bruh

AccidentalFourierTransform

no its not bruh

Balarka Sen

yes it is bruh

AccidentalFourierTransform

its the solution to an ODE

The Raiders of Las Vegas

C/D

Balarka Sen

11:56

Ok, you got me there. That's one possible way to do it.

AccidentalFourierTransform

"an ODE is a limit bruh"

Balarka Sen

Define trigonometric functions as solutions to some ODE's and then define arccos and define pi.

0celóñe7

@AccidentalFourierTransform what ode

Balarka Sen

@AccidentalFourierTransform Oh. A derivative is a limit bruh

gg get rekt

AccidentalFourierTransform

no its not bruh

its... a... vector field?

Balarka Sen

11:57

HAH

0celóñe7

Try defining real numbers without limits of some kind

Real numbers are not closed form

AccidentalFourierTransform

dude, real numbers are exact

The Raiders of Las Vegas

^

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