serious-discussion

[vast wraith]

do like Borcherds and do both mwahahaha

[dark meteor]

Nobody's helping me in help-forums 😭😭😭 like istg

[pure cliff]

why do you cry about this

people aren’t obligated to help you

they’re all doing it for free

[dark meteor]

It's just an exaggeration

[pure cliff]

anyway there’s a higher chsnc3 of help if u post in topics channels

[dark meteor]

They actually gave me a really good tip

[pure cliff]

oo

[dark meteor]

And I managed to solve

It sent at 8:24!?

[pure cliff]

based

[solemn steppe]

hello

Can i disscuss something

[pure cliff]

nice profile pic

[solemn steppe]

someone that Good at mathematics

xd

is there anyone that very good in mathematics here
I want some private discussion

its not any kind of math homework

just something (math) that pop up in my head and i discuss it with chat Gpt
and suddenly got interesting.

[ocean harbor]

!nogpt

[quasi jetty]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[solemn steppe]

sorry
but well, im still onto something (maybe )

[ocean harbor]

it is dumb

don't use it for math

[solemn steppe]

Sorry
Well im here to discuss something anyway,
are you, a guy That understand math.
im just wanted a good discussion
not anything man
im not racist

[hardy iron]

ChatGPT is certainly on something the way it hallucinates

[solemn steppe]

yea

[rancid ingot]

This is kind of a weird question, but what's the most useless math class / subject a student (grad or undergrad) would be expected to take? For example, right now I'm taking a Galois Theory course, and my professor said that the actual results from Galois Theory don't get used much today*, but it's a good class to lead into higher / more modern algebra. I was just wondering if there are more topics like this where there's a sense in which its good for a student to take the course, but they likely won't need what they learned from the course. *Besides like fundamental theorem and general extension stuff

[neat lintel]

Innit?

[eternal crow]

i tried learning arabic in

i think last year

the writing

and i haven't continued it so i forgot everything

o i know a

ا

اااااااااا

actually maybe i remember some

[neat lintel]

Your first language?

[eternal crow]

tagalog

[neat lintel]

Never heard of it

[eternal crow]

filipino

heard it?

[neat lintel]

Oh I see

[eternal crow]

yea

salamat

[neat lintel]

If you want to learn the script then it's better to learn the Persian or Urdu sounds.

[eternal crow]

salamat means thank you but I j think it's origin is arabic

[eternal crow]

oh…

[neat lintel]

In my native language it means "all right'

[eternal crow]

ohhhh

interesting

[neat lintel]

Arabic can hurt your throat.

[eternal crow]

lol

oh i see. fair enough

[neat lintel]

Persian and urdu sounds are easier.

[eternal crow]

i see

[neat lintel]

And arabic ain't got چ ژ

[eternal crow]

hmm but idt im gonna speak anytime soon

just to be able to read or write

[eternal crow]

i see. interesting

are u persian

[neat lintel]

Can you read my name?

[scenic fog]

I'd honestly find speaking arabic easier than learning the characters but that's just me lol

[neat lintel]

Somewhat, from a Persianised culture.

[eternal crow]

i learn writing first when i learn the language lolz

[scenic fog]

Ahh

Ok

[eternal crow]

i forgot that s-y character

[neat lintel]

?

[eternal crow]

i only know a

[neat lintel]

I see, why'd you like to learn Arabic though?

[eternal crow]

I'm just interested in writing and

many people speak it too

online at least

[neat lintel]

Oh I thought you were religious.

[eternal crow]

i had some algerian friends

[neat lintel]

Great.

[eternal crow]

it's been a while since we talked but yea

in case we talk again

i gotta show off

lol

and yea, just in general

[neat lintel]

Any good servers you know?

For wasting my youth

[eternal crow]

no

oh

what do u mean

[neat lintel]

Like chill servers

[eternal crow]

no

maybe I'm old enough to chill

because, responsibilities

[eternal crow]

you can chill in #chill

[neat lintel]

Doing so

Rn

[night barn]

Hey guys i have a difficult dilemma

How to decide between combinatorial optimization & analysis/geometry on manifolds (following lee's book)

I can only take one

[jagged forge]

probably best to ask in #advanced-lounge

[loud cape]

Why is that channel no access

[jagged forge]

you need to assign a role over in #info

[loud cape]

What's the role's name ?

[ocean harbor]

undergraduate

[loud cape]

Wait, isn't that an exclusive selection ?

[zealous garden]

??

Exclusive selection?

[loud cape]

Like, can only have one of the 4 roles

[zealous garden]

The roles represent where you are in knowledge and study, not where you are in academia

[zealous garden]

Wdym one of the 4

[loud cape]

Can't have all 4 no ?

[zealous garden]

It's pre-uni, undergraduate, postgraduate, I think it's clear you'd only want 1 of them at a time. And there's only 3

[loud cape]

Ah, 3 then

[zealous garden]

So I don't know what you're talking about

[loud cape]

And idk which one do I choose

I am not done with highschool but my favorite past times are type theory & category theory

[zealous garden]

Choose undergrad if you know what a vectorspace and integration by parts are

[serene ridge]

In what course did you start learning about rings, groups and fields?

[loud cape]

I do know both yes (tho I use a calculator for calculating an integral, I can't do manual integration since I never had a need for it)

[zealous garden]

I assume that happens in a first Algebra class

I don't know

I just read a book and watched some videos

Part of a book

I have not finished Pinter

[loud cape]

Will that give me access to the other channels ?

[zealous garden]

It'll get you into #advanced-lounge I think

[serene ridge]

because we started studying them at the beginning of the first year in uni, and I don’t know how normal this is.

[loud cape]

Very confusing system

[zealous garden]

If you're in for math and doing algebra that makes sense

Groups Rings and Fields are the basics of Abstract Algebra

[serene ridge]

yes, it's true

[silk birch]

Have y'all seen that video where a guy proves cbrt(2) is irrational?

[static loom]

does he say x^3-2 is irreducible by eisenstein

[past pecan]

i hope y'all remember me

[zealous garden]

A guy did something similar to that once and they killed him for it

[zealous garden]

Nope

[past pecan]

sorry

permutations

[ocean harbor]

not really confusing lol

unless if you are new to discord

[jagged forge]

yea you were supposed to choose a role during the intro screen or whatever

[lyric dove]

Hey, if anyone from UCD is good at explaining calculus (preferably with bio applications, like the MAT17 series), I’m looking for a tutor who can go over concepts with me at a slower pace

[calm musk]

Guys how do I get ,w wolfram alpha to input value of x into derivative and straight up give me the gradient?

[river moon]

you just ask it to compute gradient at a specific point

[static loom]

,w derivative of x^2+x+1 at x=-1

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by merosity

[neat lintel]

This might get quite heated, so I will try to be civil.
https://www.youtube.com/watch?v=IedVRYUNWUU

At 4:04, many comments were pointing out that the kids were saying "Kite, Hit, Steel, Plane, Must" and that this is some kind of ritual and not a coincidence, but I think it's not. At 4:35, I think it's "playing" not plane because I saw the "g" at the end of the word on the board.

[main elbow]

i def think its playing

but why would it get heated

[neat lintel]

It's about 9/11

[main elbow]

even if they did say plane like ...

yeah no i get it

but like and ???

"george bush was in a room with some kids learning word pronounciation and they said plane !!!! 😱 😱 😱 😱 😱 BUSH DID 9/11 !!!!!!!!!"

like it just doesnt make any sense 😭

[neat lintel]

that's what I'm thinking

it's probably a conspiracy theory

[past pecan]

i m back

hope y'allremember this boring kid

[wise grove]

Guys I need help or I need a formula for a specific question

calculate the sum of the first 100 positive integers

[wise grove]

Is there a formula for this question?

[hardy iron]

!help

[quasi jetty]

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

[neat lintel]

Bush did 9/11

And Bush killed dinosaurs

[shadow flax]

Aww man I love dinosaurs

[neat lintel]

Go hang Bush!

[wispy harbor]

He also plays golf

[neat lintel]

He also funded the Taliban.

[wispy harbor]

To do 9/11?

[old oak]

The most despicable crime of all

[neat lintel]

Guys can we mod dinosaurs.

[neat lintel]

No in general

[wispy harbor]

Shit, like Reagan funded contras

[neat lintel]

9/11 was al Qaeda no?

[wispy harbor]

Idk

[neat lintel]

I do.
My name is Max Muller and I was there.

[wispy harbor]

Woah

[wispy harbor]

https://tenor.com/view/toy-story-rex-shy-embarrassed-nervous-gif-4030979

[neat lintel]

W embed 😭

[neat lintel]

Exactly, it's such a fat capitalist's sport.

Any controversial opinions?

[burnt ledge]

dinosaurs aren't real

[neat lintel]

You are 6'4 your opinion doesn't count.

[burnt ledge]

? im not 6'4

[neat lintel]

What's your bio then

Status I mean

[warm umbra]

thank you @quasi jetty for always responding to our messages and clearing inconveniences in the server, you really are a superhero

[neat lintel]

Not really

@quasi jetty is a dumbass

With no free will.

[warm umbra]

Your getting banned for that

Mark my words

[neat lintel]

@quasi jetty are you a dumbass? Silence means agreement.

[burnt ledge]

its a funny instagram comment i saw a couple days ago

[neat lintel]

I didn't know this. I'm so angry 😡😡😡 /s

I don't tolerate killing innocent dinosaurs

[reef elm]

@neat lintel خودی کو کر sigma اتنا، کہ rizzler بندے سے خود پوچھے بتا تیری aura کیا ہے

[neat lintel]

واہ! brainrot کے اقبال ھو آپ!

I'm definitely storing this.

It's the funniest thing on discord.

[neat lintel]

Let's hang Bush! Let's hang Bush!

[solid snow]

what...

[neat lintel]

Bush ethnically—no, speiciecally cleansed the dinosaurs.

Get on the streets and protest!

[pale frigate]

<@&286206848099549185>

ok

[limber thunder]

yes keep this ping to your help channel please

[past pecan]

hi guys i m back

just did a 10hr physics streak nd completed my book

[neat lintel]

@visual creek make me a sandwich

In mathematic theory

[visual creek]

☠️

[neat lintel]

Is that a yes?

[timid ginkgo]

guys im new here, i see that math subjects are separated by text channels. why does competiton math has its own category? is it different from like an undergrad student math? im genuinely curious

[fresh comet]

welcome to mathcord!

as for your question, I’m pretty sure #competition-math doesn’t really fit cleanly into any category, but went into the pre-uni one because that’s where most people studying for math comps are at

I’m not 100% sure on this though

[latent edge]

Welcome! Don't ever go to competition math. Open Apostol's analytic number theory and ask questions in #advanced-number-theory

[fresh comet]

the propaganda continues…

[jaunty ibex]

DELTOID IS ACTIVELY RUINING KIDS

Langlands propaganda

[surreal sapphire]

generally competition math is solvable by elementary techniques but still has to be hard so it often relies on "tricks"

undergrad math is about building theory

deltoid isnt ruining anyone with useless comments, more just being annoying

[jaunty ibex]

I agree tho advanced number theory is cool

[timid ginkgo]

i see, for some math olympiad questions in my country, it does seem like it does not fit into any category too. i love math but i never got the chance of participating... those competitions are mostly for highschool students. now i am in my first year of uni.

[timid ginkgo]

oooh that makes total sense

[timid ginkgo]

what is analytic number theory?

[jaunty ibex]

Have you done number theory before?

[timid ginkgo]

no, i only had calculus and linear algebra

[surreal sapphire]

you apply analytic techniques (mostly from complex analysis) to study number theory

[jaunty ibex]

hmm

[surreal sapphire]

the first thing studied was the distribution of prime numbers

[jaunty ibex]

Are you familiar with modular forms

I mean modular arithmetic

[surreal sapphire]

so its more focused on large scale phenomena

[jaunty ibex]

I blame Deltoid for making modular forms stuck in my head

[surreal sapphire]

the earliest result is showing that the sum of 1/p over all primes converges

[jaunty ibex]

Yeah instead of studying a niche case, you study what happens in general

[timid ginkgo]

uhh sorry, i never heard about it before...

[surreal sapphire]

thus giving an alternate proof of the infinitude of primes

[neat lintel]

i have a dout

[surreal sapphire]

then people built on that

[jaunty ibex]

But you know what is a prime number correct?

[neat lintel]

daoubt

[timid ginkgo]

ive read somewhere that the distribution of primes are related to the natural log

[fresh comet]

check out #❓how-to-get-help for math help

[timid ginkgo]

yes

[neat lintel]

k

[fresh comet]

this isn’t the place to ask

[jaunty ibex]

Yeah true

That's the prime number theorem

[surreal sapphire]

primes grow like x/logx

its proved with techniques from complex analysis

you essentially evaluate some integral to get it

[jaunty ibex]

Evaluate more like estimate

[timid ginkgo]

i might sound dumb but primes are positive integers right? what does complex numbers have to do with their distribution?

[surreal sapphire]

funnily enough the earliest proof relies on some trick

that could appear in contest math

[jaunty ibex]

It's the fact that a special function (the Riemann zeta function) encodes information about primes

[surreal sapphire]

do you know what a taylor series is

[timid ginkgo]

yes i do

[jaunty ibex]

The proof of PNT relies on knowing what happens at s=1 in the Riemann zeta function

[surreal sapphire]

so you construct similar functions that are infinite sums

[jaunty ibex]

Do you know about p series?

sum 1/n^p

[timid ginkgo]

i know the zeta function but i dont know p series

[jaunty ibex]

Ok do you know why the zeta function converges for s>1 from elementary calculus?

[surreal sapphire]

they are of the form $\sum a_n n^{-s}$

[fathom swallow]

Lochverstärker

[timid ginkgo]

i know it converges for 2 and 3, is it for all s>1?

[surreal sapphire]

s is allowed to be complex

[jaunty ibex]

Yeah

Now we take s and extend it to complex numbers

[surreal sapphire]

those functions can be factored over primes similar to integers

and the coefficients a_n encode some arithmetical data usually

[jaunty ibex]

And we make wishful thinking and say "can we define the function for s<=1? Not only s>1?"

[surreal sapphire]

it then turns out that the poles of those functions give us other arithmetical data

[jaunty ibex]

Turns out you can by a process called analytic continuation. This will extend the function everywhere except at a pole (singularity) at s=1

This pole as Loch said is what gives u info about prime numbers

So in a sense analytic number theory is about connecting discrete things like prime numbers to complex analytic things like the Riemann zeta function

Having a bridge between number theory and complex analysis

[timid ginkgo]

wow... those things are connected

[timid ginkgo]

how does this work? i know factoring reals but how do we factor a complex function?

sorry i never had complex analysis before, i might sound stupid asking these questions

[solid snow]

find their roots

[timid ginkgo]

like finding the roots of polynomials?

[solid snow]

if you originally meant polynomials, yes

but in the precise sense that loch means, some abstract algebra is involved

[timid ginkgo]

ah okay so i need some knowledge before understanding these statements. i am really new in higher level maths (just 3 months into uni) so i still have so much to learn

thanks everyone for answering!

[jaunty ibex]

Np

Hopefully that gives you some interest in analytic number theory

[surreal sapphire]

its called an euler product

its not too hard to derive but discord isnt the best format for it

but you can look it up at least to get some idea of a connection

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

this looks pretty understandable

and maybe suffices to convince you of some connection between primes and the riemann zeta function

[jaunty ibex]

I was gonna explain that you can generalize this further but I'm not that knowledgeable with langlands shenanigans

Maybe ask nG or Deltoid for this

[surreal sapphire]

i mean you first generalize to dirichlet l functions

which isnt too hard

and this already gives you a lot

[jaunty ibex]

Yeah you just stick in a character

[surreal sapphire]

but you need more complex analysis soon

what i linked is elementary

[jaunty ibex]

At least for Dirichlet L functions are not bad

[surreal sapphire]

you soon run into hard stuff

euler himself did a lot of unrigorous (at the time) things

it took decades of research into complex analysis to justify some things

same for riemann kinda

[latent edge]

Nice discussion 2 was about analytic number theory

I'm proud

[old oak]

I agree with the first part off this message, anyway

Competition math is very much its own beast and has very limited overlap with academic math in general.

I was never remotely good at competition math, and I did fine reasonably well passably as a mathematician.

[neat lintel]

HI

QUESTION p?

.CLOSE

.close

[old oak]

Wrong channel, try in #discussion

[latent edge]

Yeah I mean my real message was the first part

Competition math is a propaganda created by liberals to sell courses. Changed my mind

[old oak]

I mean, I agree with this entirely

[plush hawk]

theres a crazy arguement happening in discussion about like trans people

[hardy iron]

That wasn't the argument...

[plush hawk]

oh

[small dust]

lmfao

[plush hawk]

whats the arguement about then bruh

[hardy iron]

DID

[plush hawk]

😐

you cant be serious

[hardy iron]

???

[plush hawk]

why are they arguing about DID

[hardy iron]

Ask them

[plush hawk]

idk man their discussion seems pretty heated

dude theyre literally talking about trans people

[small dust]

what

not at all lmfao

[hardy iron]

I don't think you read

[plush hawk]

Find me academic research about gender-affirming trans healthcare from the 1800s and I will find you academic research about non-abusive plural healthcare (it exists, but it's few and far-between and we are too tired to go search for it)

thats what the dude with the minecraft block said

[hardy iron]

Did you ignore every other sentences and cherry picked this one?

[plush hawk]

no this is literally the first sentence i saw as soon as i opened up the other channel

[hardy iron]

Then read other sentences dud

duh*

[plush hawk]

ur advice doesnt work

i asked and they didnt reply

never cook again

[plush hawk]

i tried

ASKING them

as per YOUR words buddy boy

[fresh comet]

[latent edge]

here's a C_5 for u :3

[long pumice]

a much greater alternative to Stellarium can be made, in the much more natural VR realism direction, highly professional 3D game development style

there is huge area to professionally improve astronomy simulation software, the telescope simulation in Stellarium is relatively rudimentary

the demand potential has to be high, something seems to practically lynch all sensible high quality development now

[leaden torrent]

what are you talking about my dude

[long pumice]

astronomy is a very mathematical area, lots of mathematical science history revolved around astronomy

[scenic pond]

All fun & games until u send cyclic group of order 4 DUN DUN DUN

[past pecan]

i hope you guys remember me

[limber thunder]

I think I do from the pfp alone

[rocky shuttle]

https://youtu.be/GNkPJvVEm0s

[deep mango]

<<<<
https://youtu.be/NM11WO8WE3g?si=VI0IUsOXsgMQo-gU

[rocky shuttle]

[eternal crow]

lol kano

[fresh comet]

[rocky shuttle]

[fresh comet]

[pure cliff]

Wow

9 years ago

I'm amazed at the quality of the animation and music

Even. 9 years back

[eternal crow]

2015

same year I discovered kano

no, probably 2016

[pure cliff]

first time hearing about this artist

amazing stuff

[past pecan]

i m back

[ocean harbor]

:3

[ocean harbor]

wb

[past pecan]

full form?

[ocean harbor]

shortcut for welcome back

[past pecan]

which standard do u study in

[past pecan]

thank you sir

[ocean harbor]

cs

[ocean harbor]

not a sir but you're welcome

[past pecan]

my dream

[past pecan]

Oo then?

[ocean harbor]

I'm switching to comp eng tho

[past pecan]

which field of cs u working upon

[ocean harbor]

does my roles help

[past pecan]

whats ur role

[ocean harbor]

the diamond I mean

[ocean harbor]

not the best one

[past pecan]

where?

[ocean harbor]

just regular

[ocean harbor]

canada

but not doxxing which city

[past pecan]

diamond in canada?

[ocean harbor]

no

[past pecan]

oh

but whats doxxing

[ocean harbor]

good question

[past pecan]

i m sorry i m new to discord

which field of cs u working upon

[ocean harbor]

it is like you don't wanna share information in public

[past pecan]

ohh'

[ocean harbor]

privacy

[past pecan]

whats privacy field?

never heard abt that

i mean r u in frontend , backend , full stack , database management or what

[ocean harbor]

it is regular

[past pecan]

ok

[icy locust]

DBA Full Stack DevSecMLOps

[sonic sentinel]

bruh my teacher tweakin

[icy locust]

I couldn't figure out how to stuff in more buzzwords

[sonic sentinel]

she put 40% of our grades on a surprise benchmark test, everyone got 70s or 80s (except the people who cheated)

so a bunch of people in class had their quarter grades drop by 5-10 percent

[restive flicker]

I feel like I have this problem when I self teach myself something like topology I get over my head and my thoughts feel like a inferiority complex plus the subreddit: iamsosmart

[fresh comet]

what do you mean by that?

[sonic sentinel]

ruminating?

[sleek pagoda]

Desmos added a complex mode

[neat lintel]

when I study math, I will just go through each page and do all of the exercises.
is this the correct way to learn?

specifically AoPS books

[static loom]

https://www.desmos.com/calculator/cqvkejtcyr messing around kinda fun

https://www.desmos.com/calculator/m8aiamleag obligatory

[gritty crater]

Damn, cool

[midnight vessel]

https://www.desmos.com/calculator/vh2kh3z9zz :3

[static loom]

another fun one for you https://www.desmos.com/calculator/s2ggltljqn

[static loom]

aha, try to remake it with complex exponentials now 😎

[midnight vessel]

nah i'm too lazy
here's sm else instead
https://www.desmos.com/calculator/eatigmd91u

[static loom]

you could use exp(il) or e^{il} instead

here's making an ellipse with two circles in opposite directions of different radii
https://www.desmos.com/calculator/jc8kpeybfh

[random tangle]

hey is it possible to include bounds in a ti-84 calculator?

[static loom]

https://www.desmos.com/calculator/1lgzs2yjye alright off to bed

[gritty crater]

Why my Desmos doesn't have complex number feature

[agile fiber]

gotta turn it on in the settings

(top right)

[gritty crater]

I had gone to settings, but I didn't see any setting related to complex numbers.

nvm I have to close Desmos and open it again

[gritty crater]

Yeah, I see it now. I just keep Desmos open so it doesn't get updated

[past pecan]

i m bac

[vast wraith]

ideal octagon in beltrami’s elliptical model for hyperbolic geometry spotted in the wild

though the place is better known for things like…

[solar hawk]

WHAT

RU FUCKING KIDDIND ME

FUUCK

[tender tulip]

I agree

[tender tulip]

BRUH I’ve been making my own complex number calculation shit

[brittle socket]

https://www.desmos.com/calculator/g6op54wgzn

[long pumice]

I don't seem to be able to find work development partners in spite of the involved value quality and high potential. It feels creepy lynching into total social and economic isolation. It feels like forced sick social insanity.

[long pumice]

#serious-discussion message

#serious-discussion message

I suspect that by now some publishing houses would pay me in advance to write a book. There seems to be creepy background blackmail strangulation of all work collaboration potential.

I can still do a large good work difference with the right collaboration team in spite of my medical tranquilized state that disabled my ability to do high performance software programming jobs: https://mihaiv.wordpress.com/2023/05/15/communication-problems-and-important-human-issues/

[fresh comet]

[bronze pelican]

WHAT

This is huge

[bronze pelican]

BOLZA SURFACE

[vast wraith]

mwahaha

[vast wraith]

very exciting article

am just halfway through

[bronze pelican]

[pure hollow]

oh sounds interesting

[past pecan]

nice

i am fine

[static loom]

interesting appears desmos in complex mode computes gcd in Z[i] https://www.desmos.com/calculator/kmz6abumos

[limber thunder]

i love reading about history of math

[pulsar pasture]

"mathematics. A chronicle of human endeavor" its quite interesting too.

[limber thunder]

this one is a nice survey that goes through the history of dynamics and chaos, particularly the seq. of events that led to the study of the Lorenz attractor https://perso.ens-lyon.fr/ghys/articles/lorenzparadigm-english.pdf

[ocean harbor]

pretty :3

[covert monolith]

Guys is there anything like IUPAC but for mathematics

[static loom]

in what sense, like how they have an established convention for naming organic molecules?

[quiet belfry]

chronic*

[eternal sorrel]

is dis real

a < b
c < d
a + c < b + d

[surreal sapphire]

the IEEE 'standardizes' use of mathematical symbols

mathematicians dont conform to those standards

[surreal sapphire]

why dont you try proving it

[agile fiber]

there is also the iso 80000 standard

(will run you $200 though)

[eternal sorrel]

i did it

[gusty socket]

good work

[eternal sorrel]

a < b
c < d

a - b < 0
d - c > 0

a - b < 0 < d - c
a - b < d - c
a + c < b + d

thanks

[pulsar pagoda]

IEEE trying to standardize OS interfaces

software vendors

nahh

linux

nahhh

[eternal sorrel]

[pulsar pagoda]

posix is overrated

[surreal sapphire]

which is also not used

i guess it might be important for highly technical documents

which math papers arent

at least not in that sense

[hexed pier]

Is there a way to prove stuff without actually having to prove it or be awake

[static loom]

lol

[modern saddle]

Those who know

[jaunty ibex]

Yeah it's called proof by intimidation

[hexed pier]

Now we just need computers that feel fear and math anxiety

[ripe acorn]

https://youtube.com/live/ObCg8X0AJB0?feature=share

[static loom]

.pin

[raven plaza]

Be Ramanujan

Obtain theorem via dream

[pure hollow]

theorem because i say so is also based method

[old oak]

My second-favourite footnote, beaten only by this:

[pure hollow]

oh btw i started my RA journey few days ago expect to see me shitpost in #real-complex-analysis real soon

[old oak]

Thanks for the warning!

[pure hollow]

you are welcome

[brittle socket]

Just started? Weren't you reading Abbott for some time already or something

[pure hollow]

no it was few days ago and the book i am reading is Rudins

and yes i am very slow

[brittle socket]

You're probably faster than me

[gusty socket]

can we pin this

this is so funny

like this is peak discussion 2

[ocean harbor]

you can't pin it?

[pure hollow]

iirc only senior mods can

[pure hollow]

no

[ocean harbor]

and honorable users too

since when it got changed

[pure hollow]

really?

[ocean harbor]

ye

[ocean harbor]

they pin like this

[brittle socket]

https://tenor.com/view/doubt-press-x-la-noire-meme-x-button-gif-19259237

[pure hollow]

thats the command to pin iirc but they cant pin comments

[surreal sapphire]

just ask lean

[ocean harbor]

used to

#「the-obsidian-twink-jesus」 message

[brittle socket]

I don't think you are slower than me when I'm slow + I prove all* nontrivial theorems by myself + think of and answer my own questions.

*unless I'm not planning to use that theorem and don't find it that interesting or something.

Nowadays I even have sections of self-exercises

[brittle socket]

Before wrapping Rudin up, I'm planning to try to independently develop the theory of derivatives on normed vector spaces and see how far I can get.

It seems fun

[tight gazelle]

1+1=?

[brittle socket]

Efficiency 📉

[pure hollow]

hmm good opinion but one problem I dont understand math

[brittle socket]

In Z_2, the value of 1+1 is equal to your creativity.

[tight gazelle]

2+9+9-5=?

[brittle socket]

Wdym

[tight gazelle]

"grass"?

[ocean harbor]

https://cdn.discordapp.com/attachments/952271935620915225/1296951967981109288/download.gif

[north topaz]

@zinc tartan hey saw you ask a question about your IA

it's south

[zinc tartan]

Yooo hey South

funny running into you here

could you help me out?

Im getting ghosted by the IB server 😭

[north topaz]

are you AAHL or AASL or what, remind me again

[zinc tartan]

AA HL

[frosty cradle]

Any ambidextrous Mathies in chat???

[past pecan]

Me

[frosty cradle]

Fr

[frosty cradle]

Fr?

[past pecan]

Yes

I m 14

[near prawn]

Imagine being ambidextrous. (I am dyspraxic.)

[old oak]

I'm ambisinister

[frosty cradle]

What do you do most on a daily basis

Please keep the answer pg

[pure hollow]

wise owl how should i survive the shitpost that is real analysis?

[frosty cradle]

Like I don’t wanna hear something that may incriminate the conversation

Or see

[old oak]

There's nothing shitposty about real analysis.

(Except for the recommendation of Rudin as a book for beginners)

[pure hollow]

the thing with analysis is that i am too slow and i dont feel any progress is there any method to help me do it faster?

[tender tulip]

https://tenor.com/view/whatever-go-my-scarab-gif-7579664463809719282

[old oak]

Doing it in an university course, since then the pacing is imposed on you

[steady jacinth]

same same

[placid patio]

I can’t send pictures here

Though

[vast surge]

Ah.

Sure, open a help channel then.

[placid patio]

Posted

[burnt dune]

literally math is learnt by asking the most stupid questions and working things out

yet alot of people just love acting elitist and trivializing non trivial things and hence making asking them stupid questions just more of aburden

😦

[hexed pier]

What are some ways to ask stupider questions?

[fresh comet]

an LLM might help you with that

alternatively, you can lurk in #discussion for a few hours

[burnt dune]

like okay i understand if one gets "angry" at an "undefined" question

in the sense that it says that the student is missing a key thing or a prequisite

but like

whtvers

[hexed pier]

It actually did

`Here are a few ways you can embrace asking "stupider" math questions:

Ignore conventions: Try to break rules intentionally, like asking what happens if you divide by zero, or what happens to a negative number raised to a fractional power, without worrying about whether it "makes sense."
Mix different fields: Bring together topics that don’t usually interact, like asking, "What would a complex number matrix look like in 3D space?" or "What happens if I take a limit inside a summation that's inside a geometric shape?"
Mess with dimensions: Ask questions like, "How do I multiply a 1D line by a 3D cube?" or "What if circles had volume?"
Deliberately misinterpret terms: For example, "What would subtraction mean in a world where numbers are emotions?" or "If a function is lazy, how much effort will it take to make it work?"
Ask about impossible objects: "What would a square root of a negative number be if we didn’t have imaginary numbers?" or "What if infinity was just a really, really big finite number?"
Treat math concepts like characters: Ask questions like, "How does zero feel about being used in multiplication?" or "If fractions had personalities, which one would cause the most problems in an equation?"
By making these playful connections or tweaking basic concepts, you’ll explore math in creative, unexpected ways!`

Okay, so something like this

Maybe we can make imaginary numbers real by making them into 3-D numbers?

[alpine kindle]

guh

you made chatgpt invent new crank maths

[solid snow]

this is a pretty good guide of what questions to not ask tbh

[zealous garden]

Yes

[midnight vessel]

Everyone wants to know why you can't divide by zero but nobody wants to know how's zero...

[zealous garden]

This is next level

[hexed pier]

I get so much validation here I’m like a prime number

[bronze pelican]

Cartilage

[foggy pollen]

speaking from experience, yes

but also at the same time, no

[pulsar pagoda]

pin this

[gritty crater]

Lol, I'mma stealing this

[hexed pier]

https://youtu.be/vFBK-jbZjgU?si=W3-MO7_8lhUreLI_

[limber thunder]

in the saying about "stupid questions" the "stupid" is due to the questions being simple or elementary, rather than nonsensical

or so I think anywya

[past pecan]

i do maths for about 6 hrs minimum , do some frontend codes..and 2hrs for other subjects ..i play clash of clans in my free time

[delicate sage]

What do you think of prisonmathproject?

[old oak]

I think sending people to prison for bad math is a radical but promising idea

[static loom]

i extol the death penalty

[old oak]

For bad math or just in general?

[static loom]

ah

math

[raven plaza]

What if we hack the project and train a legion of homotopy type theorists

[old oak]

Very civilized of you

[hexed pier]

I liked how Pythagoras drowned that guy for revealing something about octagons or whatever it was

You could take the centrist position of just sending them to reeducation camps

[delicate sage]

The project is actually about, getting prison inmates into math.

[zealous garden]

the one that proved that sqrt(2) is irrational?

[neat lintel]

Hi

[rain wharf]

Start with game theory… prisoners dilemma.

[delicate sage]

The project has no association with that particular problem. I think they focus on Number Theory. At least it started with Number Theory. It's just to help people behind bars to do something with their lives while inside or outside the walls.

[rain wharf]

I figured as much. I was just being facetious. Ditto the others above.

[thin mural]

Hello guys i have a math question can you help to understand the question itself.
For the function g, if g(5x-1)=x+4, what is the value of g(4)

[surreal sapphire]

please read #❓how-to-get-help

[mild vault]

any porn site

?

[rocky shuttle]

https://www.reddit.com/r/mathporn/

[tender tulip]

Isn’t that just the IRS

[neat lintel]

disscuission 1 is a bit broken, decided to come to discussion 2

[fresh comet]

[neat lintel]

what u up to?

[fresh comet]

not so much rn, how about you?

also, welcome to mathcord!

[neat lintel]

thank u

yeah not up to much as well

just an avg 10th grader

[keen merlin]

can someone get on a call with be and help me out?

[narrow talon]

Man thats tough

[worn garnet]

https://old.reddit.com/r/AskPhysics/comments/1g7wyo5/whats_a_misconception_about_physics_which_mostly/

[dark swift]

whats goin on in here guys

[frosty cradle]

How do yk you are ambidextrous?

[limber thunder]

doesn't ambidextrous just mean you have similar dexterity on both hands rather than just on your dominant hand

[thick yacht]

When you get flipped over in the 4th dimension you can use the same hands just as well.

[grand quest]

Anyone able to help me with collage algebra like asap

[delicate sage]

Why aren't you in jail?

[still walrus]

I have an interesting invariant question which I am on the brink of solving but cannot piece together what the last step should be. I will make a post for it right now but if anyone wants to see the problem/my solution and help me out I would greatly appreciate it.

[ember lance]

king charles visited my city today and I missed it! I thought a professor was kidding when he asked if we were going to go see him 🤪

[surreal sapphire]

england is my city

[ember lance]

He said the king of australia was visiting, so I was like "hmmm isn't the king of australia, the king of england? why would he be in australia?"

turns out he was visiting australia 😫

[surreal sapphire]

turns out australia is your city

is this a thing worth doing

i saw the hand of the late queen of england once

there were so many people

well, i think anyway

this was in like 2014 when someone had a baby and the queen was in buckingham palace

i happened to be there and someone waved from inside

[ember lance]

to me it's like birdwatching (which I also do) but with celebrities

so it's a fun thing to do if it's not too out of my way

[surreal sapphire]

the birds sound more interesting

[vast wraith]

hi i’m slowly dying

[old oak]

Heck, same

[vast wraith]

i included slowly with some doubt

[frosty cradle]

anybody know of a database that has lines of code to practice typing them into a text editor?
C# or C++?

[main elbow]

https://www.hackertype.dev

can problem find some other similar sites searching for 'c++ typing practise'

[ionic spoke]

I'm not sure what this means?

[frosty cradle]

Thanks

[ionic spoke]

like if you want to write code learn how to code, and you're typing speed will increase as you become more fluent with the language

[main elbow]

yh tbh this is kinda the way

[frosty cradle]

Im not realy sure how to rephrase is so you can comprehend it

[main elbow]

just go do a project

[frosty cradle]

no

Thats not the purpose

But I appreciate the input

[ionic spoke]

Ah I see if there is a different purpose to it then that makes sense

[main elbow]

the purpose of c++ typing practise is not to get faster at typing c++ code ?

[frosty cradle]

Yea, If yk of any database like that lmk

[frosty cradle]

Not necessarily the point of it or the end goal by that would natrually be a by product of practicing

[main elbow]

so what is the purpose?

[frosty cradle]

Thats not really relevant

thanks tho

[ionic spoke]

hackerrank public solutions if they have any

[main elbow]

💀 sure

yeah i mean you caould also just go through github

[frosty cradle]

Mmmmh that completely escaped my mind as a plausible option

Thanks for the information

[main elbow]

im ngl if you told us what youre trying to do then youd get better answers lmao

https://xyproblem.info

[frosty cradle]

Probably not but again I appreciate the information

[main elbow]

what is bro hiding

[frosty cradle]

Im not really hiding anything but it would be way too much of a chore to try and explain in a server filled with sarcasm and denial

[main elbow]

not my experience of this server but do what you gotta do ig

[frosty cradle]

Different strokes for different folks

[inland portal]

@hollow sundial what actually happened with you and jon though man?

[hollow sundial]

i'm not here to flame people. don't ping me thanks

[small dust]

yea, save that for hlounge

[hollow sundial]

🤐

[tranquil warren]

[thick yacht]

Where is hlounge? Is it the homotopy lounge?

[small dust]

helpers-lounge

[fresh comet]

[static loom]

https://tenor.com/view/let-me-in-eric-andre-wanna-come-in-gif-13730108

[hollow sundial]

!assign --role helpful --user merosity --sarcasm true

[static loom]

[small dust]

100 hours in the trenches for you

[static loom]

back to grinding the help channels for me to unlock exclusive bonus content

[old oak]

Doesn't seem worth it

[small dust]

it's sometimes a good channel

[old oak]

And you're welcome to it

[zealous garden]

Help channels sound terrible

[vast wraith]

imagine being a nice and helpful person

[fresh comet]

[fervent pebble]

help channels are the worst ever

i only go there if it's someone i know

[old oak]

Statements dreamed up by the utterly deranged

[heavy bridge]

why did i get banned

why did i get banned

[old oak]

For asking the same question twice

[heavy bridge]

this place is litteraly north korea

[old oak]

It's literally not

[heavy bridge]

yes it is

[heavy bridge]

1984

this is iraq under sadam hussein

[old oak]

It's an insignificant discord server.

Easy mistake to make, I know

[inner canopy]

Implying any discord server is significant in God's grace

[old oak]

The 15-person communist splinter server is incredibly significant and shitposting there is praxis which will bring about the fall of capitalism any day now.

Update, the server broke apart due to factional infighting.

[heavy bridge]

https://tenor.com/view/kim-jong-un-gif-25212933

https://tenor.com/view/search-telescope-kim-jong-un-north-korea-leader-gif-16819738

[potent nacelle]

🤔

[fervent pebble]

say it aint so

[safe crest]

Uhhhh guys. So eventually after getting an associate of arts in music, I am going to double major in Computer Engineering and Mechanical. Apart from learning math, what coding languages should I focus on?

[main elbow]

depends what you want to do

and also do you have any experience already with coding ?

what languages is your course going to use ?

as a generic answer i dont think anyone can go wrong with knowing python

[surreal sapphire]

well, if you want to do computer engineering, you wont be able to get around learning C, possibly C++ too

[safe crest]

I took Java in highschool but wasn't really good at it. I got a 1 on the AP Computer Science A exam

[warm umbra]

made you look 😉

[wintry jolt]

BRUH

ARGH

WHYYYYY

did i fall for it

[warm umbra]

W

[wintry jolt]

i am sending assasins to ur location

check the door.

[pulsar pagoda]

Average communist moment

[hexed pier]

Where is that thing where Marx debunks calculus

[tulip pulsar]

hello anyone able to help me with networks

[hexed pier]

Found https://www.reddit.com/r/badmathematics/s/ZbwPWJ63K5

[old oak]

Mathematics is heavily contaminated by the bourgeois ideology

Petition to make this the server motto.

[vivid halo]

Pinko math discord

[hexed pier]

Make a Stinner math I saw them talking about math philosophy and it made me want to claw my eyes out

They should make a creative nothing type in programming languages instead of null it does something random

[old oak]

Just code in javascript for a very similar experience.

[hexed pier]

Don like a result.. have you considered that It’s a fixed idea subjugating the individual? Things existence does not matter outside of your relation to them

He’s like your therapist. The only difference is he understands the intrusive thoughts are right

[old oak]

I mean, with LLMs we are entering an exciting new era of unpredictable programming.

[burnt ledge]

might be a goofy quote but its kinda true tho

[timid ginkgo]

i forgot to get rid of the minus sign after taking the absolute value in an exam 5 minutes ago😔. any tips to stop making this common mistake?

[hardy iron]

After finishing your calculations , recheck each line if you have time

[timid ginkgo]

i ran out of time there because im checking the problem before that one, but thanks for the tip!

im pretty sure i aced it if not for that minus sign

[hardy iron]

I see

[solid snow]

no

[strange hollow]

@jagged forge "file_dependencies.rs"? What are you coding?

[jagged forge]

database stuff

[strange hollow]

gotchya

[urban socket]

Guys what is the most fascinating use of maths you find in computer science, like it feels weird to know it

[gritty crater]

Without math, we don't even have computers let alone computer science. Because a computer is based on Boolean Algebra

So the most fascinating use of math in CS is the creation of computer

[urban socket]

Indeed its cool but if we dive deep into cs, boolean logic is the way math is done in our computers, What I am asking is like the way we use math for clever optimizations, like use of partial differentiation in neural networks.

[gritty crater]

The other application I can think of right now is computer graphics which use a lot of math. Especially linear algebra and transformation stuff

[wispy cipher]

@dusty glen freedom time?

🦅 freedom needed here

[dusty glen]

DOWN BY THE RIVER DO YOU HEAR FREEDOM CALLING ✊🏽✊🏽

[old oak]

Of course not

[fresh comet]

https://tenor.com/view/sinay-yanis-gif-18864293

[zealous garden]

Computer graphics a great application of algebras

[hexed pier]

Maybe spherical harmonics in computer graphics. Probably the most advanced topic I’ve seen used

[raven rock]

e^ipi +1=0

[fervent pebble]

me and the voice inside my head

[sonic sentinel]

it's because of seed oils 👍👍👍👍👍

[vast wraith]

who can understand my work who care

[old oak]

Precisely

No one cares about my work enough to want to understand it

[frank vine]

what tools do you guys use? I'm thinking of buying the gpt plus subscription and using it with the wolfram plugin for learning theory and as well as checking answers (currently have like 5 accounts for when 4o runs out). Do you guys use anything of that sort? (LLMs, other help programs)

[solid snow]

just use free wolfram to check computations

llms are not needed and their use is discouraged to learn math

[frank vine]

they're helping me so much to get through early college right now though, I legit feel like almost having a tutor, imo it really helps

could you expand on why they're discouraged though? aside from their inacuracy at times

[solid snow]

their inaccuracy is precisely why you shouldnt use them

if you are learning proof based material for the first time, you have little way of telling whether its proofs are bs

[mortal mesa]

I'm an electrical engineering student and I've realised that I have really great passion for very abstract things which leads me to mathematics ofc. How realistic is it for me to do a master in math and then PhD in math to land as a researcher at a university or institution? will my degree prevent me from becoming a mathematician? or is it possible? If it's, the way I told you enough or are there specific steps I need to take? Thank you

I don't feel like I will be happy if I continue to my life with this engineering stuff. That doesn't seem like what I want to do

[thick zealot]

Have any of you worked on articles with someone from the discord channel?

[leaden torrent]

"electrical engineering student" tells me nothing about your relevant mathematics background

if youre in america its definitely possible to get into a masters in math and then a phd as long as you, like, have a couple analysis and algebra courses on your transcript

(and an otherwise good GPA)

in the US, masters in maths are often seen as a "bridge degree" for students who want to do a phd in math but dont have the prerequisite knowledge

(for this reason they have something of a poor reputation, but its probably your best path nonetheless)

if youre not in america, this will depend very heavily on the school youre applying to and the courses on your transcript

(by "in america" here i really mean "looking to go to grad school in america", though this is easier for domestic students so ymmv)

that said, if the school just sees a bunch of calculus and linear algebra courses on your transcript and no "rigorous math", they'll reject you no matter what

so definitely make sure to find the time to fit those into your program if possible

even if you want to do applied math instead of pure math theyll still expect you to know basic analysis, ODEs, PDEs, ideally stats/modelling too

and if you want to do pure math they'll want you to have some (proof-based) algebra as well

and either way you really want intro topology; its not necessary but its a good indicator that youre actually taking math seriously

this sounds like a lot, but the reality is that math graduate programs in the US are very competitive (and the field only gets more competitive as you move up in your career, sadly)

internationally it can be better or worse, depending on your country

but e.g. if youre in the EU then its very hard to break into academia with only an engineering degree

theyre much less flexible

even going from CS to math is uncommon in the EU, though it does happen

i wish i had better news but like, youre gonna be competing against students who have read Munkres' Topology and Rudin's RCA

having an unusual undergrad can help you stand out in that it makes you more memorable to admissions committees, but you need to have positive traits that are worth remembering in the first place

when an application lands on their desk with an engineering degree and no math, theyre gonna go into your application suspicious; you kinda need to convince them "no no i actually know math"

[static loom]

yeah if you haven't read a textbook on abstract algebra or real analysis you should probably start

if you don't like that, you won't really like getting a phd in math imo

[leaden torrent]

also to add to this: if this is your plan, expect to pay for the masters

you might luck out and get a stipend but its rare

more commonly youll be given the masters "for free" but ofc then you have to handle living expenses for 1-2 years

and if they're really on the fence about letting you in, theyll make you pay

if youre given a phd offer with no compensation, thats a sign that they really dont want you; for masters it isnt as severe and is more common

honestly for an engineering undergrad, getting a masters offer in math in the first place is kinda lucking out, so you dont really have leeway to negotiate here

physics/econ/cs undergrads tend to have a better shot

as an EE student they might make you take complex analysis which can be helpful, but EE complex analysis courses have something of a... reputation

of being very simplified and nonrigorous

idk whether that reputation is deserved but if thats the only analysis course on your resume theyll probably pass you by

(same thing with fourier/harmonic analysis actually)

[coarse bridge]

ill preface this with saying this is anecdotal but isn't EE fairly within the ballpark of this cause there's a lot of overlap with CS and a decent portion of what doesn't overlap is physics?

or is it a perception thing

[leaden torrent]

EE's overlap with CS is like, boolean logic and thats it

and when i say physics undergrads i dont mean random people who took intro thermo, i mean people who learned basic lie theory and riemannian geometry in undergrad in order to study relativity

it isnt comparable

EE isnt physics + CS, its intro physics + circuits + a bunch of applications

not trying to downplay the work that goes into an EE degree, but the entire point of the degree (and of engineering degrees in general) is to cut out all of the "irrelevant" theoretical stuff and replace it with practical engineering material

but the theoretical stuff is the reason physics/CS majors can get into math programs in the first place

[leaden torrent]

(EE programs often teach some programming but i dont really count programming as "CS", at least not unless youre also learning algorithms alongside)

(in any case, programming experience isnt really relevant to a pure math application at all, and is a bare minimum to get into applied math rather than a real point in your favour)

[coarse bridge]

that's a fair point and probably the deciding factor yeah although i do think what you said about the EE and CS overlap is a bit of an understatement in the sense that i dont think it's majority overlap or something but they share a decent bit of degree requirements and potentially more based on choice of electives (not saying this as an argument for the math stuff just separately)

[leaden torrent]

im curious what overlap you have in mind

in my experience EE programs cover very little CS

elective choice sure but if youre taking electives to get into math grad school you should be taking math electives

(or stats)

not CS electives

like if a math program is considering accepting a CS student, theyre looking for courses like theoretical algorithms, computability theory, machine learning (preferably theoretical/statistics-based treatments), numerical analysis (often under course names like "computational mathematics" or "computer algebra" or similar), graph theory/combinatorics, number theory/theoretical cryptography

i have never seen an EE program require any of these courses

[leaden torrent]

[in addition to math coursework ofc]

and im aware that its possible to get a "computer science degree" without most of these courses, but those students are just trying to do the bare minimum CS coursework for their degree and are otherwise trying to become programmers and enter industry; they are not looking to go to grad school for CS, much less math (and if they applied to either they wouldnt get in)

the problem is less the name of the degree and more the material that gets covered

[coarse bridge]

yeah come to think of it what i might be thinking of are CS majors who choose some of the lower level/EE oriented electives when they get to upper div stuff rather than strict requirement overlap between the majors which is like the opposite direction of what a CS major would wanna do to optimize for a CS or math grad program cause those would probably be in lieu of more theoretical classes

lower level as in like

abstraction

[jagged forge]

me with no degree

[coarse bridge]

i agree with what you wrote though

[coarse bridge]

also what year are you in

think thats important in terms of advice

like i assumed by the way you were talking about it that youre almost done with ug or something and locked into your major for sure

unless you said it somewhere and im illiterate

[coarse bridge]

damn that would feel pretty shit

[hexed pier]

This

[fading sapphire]

is there a point when i should consider dropping my math major and switching to something else

im currently taking real analysis and its making me really doubt my abilities and where i can go mathematically

i take the time to understand the proofs and content in the book, but then i still do poorly with doing the homework

and if that's a struggle for me, then is mathematics even a realistic career for me? is it worth keeping going with the math major?

[granite crag]

@lapis hull Your proofs in the lecture notes are impossible to follow

[lapis hull]

lol which ones

[gusty socket]

there are going to be times where you doubt your ability to do X for every single skill or profession X that is worth doing

[granite crag]

n = m twice and wtf is a "proper prefix" and why does it matter

[gusty socket]

i am currently struggling understanding mathematics. many people struggle in real analysis

[granite crag]

We have infinite variables??? why?

[granite crag]

(from this)

[lapis hull]

Okay I did write this at like 3am

[granite crag]

lmfao

[lapis hull]

Should be n=m and phi_i=psi_i

[granite crag]

yeah that's what I figured

I couldn't figure out what a proper prefix was though

and why it matters

[lapis hull]

Because you sometimes want infinite variables (not for a single formula ofc, but for a set of them)

[lapis hull]

Formulas are strings, so you can look at their prefixes (so like if $\sigma_1\cdots\sigma_n$ is a string, a prefix is a string of the form $\sigma_1\cdots\sigma_k$ for $k\leq n$. It is proper when $k<n$)

[fathom swallow]

Keisler-(Sheli-Shelah) Theorem

[granite crag]

Ok but this makes it sound like we can only define F^n_l when we have infinitely many and we can't when there's finitely many

oh wait

nevermind

[granite crag]

oh I see

ok

you just mean a prefix that isn't the entire string

kind of like "proper subset"

[lapis hull]

Yep

Yep

[granite crag]

I would not have figured that out

ok

[lapis hull]

That's cuz you're SILLY

jkjk all good

Sorry it wasn't clear!

[granite crag]

wtf is even going on here

[lapis hull]

I think I gave an example during the lecture

Suppose I have a formula
$$ \phi = (p\land q)\to r $$
Then I can write $\phi(p,q,r)$ to mean that $p,q,r$ are the variables in $\phi$

[granite crag]

phi is phi(x) or wphi is phi(x)????

[fathom swallow]

Keisler-(Sheli-Shelah) Theorem

[lapis hull]

Ahh

[granite crag]

so w phi = phi???

[lapis hull]

"Now suppose phi=phi(x)" should be "Now suppose phi=phi(p)"

[granite crag]

oh ok

[lapis hull]

Okay these are good points

I'll fix em now

[granite crag]

ok ok I'm not crazy

thank god

[lapis hull]

I mean a little bit

[granite crag]

[lapis hull]

You're in a math discord server

[fervent pebble]

LMAO(

[granite crag]

Hopefully I can follow them now I'll let you know if I can't

[lapis hull]

Okie doke

[granite crag]

@lapis hull This still isn't clear to me, like how does this show that I can't group together terms differently to get a different formula?

[lapis hull]

It's saying you can't group together different formulas to get the same formula

So like if $\land\alpha\beta=\land\gamma\delta$ then $\alpha=\gamma$ and $\beta=\delta$

[fathom swallow]

Keisler-(Sheli-Shelah) Theorem

[granite crag]

right yes

what does that have to do with a proper prefix though?

I don't understand why the proper prefix thing is sufficient

well like

I do inuitively

but not formally

or at least I think I do?

[lapis hull]

Well look at the proof that a proper prefix cannot be a formula

If $\phi_1\cdots\phi_n=\psi_1\cdots\psi_m$, then one of $\phi_1,\psi_1$ is a prefix of the other. But they cannot be proper, so $\phi_1=\psi_1$.
And so $\phi_2\cdots\phi_n=\psi_2\cdots\psi_m$, and you continue

[fathom swallow]

Keisler-(Sheli-Shelah) Theorem

[lapis hull]

This is sorta hidden in the proof that a proper prefix cannot be a formula

oops added a dot at the bottom

[granite crag]

oh ok

[granite crag]

so either phi_1 is a prefix or psi_1, or vice versa, or both?

why can't they be proper?

[lapis hull]

because theyre both formulas

and so one cannot be the proper prefix of the other

(by induction)

[granite crag]

oh ok

so wait what even is our inductive hypothesis?

the phi_1 - phi_i = psi_1 - psi_i ?

[lapis hull]

that a proper prefix of phi cannot be a formula

[granite crag]

a proper prefix of phi_i-1 ?

or strong induction

everything up to that

also isn't n = m trivial since it's determined by the arity of s?

[lapis hull]

Okay so the inductive hypothesis is
$${\cal E}\phi=\hbox{``a proper prefix of $\phi$ is not a formula''}$$
For $\phi=\pi$ prime this is trivial since it is a single character.
Now suppose ${\cal E}\phi_i$ for $i=1,\dots,n$, then we need to prove ${\cal E}{\sf s}\phi_1\cdots\phi_n$.

[fathom swallow]

Keisler-(Sheli-Shelah) Theorem

[lapis hull]

yeah

[granite crag]

An inductive hypothesis has to be indexed I thought

[lapis hull]

well no

because you need to show the unique reconstruction property in order to prove that theres a single way to get to a formula

and so suppose there were two

like if phi1=alpha beta, then sphi1...phin = alpha beta...phin which is n+1 formulas

[granite crag]

oh so by induction we're going from prime formulas to compound formulas

is that the idea?

[lapis hull]

wdym? no it doesnt

[granite crag]

I just didn't understand the IH

I understand it now

[lapis hull]

,tex yeah formula induction is
\begin{enumerate}
\item ${\cal E}\pi$ for prime $\pi$
\item if ${\cal E}\phi_i$ then ${\cal E}s\phi_1\cdots\phi_n$
\end{enumerate}

[lapis hull]

sick

[fathom swallow]

Keisler-(Sheli-Shelah) Theorem

[granite crag]

ok right

[granite crag]

ok so we're proving by induction that a proper prefix of a formula is never a formula, how does this prove unique reconstruction?

[lapis hull]

.

[granite crag]

hmmm ok

[granite crag]

phi_1 ... phi_n isn't a formula though, s phi_1 ... phi_n is

[lapis hull]

the point isnt that its a formula

[granite crag]

oh I understand

I think

[lapis hull]

najs

[granite crag]

phi_1 can't be a proper prefix of psi_1 since psi_1 is a formula, and phi_1 is a formula

and a proper prefix of a formula can't be a formula

ok

[lapis hull]

ye

[alpine moat]

Is this like university level math

[granite crag]

This is ass