serious-discussion

[quick beacon]

(Short for You Only Look Once)

[wild panther]

I appreciate you twin

if there was a fire in a building you’d be the one I’d save

Do you know if I can use it locally on my computer?

[granite kelp]

I'm in high school at this moment. I really don't know if i should focus on advanced math (grad+ level) or master my knowledge on elemental content before graduation

[shut rivet]

do you feel like you need more practice on the elemental content tho

[granite kelp]

I think I have an ok knowledge about my age, but I wouldn't solve something on olympic level

[granite kelp]

I feel myself secure with pre calculus

[shut rivet]

are you in your senior year

of highschool

[granite kelp]

10th year of highschool

[quick beacon]

You can if you can run neural networks generally, it takes some effort to set it up

[shut rivet]

well just finish all highschool math lol

like all highschool math

in your curriculum

[granite kelp]

I already finished this.

But not at a Olympic level, as i said.

[shut rivet]

oh thats it ? precal ?

did you start cal 2 ?

and how about geometry and all

like coordinate geometry

3 dimensional geometry

[granite kelp]

No, In my country they don't teach calculus.

[shut rivet]

idk i was in a different curriculum i had cal 2 and geometry and some basic linear aljebra in highschool

[shut rivet]

well then just learn calculus if you feel comfortable with highschool aljebra and are good with trigonometry

[granite kelp]

My real question is:
Should I focus on olympic high school math (because I have some time to it) or should I try learning undergraduate stuff?

[shut rivet]

thats your personal opinion

if you want olympiad medals

then do it

if you dont care

and just want to learn math

then just learn the stuff which you haven't

for example i personally don't care for medals so if i was in your place i would learn calculus

and higher stuff

[granite kelp]

This is what I personally want.

[shut rivet]

me too

i personally don't like olympiad math

[granite kelp]

Same

Thanks for advising!

[shut rivet]

[wild panther]

If I js wanna like put a single photo thru for a design dyk anything that could do that

[quick beacon]

You still need to set everything up if you want to run it locally. There are probably services you can use online if you're willing to allow them to save your photo forever and use it for whatever and also pay them

But I don't know any off hand, and I wouldn't recommend any even if I did

[warm umbra]

welcome to the server @shell vigil

welcome to the server @shut rivet

[shell vigil]

thanks

[shut rivet]

lol

[neat lintel]

Hmmmmmmm I can't understand

[timid portal]

Ok, so a partitioning of a set X is a collection of disjoint subsets of X whose union is X itself; that is, you're putting all of the objects of X into little baggies, of which you have as many as you need, and you throw away all the empty baggies once you're done. For example, {{1,2}, {3}, {4}} is a partitioning of the set {1,2,3,4}: we've placed 1 and 2 into the same bag, and we give 3 and 4 their own separate bag. Other examples include {{1,2,3}, {4}}, or {{1}, {2}, {3}, {4}} (each object gets its own bag), or {{1,2,3,4}} (each object lives in the same bag). In all of these cases, the smaller sets like {1,2}, {3}, and {4} are called "cells".

The trick relies on the fact that every equivalence relation imparts a set partitioning (why? what are the cells of this partition?), and every set partition imparts an equivalence relation (why? what is the resulting relation?), in such a way that for any two objects a,b in your set X, we have a ~ b if and only if a and b belong to the same cell in the corresponding partition.

Hence, if we are studying equivalence relations on {1,2,3} that have 1 ~ 2, then we can just as well study set partitions of {1,2,3} that have 1 and 2 lying in the same cell. If the question is how many equivalence relations there are, we can just as well ask how many set partitions there are, which I think is a little easier to count.

[neat lintel]

Okay!! So we just need to count how many partitions of {1,2,3} have 1 and 2 in the same cell?

[timid portal]

Ye

That's how you'd get the same answer of 2 as you did with executor

You know you place 1 and 2 in the same bag, and then you just ask what happens to 3: should it go into the bag with 1 and 2, or should it go in its own bag? There's only two choices, and thus only two partitions, therefore only two equivalence relations

because they point to the relations in which 3 is related to both a and b, or only related to itself, respectively

[neat lintel]

Mhm mhm

Got it

Thankss

[timid portal]

It also makes a natural extra question easier: how many equivalence relations are there on the set {1,2,3,4} such that 1 is related to 2?

[neat lintel]

2?

[timid portal]

What are they?

or rather

what are the corresponding set partitions?

[neat lintel]

[thorn wren]

Also like there's decidedly more no?

[fresh comet]

@neat lintel welcome to the mathcord

[neat lintel]

Thanks

[neat lintel]

maybe

[thorn wren]

okay which ones do you currently have

[neat lintel]

Partitions?

[thorn wren]

yes

[neat lintel]

{1,2}, {3},{4}

{1,2,3,4}

Andddddd

Okay wait

There are more

If we put {1,2} together. {1,2} {3,4}

Anymore left?

@thorn wren

[thorn wren]

||{1,2,3}{4}||

[fresh comet]

||{1, 2, 4}{3} as well||

[neat lintel]

💀

[raven plaza]

This is just counting partitions of 3 elements

[warm umbra]

welcome to the server @neat lintel

[neat lintel]

My bad

[neat lintel]

Thankss

[warm umbra]

|| made you guys look ||

[raven plaza]

If you think of 12 as one element

[neat lintel]

mhm mhm

So the ans should be 5?

[raven plaza]

Ye

[neat lintel]

{1,2,3,4}
{1,2} , {3}, {4}
{1,2}, {3,4}
{1,2,3} {4}
{1,2,4} {3}

[timid portal]

Like a lot of things, it's easier to see this yourself if you break it up into cases

Case (a): 3 lives with 1 and 2; where do we place 4?

• {1,2,3}, {4} (by itself)
• {1,2,3,4} (in the only other remaining cell)
  Case (b): 3 does not live with 1 or 2; where do we place 4?
• {1,2}, {3}, {4} (by itself)
• {1,2,4}, {3} (in the first cell)
• {1,2}, {3,4} (in the second cell)

[neat lintel]

Oh yes! This makes it easier to think

[timid portal]

Plus it's more clear when your search is exhausted this way

[neat lintel]

mhm mhm

[timid portal]

You can riff off of questions like this pretty easily

if you so desire

you can keep adding elements to the list and asking the same question

or count relations in which 1 is not related to 2

or perhaps 3 is related to exactly one of 1 or 2

etc. etc.

at one point someone said partitioning {1,2,3,4} with 1 and 2 together was just counting partitions of a set with three elements; why?

[neat lintel]

Coz 1,2 has to be together according to the question

So we can just assume it's just one element

Can someone explain "Let R be the equivalence relation on set Z of integers given by R = {(a,b): 2 divides a-b}. Write the equivalence class {0}" What's an equivalence class

[timid portal]

for an equivalence relation $\sim$ on a set $X$, for each $a\in X$, [[a]={x\in X:a\sim x}] is an equivalence class (particularly the one containing $a$)

[fathom swallow]

Flip

[neat lintel]

🤨

[timid portal]

it's the set of all things related to a

[neat lintel]

Ohhh

Ohh

So there has to be a in every set?

[timid portal]

there's some kind of representative for the equivalence class

[0] contains 0, [1] contains 1, [a] contains a

if [a] = [b], then necessarily b is a member of [a]

(why?)

[neat lintel]

Because a= b

??

[timid portal]

no

[raven plaza]

Might be helpful to write down an example

[neat lintel]

[timid portal]

I define a function $f:\mathbb{R}\to\mathbb{R}$ by $f(x)=x^2$, and a relation $\sim$ on $\mathbb{R}$ by $a\sim b$ if $f(a)=f(b)$

[fathom swallow]

Flip

[timid portal]

this is an equivalence relation (why?), and $[2]={-2,2}=[-2]$, yet $-2\neq 2$

[fathom swallow]

Flip

[grim robin]

Yes, learn latex...

[neat lintel]

x^2 will be equal to 4 one way or another. Like if we put 2 as x we will get 4. Same goes for -2.

???

Is this correct?

[timid portal]

technically no by the way you worded it, but you're right that 2^2 = (-2)^2 = 4

what about it?

[neat lintel]

f(x) = x^2

[neat lintel]

here

[timid portal]

yeah, but so what?

[neat lintel]

Here we have the function f(x)= x^2. And f(a)= f(b) even when we have diff numbers. Why? Because of the function. only if i am not wrong

[timid portal]

I'm confused by the motive, I'm not sure what question you're trying to answer

[neat lintel]

I think i got confused too

[neat lintel]

I was just trying to answer the why in this statement

[timid portal]

ok, so your goal is to show that this is an equivalence relation

[neat lintel]

mhm mhm

[timid portal]

what are the qualities of an equivalence relation?

[neat lintel]

It has to be reflexive, Symmetric and transitive

[timid portal]

so your goal is to prove that each of these qualities hold

[neat lintel]

Yes

[timid portal]

do these one at a time; state what each quality means, and prove that the quality holds

I'll critique it in a bit

[neat lintel]

Reflexive = every element should be related to itself. But here 2 is related to -2

Symmetric = If (a,b) is a relation then, (b,a) should also be a relation. It works here

[stark pelican]

That doesn’t mean it isn’t related to itself

That just means its related to something that’s not itself

[neat lintel]

So is it reflexive or not?

[stark pelican]

The way you should write it more formally would be:
a ~ b means f(a) = f(b), and clearly that means f(b) = f(a) hence b ~ a, hence ~ is symmetric

Well, is it true that a ~ a for all a?

[stark pelican]

With less words it says:
a ~ b => f(a) = f(b) => f(b) = f(a) => b ~ a

[neat lintel]

Mhm mhm

[stark pelican]

Can you show that a ~ a?

[neat lintel]

f(a)= f(a). I mean a^2= a^2

[stark pelican]

We know f(a) = f(a) hence a ~ a

[neat lintel]

Yeah

So it is reflexiveeee

[timid portal]

the full statement regarding reflexivity is "every a in R is related to itself"

just like in programming, you must declare your variables before you use them

hence all of this must be prefaced with something that communicates a is a real number; most commonly, "let a be a real number"

the reason why a supposed proof of this "for-all" statement is valid is this: pick a real number. assuming nothing about it, we've demonstrated the goal statement pertaining to this real number is satisfied. hence for any real number you choose, you may repeat the steps taken in the demonstration to arrive at the goal statement. hence this statement is true for all real numbers

now, this particular proof is really boring, because it feels like it's over before it's even started, but it's good hygiene

if your proof is truly a one-liner, you can simply say something like "for each real a, [the one line in question]. we've reached our goal, hurray"

the logic is more important than the writing style, but it really, really helps to have a good writing style

[neat lintel]

Mhm mhm

got it

[stark pelican]

Maybe try something a bit more complex like

Suppose a, b ∈ ℤ, a ~ b if a and b are both even, or are both odd

Is this an equivalence relation?

A problem too simple sometimes feels like you’re just writing some super obvious facts but it still needs to be written so that you learn the process for when it gets complicated

[timid portal]

truth

[shell vigil]

o

even i understand it a bit better now

[timid portal]

you love to see it

[shell vigil]

yeah lol i hated solving for equivalence cause it's always so drawn out but partition sets is just

[junior veldt]

A third equivalent perspective comes via kernel pairs

Essentially the observation that a lot of equivalence relations naturally arise from something like $x \sim y \iff f(x) = f(y)$

[fathom swallow]

Pseudonium

[shell vigil]

i don't know what the tilde means here

[junior veldt]

It means “x is related to y”

[shell vigil]

ah

oh ok i understand

can that come into use while solving though?

[junior veldt]

Wdym?

[shell vigil]

like one way to solve for equi relns is just brute force and checking like i tried, then this way that flip said, so can this result help us in completing an equivalence reln from given ordered pairs?

[junior veldt]

Well what this result says is that if you can express your relation in the form of a kernel pair, it’s guaranteed to be an equivalence relation!

[shell vigil]

ohhhh

pog

damn i didnt know relations was such a detailed concept thanks yall

[junior veldt]

Moreover all equivalence relations can be expressed as kernel pairs

[shell vigil]

yeah i get that, it goes both ways

[timid portal]

I was thinking earlier that if you have a function f : X -> Y and an equivalence relation R on the image f(X), the relation ~ on X given by a ~ b <=> f(a) R f(b) is also an equivalence relation; the only significance here is just that we're replacing the equal-outputs condition with a generic equivalent-output condition

[junior veldt]

Yeah this is related to the kernel pair thing I mentioned

It’s a kernel pair of the function $q \circ f$ for $q$ the quotient map on $f(X)$

[fathom swallow]

Pseudonium

[timid portal]

ahh, the quotient map is sending each f(x) to its equivalence class?

[junior veldt]

Yep!

[timid portal]

very nice

[junior veldt]

But indeed, this allows you to “pull back” equivalence relations along a function

[timid portal]

that's so neat

[junior veldt]

Categorically you’re showing that the “set of equivalence relations on X” can be upgraded to a contravariant functor

[timid portal]

hmmm I have to parse this, because I don't know what it means for a functor to be contravariant lol

[junior veldt]

ah it's just this idea of reversing arrows

so a function from $X \to Y$ gives you a way to turn an equivalence relation on $Y$ to one on $X$

[fathom swallow]

Pseudonium

[junior veldt]

and so if we call the set of equivalence relations $\text{Equiv}(X)$

[fathom swallow]

Pseudonium

[junior veldt]

then a function $f : X \to Y$ induces a function $\text{Equiv}(f) : \text{Equiv}(Y) \to \text{Equiv}(X)$

[fathom swallow]

Pseudonium

[junior veldt]

it's contravariant cause the arrows get reversed

[timid portal]

I see, so a contravariant functor is like, a functor from a category to the dual of another category?

[junior veldt]

we'd call it the "opposite category" but yeah

[timid portal]

oh true

[junior veldt]

so in this case $\text{Equiv}$ works as a functor $\mathbf{Set}^{op} \to \mathbf{Set}$

[fathom swallow]

Pseudonium

[timid portal]

I see, neat

[junior veldt]

the idea of the kernel pair is to just pull back the equality relation on your output set

which is always an equivalence relation

[timid portal]

I think I'm seeing the picture, but honestly I'm not sure what the kernel pair is, in a literal sense

like, to whom do I point at and say "this is a kernel pair" lol

[junior veldt]

Ah so

Given a function $f : X \to Y$

[fathom swallow]

Pseudonium

[junior veldt]

The kernel pair of $f$ is the subset of $X \times X$ consisting of all pairs $(a, b)$ such that $f(a) = f(b)$

[fathom swallow]

Pseudonium

[junior veldt]

Categorically this is the pullback of $(f, f)$

[fathom swallow]

Pseudonium

[junior veldt]

And what’s neat is that this generalises seamlessly to lots of other categories

https://ncatlab.org/nlab/show/kernel+pair

[timid portal]

this is genuinely really good motivation to read more about category theory, thank you

I don't fully see the picture, but I'm becoming happier about some of the terminology, despite still lacking some of the prerequisites

huh, how do you capture the idea of an equivalence relation on a set in a category? maybe an equivalence relation on hom(1, Y)?

[junior veldt]

I’m really glad to hear that :)

[junior veldt]

What do you mean by this?

[timid portal]

well I was trying, and perhaps failing, to encode the information of an equivalence relation on f(X) inducing the quotient map q and the composition qf giving rise to another equivalence relation on X, but without assuming everything lives in Set

here are my struggles lol

I think my questions and concerns don't make sense, sorry about that

my issue is, I was getting antsy about declaring an equivalence relation on Y at the bottom like that

[junior veldt]

Well, a relation on X is just a subset of X x X, right?

That’s what the kernel pair is! It’s a subset of X x X

[timid portal]

oh, so it is lol

well I'm feeling hopeful thanks to your hint, and I appreciate you taking the time to share this

I must think on this, and also sleep lol

enjoy your morning/night

[junior veldt]

no problem! I really love category theory, after all :)

[hallow plume]

based

[junior veldt]

Natural numbers object!

[junior veldt]

sis :)

otherwise I’m doing good

[night nimbus]

can you you get ti-84 to give a function from a table?

[mint canopy]

Are you asking if you can write down a list of inputs and outputs, and obtain 'the' function corresponding to such a thing with a ti-84?

I'm afraid such a thing is impossible, because unless you can write down infinitely many pairs, there will always be infinitely many functions that work.

Perhaps ti-84s can do Lagrange interpolation, but as you've described the problem, you're asking for something impossible.

[night nimbus]

ok, thank you

[untold cedar]

British doctors who smoke have 30% lower rate of getting Parkinson's

yeah, because they die from 10 other things before they get that

[warm umbra]

welcome back to the server @junior veldt 👋

[junior veldt]

hiiiii

[warm umbra]

hey queen!

[junior veldt]

it’s good to be back!

feels a lot better since I was last here

somehow the server seems to have gotten more categorical..

[warm umbra]

when did you leave?

[junior veldt]

Few months back

Since I went into a pretty depressive phase (cause of other life stuff)

[warm umbra]

That sucks to hear, I hope you're doing better now

[junior veldt]

Oh, significantly better these days

Likely cause I accepted my transness :)

[warm umbra]

🫶

[warm umbra]

The future looks bright!

[junior veldt]

mhm!!

[warm umbra]

[untold cedar]

I thought I was imagining that u were previously with a blue diamond :3

my memory isn't that bad lol

[unborn meteor]

btw #1160361906536710265 exists

[latent edge]

same lol

[dense belfry]

Wtf

[junior veldt]

mhm yeah before I did “ask pronouns” cause I was still fairly fluid

now I feel pretty certain in wanting she/her pronouns

[dense belfry]

Yay

[junior veldt]

I’ll check it out!

[untold cedar]

ah, it wasn't a blue one

so my memory isn't that good after all

[pastel blade]

https://tenor.com/view/cringe-gif-26494931

[pastel blade]

aww man , they took my gifs 😔

[junior veldt]

they are very similar colours

[ocean harbor]

you had active role before?

https://tenor.com/view/котик-майнкрафт-лава-minecraft-cat-lava-cat-gif-12019653300971405837

[coarse bridge]

what did vro do to get his active role revoked i've never seen that happen before

[zealous garden]

Become inactive?

[coarse bridge]

Well in the sense of like losing perms along with it

Cause don’t you get another role if you had active at one point and lost it

[zealous garden]

No

If you make it all the way to very active and become inactive, you gain emeritus

Which allows you to keep the perms

[coarse bridge]

rip that guy then

[zealous garden]

Becoming very active is difficult to do in the discussion channels alone

[coarse bridge]

banished to #chill forever 🥀

[zealous garden]

Activity is weighted more heavily in help and topic channels

[coarse bridge]

Yeah I got ts before I was all that active in discussion

From the math channels

Lmfao

[zealous garden]

I made it to very active on discussion alone

[coarse bridge]

Bros a sweat

[zealous garden]

I was going to say "now I have emeritus" but I just checked and looks like I'm very active again

[coarse bridge]

LMAO

[zealous garden]

The other side effect to Emeritus is that instead of becoming active ever again, you skip to very active

[latent edge]

ts pmo

[coarse bridge]

deadass

[zealous garden]

Kinda yeah, sometimes the active color is better

[coarse bridge]

Did they change the role colors or something?

[zealous garden]

They do occasionally

[coarse bridge]

ah

[zealous garden]

I've seen it once or twice while I've been here

[coarse bridge]

At least for the current one I like the very active one better

[zealous garden]

And they do tend to change things wildly on April fool's day

[coarse bridge]

Lmfao checks out

That was whack

[zealous garden]

I was red once, it made me angry because I always want the red role

And I know I won't get the red role that doesn't exist

Such a mean joke but also nice gift

Oh shit you're chipotle!

How long have I not realized

I was going to say "how've you been" but I was there

[coarse bridge]

LMFAO

I thought you knew hahahah

[zealous garden]

No I'm fucking dying rn

[coarse bridge]

We’ve probably had a bunch of convos then in that time that u hadn’t realized

[zealous garden]

No absolutely

[coarse bridge]

I’ve been good though wbu

[ocean harbor]

lmfao

you're right

they literally joined today

[zealous garden]

I've been up, and down, and everywhere in between, so many times

I feel like a universal cover

[coarse bridge]

LMFAO

i get you

[zealous garden]

I think we're up right now, perhaps massively even

[ocean harbor]

https://tenor.com/view/job-jumpscare-job-application-job-meme-job-jumpscare-gif-5102454363566376023

[coarse bridge]

i was expecting a cat ngl LMAO

[ocean harbor]

https://tenor.com/view/eevee-breakdance-breakdancing-rmk-pokemon-gif-26492203

[latent edge]

https://tenor.com/view/fumo-call-touhou-fumo-call-fumo-plush-touhou-fumo-touhou-gif-17952274389320685721

[ocean harbor]

fumo

[true zinc]

it's quite easy imho

or maybe we're just terminally online

idk

[zealous garden]

I had to grind for it

and you aren't in discussion alone homie

I swear you go to help and topic channels don't you?

[ocean harbor]

I think i got active with 10k messages along with discussy

and very active about 20k messages

[true zinc]

veeeery rarely

most of the time we're in discussion, adv lounge, math disc

help channels is like a...maaaybe once in 1-2 months type thing

and even then only one question

[gritty forum]

are the perms the same as postgrad? Ive never even been active but can post images and stuff

[zealous garden]

really? you can?

[gritty forum]

yeah

[ocean harbor]

boosters can too

[zealous garden]

I doubt it's the same perms, I think grad has something extra

[ocean harbor]

this is new

[gritty forum]

ah ok

[zealous garden]

like I think very active has #「the-obsidian-twink-jesus」 , but I know more exist that I can't enter

[gritty forum]

ah yeah i dont have that

[shell vigil]

Even active does

[warm umbra]

welcome back to the server @shell vigil

[shell vigil]

Heh wdym lol i wasnt here b4 i just came for the first time 4 days ago

Also you already welcomed me

[warm umbra]

how did u get active already

[shell vigil]

I did a continuous 22 hour question solving streak as a challenge

💀

[warm umbra]

https://tenor.com/view/crying-emoji-gif-21922016

[shell vigil]

It was fun tho i must say

[lyric bane]

Heya everybody. I need some physics channels to learn it. Can someone recommend a discord server to ask questions

[shell vigil]

Check #old-network

[muted dune]

surely the sane ppl will talk here

surely

@haughty panther what are dynamical systems

is that engineering or still maths

[haughty panther]

#dynamical-systems
it's a field that deals with... dynamical systems. which are in general what is used to model a lot of physical phenomena, so it does intersect nontrivially with engineering applications
though it's not limited to that, every differential equation can be used to define a flow that is a dynamical system (continuous one), but there are also discrete dynamical systems which are usually obtained from repeated application of some map on invariant part of domain

it has some uses in e.g. number theory but i'm not really into that part

[muted dune]

what are u into

i imagine its pretty involved with pdes then

[haughty panther]

PDEs are usually either the object of interest or kind of "motivating example" of projects i take part in
but the main goal is usually to develop some numerical method that allows for either rigorous analysis/calculation of some topological invariant/sth else that will work in more or less general setting, e.g. for analysis of flows constructed from real-world data

it usually involves constructing some kind of combinatorial object from the ds that abstracts away some things but keeps the thing we care about intact

either some conjugation with symbolic dynamical system or things like that

[muted dune]

right

very tricky sounding

[old oak]

In general dynamical systems study iterations of a map T from some space X into itself; to be able to study that meaningfully you need T to preserve some kind of structure, which gives you three broad scenarios:

• X is a topological space and T is continuous - then you've got topological dynamics
• X is a measure space and T is measurable and measure-preserving - then you've got ergodic theory
• X is a manifold and T is a diffeomorphism - then you've got differential dynamics.

In addition instead of/as well as investigating the discrete iterates of T (which would have the interpretation of observing your system at some fixed intervals, like every minute), you could have a real-indexed family of transformations instead (which would correspond to observing your system continuously)

[old oak]

The three scenarios are often combined, for example if you start with a topological space, then there's a theorem that says that there will always be some invariant measures, so you can combine the methods of topological dynamics and ergodic theory.

PDEs are a big motivator for dynamical systems indeed, and it's what a lot of people think of when they hear "dynamical systems", but there's much more to it than that, and a lot of people work in dynamical systems without getting anywhere near differentiation of any kind.

[muted dune]

oh interesting

so it can be a very rigorous pure math field

[old oak]

For example ergodic theory is very related to probability (a measure preserving dynamical system is basically the same as a stationary stochastic process)

[old oak]

It can be and it is, and in fact I see it more as three interrelated fields (as outlined above)

[muted dune]

yea thats actually quite cool

but seems intensely difficult

[old oak]

It has some prerequisites, which is why it's usually not something taught early on.

Topological dynamics is probably the easiest to get into since you only need metric topology.

Ergodic theory requires a solid grounding in measure theory, and some experience with probability helps with the intuitions.

I don't do the differentiable things so I'm not sure what exactly the requirements are there.

[muted dune]

i see

thats pretty interesting

[old oak]

There's a fun book "Combinatorial dynamics and entropy in dimension one" by Alseda, Llibre and Misiurewicz, which has a very low barrier of entry since all it needs is some basic real analysis.

Since it's entirely about continuous maps on intervals, lines and circles.

[muted dune]

oh wait neat

[old oak]

Still very interesting results there.

[thorn wren]

Dynamical systems is the field that studies dynamical systems 💀

[haughty panther]

am i wrong chat

[old oak]

It's true, though

[thorn wren]

Category theory is the field that studies categories

[haughty panther]

that works too
but "analysis is a field that studies analysis" doesn't really work

[old oak]

Algebra is a field that studies algebras

Although it also studies other things

[haughty panther]

i've heard people use term "algebra" to refer to any algebraic structure

[thorn wren]

Algebra is the field that chases diagrams

Analysis is the study of inequalities

[haughty panther]

sociology too
isomorphic fields

[raven plaza]

Analysis is the field that studies analyses

[old oak]

Analysis analysis ||so good they named it twice||

[muted dune]

isnt that right?

[haughty panther]

it also means a specific structure, vector field with a bilinear product

[vivid quest]

This is linear and bilinear amgebra

[coarse bridge]

vector SPACE

[old oak]

https://tenor.com/view/space-tim-curry-gif-7935778

[zealous garden]

Legendario

[sinful shell]

#math-discussion

[shell vigil]

!noadvert

[quasi jetty]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[true zinc]

That's not advertising

[shell vigil]

Why?

Oh math disc isnt considered a help channel?

[fresh comet]

no

it’s a general mathematics discussion channel

[shell vigil]

Sorry, didnt know

[icy heron]

It's almost an advert tho, they posted a question in #math-discussion , then linked it here and in #linear-algebra

[shell vigil]

Yeah thats why i wrote it

[agile badge]

K=FC2?

https://cdn.discordapp.com/attachments/1379495529410461738/1380560656222261389/668b65714e2a5.png?ex=684452ce&is=6843014e&hm=2c2409aeecb58174f9d98fd64224c6eec30a4d0da73102c723b183225d338fae&

[ocean harbor]

https://tenor.com/view/gd-geometry-dash-tidal-wave-my-honest-reaction-gif-10118803229811805653

[tall solar]

Quick! What's the Cantor normal form of $2 \cdot (\omega + 1)$ ?

[fathom swallow]

castan

[tall solar]

Come on, surely someone has an opinion on this.

[old oak]

Cantor does, but he's dead

[tall solar]

That's unfortunate

It's an easy question though.

[old oak]

I'm sure it is if you remember ordinal multiplication, which I don't

I'd need to look it up, which is an effort I am unwilling to make.

[dapper rampart]

so

I find it easier to talk here

[jagged forge]

discussion 2 is a nice place

usually anyway

[dapper rampart]

it's a chill place

are you making a simple server in rust?

[jagged forge]

hm?

oh nah that's just a test file

it's part of my work codebase which is managed by a team of 7 (8?)

[dapper rampart]

what are you doing?

[jagged forge]

working

[dapper rampart]

oh ok

[jagged forge]

sorry i just dont feel like explaining

i guess i am just trying to get a data pipeline running

[old oak]

My reaction was more about the concept of working at all, not about the terse answer.

[jagged forge]

oh nah that was a response at mr manfishiinginthelakewithoutarod

but i share your disdain

work has sucked so much lately

[dapper rampart]

imo, work usually sucks, or sometimes always sucks.

[jagged forge]

well

i enjoyed my work a lot for the first 3ish years

but i've been feeling a bit burned out for the last year and a half

[dapper rampart]

yeah

burnout is annoying

[vocal zenith]

damn vegans

[shell vigil]

Hallo

@wide orbit

[wide orbit]

hi bro

[shell vigil]

How is life in chennai

[wide orbit]

IITM?

[shell vigil]

No bro no iit

[wide orbit]

not chennai though lol

[shell vigil]

Oh damn

I was asking since i hate the heat

So im thinking betn b'lore and chennai

[wide orbit]

I am in a underrated town lol

[shell vigil]

Im in b'lore on vac rn, weather is very nice

Always a bit chilly

[shell vigil]

O

[wide orbit]

You're in vacation in a chilly climate

[shell vigil]

Yess

Came to visit relatives

Your 11th vacation not on rn?

[wide orbit]

not your native lol

[wide orbit]

12th started lol

[shell vigil]

O

[shell vigil]

No my native place is a village

I mean its not a village anymore its a big town

But ive never been there

[wide orbit]

@humble viper

[wide orbit]

I see

[humble viper]

yess

[wide orbit]

oh yeah you're correct lol

[humble viper]

'responsible member' yes i remember

[wide orbit]

@shell vigil shubham is correct btw

[shell vigil]

What does that mean

Correct about what

[wide orbit]

about my join date in this server

shubham do you know that executor is our relative

@humble viper Do you know?

[shell vigil]

Oh

Yes i see that on ur profile now lol

[humble viper]

yes i read the chat

[wide orbit]

You're my senior to discord while I am senior to you in this server while you're senior to me in real life 💀 @shell vigil

[humble viper]

you both are senior to me on discord, on server and in real life

[wide orbit]

we guys aren't sleeping at this time lol

[shell vigil]

Yk each other irl?

[wide orbit]

Is it?

[shell vigil]

Nice

[wide orbit]

for a while

[shell vigil]

What

[wide orbit]

lol

[shell vigil]

You seem smart, you're not a 12th grader?

[wide orbit]

who?

shubham

[shell vigil]

Shubham

[wide orbit]

I see

He rivaled god of algebra a week ago!

[shell vigil]

I had to sleep at 10

[humble viper]

i am

[shell vigil]

Oh so just younger than luffy

[humble viper]

yes

[shell vigil]

Idk who that is

[wide orbit]

tomatoboyeet lol

[shell vigil]

O

Who proclaimed him god of algebra

[wide orbit]

himself.....

💀

[shell vigil]

[wide orbit]

shubham do you wanna challenge our new executor?

I mean our new friend executor lol💀

[shell vigil]

[wide orbit]

It seems shubham don't afford to die by his parents lol

[rancid compass]

How are you all doing guys?

[shell vigil]

Hello, doing good

[wide orbit]

fine, starlits!

[shell vigil]

Wbu

[wide orbit]

bu

[rancid compass]

I'm doing well. What's the topic you guys are discussing

[wide orbit]

just about god of algebra and his rivalry

💀

[shell vigil]

Nothing in particular, we just found at that we're both from the south and went to the same coaching institute

[shell vigil]

And also this

[shell vigil]

Went and going*

[wide orbit]

lol

[rancid compass]

I see so did you enjoy that? What do you study in that institute particularly

[shell vigil]

Jee

[wide orbit]

edit fatigue lol

[shell vigil]

And yes i did enjoy some parts

Math and phys mostly

But not chem

I dislike it

[wide orbit]

chem............

[shell vigil]

I'm on my vacation rn so im spending almost the entire day on this server since 4 days solving math for fun

[rancid compass]

It's rare to like Chem. I like math and physics too and I enjoy studying them. I like linear algebra analysis and some other branches of maths

I also play chess in my spare time

[shell vigil]

I see a lot of people that like it because it's just rotelearning uptil one point but i could never do that. Also idk what linear algebra analysis is since im at a very basic level in my education (just passed out of 12th a month ago)

[shell vigil]

Same, what's your elo? On chess.com or lichess

[wide orbit]

don't you know LA?

[rancid compass]

You took it different I meant linear algebra and analysis so Linear algebra is well known at basic level isn't it?

[rancid compass]

It's not that high wbu?

[shell vigil]

I do wish to pursue math on my own time a bit though, I'm going to be entering cs now so i think they're interrelated upto a point

[shell vigil]

Same i was 1400 at my peak but nowadays i am a 1000 (chess.com)

[shell vigil]

Oh ic ic

[shell vigil]

Yeah i do i just got confused

What does pending postgrad mean?

[rancid compass]

Oh that's amazing that would be hard to do it on your own but you will get that dw . If you ever wanted help you can ask me

[rancid compass]

Oh that's cool

I would like to play with you sometimes if you like

I'm a noob

[shell vigil]

Ok, thank you- my objective is not really to get too deep into math since that wouldnt be optimal for my path rn, i just wish to lesrn a decent amount of math so i can augment that with cs for real life systems

[shell vigil]

Ok sure can i add you as a friend

On discord

[rancid compass]

What are you willing to do in future. That's fair to learn a decent amount and that's better

[shell vigil]

But also now that i think about it i would like to learn a little bit about the basic things for an undergraduate math major since i dont want to feel completely lost like i do rn when i listen to them talk

[rancid compass]

Sure. If you want

[wide orbit]

senior's senior lol

[shell vigil]

?

[wide orbit]

want to do pg but didn't done I suppose

[shell vigil]

Its the only pcm subject that interests me enough to do that, i hate chem and physics at an undergrad level is very different from what ive learnt so far

[rancid compass]

I hopu you will do well in future

[shell vigil]

Thank you

[rancid compass]

what made you hate Chem. For me the reactions are difficult to learn

[shell vigil]

I must go now sorry

Need to sleep

[rancid compass]

Bye hope we could chess sometimes if you want

Good night

[wide orbit]

me too lol

[burnt dawn]

words like "because" and "therefore" hint at a much more fucked version of english than we currently speak

[short pivot]

huh

[vivid quest]

guh?

[burnt dawn]

like- "because" is clearly made from the words "be" and "cause". but if you said "a be cause b", then that would simply be gramatically incorrect. there used to be an english where "be cause" and "there for" were actual terms that were so commonly used that they were united into singular words

[vivid quest]

"i may not have a brain ladies and gentlemen, but i have an idea"

[old oak]

The version of English with "because" and "therefore" is not more fucked up than the version with "skibidi" and "rizz"

[burnt dawn]

thats not english 😭 thats youtube shorts comments language tm

[vivid quest]

you're unfortunately on a math server

[burnt dawn]

bruhh people talk about random shiz here all the time

u think im on a linguistics server? 😭

[vivid quest]

no, people in #serious-discussion are disstinguisshed

[vivid quest]

jkjk dw

[short pivot]

i think it literally means forward from there

[dusky thistle]

@calm kernel What answer did you get for the coloured card problem?

[vivid quest]

n*(n+1)/2

it's always the answer in combinatorics

[dusky thistle]

Erm... very much not lol

You need at least 3 factorials or it's wrong

[vivid quest]

ok lemme n!/(2!(n-2)!)

happy now?

[dusky thistle]

Much better

[vivid quest]

[dusky thistle]

Although the 2! is sus since that's just 2

[vivid quest]

ye an the whole fraction is just n*(n-1)/2

[dusky thistle]

This is the answer in summations rather than combinatorics

[vivid quest]

it's a binomial coeficient also

so pretty combinatoric by nature

[elder tiger]

Hi

4 th grade math is so hard

[fresh comet]

are you 13 or older?

[elder tiger]

Can someone help me make 1/4 bigger

[fresh comet]

<@&268886789983436800> I'm gonna preemptively ping here

[elder tiger]

What that's mean

I know what 1 4 bigger 2 8

[wild lantern]

How old are you?

[elder tiger]

I 14

[wild lantern]

How are you in 4th grade?

[elder tiger]

Jk

[tall solar]

@burnt dawn is right though. Here is a discussion on this very topic.

[cold needle]

lol

[wild lantern]

Okay? So I'm gonna assume you aren't in fourth grade.

[cold needle]

idk who timed out but its ok

[wild lantern]

I timed out

[cold needle]

ye np

they should familiarize themself with the server some more i think

[ocean harbor]

fumo

[vernal arrow]

do you know where the pre university disscusion is?

[vernal arrow]

Thanks @ocean harbor

[wanton axle]

anyone help me with math in dms?

[ocean harbor]

how about no

[fresh comet]

try asking in a help channel

[wanton axle]

I DID!!

[fresh comet]

@vernal arrow welcome to the mathcord!

oh, then just be patient

[ocean harbor]

yeah what he said

https://cdn.discordapp.com/attachments/695514882216427540/1231377074648780830/attachment.gif

[vernal arrow]

Thanks @fresh comet

[green marten]

Where is my welcome?

Like said I like to use this account as a break from my main @velvet dagger one

[vernal arrow]

@green marten welcome to the mathboard!

[green marten]

Thank you! ❤️

[ocean harbor]

wow that's dami?

[green marten]

Yup, when I am on a break from working!

[fresh comet]

LOL

welcome to the mathcord

[green marten]

Thank you, you are a very kind person

I am very excited that you are my friend!

[fresh comet]

I feel like

in another universe

we were extremely good friends

[vernal arrow]

lol

[green marten]

Well shoot, you're right. But lemme tell ya, this moderator gig’s got my back hollerin’ louder than a coyote at midnight. Ol' boy needed a breather. Took me a while to figure out if I oughta be takin’ breaks on shift or not. So I’ve started actually takin’ 'em. Apologies for always working and not checkin’ in with ya much. I ain’t been ignoring ya, just caught up trying to wrangle the chaos. Appreciate your patience! 🙂

[latent edge]

wait is this amy again

i mean ally

[vernal arrow]

oh no...

[limber thunder]

bro is NOT a 40s noir movie private detective

[vernal arrow]

anyone planning for imo here?

[green marten]

Who?

[latent edge]

research job very stressfull...

[green marten]

Brother, we work so much!

I recommend getting a break account.

This counts as utilizing the break room.

Many of those pesky children and adults always misbehavin' in discussion.

[vernal arrow]

"pesky children" 💀

[green marten]

Ah shoot, need to get back to work. Have a nice day y'all! 🤠

[jagged forge]

b r u h

[dreamy ore]

i want these

[latent edge]

amogus

[timid bronze]

https://youtu.be/eQdF8JMCYWo?t=22

[jagged forge]

and here i thought u were returning

[dreamy ore]

also is impost(e/o)r spelled with an e or an o

🤔

[jagged forge]

i always spell it impostor

[dreamy ore]

apparently it is impostor

why did i think it was imposter all this long

[warm umbra]

welcome to the server @green marten

welcome to the server @vernal arrow

[short pivot]

probably because thats how its pronounced (at least in most of NA)

[tepid hearth]

Hello is there any online resources provided here?

[timid bronze]

@dreamy ore Since u beg me so much to join

[dreamy ore]

I NEVER??????

THIS IS ON YOU

😭 😭 😭

[timid bronze]

I have the receipts

[dreamy ore]

PLEASE SHOW ME THEM

[timid bronze]

u thought i can delete fast

u

Smh its always the 21 year olds

[latent edge]

what did I do

[timid bronze]

Ur 21 already i thought not yet

oh wait shiru ur not even 21 yet

nvm im so fake

[latent edge]

yeah im 21 lol

9 more years to die

[timid bronze]

I meant 20 year olds i just wanted to cook my friend shiru

Dont diss 30 year olds

theyre kind

[dreamy ore]

BRO

ur so fake

[dreamy ore]

these arent real messages

[timid bronze]

IM SORRY

Do u even know my exact birthday

[timid bronze]

cope

[dreamy ore]

ummmmm....

july... 18th...?

[timid bronze]

.

wow fake asf

[dreamy ore]

YOU NEVER TOLD ME

[timid bronze]

its the 28th

LMFAo

[dreamy ore]

june 28th?

july 28th?

[timid bronze]

.

july

[dreamy ore]

omg i was actually so close wtf

[timid bronze]

i was born at 12 am

so nearly was born on the 27th

[dreamy ore]

ur so old
july birthday is so fast

i was born in october so im perpetually young 😌

[latent edge]

,av thisisourworld

[fathom swallow]

thisisourworld's Avatar

Click here to view the image.

[timid bronze]

Breh

harassment of my pfp

[dreamy ore]

are those bunny ears

[timid bronze]

..

WHAT?

[dreamy ore]

are those not bunny ears?

[latent edge]

bnuuy ears

[timid bronze]

on the head..? Thats a halo

Tysm for simping over my pfp guys

[latent edge]

did u draw it?

[timid bronze]

Oh no not at all

[dreamy ore]

this cant be hair can it

altho it cant be ears either

wtf is this

[timid bronze]

wings

ITS AN ANGEL?

[latent edge]

wtf

[dreamy ore]

those arent wings

[timid bronze]

Dude

[shell vigil]

The wings are the white things on the back

[timid bronze]

Ur worse than one of my friends who dirtified one of my pfps i changed so fast

[dreamy ore]

^

[latent edge]

are these the same type of wings you'd see for batwings attached to a head?

[timid bronze]

OH

I SEE WHAT UR LOOKING AT

[dreamy ore]

ally u actively said my pfp sucks

[dreamy ore]

😭 😭 😭 😭 😭 😭

[timid bronze]

BC I SAW U CIRCLE THE WING

I WAS LIKE

WTF

[dreamy ore]

I DIDNT CIRCLE THE WING

I CIRCLED THE BROWN THING

[timid bronze]

U DID

U INCLUDED IT

[dreamy ore]

NO I DIDNT

[latent edge]

wdym

[timid bronze]

yea i think thats hair

[latent edge]

we all knew what shiru was talking about

[dreamy ore]

ic

[timid bronze]

its in the circle

Ok i didnt

[dreamy ore]

its also outside the circle

[shell vigil]

[timid bronze]

I get it Ur so good at topology or wrv U know Shapes In 38945098304 folds

[dreamy ore]

me? topology?

[latent edge]

no chance

[timid bronze]

Both of u

[dreamy ore]

ew

why would u think i was into topology

[latent edge]

all what I know is donut = mug

[timid bronze]

shiru im gonna nickname u since ur added

[dreamy ore]

whyd u react to ur own message

[dreamy ore]

to?

[latent edge]

why not

[dreamy ore]

seems pointless

[timid bronze]

LMFAO

[dreamy ore]

im going to murder u

[timid bronze]

Ok do it

Lets see how far u get

[dreamy ore]

my mortar can shoot up to 3.59km

[hollow ginkgo]

That isn’t how you spell shih tzu

[dreamy ore]

so watch out

[timid bronze]

ik thats the joke

My friends dog is is a shih tzu and im so obsessed w him

hes so cute

[hollow ginkgo]

Pics?

[timid bronze]

ya one sec

[dreamy ore]

ally im never going back to my old pfp if u dont change my nickname back

[dreamy ore]

in 3

[timid bronze]

HES SO CUTEE

[dreamy ore]

2

1

[timid bronze]

his name is theodore

[dreamy ore]

oop lost ur chance

[timid bronze]

DUDE I DIDNT SEE

[dreamy ore]

dog

[timid bronze]

Ok whatv idc.

[dreamy ore]

shih tzu is a dog?

sounds chinese

chinadog

[hollow ginkgo]

It probably is

They’re Tibetan

[dreamy ore]

wow... ur so mean yk that

[timid bronze]

ur staying as shit zu

actually

lemme change it again

[dreamy ore]

ur so mean ally

i hate u

[timid bronze]

HAHAHAHA]'

[dreamy ore]

WOW

okay

[hollow ginkgo]

Ally has gone mad with power

[dreamy ore]

i see how it is

[timid bronze]

Bro

[dreamy ore]

blocked

[timid bronze]

U need to see what i nicknamed some of my other friends if u think thats bad

kk lets see how long u last

[latent edge]

hmmmmmmmmm

[timid bronze]

What

[latent edge]

Nothing.

[dreamy ore]

blocked

[hollow ginkgo]

How do you nickname someone on Discord?

[timid bronze]

Aww i wonder who it is

So cute

[latent edge]

you need to add them as a friend

[hollow ginkgo]

Does it need Nitro?

[timid bronze]

No

[hollow ginkgo]

Unfortunate

[dreamy ore]

🤔 probably someone really nice and sweet and cute

and awesome

[dreamy ore]

SO MEAN

[timid bronze]

Bro

if i sent some of my other friends names here

Id be warned

[dreamy ore]

i only have 1 person nicknamed

i dont do it to a lot of people

[latent edge]

what would I nickname ally as

[timid bronze]

Well i do it to ppl i actively talk to

And we talk a lot

[timid bronze]

Id be scared

[dreamy ore]

whos we?

me and u?

we talk a lot?

[timid bronze]

Ok how would i feel if i said u talk to me a lot

Like as if im not engaged.

[dreamy ore]

we dont talk

u bully me

[timid bronze]

.

Oh Ok~

[dreamy ore]

thats what happens in our dms

[timid bronze]

Lemme unadd u then

I only add ppl i talk to

:>

[dreamy ore]

i know u wont

[timid bronze]

Bet

I can go for long

[dreamy ore]

i know u cant

[timid bronze]

Bet

[dreamy ore]

wait

[timid bronze]

Lets give it 3 days minimum

[dreamy ore]

😭 😭 😭 😭 😭

[timid bronze]

See ur crying

[dreamy ore]

[timid bronze]

Ok ur unblocked

No but i actually like

[dreamy ore]

"3 days minimum"

[timid bronze]

had a bet w a friend in a game and

if they lost id block them for 3 days

they did lose and

they were mad at me after i unblocked them .

Like MAD

[dreamy ore]

ive never blocked a friend

meh..

[timid bronze]

I only do it as a joke

[dreamy ore]

im still blocked by that guy

[timid bronze]

i never block. in like an argument

[dreamy ore]

:///

[timid bronze]

Unless i never wanna see u again

Lmfao

[hollow ginkgo]

I didn’t even know it was possible

I assumed blocking someone automatically unfriends them

[dreamy ore]

ally accept my friend request u poopoohead

[timid bronze]

I DID BRUH

[dreamy ore]

it does

[timid bronze]

yea its annoying

so i do

ignore instead

[dreamy ore]

oh u did

[hollow ginkgo]

Discord should have an enemy feature

[dreamy ore]

ok im sorry for calling u a poopoohead

(not rlly)

[timid bronze]

i want discord to make it so deleted msgs cant show on ur screen

[hollow ginkgo]

It’s the opposite of being friends

[timid bronze]

it bothers me when i see a blocked msg notif

[dreamy ore]

u mean blocked?

[timid bronze]

Yes

[dreamy ore]

how come ur worse at english than me

[timid bronze]

dude cuz i forget words

i have brainfarts

[dreamy ore]

dummy

[hollow ginkgo]

@ mods heated argument

[timid bronze]

Ok im blocking u

[dreamy ore]

NO WAIT

😭

[timid bronze]

Exactly

Lol 😂

[dreamy ore]

poopoohead

😎

[timid bronze]

ok ur blocked fr now

[latent edge]

blocking someone doesn't really help if they are in the same server and sending messages

[dreamy ore]

cant even block me

[latent edge]

It's annoying

[dreamy ore]

bro

[timid bronze]

LMFAO

OMFG

NAH

WHATS WORSE IS

HAVING SOMEONE BLOCKED AND

THEYRE INVITED TO UR FRIEND GC

[dreamy ore]

bryh

[timid bronze]

im not in disc gcs anymore but

i was in a 10 person one and

2 of the ppl dated and sm drama happened

when they broke up

[dreamy ore]

dating inside a friend group is weird

ive always found that weird

[timid bronze]

i would never be in a friend group w my future partner im sry

[dreamy ore]

pffff

ally maybe u should try saying that after u actually get a partner

/j

[timid bronze]

bro doesnt know my love life

[dreamy ore]

cant know what doesnt exist

[timid bronze]

Jk i have no partner rn but ive been in 2 relationships

.

Ok how ab u get partner

[dreamy ore]

yeah ur alt account and ur other alt account

[timid bronze]

Mf

[dreamy ore]

im on my sigma arc rn

working on myself yk

😎

[timid bronze]

Actually nvm u can diss my 1st ex

[dreamy ore]

why
were they a bad kisser

[timid bronze]

No just a horrible person

[dreamy ore]

that sucks

[timid bronze]

bro.

[dreamy ore]

what abt ur 2nd ex

[dreamy ore]

what?

[timid bronze]

i would say we r on good terms but i wouldnt wanna reconnect

[dreamy ore]

oh

i see

man

[timid bronze]

a chapter that has ended is a chapter that has ended