serious-discussion

[tall badge]

sure we can show the sum of i^2 is that by induction

[obsidian jolt]

I bought an abstract algebra book several years ago but I didn’t have the mathematical maturity to do the proofs

[tall badge]

but how do you think we made an educated guess as to what that formula even is

[mint patio]

huh

okay

good point

[tall badge]

same for sum of i

[neat lintel]

Also, this allows you to (in theory) construct an explicit formula for sum_i i^n

Just iterate.

[tall badge]

a slick way to make an educated guess on the formula is what gauss supposedly did when he was 8

[obsidian jolt]

yeah

That only applies for sum for first power of n though

[tall badge]

(that was the case n=100 but doesn't matter)

[neat lintel]

\begin{align*}
\sum^n_{i=1} [i^4-(i-1)^4]&= n^3\
&=\sum^n_{i=1}(4i^3-6i^2+4i-1)
\end{align*}
There you go, from that you can get the sum of cubes.

[steep mountain]

[fathom swallow]

Tesseract

[neat lintel]

You can also derive it using the crank above.

Gauss's way is a lot cleaner, though.

[tall badge]

field axioms are NOT designed to be wieldy in everyday use. they're meant to give just enough to develop the algebra laws we took for granted in high school

[neat lintel]

\begin{align*}
n^2&=\sum^n_{i=1}[i^2-(i-1)^2]\
&=\sum^n_{i=1}(2i-1)\
2\sum^n_{i=1}&=n^2+n\
\sum^n_{i=1}&=\frac{n(n+1)}{2}
\end{align*}

[fathom swallow]

Tesseract

[mint patio]

I know, I understand why it was necessary. I just don't like that type of proof lol

Having to prove something turbobasic

I think I'm just being a baby

But I'm not going to stop :^)

[steep mountain]

its kinda fun

[mint patio]

Yeah no no point lol just venting

When Rokabe brought up "How do you think they came up with that formula" that did a lot for my perspective on it

I still find it annoying but him and Tess are right, it's not pointless

Just annoying

[neat lintel]

At the same time, there's a one-of-a-kind sort of feeling when you first prove that 2+2=4.

[mint patio]

LOL

Can't you just do that with Peano axioms

[neat lintel]

Yes. If you really dislike yourself, you can do it from ZFC itself.

[mint patio]

Fuck no

LOL

I'm a masochist Tess, not a psychopath

[neat lintel]

I did not say it was a good feeling, just one-of-a-kind.

[mint patio]

:^)

[neat lintel]

What did the folks in Principia start with?

[deep mango]

[tall badge]

indeed fields having quite a bit of structure makes other structures that depend on them quite nice. wieldy refers to having to go back to axioms every time when doing a typical manipulation in real analysis instead of prepping algebra laws beforehand

[mint patio]

Would you have to take an abstract algebra course to appreciate that?

[tall badge]

you can get a glimpse of it in linalg

[mint patio]

With what? Noncommutativity of matrix multiplication?

That's not very nice

That's all I can think of though

[tall badge]

sure you can compare the amount of structure fields have to rings (of which sets of matrices are an example)

[mint patio]

Right

I hate when I want to complain about things but they make sense so my complaints don't make as much sense -.-

idk how to word it

[tall badge]

specifically the comparison you may have in mind is that multiplication in fields commutes but multiplication of matrices (type of ring) may not

[mint patio]

Yup that's what I thought too

[neat lintel]

This is funny.

[tall badge]

within the first few days of an AA class, an even bigger difference can be seen in comparing a field to a group (which has just 1 operation unlike fields)

[mint patio]

I want to take AA but it doesn't interest me as much as analysis so I'd rather take analysis classes first but then all anyone talks about here is algebra stuff >.>

[mint patio]

wtf is this

"It is used at least three times in ..." lul

Well I guess they're not wrong about it being occasionally useful

Finished the problem too, this was good

[surreal sapphire]

analysts are too busy working to waste time on discord

[bronze pelican]

Fields are just places to do arithmetic

[deep mango]

[compact tartan]

funny part is that people think it's some sort of complicated nonsense

but it's really just if you union two disjoint one-element sets, you get a two-element set

[neat lintel]

my brain machine is broke rn
trying to do a cool computer thing

Say you have a 4d parametric curve p(t) = (p1(t),...,p4(t))

how would one "step through" slices of that using a 3d plotter to see a region the curve passes through

if you plot the projection (p1(t),p2(t),p3(t)) it's almost like taking the whole 4d curve and just smushing it into 3d

is there any nice way to represent the 4d curve in 3d over time?

You can do it with volumes more easily like if you have a function w=f(x,y,z) you just plot the volume you get from fixing w to some constant c and plotting f(x,y,z)=c

but what about parametric curves?

I was thinking maybe you do the same thing kinda but instead set p4(t_c)=c some constant, solve for t_c and then plot (p1(t_c), p2(t_c), p3(t_c)), would that work?

then do a lil animation like -10<c<10 or something

oh and even better, swap the functions around so that p4 is the simplest to invert of them all

and just rotate your 3d graph later if necessary

[neat lintel]

Huh, neat!

Have you read through the Principia?

[compact tartan]

I have read enough introductory chapters to get through the notation

[compact tartan]

map one of the coordinates to color?

or to time

the latter will give you a moving point

[mint patio]

[neat lintel]

TRUE THANKS SO MUCH

[vague lion]

bruh

why

[compact tartan]

expanding my horizons

[vague lion]

no

reducing them

[compact tartan]

the foundations they use are quite different from what's popular nowadays

[vague lion]

staring at badly designed cramped notation until you go shortsighted

[compact tartan]

who cares about the notation

[vague lion]

...

me

[compact tartan]

I'm talking about the foundations

[vague lion]

some notation is just better than others

[compact tartan]

again I can see mathematical content through the notation

[vague lion]

looking at the different style behind the notation is v. valid

but it just sounds like a pain

[compact tartan]

eh

it uses a ramified set theory

the "historical" connections between ramified theories, predicativity, and russel's paradox are quite interesting

[bronze pelican]

Wtf is ramified set theory

[compact tartan]

because nowadays it all just boils down to "U : U is inconsistent because girard's paradox, therefore let's use levels"

some historical perspective on why we do this is important

[vague lion]

it's like where you have a general category of sets, right

and then you apply a battering ram

[compact tartan]

yes

wait what

[vague lion]

mniip, i'm sorry but you've been scammed

who sold you that copy of principia

[bronze pelican]

What is ramification in this context

Levels

[limber perch]

a levels

[bronze pelican]

One more level mom

[compact tartan]

is this not ramification

[mint patio]

Ultra what is your favorite area of math?

You don't have anything you particularly like to do or learn?

[mortal igloo]

Should've picked ultrafilters

[deep mango]

and no period....

[latent forge]

which math had worst notation

rn im being filtered by a geometry question

is geometry worst notation wise?

like bloated

);

im talking about for reading and clarity

[woeful trout]

Well, there's this crown thing here

[narrow rock]

[latent forge]

talks oct 23

[deep mango]

#events

[latent forge]

@latent forge please

@latent forge go to his talk

[deep mango]

[cobalt cliff]

tell me something interesting

[deep mango]

@narrow rock we may be on different armies but at least we're not fencey fencertons.

[leaden torrent]

okay but unironically handwriting mathcal characters is hell

if you choose a field specifically to avoid that i dont blame you

[deep mango]

"pretend" LOL

[leaden torrent]

the pragmatic approach is probably just to do pdes research

tbh

more funding

[wild lantern]

My symbols are better than your symbols.

[deep mango]

also btw i'm also better than people who write L_p 🙂

[leaden torrent]

easier to explain what you do to your relatives

[deep mango]

hey mom can you pass the butter? anyway so back to discussing pseudodifferential calculus...

[leaden torrent]

"I study how complicated systems evolve as variables change, such as how a drumhead vibrates when you strike it with certain force at a certain spot"

[wild lantern]

Just lie to your relatives.

[leaden torrent]

it doesnt reflect anything beyond undergrad pdes but like

compare that to an algebraist

[deep mango]

hey mom i study how to solve rubiks cubes

[wild lantern]

"I study 2, other mathematicians study 3 and 4, we haven't gotten to 5 yet."

[deep mango]

15 puzzle

[deep mango]

what is this ramsey theory

[leaden torrent]

"i study symmetry"
"oh so like aesthetics?"
" "
"what the fuck does 'sully' mean and why have you said it 3 times this conversation"
" "

[wild lantern]

2-theory

[latent forge]

bruh moment

[wild lantern]

Wat

[latent forge]

everyone here gives too much attitude and is sassy and express it via sully

[deep mango]

tooth eary

tooth fairy

[leaden torrent]

im working on it but its harder than youd think

itd probably be easier if i didnt file life insurance first

[wild lantern]

Oh I did not realize that was a real thing.

[leaden torrent]

less paperwork

[deep mango]

this is like a visual novel plot...

[leaden torrent]

???

[deep mango]

everyone here gives too much attitude and is sassy and express it via sully

[leaden torrent]

no one would choose to pursue higher mathematics except to bolster their massive superiority complex

tf you expect

[deep mango]

math is an inherently sassy field

[wild lantern]

Sass-theory

[limber perch]

software as a service

the worst of all

[clever knot]

How do you feel about the "you dont own it" only have a license to use it.

[mint patio]

first time I’ve heard of this

do you learn this in pdes too

[deep mango]

much later on

[clever knot]

i thought that also neeed a limit

are you given it equals e^-2

or did you just already look at the answer

[vagrant kestrel]

(1+1/n)^2 = 1+2/n+random stuff no one cares about

[compact tartan]

do a substitution n = 2m

then move ^-2 out of the limit

no?

in the other one

?

[clever knot]

🚀

[compact tartan]

$$\lim_{m \to \infty} \left(\left(1 + \frac{1}{m}\right)^m\right)^{-2} = \left(\lim_{m \to \infty} \left(1 + \frac{1}{m}\right)^m\right)^{-2}$$

[fathom swallow]

mniip

[compact tartan]

because $x^{-2}$ is continuous at $x=e$

[fathom swallow]

mniip

[hollow ginkgo]

Is there a notion of how close two finite groups are to being isomorphic?

[mortal igloo]

Things off the top of my head include the number of homomorphisms between them, the largest possible image of a homomorphism from one to the other, but neither of them are perfect

[hollow ginkgo]

How about this: the closeness of G and H is the size of their largest shared subset?

[mortal igloo]

Subgroup* then that could be an imperfect one too

[hollow ginkgo]

No, subset

[mortal igloo]

the problem I can see with that is G and G/H for small H should be "close" but could have no nontrivial shared subgroups

I wouldn't agree with subset, if you remove the group structure, then you can just take the smaller of the two sets and associate each element arbitrarily with something in the other group

giving that the largest shared subset is just the entire smaller group

[hollow ginkgo]

Not quite

[mortal igloo]

I assume you want equal elements then?

Then there's a problem; isomorphic but not equal groups have no shared subset...?

[hollow ginkgo]

If A, B, and C are in the subset and AB=C is true in one group, it must also be true in the other.

That’s the only restriction.

[mortal igloo]

Hmm...

Sounds ugly

It could potentially in some cases be a game as to the largest independent set in A

a subset of A with no two things in A multiplying to another thing in A

that's not a very group theory-esque thing to consider

[compact tartan]

that's not a meaningful notion?

a group theoretical property does not depend on the underlying set of a group

i.e. should be invariant under a group isomorphism

an isomorphism-invariant notion would be to consider various groups K with monomorphisms K->G, K->H

and find the largest K

this can be turned into a universal property, but then existence of such universal (rather than largest) K is doubtful

but it would be kinda required to extend the theory beyond finite groups

maybe you have to consider not triangles but rather squares

[sick burrow]

I forget the term but can't every group be "factored" into simple groups?

Something with the normal series

But then isn't uniquely defined by it's factorization since you can "put things together" in different ways

[deep mango]

jordan holder and composition series

[compact tartan]

iirc the composition series aren't "natural" in a sense?

[cold needle]

oog solvable groups

the factor groups are unique but the order is not

so like the groups in the sequence can be different but you end up with the same simple factors

or something like that

[compact tartan]

sure but what I mean is that the decomposition doesn't upgrade to a natural transformation

or a functor I guess

[cold needle]

oog

[hollow ginkgo]

This is

[compact tartan]

no?

two groups could have disjoint underlying sets and yet be isomorphic

[hollow ginkgo]

Did you read what I said after that?

[compact tartan]

this?

[hollow ginkgo]

Yeah

[compact tartan]

my point still applies

[hollow ginkgo]

How?

[compact tartan]

for disjoint isomorphic groups the set would be empty

[hollow ginkgo]

What does disjoint mean here?

[compact tartan]

not intersecting

as sets

[hollow ginkgo]

That shouldn’t be possible

Every group has an identity element.

[compact tartan]

but it is a different element in every group

[hollow ginkgo]

But you can pretend it isn’t.

[compact tartan]

what about all other elements then?

[hollow ginkgo]

What do you mean?

[compact tartan]

I could take the set {apple, banana} and define f(apple, apple) = f(banana, banana) = banana, f(apple, banana) = f(banana, apple) = apple

this would be a group

[hollow ginkgo]

Yes, C₂

[compact tartan]

it is isomoprhic to C_2

but as sets, they are (likely) disjoint

because C_2 likely contains integer numbers or equivalence classes of such

[hollow ginkgo]

We’re dealing with abstract groups here, so that doesn’t matter.

[compact tartan]

abstract groups don't have underlying sets

[hollow ginkgo]

But they do have elements, so you can make a set.

[compact tartan]

and hence given g in G, it is meaningless to ask whether g in H

[hollow ginkgo]

Yes

[compact tartan]

they do and they don't

[hollow ginkgo]

Without the restriction I gave, the largest shared subset would just be the entire smaller group.

[compact tartan]

you can't talk about both "abstract groups" as if they're invariant under group isomorphisms, and their exact underlying sets (for the purpose of intersection) -- as if they're not

[hollow ginkgo]

However, I gave it, so choosing what g is in H forces other elements.

[compact tartan]

how do you "fix" any elements?

(also note that what you're doing here sounds more and more like constructing a monomorphism from another group, than talking about underlying sets)

[hollow ginkgo]

You say “this element of G is the same as that element of H”.

[compact tartan]

there are many ways to do that though

[hollow ginkgo]

Yes

[compact tartan]

how do you pick one?

[hollow ginkgo]

Any two groups will probably have many shared subsets, but I’m only interested the largest possible shared subset(s).

[compact tartan]

ok so translating what you said

you have a set K with injective functions p : K -> G and q : K -> H

such that for all x y z in K, if p(x)p(y)=p(z) iff q(x)q(y)=q(z)

and you're looking for the largest K?

[hollow ginkgo]

Yes

[compact tartan]

that's similar but also slightly different from my version

ok but note that if there's x, y in K such that there's no z with p(x)p(y)=p(z), (and also by definition no z such that q(x)q(y)=q(z))

[hollow ginkgo]

How can that happen?

[compact tartan]

we can always take K' = K + {★}, with p(★) = p(x)p(y) and q(★) = q(x)q(y)

so the largest K will be "closed under multiplication"

[hollow ginkgo]

So it’s always a group?

[compact tartan]

if K is infinite, then K' will have the same "size" as K

[hollow ginkgo]

I’m more interested in finite groups.

[compact tartan]

but I think there's always gonna be a K of the same cardinality that is a group

so yea

in some sense there's always a largest K that is a group

so really you're looking at subgroups of G and H that are isomorphic

[hollow ginkgo]

Are you sure?

[compact tartan]

kinda

[hollow ginkgo]

What if p(x)p(y)=p(a)p(b), but q(x)q(y)≠q(a)q(b)?

[compact tartan]

hmm

good point

then this sounds real ugly not gonna lie

it's kinda reminiscent of group objects in the category of partial functions?

which I don't think is a very well studied topic?

at least it seems that most of group theory tools break down there

hmmmm

there's a forgetful functor U from Grp(Set) to Grp(Set*)

and you're talking about objects over U

xy might not be defined in K, but when it is, we have p(x)p(y)=p(xy)

ah but no, that still fails to describe this structure because xy and ab are either the same point in K or not

I guess I'm out of ideas regarding what tools you might recover here

[fringe needle]

I was literally asking myself the same question this morning, hoping there might be some sort of associated metric on finite groups or smth

[gilded garden]

@leaden torrent you mentioned some time ago in #math-pedagogy that Lockhart advocates for bourbakism-with-pictures. Could you expand on that? From what I know, Bourbakism might refer to an approach to mathematical pedagogy in which the subject is treated very abstractly and hyperrigorously

[latent forge]

lol what would this mean tho

the closeness part

like their subgroups are similar?

[fringe needle]

that's the thing idk how one would do it otherwise there wouldnt be a question lol

[latent forge]

there is probably a way but idk if useful

[analog salmon]

is there an "expiration date", of sorts, for GRE scores? Like, if I take it senior year of undergrad, then take a year or two off and get a job not in academia, is it still okay to use those scores in my applications?

[ancient flame]

funny man

[jovial ember]

Yes, I do t know them off the top of my head but it’s stated somewhere on the GRE site

I think it’s in the range of like… 2-5 years???

It’s quite a lengthy time IIRC

[mint patio]

dudeee getting the integral using the limit def is so cool idk

just the fact that it works out like that

I mean it's supposed ot work like that

but you kinda just get lost in the symbol crunching after a while lol

feelsgood to go back to the roots and see it work out

[jovial ember]

Which limit definition?

Using riemann sums?

[deep mango]

[jovial ember]

Why are you sullying bruh

[deep mango]

i've seen like 2 riemann sums evaluated

both were so so awful

[jovial ember]

There’s multiple constructions of the integral

[deep mango]

disgusting

[mint patio]

oh yeah

LOL

you're right riemann integral I mean

[jovial ember]

I learned Darboux

[mint patio]

I haven't worked with any of the other types yet

[jovial ember]

Which is via like… upper and lower sums and like

Not sieves

I forget

It was similar enough to Riemann sums

[mint patio]

What is the difference between Darboux, Riemann-Stieltjes etc

[deep mango]

i think riemann is like you pick the left or the right end of the interval

[jovial ember]

Yeah

[deep mango]

or center or w/e

[jovial ember]

Not much really

I think you should learn one

Then just learn Lebesgue

[deep mango]

darboux is you pick the sup over the interval, and the inf over the interval, and these need to converge to each other as the intervals get small

[jovial ember]

You don’t gain much if anything learning multiple integrals

Besides lebesgue

[mint patio]

ANd Lebesgue is just supremum of the measure? I haven't looked into it enough no sully ty

[jovial ember]

I think the Riemann-Stieltjes is slightly stronger

But not as good as Lebesgue

[deep mango]

riemann-stiltjes is where you have a function alpha and the sum is f(x_n)(alpha(x_n) - alpha(x_(n-1)) instead of just x_n - x_(n-1)

so if alpha is like, a step function

this gives you a dirac measure

if alpha is some kinda bendy thing it gives you the gaussian weight

[mint patio]

some kinda bendy thing

[deep mango]

if it's just alpha(x) = x then you get the riemann integral

etc

[mint patio]

What the

That's interesting

[deep mango]

it's very nice

alpha needs to be nondecreasing

and like

right continuous or something

basically it's just a weight

that you put on different points

so that each part of your partition is weighted differently

[mint patio]

[deep mango]

based on how steep alpha is when you go over that part of the partition

[mint patio]

Would you learn about this in a normal undergrad real analysis text

[deep mango]

i think rudin defines the riemann integral with riemann-stiltjes

some books do

i mean it's no extra work

it's all the same exact thing basically

[mint patio]

wait what? the wikipedia article says riemann-stieltjes is a generalization of riemann integral, why wouldn't riemann come first?

[deep mango]

i mean if it's no more difficult

why not just teach the more general one

and then tell people to pretend alpha(x) = x most of the time

you see these a lot in probability

there, alpha ends up being the cumulative distribution function of your probability distribution

[mint patio]

Cool

So is there anything stronger than the Lebesgue integral

[jovial ember]

’s biceps

[mint patio]

[jovial ember]

💪

[mint patio]

chmonkey looks in the mirror every morning and calls himself a good boy

[jovial ember]

He knows he’s a good boy

[mint patio]

[deep mango]

the lebesgue integral doesn't handle conditional convergence in improper integrals well

so maybe you could come up with some way to patch that up

people use the "cauchy principle value" to do this but it doesn't always make sense

for example, the lebesgue integral of sin(x)/x from 0 to infinity is not defined

even though it is riemann integrable

this is because |sin(x)/x| has integral infinity

and like

technically if you reorganized the order of the intervals

that you're integrating on

you could make the value whatever

(this is from riemann's rearrangement theorem)

so the lebesgue integral doesn't like that, since the reason it exists is to let you reorganize countable numbers of things without changing the value

whereas with the riemann integral you can just do the usual integrate to M, take the limit as M goes to infinity, and that's fine and converges

some would say this is actually a benefit of the lebesgue integral

but

knowing the integral of sin(x)/x is useful, it's used all the time

[mint patio]

so like int -inf to -2 + -2 to 0 + 0 to inf? I don't think I'm understanding this right

[deep mango]

something like that

but like

an infinite series

so if i was to be like "oh, let's integrate this by first integrating the interval [0, pi], adding on the integral from [2pi, 3pi], then from [4pi, 5pi], then let's go back and do [pi, 2pi], then keep going on with the evens a bunch more, and do another odd, and back to a few more evens, and then add up all these results"

the lebesgue integral says "it shouldn't matter that you did this! you should get the same answer"

just like what absolute convergence for a series says.

but this is not true for sin(x)/x. if you do what i said, you'll get a different value from what you're supposed to get.

[mint patio]

So for an improper integral to be Lebesgue integrable do you need its series representation to be absolutely convergent?

I don't think I worded that right to integrate over infinite bounds using Lebesgue integration do you need its series representation to be absolutely convergent?

[deep mango]

yes

or

a simpler way of saying this is

f is only lebesgue integrable if |f| is too

[sick kite]

wait so what even are people here

like are people here mathematicians, students or just people who do math for fun?

[steep mountain]

yes

there is all kinds

from grade 8 kids to phd professors

[sick kite]

that seems trivial

probably because im asking an imprecise question

well nevermind

ty

[steep mountain]

[neat lintel]

There are definitely more high schoolers than Ph.D. and above.

However, you can still get good answers.

[candid oak]

good evening! If G a group and R is an equivalence relation and cl(x)= {a in G/ xRa}, can we safely say that cl(xy) = cl(x)cl(y)?

or is it only a special case for Z/nZ ?

nvm

I just proved it

[surreal sapphire]

but it's not true?

[candid oak]

idk, I proved it only for a particular group that I needed

[surreal sapphire]

it will be wrong for this group too, just partition into {e} and {rest} then notice
{e} = cl(e) = cl(a*a^{-1}) != cl(a)cl(a^{-1}) unless your group has order 1, 2

[candid oak]

yeah it has order 2

in fact, xRy iff y in {x, ax} such as a in G (a group)

so card(cl(x)) = 2

I should mention that every element in G is an inverse of itself

aka, x^2 = e

I used that in the proof

Am I missing something ?

[surreal sapphire]

i mean it will work in special cases, but for general equivalence relations it is really wrong

you essentially want to build a quotient group which works when the equivalence relation comes from a normal subgroup

[candid oak]

I see

I really appreciate that

[obtuse breach]

uh hii

im in highschool but i wanted to learn more about calc

[uncut socket]

Khan Academy has good videos on calc

[obtuse breach]

I just need to sit through an actual calc thing

[steep mountain]

or you can push to spivak

[obtuse breach]

they go to slow for me...

[steep mountain]

when you say actual calc wdym

[obtuse breach]

explaining the basics of it

[steep mountain]

i suggest finding a good calc book and walking through it on your own pace
coursera, edx have some nice courses as well

[torpid torrent]

redirect me to a better channel if there's a distinct subject this belongs in, cause i can't begin to guess how to go about this. these are some scribblings from a few months ago, i just got back around to them and i really wanna figure out if there's any way to explain why this relationship exists

this started with just the graph on the left, i had this idea that there would always be 3 points of intersection so long as the circle's lowest point was tangent to the parabola's vertex, and those 3 points would tend towards an infinitesimal distance apart as the parabola's coefficient would tend towards infinite.
but i messed around and found out that actually after c hits 1/(2r), the parabola only touches the circle at its vertex, and i have no idea where this relationship would have come from.

is there a taylor series that fits the curvature of a circle? my calc knowledge isn't strong enough to try and figure it out on my own, but if there is one then i wanna see if it has any correlation to 1/2r, otherwise i want to see if there's any other reason why a parabola fits the curvature of a circle so nicely when it's coefficient is a non-pi value

[swift sinew]

Yeah! They have the same 1st and 2nd derivatives at that point causing the circle to nestle into the parabola

[torpid torrent]

oh my god thank you thats the answer ive been looking for

so i was on the right track with trying to find its taylor series but i just um haven't formally learned that much calc yet

[swift sinew]

Yup! In fact, try adding (x^4)/8 to your parabola and you’ll see it hugs it even more. That’s because we’re putting in more and more of the Taylor’s series at that point

[deep mango]

For this, you could consider the function -sqrt(r^2 - x^2) and find its taylor expansion

But that sounds nasty

That's just the function for the lower half of the circle

[torpid torrent]

i actually was going to take that approach if i didnt get any response, i'd already derived that function but i didnt wanna do anything with it

because spooky scary

idk if i could find the derivative of a function with 2 variables (edit: with my current maths capability)

but i mean i guess i could just say r=1

[deep mango]

The other way to do this is to look at solutions to the system of the two equations as c varies. To do this, I would use the equation for the parabola to say r + y = cx^2 to sub in for x^2 and get (r+y)/c + y^2 = r^2. So we're looking at when y^2 + y/c + r/c - r^2 = 0.
Now we can solve for y, and see what the possible y's are given r and c. Well, one solution is y = -r. We know that from the bottom point where they both meet. What's the other? It's going to be reflected across the axis of symmetry, which is given by y = -1/(2c) (remember the axis of symmetry of the parabola ax^2 + bx + c is -b/(2a). here a = 1 and b = 1/c).
So then for there to be another solution ABOVE y = -r, we must have that the axis of symmetry reflects -r UPWARDS. i.e., it has to be above -r. Then -1/(2c) > -r for there to be more intersection points, and this simplifies to c > 1/(2r).

This is the algebraic way instead of the calculus based (analytic) way

Note that I took a shortcut using the axis of symmetry, but you could also just use the quadratic formula on our solution, find the two roots for y, forget about the -r root since we already know about that one, and then see what conditions on r and c make it so that r+y = cx^2 actually makes sense (since cx^2 cant be negative, so r+y must be positive).

r+y > 0 with y being the other root of y^2 + y/c + r/c - r^2 will imply that c > 1/(2r).

And then you can see that at c = 1/(2r), the two roots are equal.

After all, then the polynomial becomes y^2 + 2ry + r^2 = (y + r)^2

[forest jackal]

I think this para is misleading. It is of course true that this function is not Lebesgue integrable, but this is not really a distinction between the Riemann and Lebesgue integral. It is not Riemann integrable in the "basic" sense either, and improper integrals can be defined in exactly the same way for either. For things like this example of course, the value will depend on the choice of engulfing sets and it is just convention to take [0,M].

[deep mango]

That makes sense

My point was mostly that there's still work to be done beyond defining the lebesgue integral

If you want to talk about the kinds of things people need to talk about

(in particular, conditional convergence and later singular/oscillatory integrals)

[forest jackal]

Most rigorous/advanced treatments of calculus I see (eg spivak calc on manifolds) first just define the Riemann integral for bounded things on boxes, and then extend using partitions of unity to the case of integrating locally bounded things over arbitrary say open sets, and this extension is usually only made for functions that satisfy that "absolute integrability" condition which makes this definition invariant.

yeah ofc

[velvet dagger]

Yeah I think when people make that comparison it's because usually with the Riemann integral you define it on compact sets, and then the only way people seem to ever extend to stuff like integrals over R is improper integration

While in measure theory you often talk about the "non-improper" integral over unbounded things

So if you define improper Riemann integrals and get new stuff, you're strictly extending

While if you were to do the same with Lebesgue you'd be overwriting existing stuff

At least that's my impression

[glacial sable]

I had watched this recently: https://www.youtube.com/watch?v=ZYj4NkeGPdM&t=55s
And I don't think 0 and * are confused. I think one is strictly greater than the other but on a different axis. Imagine if instead of playing as red and blue, the players are the person who goes first p1 and person who goes second p2. If we choose the perspective of p1 * is strictly greater than 0. Then the blue and red lines would be confused with one another because this axis is color ambigious

it might be possible that there are more than 1 kinds of 0 using this perspective same way there is more than 1 *

[mint patio]

This is too much work

And this is such a simple PDE too wtf

uh so I kinda have to draw this

is there an easier way to do this

[clever knot]

What is this suppose to represent

[simple raven]

#❓how-to-get-help

[mint patio]

Solution to a PDE

[pale orchid]

probably some waveform over space, and the other dimension is time

[mint patio]

lul

[mint patio]

exactly this

I think I’ll just leave some empty space on my paper and then Photoshop it into the scan

[pale orchid]

the alternative is to make an animation

can't really do much more

[mint patio]

it is so long

to solve these

[pale orchid]

fourier method out the ass

[mint patio]

Yeah that’s what the notes say too

but I still don’t want to do all this

Thankfully the initial velocity is 0 so that helps

But he gave such a dickwad initial deflection function -.- why couldn’t it have been something simpler

[pale orchid]

lol

[mint patio]

@pale orchid just for fun I tried it

do you think this will work

like does it get the message across

of what the solution looks like?

[pale orchid]

that looks super cursed

sure i guess

idk if you can manage to label a couple of things on the axes

some period & amp

[mint patio]

hm

okay

how am I supposed to know the period and amplitude when it's multivariable

[pale orchid]

you can show the wavelength or wavenumber on the space axis for a fixed t

i guess that doesn't make much sense if you have several frequencies though

[mint patio]

Okay it seems wavelength is 1.5 units

at least uh

in the x direction

[pale orchid]

the periods should be linked via the wavenumber and propagation speed

but only in a straightforward manner for a single frequency

[mint patio]

I don't know what that means

,

[pale orchid]

this plot is made through the fourier method, right?

so it's the superposition of a bunch of sines and cosines

[mint patio]

oh no this is a definite solution

wait

[pale orchid]

what's the form of the sol?

[mint patio]

I just graphed cos(4y)sin(2x)

[pale orchid]

ah

right, then yes

there is a period in t and in x, and they are linked

[mint patio]

Why wouldn't it just be 2pi in t and 2pi in x

[pale orchid]

they have different frequencies and the number C^2 there is doing something

spatial frequency depends on that C

[mint patio]

c = 2 here

for the equation to be satisfied

[pale orchid]

mhm

there's a quantity commonly called the "wavenumber"

(2 pi f)^2 / c^2

[mint patio]

what is f?

I've never heard of this before

[pale orchid]

temporal frequency

in your case, 2 pi f = 4

[mint patio]

so isn't the wavenumber here just 1 then?

4/2^2

oh

Okay

So wavenumber 4

[pale orchid]

ye

and the unit is radians/meter or whatever unit you're using in space

so that's the spatial frequency

anyway yes, it's 2 and 4, but don't forget the 2 pi factor

[mint patio]

I think what I can do is

(to avoid all the mathy mess)

When I draw these lines to denote that the curve has a volume

the coordinate axes make it look weird

so I think I will color over the curves in pen and draw basis in pencil

let me try

[pale orchid]

you can always just ignore me and not indicate anything lol

or draw 2D cross sections

[mint patio]

I'm sorry 😭 I don't get it enough

[pale orchid]

since the solution is the product of 2 functions that depend on a single variable each, you can easily draw cross sections

[mint patio]

Oh

I see what you mean

Hm

I think I might do a 3d and two cross sections if I have space

Embarrassing but I'm kind of having trouble figuring out the traces 🥴

For cross sections

I think

Okay

Okay so on the y axis (right handed system) the x component is constant so it's gonna be cos(4y) and on the x axis the y component is constant so it looks like sin(2x) yeah?

geogebra just crashed so I can't check -.-

But it looks right on Desmos

[pale orchid]

bruh what

[pale orchid]

take easy ones

set the cos to 1

[mint patio]

isn't that what you meant by cross section

[pale orchid]

and then set the sin to 1

yeah

[mint patio]

okay I'm gonna try an almost final draft

I am wasting way too much time on this :^)

[wispy monolith]

hey i have a question for you undergrad students

[swift sinew]

[wispy monolith]

do you learn topics such as dot product, cross product, vector sum in linear algebra?

[mint patio]

Yes

[wispy monolith]

don't you take analytic geometry before?

[mint patio]

[mild nebula]

These are covered, but linear algebra focuses more on vector spaces, and linear transformations between them

[wispy monolith]

oh

[mint patio]

I took that in HS I’m pretty sure lol…

[mint patio]

Yes

[mild nebula]

I figure most people will take geometry before, simply because it is an earlier class. But LA doesn't really depend on geometry

[wispy monolith]

i mean i learned all that stuff in analytic geometry and it seems like in linear algebra we have it all again

[wispy monolith]

i see

[mint patio]

@pale orchid

I’ll take it

I’m not doing that for the next problem though

actually it's not that bad

[clever knot]

wait

are you still trying to graph the function

or is this a new one

cool graph

[mint patio]

I was trying to draw the first

I drew them both now

[clever knot]

I assume you worked hard on it but other than looks how does one even read these graphs?

like without units or something idk. Unless it isnt required

but then again even using geogebra I couldn't read the plane graph really

[devout pasture]

hey

just a general question

how do i know whether math grad school is for me?

i want to study more, do research, get a PhD, yes

but i'm not sure whether i will eventually stay in academic math

this is not exactly a math question but could someone throw some light?

[pale orchid]

are you currently in a masters?

i got into a research oriented masters precisely to figure that out. the piece of cardboard was anyway gonna be a plus both in salary and job opportunities, and i took the chance to figure out whether i liked research or not and how academia works

cuz it might be you like research and not academia, or you like both or none

and one kinda goes from there

[devout pasture]

i'm currently in third year of undergrad, so i will apply next year

[pale orchid]

i see. have you already begun working on your undergrad thesis? that can also give you an idea

[devout pasture]

yep, sorta. i do enjoy research, and that's why i think doing a PhD would be a great idea

but like, academic math may not be something i'd want to do - since industry jobs get you more 💰

and also it takes so long to get a tenure track job tbh

my point being, if i don't continue in academia after, is the PhD "wasted"? is it a better idea not to go through with it in the first place? or are there industry positions that could benefit from a PhD

[pale orchid]

you can still do research, just not in academia

it'll probably influence the choice of things you specialize in

[devout pasture]

fair enough, so i probably should not worry rn?

[pale orchid]

like you might wanna pick up applied maths along the way

[neat lintel]

guys

[devout pasture]

also would the field i specialize in during my phd matter?

[neat lintel]

i have a question

[devout pasture]

listening

[neat lintel]

whats 5/2 x 6/5

its my exam

i need ans

[devout pasture]

what no lmao

[neat lintel]

can u help me turn these into standard from

[devout pasture]

i mean algebra is probably not industry-oriented. i do analysis, pdes, geometry stuff so that might have applied directions? in any case i see that i'd have to pick up some applied math

[leaden torrent]

Dirty little secret: most people who employ math PhDs don't care at all about what math you did

They just see it as an indicator of being "smart", in the sense of being adept at abstract thinking and problem solving

And are cool with you learning a lot on the job

There are exceptions ofc

[surreal sapphire]

friend of mine works at siemens mobility (railways and stuff) and has a math phd in their team

[leaden torrent]

But in general I wouldn't sweat it TOO much

[surreal sapphire]

that math phd did research on graph theory

[leaden torrent]

Hey that sounds kinda relevant to railways lmao

[surreal sapphire]

siemens hired her years ago and had no idea wtf graph theory is and had her work in random teams for years

before realizing that this is relevant to railway stuff

and moving her in that position which now fits really well

[leaden torrent]

Sounds like it worked out pretty well

[surreal sapphire]

ye but it took like a decade

she apparently was a pretty early researcher in graph theory

[leaden torrent]

Yeah that's my point, many employers don't really care

[surreal sapphire]

i think the hiring persons are now more aware of what it is

[leaden torrent]

yeah in the age of google im sure theyd at least know the basics

graph theory is very, well, visual, so its easy to understand

if i told employers my research was in "algebraic K-theory"

theyd be like "idk tf that is but it works"

again, there are some more technical positions where you do need specific knowledge

some modelling gigs, security companies, etc

but these are in the minority

as long as you can program and can pick up stuff easily theyll take you

[surreal sapphire]

my (maybe bad) impression is that most employers think that a math phd (or just a degree) is a sign that this person can quickly learn whatever we throw at them

[leaden torrent]

this also applies to physics phds for what its worth

physics phds are weirdly high-earning relative to physics bachelors

[surreal sapphire]

[leaden torrent]

like obviously any phd is a pay jump but

[surreal sapphire]

why would anyone get a physics degree

[leaden torrent]

its extra big for physics phds

since undergrad physics knowledge is like, utterly useless

but a piece of paper that "proves" youd be competent at basically whatever quantitative mess you inherit

thatll get you places

[leaden torrent]

believe it or not, some people are interested in physics

(shock and awe)

though if youre saying this in the sense that "its smarter to get a math bachelors and then a physics phd", maybe i see your point? i know thats the advice for econ but idk about physics

[surreal sapphire]

all the physics majors i know started hating physics

and switched to a mathematical physics major

due to lab work

[leaden torrent]

okay fair

labs are dumb

im sure they have pedagogical merit

but monkey brain dont care whats good for it

monkey brain drinks 3 coffees a day and gets into increasingly weird fetishes for dopamine hits

and monkey brain HATES labs

[pale orchid]

[surreal sapphire]

i looked it up yesterday and 3 coffees is totally fine

[pale orchid]

your teeth probably won't like it, but it should be fine

[surreal sapphire]

oh i didnt consider this

but just from caffeine intake

its fine

[pale orchid]

yeah

[steep mountain]

why is lab work a bad thing

[surreal sapphire]

people just dislike it

[pale orchid]

it takes up a LOT of time in dumb shit

[surreal sapphire]

writing dumb reports

calculating error propagation

[pale orchid]

it also hated the physics labs in my undergrad

it would legit take like 10~20 hrs to write a dumbass report that was worth like 1 point out of your final grade

but there's like 10 of them so they build up

[steep mountain]

i feel like maybe someone in chemistry might love that

[pale orchid]

you go 2~4 hrs to measure shit at the lab

[leaden torrent]

not really

the lab itself isnt bad

[pale orchid]

and then write BS for hours on end

[leaden torrent]

its all the extra shit

[surreal sapphire]

i did chemistry labs in undergrad

[leaden torrent]

making the report

thats hell

[surreal sapphire]

it wasnt super bad but i'd rather not have done it lmao

[leaden torrent]

its like

[pale orchid]

yeah, the report

[leaden torrent]

okay the worst part of any academic job is the emails

now imagine that sort of mundanity, but you have to have a calculator in hand calculating shit

and double checking everything since it counts for a grade

i know it sounds like major first world complaints but like

it really is such a monotonous task

[steep mountain]

i mean it does sounds tedious and repetitive and i would hate it but it might just be suited for some people unlike us you know
i know a couple people who love that enviroment

most bio/chem students

[surreal sapphire]

sure, but my impression is that most people dislike labs

even people who like their subject hates (undergrad) labs

[steep mountain]

ye i suppose thats true

[small kayak]

I still would love to be a math proffesor

[pale orchid]

exactly me

i don't mind sticking my hand in a coil to measure fields and shit

but then they'd ask to compute verything by hand AND simulate, and compare the results

show propagated error

and write like 10 pages of shit explaining it, with tons of references

miss me with that shit

it takes more work than the class itself

[surreal sapphire]

we also had this ancient lab equipment

and it was super hard to measure things

you were never sure if you fucked up or the lab equipment did

[pale orchid]

lol

i remember that for circuits and electronics

[surreal sapphire]

there always was one digital of everything

and everything else was stone age analogue

[steep mountain]

writes down note:
possible lab failure or my failure but we cant know for sure

[leaden torrent]

also lab booklets at my undergrad were like $80 per course

[pale orchid]

hunched over a breadboard for 2 hrs cuz shit wasn't working. turns out either the breadboard was an open circuit cuz it was too old, or the components were burnt and ruined by the previous group

[leaden torrent]

which i hold to this day to be a scam

shit should be $15 max

it was like 40 pages of black and white text

[pale orchid]

bruh you just triggered war flashbacks

shortly after my undergrad i became a lab instructor

every single day... "measure current in series, and voltage in parallel"

5 seconds later, burnt fuses in all the multimeters

measure the current from the 12v source to ground, why don't you

[untold sapphire]

lmao

[clever knot]

relatable 😦

How was I suppose to assume the main gnd wire was broken and not properly grounded 😦

[pale orchid]

smh

[clever knot]

we had something like this

but layed out a bit different

[pale orchid]

ye boi

we used these bad bois

oops LOL

[brave hollow]

no memes in #serious-discussion

[pale orchid]

here, i copied the wrong thing

NI ELVIS II+

pretty good tbh

[clever knot]

well actually closer to this

[pale orchid]

but students managed to fry them

[pale orchid]

the uni was not happy

aha

yea these look more for like basic digital electronics tho

[clever knot]

you threaded the wire through a little hole

and screwed it down

and i guess it was broken and not making proper connection

Then I also had a bad little cihp

chip*

[clever knot]

was the bread board all attached

[pale orchid]

yeah

couldn't be removed

[clever knot]

the thigns we have they just have like velcro

[pale orchid]

no need to screw anything, only thread the wires in the breadboard

oof

[clever knot]

but seeing other people use the lab you can just take your crap and put it somewhere in the mean time

hopefully next semester math class is good :V

Do you study math outside of classes or do you get enough through classes?

[steep mountain]

my classes miss a lot of details and proofs due to the pace so most of the time i have to prestudy/overstudy to get the most out of a class im interested in

[surreal sapphire]

most work is done outside class

[clever knot]

but does it align with your classes?

I guess I mean almost like a 2nd class

[frosty zinc]

Looks like you started off as an EE/Physics person and then transitioned into a sig.proc. chad. Noice

[clever knot]

and how much time are you able to dedicate and treat as if it was a full class

[surreal sapphire]

even busy semester i had < 20 hours per week of actual classes

so its kinda expected to spend at least as much time outside of class

[clever knot]

maybe i phrased it bad

I meant outside of the classes you take

[surreal sapphire]

i mean just a weekly homework sheet takes like 10 hours per week

[clever knot]

like say you are interested in a some topic or subject

do you have enough time to study that while doing your actual scheduled classes

[surreal sapphire]

if im interested in something, i usually will try to take a class on it

[clever knot]

makes sense

[steep mountain]

i tend to do things i cant do in college in summer

like studying philosophy/justice
mostly none-math

but it might be just me

[leaden torrent]

yeah i study justice

i play ace attorney

😎

[steep mountain]

[surreal sapphire]

make me mod so i can study justice

[clever knot]

do you take summer classes also?

idk if that is common or not

[pale orchid]

started as telecom, a branch of EE, yeah

[clever knot]

i know some degrees you might need to

[steep mountain]

nah my sems are too tight already

summer is only time i chill out

[mint patio]

Integral transforms are so cool

And series

[candid oak]

good evening everyone, I found this statement in a problem: let (G, .) a group contained in Mn(R), we clarify that G is not necessarily a subgroup of GLn(R), which makes it possible that G contain matrices of r<n such that r is the number of linearly independent vectors

in the french notation we call r ''rang"

this statement doesn't make sense to me at all

[fast ivy]

Why not tho?

This is definitely weird tho

[candid oak]

if G a group then all of its elements are invertible

[fast ivy]

Because in order to G be a subgroup, every element must have an inverse

Don't they mean like

A subgroup of M_n(R) under addition?

Because that would make sense

But again

GLn(R) is not a group under addition too

Which makes this even worse

Yeah, that statement is totally flawed.

[candid oak]

they said: if A in G then A has, for multiplication, an inverse A'

[fast ivy]

Oh, ok so it is a multiplicative subgroup.

[candid oak]

wait

there's something crazier

in first line the wrote: let G a multiplicative group that is not reduced to {0}

shouldn't it be {In} ?

where In is the neutral element for Mn(R)

[fast ivy]

Yeah, it should be Id_n.

The identity

There's definitely some weird stuff in these problems.

Where did you find these?

I will give the benefit of the doubt and like

Just assume these are typos or misprints.

Or maybe mistranslation

[candid oak]

maybe typos

I translated the problem to eng so we can discuss

here what it says in case there are french ppl

[neat lintel]

Damn, I have a french test tomorrow

Dont put the translation lol, let me try

"In this party, one considers a multiplicative group G non reduit â (0)" ok I stopped understanding

[candid oak]

sure

[neat lintel]

Lol

is it at least close (my start)?

[candid oak]

close enough

[neat lintel]

"the multiplication of matrices, an inverse in G one notates A'"

[neat lintel]

Ok, thx

LOl

I wont worry at all 😉

[candid oak]

in this part, we consider a multiplicative group non reduced to..

[neat lintel]

Aha

[candid oak]

on <--> we

[neat lintel]

I guess I could have guessed reduced

[neat lintel]

ic, but don't you also use it for "you" in some cases?

[candid oak]

nope

we say on for "they" in some cases and for "we" in other cases

confusing I know

[neat lintel]

ok

thx

[simple raven]

It's said that the neutral element isn't necessary the identity matrix

We could imagine that with another neutral element than id, there could be matrix non invertible regarding to I_n, that is invertible for this convention

If $E$ is your neutral element and $M\in G$, then $M$ is invertible in $G$ if there exists $N$ in $G$ such than $MN=NM=E$
So the inverse of M has no reason to be the inverse matrix for the usual conventions, if it happens that the rank of $M$ is maximal.

[fathom swallow]

Adrien

[candid oak]

that makes total sense

[simple raven]

What book is it from ?

[candid oak]

but what makes us sure that E.E= E

[candid oak]

just homework

[simple raven]

It's by définition of E

[candid oak]

then they should demonstrate its existence before defining it no?

[simple raven]

You see, the notation for the inverse of $M$ is $M'$ and not $M^{-1}$ because there's no reason for them to be equal

[candid oak]

do you want the full problem? (if you're familiar with french notations)

[simple raven]

No, you suppose than there exists a group G and a neutral E such than ... (the usual properties of a group)

[simple raven]

I'm French

[candid oak]

yaay

[fathom swallow]

Adrien

[simple raven]

Yeah why not

[simple raven]

You have $E^2=E$ so E is a "projecteur" !

[fathom swallow]

Adrien

[simple raven]

I assume your problem studies which $G$ and $E$ can exists with these properties, and there will be not much

[fathom swallow]

Adrien

[candid oak]

I thought they supposed that their exist an E other than In, and then conclude a contradiction to demonstrate that E is unique

[candid oak]

that was a good example

[simple raven]

If it's not said, it's not supposed !

[candid oak]

I see

[simple raven]

If you have difficulties with problem 2 , try to review your lectures about projections

@candid oak

[candid oak]

I will

[bronze pelican]

@surreal sapphire How do you export your notes from the nova pro

[surreal sapphire]

that doesn't work well i think

[bronze pelican]

[surreal sapphire]

you can export them some way, but it wont look good

mostly size issues

and on pdf it doesnt work at all i think

the notes are stored separately from the pdf

[bronze pelican]

i like using one note for notes because its synced to your account

[surreal sapphire]

if its available on the google play store it can be installed but no idea how well it would work as i personally dont use it

[round umbra]

Any tips on how to not get bored during math class?

[steep mountain]

let me ask something instead
why do you think you get bored during a math class?

[round umbra]

Its too ez

We do the same thing like 10 times while I already understand it after 1 time.

[steep mountain]

sounds like a chance to teach yourself new things

study harder mathematics ahead of your class

[vague lion]

speedrun the questions then flip the sheet and fiddle with things by yourself

try and find interesting questions

and then try and answer them

for example, 'what are the differences between the square numbers? the cube numbers? the fourth powers?'

that's one i remember doing

by interesting questions i mean more like. open-ended exploration vs just specific problems from a competition or something

[round umbra]

Good idea. I never thought about trying such problems during class.

I once tried finding out a formula for the maximum area of a right angled triangle when you have the length of the perimeter.

[vague lion]

ah, that's interesting

[round umbra]

It turned out to just be a proof of that the maximum area would be achieved with an isosceles triangle.

[vague lion]

yes

[round umbra]

But it was nice to use things I learned in class like the quotient rule.

[vague lion]

yeah, exactly

just fiddle with stuff

[round umbra]

Ok thanks for the idea.

[agile wedge]

@devout nacelle 👀

[long anvil]

Manan likes to fuck a lot

[devout nacelle]

I feel with a substantial understanding of the subject, one might be able to discover connections or perspectives that weren't realised before.

[long anvil]

Sully back

[devout nacelle]

I suppose that is the case with mathematics usually as well.

[agile wedge]

No I mean, the guy would have no creativity, like, he would be perfectly unable to create new knowledge, no matter how (seeing new links being creating new knowledge )

[devout nacelle]

Oh hurb

Hmmm

Then yeah, it's just a repository which can fetch information

Nothing more and nothing less

[agile wedge]

Yeah, I think too

[leaden torrent]

please dont

[deep mango]

I feel with a substantial understanding of the subject, one might be able to discover connections or perspectives that weren't realised before.

[elfin fog]

How can I change the my nickname in this server?

[leaden torrent]

you can ask

what do you want it changed to?

[elfin fog]

"Chris"

@leaden torrent

[leaden torrent]

[elfin fog]

Thank you

[neat lintel]

break the rules of math; do whatever the teacher tells you not to do in math and see how far you get until it does not make sense anymore

[neat lintel]

Can confirm this

[neat lintel]

😉

[round umbra]

Lol

[trim stratus]

Should've added in the ""

[swift sinew]

I really think this server could use a “Venting” channel. With the amount of frustration people get with math, it’s not uncommon for people to want to vent, and often times they decide the math discord is the place for it. Sometimes however, this bleeds into other channels, so it’d be nice for people to have a specific place for them to just let things out with or without looking for people to really respond to it. I think chill is currently the best channel for that, but it’d probably be nice and I think a lot of people would enjoy just having a channel specifically devoted for being able to vent in. I’ve noticed some other servers have a Venting channel and it seems to benefit the server overall in many ways, including boosting bonding between community members

[sick kite]

I feel like that would just make this place toxic

[swift sinew]

How is that?

[sick kite]

I mean, as you said, venting can leak into other channels and potentially cause disdain among community members if they say something a little shitty while venting

i suggest we just encourage deskslamming and moving on

[swift sinew]

I mean obviously expectations of being respectful to community members would still exist in such a channel.

[sick kite]

Sure, but just by having a venting channel could increase said disrespect because thats typically what venting entails. Even if you put a rule in against it

[deep mango]

le vent 🤓

How about #the-teapot

We can all post gossip toward others in the server there

If you enter the teapot, be prepared to fight off a million critiques.

We could make it so that you opt in with a role to see the channel. That way if someone doesn't want to see all the gossip about them, just dont take the role! It's that easy.

[untold sapphire]

that's great. i've been looking for a fight recently

[swift sinew]

Give it a voice channel too for good measure

[wild lantern]

I propose a #galois channel for organizing pistol duels.

[neat lintel]

Lol, my school server was basically only ever active when there was a conflict. Otherwise it was practically dead.

[velvet dagger]

I cackled out loud

[neat lintel]

crackled?

[gentle bay]

[leaden torrent]

I have had an epiphany

the "dont pin anything in #serious-discussion " meme was never actually funny

therefore

[pale orchid]

[pale orchid]

i had pinned a good one at the beginning on the channel history and you removed it

such hurting of the butt right now

[inner finch]

lol