serious-discussion

[tacit tulip]

nice

[surreal sapphire]

once its published, come back

[tacit tulip]

good for u

[frail snow]

Only over function fields though

[alpine kindle]

<@&268886789983436800>

[mental stratus]

wtf fuck off

[upbeat shore]

@cold needle

[neat lintel]

alright @mint patio

it's easiest to start with the inverse function theorem

[mint patio]

I wrote what I interpreted then got told it was kinda wrong immediately after

[neat lintel]

i can look after

food is consumed

username attained

ready to game

[mint patio]

let us game son I’m ready to learn

[neat lintel]

the inverse function theorem is basically: if the best linear approximation at a point to a function is invertible, then the function is locally invertible around the point

why is this plausible

[mint patio]

I can give you an intuitive answer but not a formal one lol

[neat lintel]

well the best linear approximation at p is the linear map Df(p)

and what that means is f(x) = f(p) + DF(p)(x - p) + o(x - p)

o(x - p) meaning terms going to zero faster than x - p does

[mint patio]

Mhm

[neat lintel]

these are negligible if you get reeeealll close to p

[mint patio]

Yep

[neat lintel]

so rrrreeeeeeallll close to p you have f(x) = f(p) + DF(p)(x - p)

not = but you know

squiggly equals

[mint patio]

Yes

[neat lintel]

well when is this simpler guy invertible

when DF(p) is

[mint patio]

ayaya

[neat lintel]

so if f(x) ≈ f(p) + Df(p)(x - p) then you would expect to have something like f^{-1}(y) ≈ p + DF(p)^{-1}(y - f(p))

did i get that one right lemme look

yeah

please forgive me using f and F interchangeably

[mint patio]

mfw I didn’t even notice (I am converting mentally 🤓)

[neat lintel]

some harder thinking and you might even say f^{-1}(y) = p + Df(p)^{-1}(y - f(p)) + o(y - f(p))

the actual proof of the inverse function theorem, at least the one in spivak, is just making sure you can actually go from "really close to invertible map" to "invertible map"

implicit function theorem

the corresponding linear algebra thing is solving systems like Ax + By = 0 for y in terms of x

why

well say you have a nonlinear system of equations f(x, y) = 0 and you want y in terms of x near a point (a, b)

when you take the linear approximation at (a, b) you'll get a linear system of equations (a breeze to solve. so easy)

f_x(a, b)(x - a) + f_y(a, b)(y - b) = 0

i probably should have mentioned i wanted B to be square

[mint patio]

any determinant needers in the chat

[neat lintel]

[neat lintel]

so this is the best linear approximation to the nonlinear system of equations f(x, y) = 0 near (a, b)

solve.

to get y in terms of x you need f_y(a, b) to be invertible

the implicit function theorem says that, if you can solve this approximating linear system, then you can solve the non-linear system locally

[mint patio]

I sort of see why they’re the same

[neat lintel]

in linear algebra, invertibility of a matrix and the condition of whether you can solve a system of equations involving the matrix are the same

so of course the theorems in calculus should be the same!

proof: just try to adapt the linear algebra proof to calculus

[mint patio]

I never really learned rank stuff properly so that’s the one I don’t know or understand

[neat lintel]

if the rank of a matrix is r then it can be put into the form

I_r  O
O    O

I_r the r by r identity matrix

this is the only fact you need to know for the constant rank theorem

(the Os may be of different sizes but they're all just matrices with only zeros)

[mint patio]

Yes

[neat lintel]

so well

you can probably guess how it's going to go

if a mapping's best linear approximation looks like this I_r OOO thing then the function ought to look like it locally

there is one small issue

[mint patio]

I’m guessing it’s just if constant rank within nbhd then you guarantee invertibility within nbhd

[neat lintel]

not invertibility

constant rank applies to maps from any R^m to any R^n

but yes constant rank is the condition

[mint patio]

If the differential isn’t square?

but isn’t that related to invertibility

[neat lintel]

only square ones can be invertible, and, in that case, invertibility is the same thing as maximal rank

anyways

[neat lintel]

if the mapping looks like this, i.e. looks like (x_1, ..., x_m) -> (x_1, ..., x_r, 0, ..., 0), then that forces its derivative to have rank r not just at one point, but near the point you were considering

so constant rank is a necessary condition for the result to hold

it is also sufficient. cool

because a matrix has rank at least r if it has a non-vanishing r by r minor, the rank of a matrix cannot drop suddenly

so you just have to make sure that the rank isn't jumping near your point

in particular if you have maximal rank at the point you have maximal rank near the point

this is how you get the inverse function theorem out of this

when square maximal rank is equivalent to invertibility

[mint patio]

ahh ic

that one’s cooler than the other two

maybe that’s bc I’m less familiar with it though 😛

[neat lintel]

so true

[mint patio]

Thank you for explaining

[neat lintel]

tu's manifolds book has an appendix going over all of this

[mint patio]

I don’t think I’m ready for this subject

I mean I understand the concepts, I’m just an absolute Cox-Zucker when it comes to proofs and manipulating objects lol

but ig that means I don’t understand very well huh?

[molten ibex]

why chatgpt chan nit solve elementary algebra problems?

[mint patio]

bc it sucks for math

use a CAS

It’s a text generator

[molten ibex]

cas is artificial inteligence?

[mint patio]

As in Computer Algebra System

Wolfram, Sage, MATLAB, etc

[languid marten]

ChatGPT is good with providing correct definitions but can't do even simple arithmetic correctly

[mint patio]

Funny enough

it helped me a lot with my fluids hw

LOL

I had it solve some NS for me

[neat lintel]

nah, it's not even good for this as well

[mint patio]

just ignore viscous terms

easy 👍

[neat lintel]

i saw someone try to ask it what the third isomorphism theorem was and it produced a blatantly wrong statement

literal nonsense

[languid marten]

yeah it does some errors in defn as well but not as much as in computations

[mint patio]

the third isomorphism theorem according to chatgpt

[languid marten]

isn't stokes thorem or generalized stokes thm

[mint patio]

just call it stokes

generalized stokes if you want to be specific ig

[languid marten]

yeah

[mint patio]

That’s Stoke’s Theorem yeah

Man I remember

When I learned it the first time (or Kelvin-Stokes, rather)

And Moth was explaining the intuition to me here

That feels so long ago but also just like yesterday

[alpine comet]

Lmfao, Stokes at its finest

[mint patio]

That’s Yoneda’s lemma, excuse you

according to ChatGPT at least

[languid marten]

you can convince chatgpt into believing anything

[alpine comet]

Even if ChatGPT gets better at math, I will still study math tbh

There's no good if I can't verify if a proof is correct

[mint patio]

So true

[neat lintel]

<@&268886789983436800>

"frist trun off your antivirus"

any mods online

[livid gull]

Do you think it will get better at math?

It doesn't have any intuition

[alpine comet]

It doesn't need intuition

Math a lot of times boils down to knowing and applying tricks

And AIs are way better than us when it comes to that. Just look at AlphaZero

[neat lintel]

[languid marten]

does it mean it will not be able to come up with "new" proofs ever ?

[alpine comet]

These mfs discover new tricks in chess. I don't see why it's not possible for math

[alpine comet]

Oh, i'm sure it will

[languid marten]

that'll be cool specially the algorithms which will make it possible

[alpine comet]

There will be no algorithms for it tho

At the very end of the day, it's a hell lot of knobs being tuned just right so that it stumbles upon something

I think there's technically an algorithm to generate proofs: just enumerate all possible combinations of logic symbols. But it's so useless that you better just study math and do the proofs yourself

[languid marten]

hmm Can we solve open problems with AI somehow ?

like using that algirothm of enumerating all possible combinations of logical symbols

[alpine comet]

We did solve open problems with computers before

[languid marten]

hmm but mostly using it's computational powers ?

[alpine comet]

It's like enumerating all possible games of chess to find the winning moves

[languid marten]

how does this algortithm halt tho ?

like how does it get to the "correct" proof

[alpine comet]

You don't

that's the point of halting problem: you can't decide if a given program halts

[alpine comet]

this one halts because we know all chess games must terminate

but there are statements that are correct but not provable

[languid marten]

ig some of the open problems fall into this category ? like we don't know if it's provable withinn the given axiomatic system

So the task is to prove that it's unprovable within the given axiomatic system

[alpine comet]

We don't know 😄 we haven't found any statements like that

We know they exist tho

[languid marten]

CH ?

[alpine comet]

Nah, We proved that one is independent

[languid marten]

ig it's proven to be unprovable

ohh yeah independent of zfc

[alpine comet]

Godel's first incompleteness theorem implies that for any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system.

I think the second theorem shows that the consistency of the system is such a statement

either a system is inconsistent, then it's demonstrable, or it's consistent, but it cannot proves the consistency of itself

Idk, I don't study logic. And for good reasons

[languid marten]

idk if it's silly que but how do we extend that to talk about other domains in maths , like statements about abc... that are true but that are unprovable withinn the formal axiomatic system or we don't ?

[alpine comet]

They apply to all domains in math

You don't have to extend anything

[languid marten]

hmm then why godel's 1st incompleteness thm talks about natural numbers specifically

[alpine comet]

It's the weakest system you can possibly hope for

Anything below that is too weak to be interesting

[languid marten]

ohh yes So it's godel's weak thm

[neat lintel]

isn't this the theory of singularity

[sudden thunder]

Can anybody help me take this godforsaken calculator off test mode i'm about to claw my eyes out

[neat lintel]

what calculator is it

[woven whale]

ti nspire?

[sudden thunder]

yes cs ii t

i have the application

windows is recognising the calculator

but the application isn't

[woven whale]

I usually just use another calculator of the same model

[sudden thunder]

do you work for texas instruments and want me to purchase another calculator?

[woven whale]

Yes

do you like not

have anyone at school that has the same calculator as you

[sudden thunder]

i graduated

[woven whale]

skill issue

[neat lintel]

[sudden thunder]

thank you both this has been enlightening

[neat lintel]

if your only problem is getting it out of test mode there should be plenty of help online

could you not find anything?

[sudden thunder]

well my problem is that this is happening

getting it out of test mode should be fine assuming the app they made for it works

[neat lintel]

oh

[sudden thunder]

the only way to do it through a computer involves TI Inspire Computer Link

i have my calculator plugged into the computer

the computer is turned on since i'm using it to send these messages

and windows recognises it as a TI Inspire CX II-T

but somehow the app can't see it

oh god. i just realised that the free app doesn't work with my calculator and that I have to buy the student software

[eternal glen]

Texas instruments my beloathed

[sudden thunder]

damn right

[storm sage]

Be nice

[storm sage]

Be nice

[solar hawk]

english totally robbed latin for like half of its (english's) words

[bronze pelican]

@solar hawk what does your name mean

[solar hawk]

It doesn’t really have a meaning

Is it partially made of my initials though

[bronze pelican]

Amukh

[solar hawk]

I would explain but I don’t wanna dox myself 😭

[bronze pelican]

Don't

[echo tundra]

In hindi mukh means mouth so a mukh means mouthless

[echo tundra]

wait, I didn't dox you right? Should I delete my comment?

[solar hawk]

you didnt

lol

[echo tundra]

thanks xD

[solar hawk]

mukh means mouth/face in bengali too, what a coincidence

[echo tundra]

I mean north languages are pretty similar so not a big coincidence

[solar hawk]

ig

[jovial ember]

Chmonkey

[fervent seal]

im back

[neat lintel]

why did you name your account chmonkey

[jovial ember]

Hi pikachu

[mental stratus]

https://tenor.com/view/joie-pikachu-pokemon-bohneur-gif-20062195

[jovial ember]

Lol “bohneur”

[bright hill]

chmonkey french pilled

[jovial ember]

No it’s in the name of the gif they sent

[long matrix]

hi dqstupid

[echo tundra]

hey darq can I talk to you for a bit

[bright hill]

yes, but you recognized it

[bright hill]

sup dummy cat

[echo tundra]

@bright hill hello, just want to talk about the custom server

[rocky shuttle]

[long matrix]

hssssssssssssssssss

[hollow widget]

yo guys i really need hhelp
i have a finaly exam after tmrw
and i cant find my geomerty book
its called "geometry 2018 student edition"
if anyone has it please dm me

[river moon]

search up Pontryagin

the dude was blind from like the age of 14 and has quite a bit of theorems named after him

[alpine kindle]

mathematics is, with one viewpoint, entirely abstract so yes probably

[zealous garden]

That's how computers do it

[little vine]

Is Euclid the best Geometry book? Not for someone in junior high but for an older student/mathematician who'd care to learn it for some unknown reason

[solid yarrow]

Any recommendation which book I should get, after the "Book of Proof" in terms of preparation for university?

[woven whale]

terence tao's analysis

[solid yarrow]

I read the discription. Sounds quite interesting.

[mental stratus]

and gallian for aa

[solid yarrow]

What is aa?

[mental stratus]

abstract algebra

axler for linear algebra is good too

these three are like classic recs for anyone begin the next step

[solid yarrow]

So for abstract algebra gallian, analysis terence tao and linear algebra axler?

[vast surge]

I'd say pinter for abstract and ladw for linear.

[solid yarrow]

I am not so sure if I get them through till uni starts 😦

[vast surge]

Axler is not a good book. Determinants are an important part of LA, and his "determinant-free" approach is mind-boggling.

[solid yarrow]

So I should swap axler with pinter?

[vast surge]

Swap axler for ladw

[solid yarrow]

Ladw?

[vast surge]

I like Pinter better than Gallian for the exercises, but I think Gallian is fine

[vast surge]

Linear Algebra Done Wrong

[bronze pelican]

Axler is good

[vast surge]

Except for how he does determinants.

In the very last chapter

[river moon]

"determinants are an important part of LA"

[vast surge]

They are!

[solid yarrow]

Ok quick question. What do you think about the "Book of Proof"? For introduction purposes.

Bc I am currently reading it.

[vast surge]

It helps you learn to write proofs

[solid yarrow]

So useful?

for uni

[vast surge]

It's useful

Axler does eigenvalues and eigenvectors before he does determinants though

[river moon]

now that's sus

[vast surge]

Yeah

[solid yarrow]

The questions is, am I able to work through those books till uni or even do I have to?

kind of worried

a bit

[vast surge]

Those are all textbooks for courses you're expected to take in your first year or so

If you're American you might take 3 years going through them. If you're a Brit it might just be your first year.

[solid yarrow]

So it's supporting material after the courses?

[solid yarrow]

German.

[vast surge]

No, it's the textbook for the course.

[vast surge]

Ah. I'm not as familiar with the german system.

[solid yarrow]

You get textbooks for the courses?

Thats new

[vast surge]

Yes.

[solid yarrow]

Interesting.

[vast surge]

You need to read the textbook as well as attend lectures

[solid yarrow]

Are solutions in the books?

Or do you get solutions?

Or something alike

[vast surge]

Generally there are not solutions to exercises in textbooks at this level

I think Pinter includes some hints

And solutions to very simple computational problems

[solid yarrow]

So how you does one find out if you he's right?

guess work?

[vast surge]

You generally know.

[solid yarrow]

ok

Man I wish I could do more advanced math... I find those topics I see around so interesting. And then I realize that I am not even at the beginning.

[vast surge]

Just start studying and keep studying and you'll get there

I'm starting my PhD in a couple months and I'm still just starting off in math

[solid yarrow]

What topic?

[vast surge]

Mathematics.

I'm not sure anything more specific than that yet

[solid yarrow]

Hm.

What does a math PhD do?

[vast surge]

Math

I'm going to be grading probably calculus

And taking advanced courses

Then in a couple years doing research

[solid yarrow]

What do you do in calculus?

[solid yarrow]

Sounds interesting.

[vast surge]

I will probably have a discussion section, and then I will grade homework.

That is my guess.

[solid yarrow]

Hm.

[vast surge]

Unless you mean, like, what is calculus

In which case it's calculating derivatives and integrals

[solid yarrow]

That would have been my guess.

[vast surge]

So in calculus you learn to compute things like this integral: $\int_{0}^{1}x,dx=\frac{1}{2}$

[fathom swallow]

Zorn's Lemming

[solid yarrow]

With compute, you mean what exactly? Typing it in a program?

[vast surge]

Calculate

[solid yarrow]

Hm.

That's what I have been taught at school.

[vast surge]

Yes, the American curriculum is a bit slower.

Lots of people don't see calculus until they start college

[solid yarrow]

Ok. In Germany we see integrals in "Gymnasium". I don't know the correct school system, so...

But it is the "highest" school, but still under university.

[bronze pelican]

Thats a good integral

[vast surge]

In America a gymnasium is where you go to do exercises, run on treadmills, use those bike things, lift weights, etc.

[solid yarrow]

xD

[vast surge]

It's the best one that I know.

[solid yarrow]

I am still wondering which books I will have to buy when i enroll uni.

[vast surge]

It depends a lot on the professor teaching the course

[solid yarrow]

Because it could become a problem, if i buy a book which i then won't use.

[vast surge]

At my UG some professors used Pinter, some used Gallian when teaching algebra

It depends on who's teaching it when

[solid yarrow]

so i should wait with buying?

[vast surge]

Buy if you want to self-study before you start

If you only want the books you'll use in your courses, then wait

[solid yarrow]

i mean i want to study math, but i am worried that i might buy books that i will later on not use. i mean i only have a few months till uni, so...

[vast surge]

Then finish reading book of proof now

What math courses are you in next semester?

[solid yarrow]

I am at the last big chapter.

[solid yarrow]

I am starting uni. So I am not sure.

Propably linear algebra, i guess.

[woven whale]

linear algebra 1 and analysis 1 is the standard for first sem in germany

[vast surge]

LADW is free on the internet.

Read that

[woven whale]

maybe also an intro to programming

[vast surge]

Are German undergrad programs more analysis-oriented than algebra-oriented?

[woven whale]

Yes

at least at my uni you are required to take analysis 1, 2, 3 which includes measure theory and analysis on manifolds

and algebra 1 is optional

[vast surge]

Oh, wow.

[solid yarrow]

?

[vast surge]

That is a very strong analysis bias

What do the germans who want to do algebra do?

Suffer?

[woven whale]

you can take like numerical analysis instead of algebra 1 lol

[woven whale]

maybe other unis are more algebra pilled

[vast surge]

Maybe

[woven whale]

my uni has a big numerical department

[vast surge]

Ah that makes sense then

[solid yarrow]

Where do you study?

Do you get books recommended by your prof? Like at the beginning of your courses?

[woven whale]

yeah profs usually give literature recommendations

or say what book they are basing their course off

[solid yarrow]

i like the approach, idk why though

[vast surge]

Do you have any German textbooks or do you just use the popular ones in English?

[woven whale]

I have this one german category theoretical algebraic geometry textbook

and one on numerical analysis

but nowadays I just use online pdfs

[solid yarrow]

Wait... are most math books free online pdfs?

[woven whale]

first book of the bible in your favorite library...

[solid yarrow]

?

[vast surge]

Ahoy, maties! Walk the plank! Arr!

That's how to get free pdfs.

[solid yarrow]

But you need to sign up.

[woven whale]

usually I just search for "<book title> pdf" though lol

fwiw you can log in with your uni account on springer and get books that your uni purchased

[solid yarrow]

hm

Do you keep notes of those books? Or do you just do the problems?

[woven whale]

I do notes if I feel like it

or if I can't ctrl + f the book

[solid yarrow]

So in general just the problems.

[woven whale]

wait you guys do the problems?

I just play spectator

[solid yarrow]

but if the pdf is longer than 100 pages, how do you keep track where you left off?

[woven whale]

I use obsidian to read pdfs

if you close the app on page 69420 then next time you open it again it will resume on page 69420

[solid yarrow]

is it free?

[woven whale]

yes

https://obsidian.md

[solid yarrow]

interesting

Got any more tips I need/ should know before uni?

[woven whale]

git gud

[solid yarrow]

that was the plan

xD

[solid yarrow]

I was looking up this book. Do you mean "Contemporary Abstract Algebra" by Gallian?

[mental stratus]

yep

[solid yarrow]

k thanks

[mental stratus]

Heard good things about it

[livid gull]

yeah dude

i feel like uni is needlessly hard in germany

[storm sage]

BASED

[velvet dagger]

How have your opinions gotten that bad

[neat frost]

use LaTeX dummy

[woven whale]

it's mathjax + markdown

[mint patio]

@storm sage what’s your youtube channel

also I’m going to get you to help me learn algebra

also also I think I’m going to become algebra pilled just so I can get away from point set topology

@woven whale I like projective :3

[woven whale]

I am planning on changing my minecraft name to that too

[mental stratus]

about me

[mint patio]

I forgor my MineCraft account :sadge:

Maybe once I’m a big boye and can play games as much as I want

[neat lintel]

[woven whale]

🫂

[storm sage]

They always were

I wanna learn numerical analysis 🥺

[storm sage]

https://www.youtube.com/channel/UCfphydDz_mF1ICH0N18QwrA

[storm sage]

Sure thing fren

[neat lintel]

what is wrong with point-set topology?

[mint patio]

open and closed sets

why’s there gotta be two :sadge:

and then there’s CLOPEN too like wat the fuck

it’s that hitler video all over again

[neat lintel]

this really isn't that confusing

[mint patio]

why can’t there just be

set

(excluding category theory fuck that too)

[mint patio]

no idk what I’m complaining about LOL it’s just hard writing proofs :sadge:

[neat lintel]

most of basic point-set topology is supposed to be incredibly straightforward

it's good proof writing practice

[mint patio]

shh let me whine in peace I’ll come back to it one day :3

I do the algebraic analysis 👍

become new eric tao

[neat lintel]

if you do commutative algebra you are going to have to grapple with open and closed sets

if you do analysis you are going to have to

like

this isn't really something you can reasonably avoid

[mint patio]

yes I know :hehe: but it’s so much easier than the spaghetti that goes on in m*nifolds

[jovial ember]

They’re all the same thing

Bruh

[neat frost]

im aware what it is
Doesnt change my opinion
use LaTeX dummy

[jovial ember]

This is like saying there’s blue and not blue

I guess not the perfect analogy

[solid yarrow]

What is LaTeX? Have only heard of it.

[neat frost]

It's a language for typesetting documents

It has very tools for typesetting math and so is very popular in academia

[solid yarrow]

Do you learn that in university?

I mean like writing it

[neat frost]

you learn it yourself

idt unis usually provide a course on it

[solid yarrow]

do you need a specific program for it?

to write it

[leaden torrent]

no, its a language

so you need a program or software to compile it

but you can write it with any text editor

[solid yarrow]

hm, interesting

[leaden torrent]

like how you can write C++ in any IDE, but you need gcc or something to compile it

[solid yarrow]

like vscode?

or something similar?

[leaden torrent]

sure

there are dedicated latex editors though

but again those dont usually come with a compiler

the standard latex distros on windows are miktex and texlive

idk about other platforms

and then you can write it in whatever text editor you prefer, though there are dedicated latex editors (e.g. texstudio)

there's also overleaf, an online latex editor

good for collaboration on the same document

[solid yarrow]

what would be your recommendation?

like for an absolute beginner

[neat frost]

vim+TeXlive is the way to go

[leaden torrent]

personally i use miktex + texstudio

[neat frost]

overleaf

[leaden torrent]

but overleaf is the most beginner friendly

no need to install anything

it holds your hand a lot

[solid yarrow]

might give it a try in the future.

by the way... i was wondering about implications. Why does math have two symbols for that? Like an single arrow and a double arrow?

Are they used in different ways?

[neat frost]

like $\rightarrow$ vs $\Rightarrow$?

[solid yarrow]

yes

exactly

where's the difference?

[leaden torrent]

just down to the preference of the author

no real difference

anecdotally $\rightarrow$ feels more common among philosophers and logicians, and $\implies$ feels more common in most other settings

[fathom swallow]

namington

[neat frost]

Though single-stroke arrows are used for many other things in math as well, so double-stroked arrows stand out more

[leaden torrent]

yeah i personally prefer \implies since its less likely to get confused

[woven whale]

my uni has a semesterly latex course organized by the faculty

[solid yarrow]

obligatory?

[leaden torrent]

$\exists f^{-1}\colon ℝ \to ℝ \implies f$ is bijective

[woven whale]

no

[fathom swallow]

namington

[woven whale]

wait people use rightarrow for implies Lmao

[solid yarrow]

so in general use the double arrow, just to make sure.

for implications

[leaden torrent]

yeah, ive only really seen the single arrow used in the context of formal logic or philosophy

(and in formal logic its because theres often a distinction between syntactic and semantic implication)

[solid yarrow]

Good to know.

Hopefully my uni also provides that.

When I am enrolling.

[woven whale]

what uni will you be going to?

[solid yarrow]

Still not so sure.

[neat frost]

I think LaTeX is not too hard to self-learn

[solid yarrow]

You think? I looked up some and it seems like HTML code to me.

Or in other words, complex.

[neat frost]

it is very different from html

for one it is not stupid

and its meant for typesetting documents, not webpages

[fathom swallow]

pikachupikachu

[solid yarrow]

I know. But it still seems so new to me.

But I guess that comes with practice and stuff.

[neat frost]

everyones new before they learn something

[solid yarrow]

true

[neat frost]

read a few tutorials and whatnot

[solid yarrow]

any recommendation?

[neat frost]

sure

,help tex

[fathom swallow]

`tex` command documentation. (Aliases `,`, `mtex`, `align`, `latex`, `texsp`, `texw`, `tikz`.)

Usage

,, <equations>
,tex <code>
,align <align block>
,texsp <code>
,texw <code>
,tikz <code>

Description

Compiles and displays LaTeX document code. For a quick introduction to using LaTeX, see one of the resources linked below.

The output is extensively configurable, see ,help texconfig for more information about the possible configuration options.

LaTeX macros and packages may also be used in this command via inclusion into the preamble, see ,help preamble for more information.

If a guild or user has latex recognition enabled (see ,config latex and ,help autotex), messages containing LaTeX will automatically be compiled and this command is generally not required.

Aliases

​ ​ ​ ​ ​ ​ tex: Code is compiled in the default document environment.
, or mtex: Code is rendered in math mode, in a gather* environment.
​ ​ ​ ​ align: Code is rendered in math mode, aligned in an align* environment.
​ ​ ​ ​ texsp: Same as tex, but ||spoiler|| the output image.
​ ​ ​ ​ ​ texw: Don't pad the output (with transparent pixels) after compilation.
​ ​ ​ ​ ​ tikz: Code is rendered in a tikzpicture environment.

Related

​ ​ autotex: Toggle whether your LaTeX is automatically rendered.
​ preamble: View or modify your LaTeX preamble.
texconfig: View or modify your personal LaTeX rendering options.

LaTeX Resources

Our own LaTeX cheat-sheet
LaTeX Mathematical symbols for undergrads (and everyone else)
Find a LaTeX symbol by drawing it on Detexify
Friendly introduction to mathematical LaTeX, with links
TeX Stackexchange, where every question has been asked before
The LaTeX Support Discord server, origin of the LaTeX Support Network!

Examples

,tex This is a fraction: \(\frac{1}{2}\)
,, \int^\infty_0 f(x)~dx
,align a + 1 &= 2\\ a &= 1
,tikz \draw(0,0) circle (1);

Have more questions?

Visit our support server here to speak to our friendly support team!

[optional] and <required> denote optional and required arguments, respectively.

[neat frost]

Under LaTeX Resources are a few

Overleaf has many good ones

[solid yarrow]

Overleaf saves the day again.

[velvet dagger]

For some reason I forgot to respond to this all day but I opened my computer and this was one of the first messages shown since it takes a sec to load

So I remembered it

Honestly? Numerical analysis I could see being interesting

Like idk much about it but

I'm guessing the idea is like, hey here's some shit you may wanna do

Solve some matrix equation or differential equation or whatever it may be

What are some methods to estimate shit? How quickly do they converge? etc

Probably not my cup of tea but I could appreciate it

I have analysis psets from a couple years before I took it and one problem they had is what I imagine numerical analysis to be on some level

Like that's kinda nifty. The coding part would probably make me wanna commit sudoku, healthy as it is

@sharp mulch maybe confirm I'm not talking too much shit?

Anyway my thing earlier was more just the fact that you didn't have to do algebra lol

[sharp mulch]

Huh what

[velvet dagger]

Just like, was that a total mischaracterization of numerical analysis lol

[sharp mulch]

A big part of numerical analysis is numerical linear algebra so solving Ax=b, factoring A=PLU/LL^T/QR/USV^T, multiplying C=AB effectively

Another big part is solving ODEs/PDEs

And you do want to have error bounds and convergence rates

[velvet dagger]

Gotcha

[lavish hull]

I never heard of PLU

Cholesky,QR and SVD I get

Not sure what PLU is

[river moon]

have you heard of LU decomposition

[mint patio]

The classic

[lavish hull]

Yes

what is the P matrix?

[river moon]

PLU or LUP is just LU with some Permutations

[lavish hull]

oh cool

if you dont mind what do you study?

[river moon]

optimization and machine learning

[lavish hull]

cool stuff id say

i took a computational stats class

all my exposure to numerical linear algebra was in one class

i enjoy the topics

im assuming ur in academia

so what specifically do you study

[river moon]

no

[lavish hull]

o cooler then

industry is cool

[neat lintel]

Hmmm

Is $\mathfrak L$ better or $\mathcal L$ better for Laplace transforms?

[fathom swallow]

brotherImusttalk1234

[mint patio]

The latter

Please

[neat lintel]

Hmmm I use that for lagrangians

$\mathscr L$

[fathom swallow]

brotherImusttalk1234

[neat lintel]

Huh

[ripe dirge]

L moment

[river moon]

use \mathfrak if you want to have a book that feels like it has been written in 1950s

[alpine kindle]

$\mathcal L$

[fathom swallow]

ally ❤ (semaluhtounuyulohowwah)

[echo tundra]

$\mathfrak L$

[fathom swallow]

numbpy (anti-glomed)

[midnight kayak]

$L$

[fathom swallow]

MochaOhwelp

[fervent seal]

hi

[eternal glen]

I once attended a talk on Lie algebras where they referred to mathfrak as the "spooky vampire font" and honestly valid

[little vine]

$\mathfrak{I've come to suck your blood}$

[fathom swallow]

cali5nia

[little vine]

Checks out

[solid yarrow]

weird flex?

[eternal glen]

is that seriously what $\mathfrak{y}$ looks like ew

[fathom swallow]

dirichlettt

[eternal glen]

I was wondering why there was a random eta in there xddd

[neat lintel]

wtf

eta on

drugs?

[cyan goblet]

$\mathfrak{S}, \mathfrak{G}$

[fathom swallow]

anamono for anamono 🍓

[vocal vessel]

Why are you mad at y? Look at k!! 😱

[zealous garden]

,, \mathfrak{Transylvania} \subset \mathfrak{Romania}

[fathom swallow]

wraithlord_kobordism

[zealous garden]

That's so not a T

That's an I

[cyan goblet]

$\mathfrak{J} \mathfrak{I}$

[fathom swallow]

anamono for anamono 🍓

[eternal glen]

Professors using p and rho as variables except so much worse

[trim vessel]

yo dm me if you can help me with something that involves joining a server a using the search bar to find something

[jovial ember]

Chmonkey

[neat lintel]

Yo is Khan Academy and a few past papers enough for an AP Exam

[solid snow]

Most likely not

[rain plinth]

1-905-442-4151

[wet berry]

The hell

[neat lintel]

what else would you recommend

[solid snow]

some book

james stewart or ron larson's "Calculus" books

[neat lintel]

do they cover all of single var

[solid snow]

yes

[languid marten]

Okay , So Linear transformations are a type of vector valued functions that maps V to U such that L(x+y) = L(x) + L(y) and L(ax) = aL(x) where x , y ∈ V and U respectively and a ∈ F(X,+,×) have I understood this correctly or Am I missing something ?

[mental stratus]

what are F and X

[sturdy kindle]

They mightve been hacked

Same message in 3 different channels on the same minite

[languid marten]

any field over a set X

[mental stratus]

and X?

[languid marten]

a set

[mental stratus]

so what is the relation between X, and U,V

Because you can't leave that unspecified

[languid marten]

hmm U and V are any vector spaces and F is a field over a set X , wdym by relation between X and U,V ?

[mental stratus]

That makes no sense, a linear mapping is only defined between vector spaces that are over the same field

[languid marten]

ohh yes right So vector spaces U and V are defined for scalars belonging to X (i.e over the field F)

[mental stratus]

So if F is your field then your v.s. U and V have to be over the field F and a linear mapping from U to V is any mapping that preserves the alg str.

[mental stratus]

If your field is X then yes

[languid marten]

yeah sorry I forgot to mention that

[bronze pelican]

Chair monkey!

[fair mural]

looks like some weird character from gumball

[languid marten]

Does it hold for finite elements fields as well ? (Sorry for the ping)

[solar hawk]

what does over mean

like a vector space is over a field means it gets it scalars from that field

what does a field over a set mean

[languid marten]

It means the elements of the field belong to that set

[solar hawk]

so X is F?

[languid marten]

F is a algebraic structure equipped with two binary operations and it's elements belong to the set X

[solar hawk]

okay

a field is a set itself though

[mental stratus]

the definition doesn't care about that but a lot of the theory developed in linear algebra is over fields with characteristic zero, and these are infinite. the mapping N^{X} to the field F defined k |--> k.1 is injective, indeed if for m, n in N^{X} if m.1 = n.1 then (m-n).1 = 0 and by the fact that a field does not have divisors of 0, m-n=0 which means m and n are the same therefore proving the injectivity of the said mapping

[solar hawk]

pika where did you learn linear

from a book?

[mental stratus]

N^{X} is just naturals without 0

Haven't finished learning it entirely lol, mostly axler, and morton curtis and a bit of this bit of that, did some abstract algebra from hungerford to make myself with some of that terminology, helps out a lot when you get to linalg knowing some group thelry and basic facts about fields like the fields of characteristic zero being infinite

Also cosets

[solar hawk]

so you need abs alg for linear?

[mental stratus]

Nope.

[solar hawk]

ik what groups,rings, and fields are but idk anything further

[rugged blade]

trying to understand the mathematics behind general relativity a bit better. I know it's a long shot, but does anyone have any useful recommendations on books about Rieminnian geometry/differential geometry?

[blazing pawn]

Have you seen any differential topoology before

What is your background going in

[velvet dagger]

I think people like Wald? It seems like it discusses a good bit of math

But yeah your background is pretty relevant

[fallow pawn]

bye they didnt even help me i literally cheated my way to finish

[south kelp]

who u

[umbral forge]

is there a general number of classes a math major should take per semester in uni?

[forest vale]

i remember i took 6 classes per sem?
but it differs from each uni

[umbral forge]

thats fair

i can send the list of what i have to take if that helps

im ofc talking with an advisor but rn its by mails so its rly slow

[forest vale]

i think your advisor would give better opinion than me lol

[umbral forge]

thats fair

[forest vale]

so, even if it's slow, it worth asking

[umbral forge]

basically im gonna be taking at least algebra 1 and analysis 1

[forest vale]

sounds good

because the stuff in year 1 is generally easier, i took around 4 classes only in my last year

[umbral forge]

but yeah im in quebec so its different, i basically start as a U1 student

[forest vale]

each sem

[forest vale]

i see

[forest vale]

did you go through the syllabus or have you bought the books?

[umbral forge]

For the classes I’m taking next semester you mean?

[forest vale]

yep, i will usually skim through the websites of the class in the previous years and take a look at the table of contents

[umbral forge]

Thats a good plan yeah

I haven’t chosen everything yet cause I’m waiting on something but I can do that for the 2 I’ll be taking at least

[forest vale]

then you can try reading those stuff online and see if you can get used to them

[umbral forge]

Yeah I’ll try that

[forest vale]

i didnt prepare well enough for my analysis class in my first year, i failed it...

[umbral forge]

Is it because of difficulty or the different approach to math

[forest vale]

latter

[umbral forge]

That it’s like challenging

Yeah I heard everything is proof based

Well, a lot at lest

[forest vale]

I was so not used to the thinking process of it back then

[umbral forge]

Is it the same for algebra 1

I mean it does say methods of proof so I imagine so

Im just not sure the pace that’s expected to do everything

Anyway I’ll think it over and just wait for more answers from advisor thx

[forest vale]

I'm not sure if it is abstract algebra

[forest vale]

you'll have to get use to stuff real quick in year 1, then you'll be more comfy in later years

[umbral forge]

Mathematics & Statistics (Sci): Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.

That’s the info given on the class

So yes I think

[forest vale]

ah

[umbral forge]

I should probably take a good look at my linear algebra notes from half a year ago before I start this

[forest vale]

the divisibility and on stuff is kinda hard to understand at first

tbh it really depends on the lecturer/prof

but it's fun if you understand those!

[umbral forge]

Not sure what’s meant by divisibility theory

I already had a class that went into methods of proofs and complex numbers tho

[forest vale]

for that, you don't really have to learn in advance

I'd trust lecturer/prof's design of studying pace

(although some don't really care XD)

[umbral forge]

I just hope I get lucky

It’s for an honours class so it should be fine

Oh also last thing before I go

[forest vale]

yea?

[umbral forge]

I have 4 classes of algebra and analysis in total required

Is it better to do them like in a row

[forest vale]

hmmm

[umbral forge]

Aka not skipping a semester of one of those

[forest vale]

yea

i bet you'll have some guidance when your in the welcoming week of the department

senior students might help planning

(that's what i get, I'm not sure if you have the welcoming week though)

[umbral forge]

Pretty sure I do

[forest vale]

that's great then!

[umbral forge]

But yeah ill ask a lot of questions cause so many classes are required and the order is a bit not clear even with the prerequisites written out

[forest vale]

don't be too shy to ask, and you'll be fine

[forest vale]

ah

[forest vale]

my seniors did a list / table / mindmap for those

you can construct one in case you dont have it when it's time to apply for classes

it's a good logic practice

[umbral forge]

Mindmap is like a tree I imagine?

[forest vale]

yea

[umbral forge]

Yeah probably should do that

It will give me something to do

Alright see ya 👋 and thx

[forest vale]

cya!

[bronze sun]

Guys, please me help with this VSCode problem. I don't know what to do.

[ashen pike]

You're asking on a Mathematics server

[bronze sun]

I know.

Just asking in case anyone knows how to fix it.

[ashen pike]

Well this isn't a help server, so don't expect anyone to know. Just ask on a discord server thats designed for programming, or better, VScode

[bronze sun]

Okay, fair enough.

[pulsar pagoda]

the problem is using vscode at all

tbh

just use vim

and dont use language servers

[stuck meadow]

what kinda of problem is it?

[midnight kayak]

#old-network

[stuck meadow]

also u can use sublime text

just, vsc code nice, but insome specific situations its not the best editor

[neat lintel]

U need to edit your spacebar

[neat lintel]

ok

yeah

but what is the real and imaginary axis really

[inland raft]

Yes

[velvet dagger]

The real axis is the x axis, imaginary is y axis. If you're thinking about complex numbers

[neat lintel]

like what if you alrdy plot the equation on its real x and y coordinates and now u need a imaginary axis idk

ok ig im just over complicating it for myself

(x^2+1)(x+1) =0

this has a real solution AND an imaginary solution right

yess

now

suppose you plot the rest of the equation too

yeah

where would u plot that

in the z axis?

but then what happens to x = -1 when y = 0

y is 0 in that example

equation is (x^2+1)(x+1) = y

ok

i dont have to but i still do🥲

fair enough

[solid yarrow]

what's the most interesting conjecture you know of?

[digital furnace]

a b c

[woven whale]

an already solved one or an open problem?

[solid yarrow]

if you ask like that, both

[woven whale]

whitehead problem

[neat lintel]

Pre-uni student here, can anyone explain me to me how complex numbers can exist in real life, want to know out of pure curiosity

[vast surge]

Ask a physicist to explain quantum mechanics.

[neat lintel]

Do you know if complex numbers exist in any other fields outside of physics

Seems so hard to conceptualize imaginary numbers existing

[vast surge]

I guess quantum computing is sort of a cs subject?

[umbral forge]

I think they’re used when working with electricity too

Im not sure if they’re needed for it or it’s just more useful to have them as a tool

[hallow blade]

do you also conceptualize why -4*-3 = 12?

If you accept that multiplication correpsonds to reflection, then you should also accept that complex numbers corresponds to defining a number system on the plane

[steady sparrow]

can someone help me with this question. Expand and state your answer as a polynomial in standard form.(4x-y^(3))y^(2)

[lavish hull]

do you know how to expand+multiply?

[steady sparrow]

nope

[lavish hull]

you should go to #❓how-to-get-help
but do you know how to expand 3x(x+y)

[neat lintel]

Sort of. My understanding of that is subtracting -4, 3 times which is 12

[neat lintel]

No clue what that means, but my main motivation for studying math as of now is to one day understand complex numbers, so hopefully I will soon

[umbral forge]

If you have the real numbers as a line with 0 being at the middle, then -1 is just the reflection of 1 through 0

Not sure if this helps

[hallow blade]

But why should multiplication by a negative be repeated substraction?

It's just arbitrary no?

in the same way, you can define a certain number system on the plane

which extends the number system defined on the line

[neat lintel]

well multiplication is just adding no, and I can re-write adding -3, -4 times as subtracting -4, 3 times

[hallow blade]

for example, what if you just forgot about complex numbers

and just thought about defining a number system on the plane

What then does multiplication represent?

[neat lintel]

a number system is a number line right

[hallow blade]

by number system i mean a field

i.e. one where you can do addition, multiplication, substraction, division

[neat lintel]

Well to be honest I would've just said addition/subtraction multiple times, but it seems that is not what you're getting at

[hallow blade]

i mean my point is this: it's actually somewhat arbitrary that someone decided multiplication by a negative number means repeated subtraction

you first define multiplication for positive numbers and say it means repeated addition...fine

[neat lintel]

oh I see what you're trying to say, if multiplication is adding, then negative multiplication is adding negative times which doesn't make sense, so we just decided it was repeated subtraction

[hallow blade]

yeah

now let's say you want to extend to a number system on the plane

if you represent everything using rectangular coordinates, it's not actually so clear what's going on.

Let's say you have rectangular coordinates and you want to define (a,b) x (c,d)

What is the geometric interpretation of (a,b)x(c,d) being defined to be equal to (ac,bd)?

and also, does it make it into a number system/field if you define it like this?

Because remember, you also want to define (a,b)+(c,d) = (a+c,b+d)

Which implies that the additive identity is (0,0) which means that anything else you should be able to divide by

But then... how do you divide by (1,0)?

so you immediately see that you can't define it like this if you want a number system

[mental stratus]

(1,0)*(0,1)=0 so zero has divisors therefore not a field

[hallow blade]

Of course now it's not at all obvious how to define multiplication. But interestingly, if you switch to polar coordinates, stuff becomes perhaps more clear

If you now think about how to define multiplication on (r_1,theta_1)x (r_2,theta_2)

you end up with (r_1r_2,theta_1+theta_2)

[neat lintel]

I'm not sure what you mean by geometric interpretation but I imagine it is the same thing, (a,b)x(c,d) is adding A c times on the x axis, and adding b d times on the y axis

[hallow blade]

well okay just forget about that point its not so important, the bigger point is that you cannot define a number system

[neat lintel]

Okay so what you're saying is, multiplication is sort of arbritrary and hence to try and understand complex numbers, you have to take this into consideration

[hallow blade]

to motivate this, we should have in rectangular coordinates (1,0)x(-1,0) = (-1,0)

Which translates to polar as (1,0)x(1,pi) = (1,pi)

[neat lintel]

wouldn't it be, theta1 * theta2

[hallow blade]

read what I replied to it

[hallow blade]

Well my objection to your objection about complex numbers seeming to not exist is that not everything in math neccessarily has some sort of physical interpretation

The example I gave being multiplication by negative number

[neat lintel]

Okay I see, just out of curiosity when did this idea come to maths, from my understanding, when imaginary numbers were first created, they were seen as literally imaginary and non-existing

[lavish hull]

yeah i disagree here

maybe not physical, but existing in reality

actually i can agree because a lot of concepts are too hard to make analogies with reality

[neat lintel]

at what point did we say, okay hold on, just because it doesn't have a physical interpretation it can still exist, was it when we started seeing complex numbers in real life equations or did this idea exist prior to it

[hallow blade]

not sure about the history of it all

[lavish hull]

maybe before math was invented @neat lintel

[hallow blade]

According to veritasium's video, complex numbers were introduced as a computational aid when solving polynomial equations

[lavish hull]

language gets pretty abstract too

[neat lintel]

i'm wondering if there was something specific we discovered that enabled us to say okay it doesn't need a physical interpreation to exist

[hallow blade]

i mean what is the physical interpretation of the quadratic equation?

[lavish hull]

trajectories

[neat lintel]

Right I'm speaking from that, in that video it mentioned when they were first introduced, people didn't believe they actually existed because there was no physical interpretation, hence at some point mathematicians changed ideas

[hallow blade]

fair

[neat lintel]

I believed they use geometry

[hallow blade]

though Im not familiar with how projectile motion is derived without calculus

[lavish hull]

even more generally polynomial equations can be representitive of a lot of things

[hallow blade]

There is this guy on youtube that you might find interesting @neat lintel nj wildberger or something

[neat lintel]

I'll definitely check him out, is he like a 3b1b type of guy

[hallow blade]

no he is a guy that likes to talk about how modern mathematics is wrong

[neat lintel]

that sounds awesome haha

[lavish hull]

no he is a professor

[hallow blade]

because the objects we use, namely real numbers, do not exist

[neat lintel]

Is there a specific video you'd recommend, skimming through his youtube channel, there's a lot to choose from

[tiny forge]

nj wildberger has very "non standard" views on things from what i remember

[hallow blade]

https://www.youtube.com/watch?v=edh5bbgSKqo&t=2025s

[tiny forge]

hes a finitist iirc

[neat lintel]

what's a finitist

[hallow blade]

for context,you probably want to first understand what a real number actually is

[tiny forge]

people who do not accept the existence of infinite objects

[hallow blade]

though im not sure if its strictly necessary to understand his viewpoint

yes he is very very outside of mainstream mathematics in that he is literally trying to make a new mathematics on his own

[lavish hull]

you dont know this

[hallow blade]

but the idea that real numbers actually don't exist, nonetheless are very convenient is quite interesting

[lavish hull]

and every mathematician wants to make new math

[hallow blade]

no I do know

[neat lintel]

Is this a popular mathematical academic take, or is it generally accepted by pretty much everyone that infinite objects do exist

[hallow blade]

he has content where he builds math up "rigorously" using his viewpoints

and he even sells it iirc

[tiny forge]

Most people don't even think about whether or not they should exist, they just use them

But the people who do think about these kinds of things generally accept them as existing yes

Otherwise things are very difficult

[solid snow]

avoid cranks

[neat lintel]

.

[woven whale]

lol

kids these days

[jovial ember]

Chmonkey

[quiet geode]

oi mods

my ass is patiently waiting for 'very active' role

[echo tundra]

very active role is not controlled by the mods

[quiet geode]

thats what they said to me last time around as well

truly believe its an escape hatch

[neat lintel]

You last messages were over 9 months ago so. not ver active

[quiet geode]

i am very actively promoting this server irl

[echo tundra]

That doesn't count sadly

[quiet geode]

nice discussion

YOOO

WE HAVE @strange meteor

are we going to war

[neat lintel]

I thought/assumed that the things we talk about in formal systems are confined to just the formal system. The interpretation of the formal system I assume can then be used to see if a different formal system can be interpreted in the same model?
And if you want to capture some idea it needs to be written in formal language, and all that captures is just the formal definition according to the formal system.
And natural language I assume doesn't have an exact mapping to formal language, so you don't know whether the idea expressed in natural language matches your formal definition or not.
I assume physics then is a bunch of models that are gathered by thinking about replicable measurements of what we perceive to be the external world, and then expressing these replicable properties in formal language? And then using what we know about formal language to talk about them?

[quiet geode]

i have a snippet from a book that is a hard counter to this argument

apparently i am not allowed to upload images 😢

[neat lintel]

Lame. U could post in chill and link to it here

[quiet geode]

i can do that but i want the mods to acknowledge my helpfulness and promote me to a greater being as well

here you go

#chill message

[neat lintel]

I've heard that there are philosophical problems with each philosophical interpretation of mathematics, but I don't understand how the picture is a counterargument? It seems to say that you should think about mathematics in terms of the formal definitions as written in formal language

[quiet geode]

the natural medium

[neat lintel]

I interpreted this as 'The formal language is the natural medium of mathematics.'

[quiet geode]

there is no natural medium outside of the formal language

it is as natural as it gets

[neat lintel]

I don't see how this is a counterargument?

[quiet geode]

my subscription for a working brain ends here, i cant help you anymore

back to my troller self

[neat lintel]

https://www.youtube.com/watch?v=GZgIYGaeWy0 don't be like this

[neat lintel]

Wow the video was actually quite interesting

[quiet geode]

i feel attacked

Also

#chill message

[neat lintel]

Losing my mind

tried 100 different names for my 2nd account

all taken

[fair mural]

random numbers go

[neat lintel]

652336711325712386

[ocean harbor]

69

[granite hound]

Oh cool an Abstract Algebra study group starts up just when I started actively self teaching it 🙂

I should power through the last chapter of Understanding Analysis before it starts up

[tawny iris]

hey guys

[solid yarrow]

hello

[granite hound]

Hi

[ocean harbor]

ded

[quiet geode]

dead is good

[olive basin]

can any1 help me

[quasi jetty]

Please read #❓how-to-get-help

[neat lintel]

Lol

Is that automatic

Help

Help me

Can anyone help me

Ok it’s not

!help

[quasi jetty]

Please read #❓how-to-get-help

[neat lintel]

Hmm idk how it did that

Can any1 help me

weird

!help @neat lintel

[quasi jetty]

Please read #❓how-to-get-help

[neat lintel]

yeah idk

[magic owl]

reading too hard

[neat lintel]

is capital pi notation useful or can it be expressed with summation

I don’t think it’s used all that much tbh but I’m wondering

[storm sage]

It is useful

It works the same way as the capital sigma notation

So it's not like you have to learn anything special with it

[neat lintel]

They are the same?

[fervent pebble]

capital pi is multiplication and capital sigma is summation

i mean you can represent each in terms of the other (for real positive terms) but why would you want to

[neat lintel]

Ok that makes sense. I was just wondering if capital pi was easier to write in terms of a sum or if it’s good on its own

[fervent pebble]

ofc

[neat lintel]

g

[fervent pebble]

if you want to, for $x_k$ positive and real, see how you could turn $\prod_{k=0}^{\infty} x_k$ into $\sum_{k=0}^{\infty}y_k$, where each $y_k$ is real

[neat lintel]

\prod

[fathom swallow]

valley

[neat lintel]

I don’t know how to otherwise I would try

[fair mural]

x = e^ln(x)

use that

[neat lintel]

I haven’t taken precalc so I haven’t used summation or natural log yet

Only practice problems with logarithm rules

no actual applications

[fair mural]

i mean, that’s literally all you need though

[neat lintel]

I don’t even know where I’d begin. My first thoughts were using a tower of exponents or putting another summation inside of the first

idk how to do anything with e^ln(x) it means nothing to me

[neat lintel]

valley what exactly do you have in mind for this

[small dust]

y_0 = \prod x_k, y_n = 0 for n > 0

[neat lintel]

lol

[solid snow]

Could you elaborate

Oops

Chat didnt scroll down lmao

[fervent pebble]

||ln||

[neat lintel]

i want to know what final expression you have in mind

[fervent pebble]

ohh

||ln(prod) = sum(ln)||

[neat lintel]

of course

[fervent pebble]

is there a different way to do it

[neat lintel]

maybe i just misunderstood what you originally meant by "turn into"

i read it as "make the product literally equal to the sum"

[fervent pebble]

ohhhhhh

x_k = y_k = 0 hehe

[neat lintel]

yeah alright this is fine

i just misunderstood you

[fervent pebble]

in your defense "turn into" is definitely not a very mathematical term

[neat lintel]

https://tenor.com/view/bro-high-five-fist-bump-cats-gif-9405911

[echo tundra]

We plan to start today itself

[storm sage]

Good book!

[fair mural]

i forgot to fill it out before now but i just did

[woven rapids]

bro there's a latex bot? that's so coollllll

[fervent pebble]

stop 💀

[lavish scaffold]

@cold needle please ban @wild comet this spammer from this server

[echo tundra]

@cursive token can I DM you about the abstract algebra group?

[cursive token]

Feel free