serious-discussion

[surreal sapphire]

i think it should be notfallmöhre

we don't really do -

[pale orchid]

for foreign words, sometimes

[surreal sapphire]

als it inherits caps from the noun Möhre

Notfallmöhre

Möhre

nouns are capitalized

beginning of sentences

headings start in caps as well

also in english?

i think so, yes

i am sure

[frigid lark]

ah thank you. Is it worth to learn tikz

I have some html5 canvas experience, should be easy to learn it I guess. tikz-graphs fit so nicely to the text.

[limber thunder]

definitely worth it, another option would be to use e.g. inkscape but I find tikz gives a finer control over the picture layout and how it relates to the whole document

plus there's fun stuff you can do with for loops

[frigid lark]

nice nice, gonna learn

[maiden bear]

I'd like to know the context behind this

about carrots

[surreal sapphire]

Szene 1: Die Möhre betritt den Raum. In einem Sessel wartend der Sellerie. Ungeahnt derer, vor dem Fenster schemenhaft für die Zuschauer zu erkennen: die Gurke.

[devout nacelle]

Scene 1: The....for the....the

[pale orchid]

in front of

[devout nacelle]

[surreal sapphire]

Sellerie is celery

[devout nacelle]

Oh

[surreal sapphire]

thats sad i tried to use vegetable names that are different in english

[devout nacelle]

Sessel?

[surreal sapphire]

like Möhre isnt common, Karotte is more common

which is carrot

[devout nacelle]

Ah

[surreal sapphire]

Sessel is armchair

[devout nacelle]

[pale orchid]

i don't understand the sentence structure of the celery sentence

i would've used erwartet

oder wartend + sein; wartend, ...

idk

no verb = scary

[surreal sapphire]

hmm

[devout nacelle]

[surreal sapphire]

i dont enough linguistics to explain

but its the same in english

maybe its a stylistic device

[pale orchid]

i would buy that, sure

[surreal sapphire]

this is common in scene descriptions for theatre

[pale orchid]

for poetic effect

[surreal sapphire]

(which this was supposed to sound like)

[pale orchid]

that's the impression i got

big words from someone that just failed a safety instruction, but yeah

[surreal sapphire]

i bet more people failed

cant you just retake?

imagine failing and not being able to blame it on the german language

[pale orchid]

yeah it can be retaken as many times as you want

and indeed, native speakers failed it lol

i took it twice and got 39 both times

then i gave up

[surreal sapphire]

lol

tbf admin probably just needs some proof you took it

[pale orchid]

watched a fucking 51 minute video and then spent 2 hrs going through the 10 questions

no, they want you to send the certificate with a digital signature

and you can only get the certificate if you pass

[surreal sapphire]

what kind of safety stuff is this

how to act in case of fire?

[devout nacelle]

What kind of test is this?

[surreal sapphire]

amokläufe

[devout nacelle]

Don't you already know German?

[pale orchid]

brandfall, sure, but also how to deal with dangerous substances and what to do if there's an accident

[surreal sapphire]

ah ok, you deal with dangerous things

[pale orchid]

brief shoutout to different kinds of fire extinguishers, how to use ladders and defibrillators, etc

i don't

i deal with a laptop

[devout nacelle]

Very dangerous

[pale orchid]

but other people in the institute do

[surreal sapphire]

they can explode

well ok

[devout nacelle]

Edd can explode solving those big matrices

[surreal sapphire]

my security briefing was "sign here"

at my first job in industry we skipped the security stuff

and there was an accident

one of my coworkers lost a hand

[pale orchid]

i could brute force it, too. unlimited tries, and there are 10 questions only. multiple choice, you can select as many as you want from 4 options

[surreal sapphire]

and our boss got in big, big, big trouble

because he couldnt prove there was a security briefing

[devout nacelle]

That sounds awful

[surreal sapphire]

it is

[pale orchid]

so something like $\left(\sum_{n=1}^4 \binom{4}{n}\right)^{10}$ options

[fathom swallow]

Edd

[pale orchid]

yeah i think they're being more careful since a mofo forgot to put on safety glasses during a laser welding thing

[surreal sapphire]

thats finite, which concludes the proof

ye, once something happens they make everything way more strict

[deep mango]

[pale orchid]

i do sigproc stuff, but the applications are very industry-oriented

we coop with some institutes that do stuff like inspect railroad tracks, weld stuff, use radar to detect buried mines, and other fun (c.f. super dangerous) stuff

[surreal sapphire]

pinpointing your location

[neat lintel]

wait what do you work in?

[pale orchid]

sigproc

[neat lintel]

what's that?

[pale orchid]

signal processing

i sit in front of a computer and go "lmao correlations"

[neat lintel]

lmao

[analog salmon]

I love how operator calculus always looks like bad math, but works out

[neat lintel]

[neat lintel]

You cant tell me that all of this notation is good, or that all of it is needed

[shy pollen]

ij wasted 3k on a raincoat

why am i this stupid

[chilly wigeon]

Is there a channel for analysis

[deep mango]

There are 2

Go to #get-advanced-access

And then go to #real-complex-analysis or #advanced-analysis depending on what you need

[sonic ether]

Shieeeeeeeeeeeeet

[neat lintel]

did they find it?

[honest veldt]

Wtf new analysis channels?

[mint patio]

I thought I liked power series

now seeing this stuff for ODEs makes me head go

looks like a lot of work for such an ugly solution

[cold needle]

wait till you see frobenius

[limber thunder]

tbh these are outdated methods

people in like the 18th or 19th century cared about solving ODE by power series

nowadays you just approximate a solution by runge-kutta or smth

[mint patio]

why is y'' - y = 0 the classic example

because you get sine cosine out which is satisfying ig

[cold needle]

and matches the other methods we have

[ancient flame]

geometric calculus is cool af

like $\prod_a^b f(x)^{dx}$ is the geometric integral

[fathom swallow]

gmod

[ancient flame]

when I learned about this I think I came

[deep mango]

[cold needle]

STOP BEING HORNY FOR MATH

[fair mural]

bruh

how do you even respond to this

[honest veldt]

You don't

Just let it sink in silently

[ancient flame]

LOL

[swift sinew]

What’s the intuition for a staircase with n stairs from (0,0) to (1,1) not having a limiting length equal to sqrt(2)?

[untold sapphire]

i mean have you tried working out the length manually in the case n = 1, 2, 3

[swift sinew]

I mean obviously the length is gonna 2 for all n but why does it differ from the expected limit if you look at “the limit” geometrically?

[untold sapphire]

ok, i see

imo calling it the "limit" geometrically is up for debate as jagged things and smooth things have big differences between them, i mean you know the old question "How long is the coastline of britain"

it depends on the scale at which you measure it! do you post a marker every mile, every ten miles, etc

or if you looked at a picture of the stock market graph from today and asked "what's the total cumulative change in the value of the stock, counting all ups and downs, all highs and lows"

if you looked at the change every five minutes and added them all up you'd get a different answer than if you looked at the change every hour

the "limit" you're talking about of the staircases is IMO an infinitely jagged thing and we shouldn't expect it to resemble a smooth thing

[swift sinew]

Ah that makes sense. Though if you decided to define the limit in some fashion similar to being contained in an arbitrarily small rectangle around the straight line, would the difference then be that the staircase has some “measure” (in a loose sense) that’s different than the straight line?

[modern bramble]

Maths is my crush, i will do what i want.

Darling Mathematics,will you marry me?

[untold sapphire]

hmm ok i have come up with an answer

[deep mango]

You could make the zig zags go more steeply and then the length would be even longer

You could make the length infinite

[untold sapphire]

my idea is that the length of a curve c is like

[deep mango]

Sorry triangle inequality

[untold sapphire]

$\int_x T(x,f(x), f'(x)) dx$

[fathom swallow]

diligentClerk

[untold sapphire]

where $T$ is a function of both $x, y and dy/dx$

[fathom swallow]

diligentClerk

[untold sapphire]

so we should only expect length to be well behaved with regards to the limit of a sequence of functions $f_n\to f$ if $f_n\to f$ not just "pointwise" but also in terms of the derivative we also have $f'_n(x)\to f'(x)$

[fathom swallow]

diligentClerk

[untold sapphire]

I think for complex analytic functions you get this automatically but not in our example

[swift sinew]

I’m having a bit of a hard time understanding why the length of a curve is some int{T(x,f,f’)}

I guess I get it, but I have a hard time seeing why x and f’ also need to be arguments for T. Isn’t just f sufficient

[untold sapphire]

https://tutorial.math.lamar.edu/classes/calcii/arclength.aspx this is what i'm talking about, i just abbreviated some stuff

as we go from $x$ to $x+\Delta x$, if we assume that the curve is locally linear then the length is roughly given by the pythagorean theorem, i.e. $\sqrt{(\Delta x)^2 + (\Delta y)^2}$

[fathom swallow]

diligentClerk

[swift sinew]

Gotcha gotcha

[untold sapphire]

and i'm using the approximation $\Delta y \approx \Delta x \times (dy/dx)$

[fathom swallow]

diligentClerk

[untold sapphire]

so it simplifies to this $\int \sqrt{ 1 + (f'(x))^2} dx$

[fathom swallow]

diligentClerk

[untold sapphire]

which is what i mean we should only expect length to behave well wrt limits of functions if we also have $f'_n \to f'$ because $f'$ is what actually appears in the definition of length

[fathom swallow]

diligentClerk

[swift sinew]

That makes sense, does this seem like something that might have an already-existing formalization?

[untold sapphire]

uhhh i don't really know enough analysis to answer that but it I think that we should have the precise theorem that if $f_n \to f$ (where $f_n, f$ are continuous and differentiable) on the interval $[a,b]$ and so does $f'_n\to f$ on the same interval, then the lengths of the $f_n$ should converge to the length of $f$

[fathom swallow]

diligentClerk

[swift sinew]

I feel like that implication is in the opposite direction than what would answer my question, but I guess it’s satisfying to the extent that for the staircase, the antecedent doesn’t hold so I shouldn’t expect the consequent to hold

Sorry if that was worded confusingly

[untold sapphire]

nah i get what you mean

it's not a direct explanation, it's more just showing that the obvious theorem you would write down doesn't imply that this is true

[swift sinew]

Seems this question has already been asked on stack exchange: https://math.stackexchange.com/questions/1810336/does-there-exist-a-if-and-only-if-condition-so-that-arc-length-of-a-convergent-s

Not much new there outside of what you’ve explained here

[untold sapphire]

mm nice

[honest veldt]

the only dog person in this discord, this is shocking stuff

[mint patio]

why do we care about phase portraits and trajectories and whatnot

[deep mango]

to understand what happens when the equation can't be solved

at first you just do them for linear equations

but later you do them for nonlinear equations (in particular, you often look at their linearizations around equilibrium points)

and the phase portraits can tell you a lot about solutions without you knowing how to actually solve for them

[mint patio]

how are you supposed to obtain the trajectories without having the solutions?

[deep mango]

(e.g. the poincare bendixson theorem is a big theorem in this regard)

[deep mango]

i mean you can't get analytical descriptions of them but you can understand what they do topologically by looking at the vector field that the system of ODEs gives

"topologically" isn't really a technical term here

i guess the better word is "qualitatively"

so, for example, maybe you don't know what solutions are, but using the phase portrait you see that all the solutions are converging to some stable equilibrium

like a sink

[mint patio]

so important things to consider would be the limiting behavior of solutions, holes/regions where they blow up, etc?

[deep mango]

yep

and sure, just looking at a picture isn't a proof

but the picture can tell you what to do to get a proof

[mint patio]

And solutions x(t), y(t) only differ up to constant right?

[deep mango]

uhm for linear inhomogeneous equations

or

idk

that might not always be true

[mint patio]

This is what I have

[deep mango]

no that's not true usually

[mint patio]

So one ODE/system can have multiple solutions?

Ignoring constants

[deep mango]

well

no

or

at time t_0, you give an initial condition

the initial condition is just the point where you start

the ODEs tell you how to move from that point

[mint patio]

ok that's what I meant, mb. the only difference between different trajectories is different ICs

[deep mango]

yeah

but the trajectories don't need to be like

translates of one another

[mint patio]

oh

[deep mango]

they could do totally different stuff

[ancient flame]

imagine math papers using comic sans

[swift sinew]

Isn’t that not necessarily true for non-convex sets or am I misremembering

[deep mango]

(the important thing is, if you pick 2 points, then either the trajectories they are on are disjoint, or they are the same trajectory - as long as time goes forward and backward)

this is just cause if the two trajectories ever collided

then from then on, the derivatives along both are the same

and by the fundamental theorem of calculus, if two functions have the same derivative and are the same at a point, they are the same function.

[deep mango]

idk what you mean by this

[mint patio]

I'm confused, aren't we multiplying constants most of the time anyways? Why is"don't need to be translations of one another" something important to mention? Aren't they usually not translations of each other?

[swift sinew]

Like if you have this system over that kidney-bean shaped set, multiple functions can satisfy this system and have the same value c_1 but different values c_2
(Feel free to ignore this if it’s obtrusive to the convo)

[deep mango]

i just meant when you said they differed by a constant, to me that means if i take one curve (as a function of vectors in R^2) and another curve and subtract them i get a constant

and that's not always true

(if it were true, one curve would be a translation of the other)

but that's not what you meant so it's fine

[deep mango]

i mean i don't consider f here as one solution

i get what you mean but

like to me a solution is only valid on a connected interval

[mint patio]

Oh wait

hm

I'm testing it with x = e^t, y = e^(-t) and different constants and they are translations of each other

let me try other functions

when I subtract them I just get 0

oh

idiot

ok nvm I am not getting constantw

yeah I'm so confused

how are solutions supposed to be different besides with constants like this

any ode's gonna have a unique fundamental set of solutions right?

[shy pollen]

everyone is mac at me

[mint patio]

so the only way we can get different trajectories is with different linear combinations of the fundamental set

[shy pollen]

but i just blocked my friend bc i made fun of her career path

[mint patio]

what am I misunderstanding?

[sick burrow]

Alg top is weird

Like this feels like the next big step up in abstraction for me

[crystal stone]

eh

[sick burrow]

Because it's like my first real encounter with the whole approach of turning one thing into another thing and then studying the properties of that new thing

Like even in my other advanced math classes, I'm still studying the properties of a thing in "its own language" so to speak

Idk. Like I'm getting it, but it feels harder than anything else I've done.

[swift sinew]

Can we get a “how to get help” mentions over time graph, possibly normalized to number of users?

It really feels like we’re saying it extremely often

[uneven steppe]

^

[swift sinew]

And a ban count tbh holy crap

[leaden torrent]

theres no easy way to get those numbers without running a bot

if you want it to be measured over time that is

mniip could probably easily add it to bot, but im not sure what that'd help with.

[sick burrow]

What are the most common reasons for a ban

[leaden torrent]

if you just want a total ban count, we have 3147 banned users

this is different from the total number of bans though

since bans from about 2 years ago have all been thrown out

(when we shifted over to the ticket system, we undid a lot of old bans)

[leaden torrent]

scambot.

by far.

[sick burrow]

Besides that

Like bans of actual users

Not bots

[leaden torrent]

just trolling i guess

[primal crater]

got 2 users banned due to rude behaviour

[leaden torrent]

if youve only sent 8 messages on the server, all in #chill , and 3 of them are racist or transphobic, we typically wont give a second chance

we're a little more lenient (read: mutes with strong warnings instead of bans) if the user has contributed to the server in another way

since perhaps they just said whatever message out of ignorance

but thats less common

[uneven steppe]

Period

Anyway need advice on something

[sick burrow]

I wonder what the ratio is of the different types of bigotry for banned users

[leaden torrent]

in my anecdotal experience, transphobia is the most common

[sick burrow]

That's what I've noticed too but I'm obviously biased to notice it more

[leaden torrent]

also a lot of people in help channels calling others idiots/r*rds/autistic or whatever

which i guess you could classify as bigotry

thats gotten less common recently though

like, even before the new help channels, it was on the decline

which is nice

[uneven steppe]

He was 13 anyway and annoying

[sick burrow]

Like the people asking for or giving help

[leaden torrent]

both

[uneven steppe]

Wait anyway I teach a recitation at 9:00 tomorrow but I’m not tired bc I took a nap should I just stay up and study all night lmao

[leaden torrent]

youll feel tired eventually.

[sick burrow]

Honestly this server is impressively well moderated

[leaden torrent]

no it isnt

[sick burrow]

Ok there are some annoying emote spammers that should be banned or at least muted

[light needle]

if it were well moderated how am i not banned

[sick burrow]

Spamming and whatnot

But besides that

Idk I just feel like "public discord math server" are not the words that make me think "good community"

[light needle]

yeah to be fair for a public discord server this is like

surprisingly good

[crystal stone]

no it isnt

[light needle]

we could have been like, the physics server

[crystal stone]

what are they like, sir john

[swift sinew]

How’s that server doing btw

[light needle]

A lot of racism and stuff in the upper ranks from what i understand

[sick burrow]

Smh I'm trying to suck up to Namington here so I get Honorable

[light needle]

I mean public servers are like

a menace to humanity usually

[crystal stone]

why do you care if you get honorable or not

[light needle]

ya know

[sick burrow]

Don't interfere

[sick burrow]

Status

(I'm meming)

[crystal stone]

Ah I c

Some people really overly value that stuff

[sick burrow]

I kinda want to join a large public server

And just die

[light needle]

you already are in one

already dead sorry

[sick burrow]

No like a larger more mainstream and toxic one

[light needle]

probably joining a gamin community will do that

[leaden torrent]

WHAT IF I WAS WRONG AND NO ONE CARED TO MENTION
WHAT IF IT WAS TRUE AND ALL WE THOUGHT WAS RIGHT WAS WRONG

[light needle]

is this from a song?

[sick burrow]

I've already seen old discussions of this so I know the majority of you will disagree and claim that mutate is weak. Lots of gas lighting trolls up in here. I pretty much just play Arena but I win the majority of my games. The only thing I consistently lose to is mutate decks or one of several super combo decks where suddenly I'm hit for 50+ damage in 1 turn. Mutate literally beats anything that doesn't play faster or isn't more or less an antimutate deck. So then your only options are mutate deck or antimutate deck. I can't even think of another set of cards that comes close to buffing like mutate does.For anyone who disagrees, please tell me how YOU would beat a mutate deck without saying "cancel deck" that's not playing. That's nobody playing.
p.s. Whatever you assume of my deck construction it doesn't change the fact that mutate is the only deck type that I struggle against. In Arena I'll quit discard/ mill matches cus I just don't want to deal with it.
TLDR Most deck types are useless trash against Mutate decks.

Ok what is the best copypasta

[leaden torrent]

negate revel in riches

[leaden torrent]

https://www.youtube.com/watch?v=PaMiVDZu_T4

[sick burrow]

Before this gets deleted by reddit admins this asshole took it completely out of context

[leaden torrent]

its an incredible pasta since its 100% genuine

[pale orchid]

namington is poorly moderated

[leaden torrent]

and he actually thought itd make him look better

[sick burrow]

The best pasta are always the ones originally written unironically

[light needle]

[sick burrow]

DesolatorMagic moment

It brings me great joy that in addition to be a raging bigoted asshole, he's also just shit at mtg

[inner finch]

mm oo mmm ooo mmmm oooo

[compact tartan]

yea

now I've become one

the vicious cycle continues

nah that's just being an asshole

is this happening on here or elsewhere?

that should not be happening in here

[distant vortex]

If you make a typo, that's one thing. But if you don't know how to spell a word and keep getting it wrong, I'm sure the intention is to just tell you so you learn how to spell it.

It's not cocky.

I know what incident you are referring to, and you misspelt it the same way more than once.

No, you think it's cocky for them to call you out for disappearing for 20 minutes while they are waiting in the channel to help. That's not cocky.

she

After she said that, it still took you 25 more minutes to actually reply

So I don't think it matters what she said, you weren't there

Lol

You are way too sensitive, but okay, I'm not interested in arguing with you. Just letting you know that from reading the exchange, I don't think she did anything wrong.

[neat lintel]

Hold on.

Somebody clue me into this?

[distant vortex]

Okay, next time tell her you will wait for someone else to help you rather than continuing to let her help you and then once you get what you need, you come here to complain.

[blazing pawn]

This is so sad

[distant vortex]

No one is responsible for what other people have said to you in the past. Nothing she said is very egregious, so it really shouldn't have upset you this much.

[neat lintel]

That's a good analogy.

[distant vortex]

Please stop pinging me when you reply

[blazing pawn]

This is so silly

[distant vortex]

I'm done here since I think you are unreasonable

[neat lintel]

Strike, we all have bad days, but that isn't the way one should cope up.

[blazing pawn]

Getting your spelling corrected is not a valid reason to rant here for 20 minutes

[distant vortex]

No, the problem is that you think someone correcting you is them being cocky, when it's just them correcting you.

[neat lintel]

Heard about displacement defense mechanism?

You're frustrated, so since you're frustrated you take it all out on somebody.

On everyone?

Then who?

[blazing pawn]

Please stop ranting here

[neat lintel]

There's a better way to channelize all your frustration.

this chat belongs in #vent

Hope you could take that into account.

Hmm???

[distant vortex]

My time to vent: I am in shambles that I was blocked by Read.

[neat lintel]

That's sad.

[frail lagoon]

dino

[neat lintel]

Hang on.

He edited a message.

[deep mango]

Lol

[maiden bear]

LOL what is that whole convo

i saw the help channel earlier

[distant vortex]

Don't laugh at my despair

[maiden bear]

didnt expect it to escalate like this

[neat lintel]

Let this one slide.

And i never saw the help channel.

Oh.
I thought "help channel" to be a vent channel or something.

[maiden bear]

HAHA

[neat lintel]

Didn't catch you there.
Discord servers who offer to help someone?

I've seen many vent channels. Maybe they do.

[maiden bear]

[frail lagoon]

[reef carbon]

what happened here, god damn

[toxic schooner]

[neat lintel]

[thorn brook]

[reef carbon]

nice vaguepost btw

[neat lintel]

toki mfking doki

[shy pollen]

fortnoight

[neat lintel]

Toki is amazing. Toki is cool and trusted and talks and is very active

[paper peak]

hello

can anyone help me on a simple matrix problem?

[neat lintel]

#❓how-to-get-help

[swift sinew]

Why do the discussion channels feel post-apocalyptic? Feels like it’s just a whole lot of wreckage

[leaden torrent]

early morning hours

they always get like this

[neat lintel]

this is #serious-discussion not #vent

thank you.

[neat lintel]

however, you got no excuse

mniip said yes

i mean, we discourage venting here, so it's best to vent on private server instead

also i'm not man

but ok

yes, why are you still asking?

[maiden bear]

read their about me

[deep mango]

in shambles

[maiden bear]

in shambles

[honest veldt]

in sandles

wait

That's not how you spell that

[maiden bear]

in sandals

[honest veldt]

day ruined

Thanks

[distant vortex]

I don't think anyone wants that

Rate My Helper

[fair mural]

helpers pretty much don’t even respond to pings lol

i imagine that they all have pings disabled

[primal crater]

u don't need to imagine, it's the truth

ppl take the helpers role for the 'color' only

[fair mural]

lol

[primal crater]

I got blue so I don't need green

[fair mural]

this blue is pretty cool though

[primal crater]

cyan's my fav tho

🌈

[distant vortex]

They set everyone's nickname to a random number

[fair mural]

make me grahams number

[primal crater]

if a custom bot does it then no

[primal crater]

a prime number

[fair mural]

oof

[leaden torrent]

that is literally what we did

this april fools

[fair mural]

wow

[leaden torrent]

next one probably wont be nickname related

[fair mural]

why

[primal crater]

[leaden torrent]

because itd be the same joke twice?

[fair mural]

beaned

[primal crater]

this time make it a prime number

[leaden torrent]

how long

ok.

[primal crater]

make everyone a MOD

a fake one

[fair mural]

@primal crater assigning a role to 70k people

[primal crater]

a bot will do it in seconds

[maiden bear]

depends on where its hosted ig

[compact tartan]

as if we've ever planned ahead

[toxic schooner]

how did i miss that

[analog salmon]

I didn't realize I was gonna have to learn so much german for alg. geo

first hilbert's nullstellensatz, now Krull's hauptidealsatz

wtf is this

[maiden bear]

LOL

[honest veldt]

How do you even say that, my guy

[maiden bear]

i mean the first one is just hilberts root theorem translated i guess

the second one idk

my english maths vocab is not sufficient there

[fair mural]

i love math but i wouldn’t learn another language for it lol

[analog salmon]

I think it's "principal ideal theorem"

[maiden bear]

yeah the thing with ideal is always

its several meanings

in english and german

[analog salmon]

I swear I remember reading that back in the 70s or 80s or something at yale you had to learn a language commonly used to publish math to get a math major

or maybe it was in their grad school

had to learn russian or french or something

[wild lantern]

I think that used to be a thing at several places.

My school has a language req

I can't remember if it's just the math dept or not tho

[mint patio]

I do not like systems of differential equations

For the sole reason of I do not understand drawings

[frigid lark]

I like euler method, cus its simple to solve those equations. But I didnt bother yet with the analysis approach

[ancient flame]

math major moment

[mint patio]

I'm an engineering major

I think we would do better with STEM major moment

[ancient flame]

lol true

[maiden bear]

nah what

drawings slap

even though i cant draw for shit

[ancient flame]

lol

[simple cliff]

calculus is the best

🙂

[fair mural]

it is pretty cool

[simple cliff]

quatum phyics in interesting got to learn calculus to understand it tho

[fair mural]

i haven’t actually gotten to calculus 3 yet but i’ve looked over it a bit and it looks really cool

[simple cliff]

im in cal 1 going for engineering

aerospace engineerin going to a college close to get regular classes done

hope i can transfer to georgia tech

[untold sapphire]

satz just means statement (theorem)

hauptsatz means something like, principal theorem or main theorem

[tawny spoke]

haup-on-deez-natz

[leaden torrent]

if only calculus was sufficient for quantum stuff

maybe people would stop overhyping it so much

[river linden]

relevant xkcd:

[leaden torrent]

id swap special relativity and magnets tbh

you can visualize the underlying mechanics behind special relativity quite easy even without an understanding of the mathematics that births it

good luck doing that with magnets

why do magnets need a north and south pole??? why arent there poleless magnets?

[limber thunder]

I feel old

[wild lantern]

On the bright side I suppose faygo soda is fairly cheap.

[simple cliff]

really

?

[leaden torrent]

really what

[toxic schooner]

calc is not sufficient for quantum mech lol
nami was saying if only it was, maybe then it wont have been so popular

[timid spindle]

quantum mech is overrated.
You sussy baka, Nyah

can't even solve classical problems 😐
You sussy baka, Nyah

[inner finch]

You sussy baka, Nyah

[toxic schooner]

but i have wanted to do it for over 10 years

[cold needle]

what

bro i didn't even know i was gonna do math until literally maybe 3 years ago max

how do ppl find out about this shit so soon yo

[timid spindle]

BRUH!
you know you have to go through books.
You sussy baka, Nyah

[toxic schooner]

probably coz my dads a physicist

[toxic schooner]

yeah ik i have to go through books

[primal crater]

too advanced for this channel

[inner finch]

lol

[compact tartan]

I think that chart is referring to the way they are typically introduced in a physics curriculum. So the necessary math for magnets is multivar calc, not fuckin lie theory

[leaden torrent]

idk man, multivar doesnt help me understand why they work

it helps me compute shit about them sure

[neat lintel]

lol

[deep mango]

I want to do quantie!!!!!

[neat lintel]

Really?

[turbid epoch]

math makes me feel very self confident but then I realize I'll die broke and lonely /s

[toxic schooner]

yeah

[primal crater]

https://fb.watch/9fwGqP34D9/

for my indian friends

[turbid epoch]

I'm getting out of here

[devout nacelle]

Bruh

[turbid epoch]

This video gave me blood pressure.

[primal crater]

ok

[raven vector]

Lmfao

[round umbra]

Lol

[neat lintel]

fuck fb

[neat lintel]

That is so cool

[toxic schooner]

[neat lintel]

do you guys know of any good website to practice trigonometry, which has a choice of practicing basic things or advanced. just annoyed of looking at worksheets which don't even have answer keys

[distant vortex]

Khan academy?

[neat lintel]

any other too?

[distant vortex]

I don't know any

[neat lintel]

youtube.com

google.com

khanacademy.org

brilliant.com

[distant vortex]

Read got rid of the Helper role

I would tell her that's based, but she blocked me

[neat lintel]

brilliant costs some dolla dolla bills, i am broke, but everything else works, khan academy looks fine

[sterile hare]

stepdatabase.maths.org/

and then type in 'trigonometry'

😎

[neat lintel]

aops

i forgor

[sterile hare]

http://jeeadv.ac.in/pastqp.php

[neat lintel]

[neat lintel]

HOLY SHIT! thats a gold mine Right there!

[neat lintel]

Give my boi azeem321 helper role please'

he deserves it

ask mods for helper role

[devout nacelle]

Helper role is literally punishment

[sterile hare]

lol i posted it as a joke because those are quite hard problems, but if you think you can do them then glad to be of assistance

[neat lintel]

i agree with janman

[neat lintel]

just give the man a role, he Deserves some colorful text in his life.

[devout nacelle]

[fair mural]

someone getting helper role is just giving them 500 pings a day

[neat lintel]

1984 pings

[neat lintel]

if i can't do them now, ill do them in the future regardless. Slowly climbing the ladder. no one knows math at the start, but they eventually get it.

[surreal sapphire]

helper role has rights now though

[fair mural]

like what

[surreal sapphire]

close question channels

[sterile hare]

need a hint on help-20 pls

[hollow vale]

anybody know if this paper is legit? Looks like it proves the remaining unknown Moore graph does not exist, the one with degree 57 and diameter 2. If so the wikipedia page for moore graph needs to be updated, as it's no longer an open problem. https://arxiv.org/abs/2010.13443

[devout nacelle]

Have you checked if this paper has been submitted/accepted for publication anywhere?

[neat lintel]

this is beautiful

[neat lintel]

...

[fair mural]

you have role pings disabled don’t you @neat lintel

[neat lintel]

nope

[fair mural]

how many pings do you get a day

[neat lintel]

...

ignorance is bliss

i dunno, ask Google 😎

fuck google

[ancient flame]

is there any way to think about $\int \frac{f(x)}{dx}$?

[fathom swallow]

gmod

[icy forge]

No clue, but the person has a Math net ru page and it seems pretty extensive.

[mortal igloo]

Yeah, you're dividing a function by a differential form to get section of the tangent bundle, but you can't integrate that kind of thing

[ancient flame]

alright thanks

[subtle mortar]

anyone mind answering this question for my data project?
How Much Phone Screen Time Do You Have per Day? (In Minutes)
and
How Much Computer Screen Time Do You Have per Day? (In Minutes)

[neat lintel]

[hollow vale]

Thanks ShatteredSunlight, yeah it seems like the author is legit

[shy pollen]

fortnite

[swift sinew]

This might be heresy, but is there anyway to get a role where the help channels are inaccessible/not visible?

[sick burrow]

You can mute them

Then if you minimize the category it hides everything

[leaden skiff]

you can also tick the "hide muted channels" in the server settings and hide them.
but you will have to manually hide each channel and can't just hide the category

[timid spindle]

computer time -> infinity

[leaden torrent]

0.2103495009000539124852931855 minutes (how long it takes me to turn my alarm off in the morning and turn it back on at night, measured using an atomic clock)
3.419 * 10⁵² minutes (measured using observations from a collection of telescopes around the earth's orbit, time dilation effects unaccounted for, accuracy subject to atmospheric effects)

you're welcome

[cold needle]

thanks

[timid spindle]

[limber perch]

not the atmospheric effects

[real sigil]

hey i wanna talk maths

i got a question or two

[raven vector]

Dont ask to ask

Just ask

[shy pollen]

no don’t ask pls

[real sigil]

i will, i am sorry, they left me no other choice, i want my family back ...

anyways

lets see

when we say complex numbers

do we mean the unreal numbers, or real numbers + imaginary ones

[raven vector]

Only imaginary numbers

[real sigil]

so this image is wrong right?

[raven vector]

Ig

[real sigil]

what we would we call the set that contains real + complex numbers

would it be computable numbers?

[neat lintel]

complex numbers are in the form a + bi

[honest veldt]

You'd call it the complex numbers

[neat lintel]

so you could say real number + imaginary

[raven vector]

No, a + bi is a complex number

[neat lintel]

yea

[raven vector]

it has a real ‘part’ and imaginary part

[neat lintel]

where a is the real component and bi is the imaginary one

[honest veldt]

Imaginary numbers are just complex with a 0 real part

They're all in c

C*

[raven vector]

Complex = imaginary

[real sigil]

oh that make sense

[neat lintel]

don't think so

1 + i isn't imaginary is it?

[honest veldt]

It's complex

[neat lintel]

yea

[real sigil]

yeah its kinda confusing

[honest veldt]

Complex and imaginary aren't the same

Imaginary is a part of complex numbers

[real sigil]

based on what i understood, complex can be non real, while imaginary has to be non real

[neat lintel]

yea?

[honest veldt]

yeah, that checks out

[raven vector]

Ah ic i acc didnt know that lol

[surreal sapphire]

0 is imaginary probably

[honest veldt]

Yeah, in a+bi, you say the real part is a and the imaginary part is b

[surreal sapphire]

it is also real

[raven vector]

Ik just thought complex and imaginary were the same smh

[surreal sapphire]

ultimately it doesnt matter though, i have never encountered a reason to consider purely imaginary numbers

[honest veldt]

Ah gotcha

[neat lintel]

yea ig it's easy to think that

[neat lintel]

I know complex numbers have actual applications but I guess imaginary numbers don't?

[surreal sapphire]

the imaginary numbers are just another copy of R inside C

[raven vector]

They have applications

Qm, qft

[real sigil]

is there a name for the set that contains algebric + non algebric numbers

[neat lintel]

yea it's used as a complex number

[real sigil]

or would we just go with complex

[surreal sapphire]

every (complex) number is algebraic or not algebraic, so ...

[real sigil]

oh i guess

is there a non complex number?

[surreal sapphire]

number isnt really a well defined term

[real sigil]

then, infinity?

[surreal sapphire]

no

[raven vector]

Infinity is not a number

[real sigil]

what even makes a number?

is it the "value"

because imaginary numbers dont really have that known concept of values

yet they are considered numbers

[surreal sapphire]

well

i would define a number to be an element of a skew field

numbers are things you can add, subtract, multiply, divide (with an exception of division by 0)

[real sigil]

make sense

also, lets say a graph, with a curve, we made sure that each Y has no more than one X

does that mean that this graph has a function ?

[leaden torrent]

it means that the curve is the graph of some function

(in absence of any other disqualifying information at least)

[real sigil]

damn, theres like an infinit possibilities of graphs, didnt expect each of them has an functional expression

[compact tartan]

"function" doesn't mean "formula"

some functions don't have formulas

[real sigil]

oh for real?

lol

didnt know that

so basically, if i see a graph, that doesnt mean it has a formula?

wow

[river linden]

yeah just draw some squiggly line, that squiggly line doesn't have a formula that's exactly equal to it at all points

though you can find formulae that approximate any graph arbitrarily well @real sigil

[real sigil]

yeah i guess you can aproximate a formula for every curve you see

[river linden]

you can actually prove that you can for reasonable curves, ie. all the ones you could draw without picking up the pen

[real sigil]

it sounds quite weird to me how you can formulate every curve

[river linden]

well, you can approximate any function with a polynomial as well as you want, so that lets you formulate any curve as close as you want

i can't really explain in detail since you don't know calculus

[real sigil]

sadly

[river linden]

the main idea is that you can approximate any function with a piecewise linear function

basically a bunch of small connected lines

by making the lines small enough it approaches the function

then you can approximate the piecewise linear function by a polynomial as well as you want, so overall you're approximating any function arbitrarily well by a polynomial

[real sigil]

so we transform the curve into tiny lines?

like old people used to do to circles in order to calculate their perimeter

[river linden]

yeah exactly

[real sigil]

in that case, is it easy to make a formula for those lines?

[river linden]

well it depends on your definition of "formula", you can get a piecewise function that describes those lines

it would look something like
$$
f(x) = \begin{cases}
m_1x + b_1 &\text{ if } x \in I_1 \
m_2x + b_2 &\text{ if } x \in I_2 \
\vdots \
m_nx + b_n &\text{ if } x \in I_n \
\end{cases}
$$

[fathom swallow]

uli

[real sigil]

in this case we have divided the curve into 3 lines right?

oh wait nvm

[river linden]

i've named the intervals $I_1, \dots, I_n$

[fathom swallow]

uli

[river linden]

so we basically cut the function into a lot of tiny bits that are very close to being linear

[real sigil]

oh nice

that makes it really clear now

[river linden]

yeah thats one of the main ideas in calculus

if you zoom in closely something is linear

then if you take lots of those linear guys and add them together you get the function

[real sigil]

this cant possibly contain all of the graph, but will sure makes it alot easier to understand

[real sigil]

makes sense

[compact tartan]

you're not capturing the function exactly

rather forming a sequence of approxmations

that can approximate the function arbitrarily well

[real sigil]

yeah its sad how this is the best thing we can do

ill try to invent a computer that can make formulas

gimme a good 15 yaers

[compact tartan]

well

[real sigil]

and aloooooot of patience

[compact tartan]

forget functions

there are real numbers that don't have formulas

in fact "most" of them don't

[real sigil]

dude....

how come ive never realised that

lmfaoo

[compact tartan]

the argument is really simple

[river linden]

computable numbers

[compact tartan]

there's only a countable number of formulas, but uncountably many real numbers

[real sigil]

yeah theres like a ton of nonfinite numbers with no formulas to represent them whatsoever

infanct its an infinit amount of numbers

[river linden]

do you know what countable/uncountable means?

[real sigil]

i guess?

countable means it has some sort of representation

like sqrt x or cos x or something

[river linden]

countable means you can enumerate them all, the natural numbers are countable since 1,2,3,... enumerates them

uncountable means you can't

the natural numbers, integers and rational numbers are all countable

[real sigil]

oh so we are talking about decimal numbers and non decimal

[river linden]

but the real numbers are not

no

well

[compact tartan]

words in a finite alphabet are countable

you can enumerate them by listing first all 1-letter words, then all 2-letter words, etc

every word will be eventually listed

[river linden]

the way I like to think about it is every computer program can be represented as a finite list of zeros and ones, therefor they are countable

and since the real numbers are uncountable there must be real numbers that cannot be calculated by programs

[real sigil]

what are examples of something uncountable

[compact tartan]

subsets of N

there's no way to list all subsets of natural numbers

[real sigil]

it pains me to say that i dont cognize what that is

[river linden]

the real numbers, the set of all infinite binary strings 00010101... (which is equiv to reals in base 2)

[compact tartan]

"equiv" is a strong word

but yea

[real sigil]

is countable and uncountable a state of one single number or a set?

[compact tartan]

it is a property of a set

[real sigil]

in that case, no set is actually countable

right?

because they have equally infinit amount of numbers

[river linden]

[real sigil]

well maybe not equally

[compact tartan]

"uncountable" is in a rather precise sense a "larger" way for a set to be infinite

the set of natural numbers, while infinite, is not very "large"

[real sigil]

||damn, its 2021 and people are coming up with things bigger than infinity ||

yeah

[compact tartan]

when were cardinal hierarchies invented? gotta be 1910s

[river linden]

two infinite sets are said to have the same size if you can map one to the other and back again in a 1-1 fashion

[compact tartan]

the idea of uncountable sets probably comes from 1700s

[real sigil]

the infinity provided in the amount of numbers of the natural set
should be smaller than the
infinity provided in the amount of numbers of the rational set considering it has the same numbers + more

am i collecting you this way?

[compact tartan]

actually maybe 1800s

[compact tartan]

funny that's actually not true

[real sigil]

how come lol

[compact tartan]

they're actually the same "size"

[real sigil]

becuase inf = inf

yeah it makes sense

but still kind of paradoctic

[compact tartan]

.

there's as many natural numbers as there are even numbers

and as there are rationals

but less than there are real numbers

but there's as many real numbers as there are complex numbers

[real sigil]

this is weird lol

[river linden]

they all make sense once you see the proofs/reasoning

[real sigil]

its like we are no using the same constitution in different comparisons

[compact tartan]

it is a finicky notion

[real sigil]

ok i get whats before this, but what changes exactly so that real numbers are said to have more numbers

[compact tartan]

hard to say "what changes exactly"

[real sigil]

cant we still do a 1-1 fashion in between real and natural?

[river linden]

no

[real sigil]

we have like, a batallion of naturall numbers

still not enough?

[river linden]

too many, that's the problem

[compact tartan]

we don't have enough natural numbers

[river linden]

you can always find a real number that isn't on the list

https://www.cs.virginia.edu/~lat7h/blog/posts/124.html

[compact tartan]

so maybe to motivate this a little

there's this thing called the pigeonhole principle

[real sigil]

so basically, this theory (rule) indicates that infinity is equal to infinity, but only in some cases

[river linden]

where if you have n+1 pigeons and n holes then two of the pigeons have to get comfy

[compact tartan]

if you have a function f : X -> Y, where X and Y are finite sets, with, say, m and n elements respectively

if f is surjective, then necessarily m <= n

if f is injective, then necessarily m >= n

if m <= n, then there exists a surjective f, and if m >= n then there exists an injective f

this is why we use surjections and injections to talk about "sizes" of sets

because these generalize beyond the finite case

albeit you lose some things

e.g. an infinite set can inject into a proper subset of itself

[river linden]

surjective means every y has an x with f(x) = y

[compact tartan]

but this is why, generally, when we ask, is X a larger set than Y, we are really talking about whether there exist injections/surjections between X and Y

[river linden]

and injective means f maps every x to a unique y

[real sigil]

so if we represent X with natural numbers, and Y with real numbers, we would have F (x) = y being an injective function

?

[compact tartan]

we could come up with an injective function yes

[river linden]

you can form an injection from N -> R because the size of N is less then R

[compact tartan]

but we wouldn't be able to come up with a surjective one

[real sigil]

but you cant form an injection between N and, say Q?

[compact tartan]

yes you can

[river linden]

you can

[compact tartan]

this is like

bog standard intro to proof topic

[real sigil]

this "function" we are using, can it be any type of function?

[river linden]

you represent the rationals in a square then you take the diagonals to get a list [r1,r2,...] of all the rationals

since any rational number is somewhere in the square, say at (x,y) you have the rational number (x/y) then eventually it is in our list

since we made a list you can make a function from a natural number to that element in the list f(n) = r_n

bing bang there's your surjection

[real sigil]

so basically, this shows how clear it is that Q contains N

[river linden]

no, see this

[compact tartan]

"contains" doesn't mean much when it comes to size

[river linden]

it shows we can find a map from N to Q that "hits" every rational number

[compact tartan]

this is precisely what I meant when I said

[8:48 PM] mniip: e.g. an infinite set can inject into a proper subset of itself

[real sigil]

so this is a surjection

[compact tartan]

sure

[real sigil]

do we not have a surjection when it comes to even numbers To whole numbers?

[river linden]

we do

[real sigil]

but still he said theres as many natural numbers as there are even numbers

[real sigil]

wait my bad i meant natural

[river linden]

yeah, so we have a surjection

whole numbers? you mean integers? [0, -1, 1, ...]

[compact tartan]

surjection means more-or-equal

injection means less-or-equal

[real sigil]

no i meant, naturals, sorry

surjections means more or equal

[compact tartan]

you can build a surjection both ways

so they're more-or-equal than eachother

i.e. equal

[river linden]

yeah so if we show N is more or equal to Q (the rationals) then they must be the same "size" since N is in Q so N is also less then or equal

[real sigil]

this equal thing is the problem, i see

"equal"

[river linden]

no its not a problem if you show a >= b and b <= a then a = b

"equal" refers to our invented notion of equal size

[real sigil]

but we already know that N=/= Q

[river linden]

you're confusing set equality with cardinality equality

N is not Q but their size is the same

since you can map N -> Q and Q -> N in a 1-1 fashion

[real sigil]

is there somehow a dependable term that is exactly like sur/in jection but does not include "equal", making it absolutely bigger/smaller than the given value

[river linden]

well if you had >= and != then you get >

(greater equal, and not equal implies greater then)

[real sigil]

so what is the function surjection helping us prove here? if it isnt for determining the > or <

its kind of null how we go back to = from >= and <=

[river linden]

do you know what a bijection is?

its basically an invertible function

ie. surjective and injective

[real sigil]

like, the amount of X = Y

[river linden]

if f : A -> B is bijective then A and B have the same size

this is our definition

[real sigil]

yeah thats it

[river linden]

for finite sets it makes sense, since {a,b,c} and {1,2,3} can have the mapping f(a) = 1 ... etc

now for infinite sets it gets tricky, but this is the definition of size we're using

listing the integers as [0, -1, 1, -2, 2, ...] gives us a function from N to Z that's bijective

therefor size(N) = size(Z) by our definition

[river linden]

a similar thing can be done with Q by taking diagonal slices

[real sigil]

isnt every infinite set-contained function bijective?

as either >= or <= will deliver us back to = which bijection

[river linden]

not either, you need both

[real sigil]

yeah...

[river linden]

wdym "infinite set-contained function bijective"

[real sigil]

i mean, the function where X and y are infinite set

sets

[river linden]

ah

1 sec lemme show you the proof that R is uncountable

meaning it is not bijective with N

basically, suppose f : N -> R is bijective

we can represent each real number as an infinite decimal (rationals become 0.400000000000...)

then we flip every digit in the diagonal creating a new number

since we flipped the first digit it is not equal to the first number, since we flipped the second digit it is not equal to the second number...

our new real number cannot be in the set

by construction

therefor f is not bijective and so R is uncountable

https://youtu.be/elvOZm0d4H0 is a good video if my explanation is bad

[real sigil]

f : n -> R is not bijective, meaning R is absolutely bigger than N

can we prove also that Q is asbolutely bigger than N?

[river linden]

no, card(Q) = card(N) but card(R) > card(N)

since we can find a bijection from N -> Q by taking the diagonals of

[real sigil]

given that q=n, then r>q

[river linden]

yes

[real sigil]

oh makes sense

so R is the bigger one, whilst the ones below it are equally equal to each other

[river linden]

yeah

[real sigil]

damn thats an interesting way to validate it

[river linden]

actually it gets hairy, there might be infinities between N and R

[real sigil]

wdym infinities

[river linden]

that was a famous problem in math

like, a set A with card(A) > card(N) but card(A) < card(R)

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

it turns out it's independent, ie. there might or might not but either way we'll never know since our axioms are not strong enough

or: you can assume its true or its false and it doesn't effect anything

[real sigil]

i think the safest choice is to assume bijection

if its not right then its not wrong

no?

[river linden]

i'm not a logician so idk ¯_(ツ)_/¯

[real sigil]

yeah i get it

[river linden]

there are also sets larger then R

theres a theorem that the set of all subsets P(A) is always larger then A

so the set of all sets of real numbers is a bigger infinity then R

[real sigil]

what???

the set of all sets?

[river linden]

the set of subsets

[real sigil]

like the sum of whats inside R

[river linden]

P(N) = {{1}, {1,2}, {1}, {1,3,4,9}, ...}

the set of subsets

[real sigil]

this looks kind of weird but ok

[river linden]

in fact P(N) = R which kind of makes sense if you consider decimal expansions as lists of natruals

[real sigil]

is it equal or bigger?

i think its =

[leaden torrent]

is what

|P(A)| > |A|

this is a strict inequality

youll never have |P(A)| = |A|

https://en.wikipedia.org/wiki/Cantor's_theorem

in the finite case, it turns out that |P(A)| = 2^|A|

this isnt hard to justify with elementary combinatorics.

[real sigil]

i think so, yeah

[leaden torrent]

(though formally speaking, such a justification is probably circular... but meh)

[river linden]

proof by thinking: for each element of A we could include it or not include it in the subset, that's 2 possibilities for each element of A so 2^n possible subsets

[real sigil]

i mean i guess you can justify it as long as |P(A)| = 2^|A|

[river linden]

well, that doesn't work in the infinite case

basically another contradicty boi

also why tf does wikipedia use xi for an element of A

[real sigil]

thats pretty random lmao

[river linden]

suppose $f : A \to P(A)$ is surjective, and consider $$B = {a : a \notin f(a)}.$$ there must exist an $a \in A$ with $f(a) = B$ since $f$ is surjective, but this causes a contradiction since $a \in B = f(a)$ contradicting the construction of $B$ which implies $a\notin f(a)$

[fathom swallow]

uli

[real sigil]

surjection usually cause thus kind of paradox

thats why we take bijection for infinit sets

[leaden torrent]

bijections are just 2 directional surjections

(assuming the axiom of choice)

https://en.wikipedia.org/wiki/Schröder–Bernstein_theorem

(its phrased using injections, but you can just flip the arrows of an injection to get a surjection)

[river linden]

the paradox is what makes f : A -> P(A) impossible to be bijective

[real sigil]

yeah its meant to simplify it

[river linden]

I could have assumed f was bijective as well since bijective implies surjective

[shy pollen]

obviously lol

[neat lintel]

What are some interesting/cool facts or properties of Lagrange Polynomials?

[swift sinew]

They were not discovered by Lagrange but instead by Edward Waring

They can be used to give very high order numerical approximations of integrals (see Gaussian Quadrature)

[crystal stream]

Is it just me or can they be derived by using cramer's rule on a vandermonde matrix system

[neat lintel]

That sounds very interesting, thanks!

[neat lintel]

A matrix of matrices

[elfin thicket]

a matrix of matrices of matrices

[elfin thicket]

a matrix of matrices of matrices of matrices

we now just invented “infinite matrix composition” cool name huh?

M[(a(b(c(d(e……….if there were infinite letters in the alphabet)))……)]

[toxic schooner]

i present to u, matrix cat

[pale orchid]

how about matrix cat transposed

[turbid epoch]

really tho, can we have a matrix in a matrix?

[toxic schooner]

i can do that

but i dont want to

[simple raven]

Yes ! You can look at matrices with coefficients in any ring

And there exists a lot of rings of matrices

[turbid epoch]

I'll... pretend I understand this for now.

I just started abstract algebra.

[simple raven]

Any commutative rings* (I don't know otherwise if it works well)

[toxic schooner]