#serious-discussion
1 messages · Page 11 of 1
in the context of limits infinity is not a number
unless
you use the extended real line
which is the real numbers extended with +infty and -infty on either end
to start u can google ‘epsilon def of limit’
I know that one
then u should know that divergent limits are undefined
why should I know
neighbourhood definition of limit is better
because "the limit exists if L exists such that..." is pretty clear
topology my beloved but we have no time
well...
so if you use the extended real line, you can multiply infinity by itself
but infty/infty is undefined
this whole discussion could've been these two lines
I think I didn't even need that
i stg
Roketto being ignored 

ok but i wanted to actually explain what's going on with infinity
i cant care enough to put down my margarita and engage at a higher level
infinity is a really broad concept
yeah
i think it makes more sense to think of infinity in this context as equivalence class of limits
exploring that should've been beyond the scope of this discussion
that explains better why inf/inf is undefined
so i wanted to at least introduce the idea
all illuminator need to know is that +inf isn't an element of a field
that's not a satisfying answer
because you can just use extd real line
extd real line isn't a field
right
is that better?
yes but you can use it for analysis
the reason to leave inf/inf undefined is because given two sequences u_n -> inf and v_n -> inf you can have many different behaviours of u_n / v_n
also a bad answer because there are infinities that are
it could ->0 or -> inf, ...
so there's not a unique choice of what to pick for inf/inf
I didn't need $\infty \cdot \infty$ but $\infty - \sum \infty$
illuminator3
it's much better to properly pin down the context first
what's $\infty - \infty$
thats also undefined
illuminator3
undefined yeah
mehhhhhh
because for example x² -> inf and x-> inf and x²-x -> inf however x²-x² -> 0
the point is that you can't expect mundane operations that work with real numbers to also work with the ext real line
there is one more sense of infinity that's important to talk about here
hyperreals
ahh
Have you ever heard of the tragedy of infinity-categories
mentioning other infinities at all is a bad idea
hyperreals basically make infinities work like real numbers
the point is that you can't expect mundane operations that work with real numbers to also work with the ext real line
where infty² ≠ infty
yes i saw
sorry
why
maybe because it can confuse them more
the moral of the story here isn't that "there is more than one infinity"
"infinity" means different things depending on context
it's that "you have to be careful when working with infinity"
this was my initial aim because they posted ∞•∞ with no context
just finished my drink
Roketto i think i have a crush on you
seems noone wrote the def of lim=infty yet
i can write
lol
ly2 ❤️
I dunno, I think it was pretty clear that he was treating inf like a real number
$\forall \epsilon > 0 \exists \delta >0 \forall x\in D 0<|x-a|<\delta \implies |f(x)|>\epsilon$
Carla_
D domain, a limit point
no bars on f(x)
if to inf then bars
btw i think illuminator was doing sequence stuff
if to +inf no bars yes
so i meant lim for sequences
+inf
$\forall \epsilon > 0 \exists N \forall n>N u_n>\epsilon$
Carla_
tybb
,, \lim_{\mathfrak{I}0 \to \infty} \sum{0\leq \mathfrak{n}_0 \leq \mathfrak{I}_0} \blacksmiley\left(\mathfrak{I}0 - \lim{\mathfrak{I}1 \to \infty} \sum{0 \leq \mathfrak{n}_1 \leq \mathfrak{I}_1} \mathfrak{I}_0 - \mathfrak{n}0\right) - \lim{\mathfrak{I}2 \to \infty} \sum{0 \leq \mathfrak{n}_2 \leq \mathfrak{I}2} \blacksmiley\psi (-1)
uhh
nty
illuminator3
is there anyone who took ap calc right after algebra 2 in highschool? I didnt know my teacher recommanded me in ap calc ab till today where i got my classes. Idk if I can pass the readiness test on the first week
also, @alpine kindle wdym divergent limits are undefined
(sry for replying too late, I was sent on some errand)
I swear I saw that but i ignored it thinking I was missing some context
What’s this for?
I forgot after writing it down
this is really bad motivation for people who want to learn pure mathematics
I don’t see why this is bad motivation
Being useful is a great motivation to learn anything
It’s not what motivates me to do math but I can see why it would be a strong point for others
im not saying its bad motivation for everyone
im saying its for bad motivation for pure mathematics
I mean just cause you’re not applying it yourself doesn’t make it less motivating
But I see your point
Judith Butler is at Berkeley???
Why have I not realized this until now
Time to bump them up from my 1st choice to my 0th choice
eg. lim e^n is undefined since it diverges
1st choice it is
well
you can define it to be inf 🙃
lmao
how can it be the Infinium if it gets arbitary large...
also, convergence/divergence is a property of sequences, not limits in general
literally everything
rank nullity is literally just first iso from vector spaces
schur's lemma can be proven pretty quick from first iso is the first one that comes to mind
uhhh every normal subgroup is the kernel of some homomorphism
so you can prove some subset is a normal subgroup by finding some homomorphism it's the kernel of
very useful for example proving A_n is a normal subgroup of S_n
again, these are just the things coming to mind - there are many more
it is
so powerful it's actually true for a lot of objects
vs, groups, modules, rings
anyone have any tips on making life more exciting?
i'm just
insanely bored
like
really badly bored
usually when this happens i manage to find smthn to fixate on for a few months but its not working rn
and i just hate everything
and schoooool is starting up again and it's pain and suffering
anyways
anyone got anything?
Have you tried to make origami or to build polyhedra? It's a very nice hobby and can be done from home.
ive been through my origami phase already, sadly, so it doesn't really interest me anymore
rock climbing sounds interesting 👀
where in India btw? I'm too from India
Kolkata
Pizza.
OOO
Learn latex!!!!!!!!
Yesh yesh yesh
Tried reading books?
i'm trying to print my thesis and i sent my printer person some test files with certain crop marks and bleed margins and i'm really confused about their response
"The cut marks that are now only placed on one side of the design are not needed. All we need is the bleed margins."
but how do I indicate the bleed margins without the crop marks
i do not understand anythink
ik latexxx
i've read every book i care to read for now, at least
besides the ones on my to-read list
currently on 'a portrait of the artist as a young man' by joyce
ayyy I love that book
have you read the christmas dinner scene yet
it's so visceral
||the one where mr dedalus, casey, and dante have the argument over the irish priesthood? yeah i thought it was really fuckin well written, i was like||
||invested and shit||
yea that scene is amazing oh my god
"I've read all the books I care to read besides the ones I haven't yet"
x post
what do career statisticians find themselves doing most of the time, outside of administrative/bureaucratic fluff? does it largely vary by industry? does anyone have industry experience to talk ab this?
yup!
my closest exposure to it is just what statistical studies manufacturing engineers find themselves doing in mfg companies
so not professional, trained statisticians
I have purchased everything on my list for college!!
yay!
Then learn tex
i'm no masochist
Tex is fun until you include a graphic
Why would you ever do that
Also using pdftex I don’t think it’s that hard
I’m just too lazy to read the manual
Everything is better than word
Hell fucking lyx is better than word
How expensive was it?
I was going towards 800 dollars
Which sucked
Big tip buy stuff as you need it
well I already had most of my list done
we were just getting the last few things
but we spent like $150-200 today
nG congrats on honorable!!
Uncongrats to nG
Slurp (ryc for admin)
Ryc for helper
why is the prime spectrum of an ideal important
of a commutative ring you mean?
Zariski Topology
if you have a commutative ring R, the prime spectrum Spec(R) is sort of the universal space such that the ring of functions on this space is R
We had modular forms for SL(2,Z), then we put in some congruence subgroups and get modular forms for that...but now why would one want to get more such crazy functions by defining functions in crazy objects like fuschsian groups.
The condition of primality seems to be like finding a sublattice of the lattice of ideals that specifically has closure under binary unions
It is addition of more and more parameters to generalize the theory. And now these classical automorphic forms seems like a date of hyperbolic geometry with complex analysis to generalize classical modular forms
I mean the reason is that we have many more interesting kinds of groups acting on the upper half plane other than congruence subgroups of SL_2(Z)
crucially none of the examples like SL_2(Z) or \Gamma_0(N) or \Gamma_1(N) or \Gamma(N) are cocompact, meaning the corresponding modular curves are not compact, they have some cusps that you have to add back in
but there are cocompact Fuchsian groups like the triangle groups that give you compact quotients of the upper half plane
This has to do something with their fundamental domains being compact and stuff. Most of times for congruence subgroups it is not compact. Right?
yeah this is never compact for any of the congruence subgroups
But how did the aim to generalize modular forms for SL(2,Z) comes from changing groups is the only reasonable way to generalize?
Is it because we want functional equations
Later
I mean changing the group is an obvious way to generalize yes
I mean here we're not even changing the underlying group G=GL_2 that much, we're passing to an inner form essentially
Moreover we now have general automorphy factor etc stuff which satisfies some rules. But ultimately at the end what kind of L functions it leads to ? Must be very similar to these modular forms L functions
But do we have modularity ?
yeah you basically end up with the same GL_2 L-functions
I think the way this much theory is needed to go from SL(2,Z) to any discrete subgroup of PSL(2,Z), which is by introduction of hyperbolic geometry and automorphy factor etc...i hope for GL(n,Z) kind of stuff it is not much different
Or there are much more theories needed again
well so you can write down automorphic forms for GL_n in the same way as you can for GL_2
there's a little more bookkeeping involved but it's not that different
one big difference is that you never have any holomorphic modular forms for n>2
so you pretty much only have Maass forms
And i hope mostly we would be studying GL(n,Z) functions by studying how it breaks into lower GL(d,z) d<n type functions. Like is it same kind of how representation are broken into irreducible ?
that is sort of what you do yeah, for GL_n you have cusp forms for GL_n, and then you have Eisenstein series coming from Levi quotients of parabolics of GL_n
those Levi quotients will look like GL_n_1x...xGL_n_m
It's always the algebraic objects being introduced for getting generalized stuff ...like Riemann Zeta function was purely complex based functions and generalized to dedekind Zeta function and then to Artin L functions. All this is due to algebraic thought process. On the other side no one cares much about Hurwitz Zeta function. Thank God multiple Zeta functions saved some respect of analytic nt people. And now i see that in modular forms also it is the groups and their geometry generalizing this classical analysis type objects. Do we have multiple GL(n,Z) type stuff too like MZV
I don't think much is known about the "multiple" analogues of this automorphic stuff
Yeah that would be crazy book keeping
Just Artin L functions only had me rolling through algebra a lot
that starts to run into foundational Langlands stuff that we don't really how to answer
anyways an example you should look into going back to Fuchsian groups
the relationship between the (2,3,7) triangle group and Hurwitz curves
DID WEW GET HONORABLE
those are some really nice examples of compact quotients of cocompact Fuchsian groups
no lol
What is honourable?
I mean what is special about yellow ?
Oh ok
I am stupid..i never noticed it...i thought these colours are by choice
most of them are automatically assigned by a bot
like active and very active are based on chat activity
Ya I think I ain't active because it is taking weeks to read just 1 page of that iwaniec book...so it's sometimes torture. On the other side Artin L functions although they look innocent but i know they'd strike harder then GL(2,Z) stuff later.
That is why trusted is better
if you actually think someone like me gets honourable you're mental
" @neat lintelable — these are people who have consistently demonstrated courtesy, reasonability, and helpfulness around the server; and whom we consider to be exemplary members of our community."
courtesy: youve said nice things to ppl smtimes
reasonability: never have i ever seen a more reasonable person when it comes to trolling ppl
helpfulness: very helpful when you want ot be
exemplary member of community: duh
Hello Mr. Honor
...
Wew for honorable except on a set of measure zero
and since this server's set is isomorphic to the set of rationals, that'll never happen.
I’m putting the counting measure on Q, biatch
Zoinks! Looks like you have been coaxed into a snarfu of your own construction
Proof: Wew Lads diagonalization argument
Lets say we have a bounded lattice with maxima and minima, and every subposet of the lattice has a supremum. Define an element to be prime if for any two elements, their meet is less than the prime element if and only if either of the two prior elements are less than the prime element. For any element, we can define the Lead of an element to be the set of prime ideals greater than the element.
The intersection of the leads of any set of elements is just the lead of the supremum of the set, obviously, and is closed under uncountable intersection. The union of the leads literally is just the lead of the meet by the literal definition of primality. The lead of the maximal elements is the empty set. The lead of the minimal elements is the set of all primes. Thus we have an “antitopology” over the set of prime elemenrs, or a topology where the closed sets are these leads
this is useless though because we pick out prime elements just so we have a topology
This server is isomorphic to the free group on all peoplewith active
Or maybe honorable
i also satisfy all these criteria!
i deserve honorable!

helpfulness
LMFAO
i am more helpful than u are!
i help more people
coz i am online all day
$dx\wedge dy(\hat i, \hat j)=1$
I may help only once in a while but my help is worth its weight in gold
gmod
:D
and since its all online, the weight is 0.
wtf is this
do you guys write i-hat and j-hat with or without the dot
😵💫
differential forms!
with the dot
teach meeeeeeee
What... Fuck you
my phone autocorrected j-hat to jihad
delete this
you got owned.
exemplary member of the community
why
I am exemplary

how am I supposed to do it then
tterra, its just physics notation
wait what
no need to be scared of it
don't take me too seriously i've had some drinks
but no one uses i and j for basis vectors
In differential geometry we often use \partial_x and \partial_y for this
???
Cool
Or \partial_j for j = 1, ..., n
I meant for like R²
for what
Has to do with equating vectors with directional derivative operations
For the unit vectors
oh rly
oh wait what's the difference between basis vectors and unit vectors
unit vectors are more general right
basis vectors are a type of unit vector?
Yeah or people use \partial / \partial x, ...
Sorry I meant the basis vectors
unit vectors are just any vector with "length" 1
they dont have to 
oh what
These do though
A basis vector is linear independent and span the entire space
ok
basis vectors need to be linearly independent, and span the set
they can be whatever u like
Probably the best word for it is the coordinate vectors

icic
Anyway feel free to use ijk for now but that will fall out of practice quickly
in about a week and a half I will have to unmute #probability-statistics
since I will be taking the course
yeah it's more of a linear algebra thing right
just another reason to hate 4 manifolds...
l
yup you took the L
is the ti nspire cx ii is better than the ti nspire cx ii cas?
LOL
Also
what is a wedge product
Whatever
Helpfulness
$\omega_1\wedge\omega_2(v_1,v_2)=\det\begin{pmatrix}\omega_1(v_1) & \omega_2(v_1) \ \omega_1(v_2) & \omega_2(v_2) \end{pmatrix}$
lol
wtf
Lmao
gmod
there we go
I dont know what a damn wedge product is
where omega's are differential forms
I know how to define it in like 4 ways
oof
But idk how to tell you what the picture is

determinant of that matrix
Basically you pop two vectors together into a parallelogram
which is like the area of the parallelogram bounded by the vectors
Thats it
k-parallelepiped moment
Its the same in higher dimensions, you're still popping k parallelopepids onto l parallelopepids

And you're like
icic
Idk
They're signed
By the orientation
That comes from the order you list the edges
damn like

I feel so much better that I can talk about this kind of stuff now
after like
basic videos
this shit is interesting
indeed!
thats why i have been trying to half ass and still learn it
its so much fun
lol
like I said earlier I think I've found the right path I want to go down
bc like algebra is cool but I don't seem to have enough motivation to learn it
lol
TRUE
:D
Algebra is cool n all and so is analysis but i think i prefer number theory since both are present (although id go more towards analytic number theory)
analytic number theory 
They could have called it anything and yet they chose "analytic number theory" over "numbernalysis". 
Analytic number theory makes it clear that there’s some kind of analytic structure in place
bruh what does this mean in general
i always find it weird how analytic methods come into some problems
We usually equip a set with structures and make couples or triples etc
Not all number theory has an analytic structure involved
ive heard of this in many different contexts
Im still drunk from last night
ok
Yeyeyeye
should i try to learn the violin
defo
i have no previous experience with any instrument except vaguely with the ukulele (and the recorder from elementary school)
if you arent expecting too much of yourself, yes
friend of mine got an electric violin somewhat recently
without prior experience
No #serious-discussion is mine
shut up
No. Mine.
@errant ridge it depends on what you're looking for.
are you looking to become a good/respected practitioner of a traditional martial art
that takes decades
You can get a black belt in most styles in the 5-10 year range.
Tournaments are a different story
i used to do competitive martial arts
you can start doing them early on
tbh I wanna participate in some tournaments/be able to defend myself (if I did find myself in such a situation, which is unlikely yes)
just don't expect to win them at the beginning lol
Lol yeah
those are 2 entirely different things
But if you really want to "know" martial arts then it's basically endless. I started when I was 8 and am approaching 20 years with the school.
you can't do both?
you can i guess but they are different
makes sense
You can but they're very different goals with different timelines.
you wouldn't want to train traditionally if your goal is to defend yourself
I see
how are they doin' with it
I mean, obivously no matter how good i get my first thought is to run away
because why wouldn't you?
there is a big difference between martial arts and actual fighting where you need to defend yourself
but martial arts does help with that
some more than others
But even "defend yourself" can mean a lot of things. Like, do you mean defend yourself when an MMA fighter that's getting aggressive in a bar or do you want to stay safe in everyday life?
stay safe in everyday life I guess
Honestly that's the best start you can have lol
Lol yeah
I agree
I've never met a lifelong martial artist who would say otherwise.
but im talking about, if I couldn't, then I'd have to defend myself and I don't wanna be totally helpless
you never know if the other person is armed
or has people who will help them that you havent noticed
hm true yeah
punch to the nose 
he gets to play in some band and is enjoying it
Throw your wallet in their face, punch, run.
oh cute
a punch to the nose is a nice distraction but won't knock them out
in a band without prior experience sounds like a jump
gets tears in their eyes tho so thats a plus
My favorite quote that I've heard I response to "what is the best technique in the martial arts" is "don't be there when the punch arrives"
I'm thinking about getting into martial arts for multiple reasons, a 3rd one is developing discipline
Lol I agree. That was from Fumio Demura about 30 years ago I think? I'd need to check my books to be sure. He's a Japanese master and has been extremely devoted to the art since long before I was born.
i don't think it's very funny tbh
Lol I love that this is where you chimed in 😘
I find people who stay with traditional martial arts pretty cool
like at some point you see that it's so much more than just the techniques and fights
all the culture behind it
honestly great
i just opened chat now. what do you think about public kissing?
ab = a . b + a
b
kissing my copy of introduction to differential geometry in public
I say yes
I quit "traditional" martial arts for boxing and kickboxing a long time ago tho
sometimes i miss it
Another quote that I heard in a documentary on Musashi from when History channel had history: "martial arts is a language and a black belt means that you know the alphabet"
what about a non-black belt
that's a great one as well damn
I enjoy it but we may get banned 😅
i dont mind getting banned of lowmath
That comes down to what I said about different goals. A non black belt can defend themselves just fine. If you internalize that "avoiding a fight is the smart choice" then you'll do very well safety wise. But it's not the same as really being a martial artist.
Ok but if half of what we say in DMs ends up here then I feel like they'd find a way to IP ban us 🤣
And I like this server, I'd like to avoid that lol
🤧
So one of the styles that is taught at our school is an old iaido style and I really enjoy it because it has a very heavy emphasis on philosophy from the start.
If you want personal safety, tournaments, and discipline then I'd look for a traditional school that competes in public tournaments. I'm not saying that you won't get discipline from a non-traditional school like an MMA gym but they usually aren't run with the same emphasis on structured formats that traditional styles do.
Also for anyone interested in martial arts who likes movies, watch the Karate Kid series (not the Jackie Chan one) and then watch Cobra Kai on Netflix.
hm I was hoping MMA would be good for that, but I guess I can go for other forms it as well
what are you sayin my guy
"a traditional school that competes in public tournaments"

the Jackie chan one is the best
Doing staff for 8 years in martial arts tournaments gave me trigger finger in both my pinkies
The movies are wonderful 80s camp and the show does an amazing job of recapturing and embracing that while also being more self aware.
the payoff is I can make an ungodly whooshing noise with any elongated staff-like object
miza badass
Oh I like it to but it's not a part of the same franchise. At least not yet.
Oh my god I want Smith to show up in Cobra Kai now 🤣
most people do sword or nunchucks as a tournament weapon and my dumbass chose staff
btw what do you mean by that "structured formats that traditional styles do."
Bo is fun but I prefer eku because just carrying it turns heads lol
ye
that and fan
fan forms are fun as fuck
useless but fun
unless you have a very sharp edged fan like my old grandmaster has and then it’s just a horrifying dagger
I wonder if it's possible to practice martial arts by yourself after training for a few years? 
So traditional styles are pretty universally rooted in one of two things: formal military or informal resistance movements. As such, the style was taught in a very rigid, repetitive structure with things like ranks, titles, a lot of formality, etc. It's not for everyone and I wouldn't say that it's better than the alternative but discipline naturally follows.
That, again, depends lol (sorry, that's just pretty universally the answer). You can certainly train and then keep practicing on your own but there are things that you won't be getting, namely partners to work with and the corrections of an instructor. No matter what you learn and how hard you try to stop it, you will change what you learn. It just naturally drifts. If you don't have someone who knows the original to correct you then you'll start mutating it.
haha don't worry I'm used to hearing/saying "Depends" as an answer
Fans are so cool. On the other end of that is the kanabō but I haven't used either lol
Ye
so you can't perfectly learn new things on your own but you can maintain the skills you already have?
"No matter what you learn and how hard you try to stop it, you will change what you learn. It just naturally drifts." hm yeah okay
Wonderful! Then I'll lean into it: martial arts is an extremely personal journey. Who you are, what you want, what you're willing to do, and who you find to help you will lead you in INCREDIBLY different directions. None of those directions is necessarily "better" or "right" outside of subjective opinion. Like I can answer questions but (especially without knowing you better) it's all steeped in my perspective and is almost certainly not perfect advice from you.
We do use a really cool Chinese weapon that I always struggle to find info on. The name that I can most consistently find info under (which isn't saying much) is "crescent moon saber"
scythe
handheld scythe
Used for farming (cutting stalks) but repurposed as a weapon
No it’s a Sickle
handheld scythe is a sickle
same purpose but smol
That's extremely subjective lol. In my case, I didn't choose my school. My mom and her brother had trained together as teenagers and she had plenty of her own opinions on it (chief among them that if I was going to train then it would be in the furthest thing from her school lol). She had a friend in one of the other moms at my school. Her son's (my friends) and she had both trained at a local school and she had become a black belt in the style. I was told that if I was going to train, then I would train there. In 2024 I'll have been there for 20 years.
god damn, that’s epic
wow nice
Kama is the word that you're looking for lol. Traditional (and still in use in rural areas btw) Okinawan farming tool. Very fun, and I recently learned that the professor I've been working with was a 3rd Dan in a traditional Okinawan style and had used the kama extensively.
karma police
Lol, I wouldn't say epic but I'm proud of it
Funny thing about that school: the kids that became black belts are VERY likely to have pursued ambitious higher education, especially in engineering. 5 of the people that I came up with became engineers, a couple of those with MS degrees and one just left for California to get his PhD in biochemical engineering. Another is in med school, another is in law school, and I'm working on getting into a PhD for math.
There are other examples that I don't know as well personally but my "group" held to this trend.
Oh! And one joined the national guard and they sent him to Serbia to get his MS in environmental engineering.
So while I will not say that my school is the best school, I firmly believe that it's the best school for me and it's absolutely the first one that I recommend for kids.
Hey guys
Hey
let me dm a question
basic stochastic calculus
Lol if it warrants a DM then I almost certainly don't know it but go for it
Is the “subset product” of two normal subgroups the “smallest” normal subgroup containing them
aka, does normal subgroup-ness form a lattice where the join is the product and the meet is the intersection
yes cuz any subgroup containing H and K must also contain all elements of HK since closed for the operation
if R is a ring, then the ideals form a sublattice
but do prime ideals form a sub-sub lattice
no they don’t, cry
if i want an exponentional function from x=0 y=100 to x=69 y=900, is it possible to create?
or at least close like y in range 875-925
Sure
yeah you can ask wolfram to do it
,w plot e^x, x=[0,69], y=[100,900]
Uhh
I think they mean an exponential that interpolates those two points
Like
y = 100*a^x
oh i read the question as plot within these bounds
And then we need to pick a so that 900 = 100*(a^69)
Now it's your job to figure out what a is @dire beacon
ok
how do i get the equation out of that?
or the thing you type into the graphical calculator with just one variable
i read the question as 'plot e^x with these axis bounds'
if thats not what you meant then disregard
i used x^2/6
but the start was too slow
and the end too fast
but i dont want it to be same rise everywhere
can u clarify what ur asking for?
first it needs to look like this
it kinda reassembles 2^2/6.1+100 but that haves too slow start and fast end
idk, im bad at explaining
if you dont know what i mean, then nevermind
ill just combine multiple functions together
u wanna fit the curve
yes i guess
and u first picked an exponential fit
i have this as the main curve
ill just make additional curve with something smaller than 6.1 at lower x values
it does not have to be one continuous curve
u can use the fit ryc suggested
ok
y = 100*a^x
plug the point (70,800) to find a, u also need to add a constant so that it hits (0,0)
ok, mabye im just too stupid for that
lets add -1 first so it hits (0,0)
y=100a^x-1
ok
@misty lake dont shitpost here
society
Society
society
sobriety
society
whats everyones favourite topological space
Top
Zariski Topology
My answer isn't family friendly
tell me in dms
ok fine i thought that nobody would notice
Q endowed with the usual metric
long line
it's nice and simple...
real numbers are scary
the best topology is the discrete topology, i don't want any constraints on my open sets 😁
my favourite space is
my favourite is the Baire space maybe
Best topological space is the hyperreal number line
neither of these are topological spaces either, they are families of spaces
Sierpinski Space
sierpinski space is a good
did you know that a topological space is T_0 iff it can be embedded into a power of the sierpinski space?
ok fine euclidian n space
there??
I did not know that
I remember using it for some counterexamples concerning seperation axioms
But it’s been a while
Stated categorically, this means that the sierpinski space is an M-coseparator in the category of T_0 topological spaces with M being the class of topological embeddings
I see
i like the name "alexandroff cube" more
falls in line with cantor cube and tychonoff cube
do you like polish spaces?
I didn't know that was a thing :O
i can relate to that
my favorite topology theorem name so far is the Hewitt-Marczewski-Pondicery
I got algebra honors for 8th grade is it hard
what the hell is algebra honors for 8th grade
its says algebra I honors @neat lintel
which n
n=pi
💀
each school or district has different curriculum , and whats hard for one person may not be hard for another so its really just subjective.
yeah there's no real way we can answer this
is there a way to specify normal extensions and seperable extensions through homomorphisms or smth
The main problem i face is specifying if a given polynomial is linear without referencing it’s degree
originally I was going to try to “compare” the extension somehow to F[X]/<P(X)> where P(X) is irreducible
but field homomorphisms are always injective and that kinda breaks down
also seperability is prime characteristic might be an issue
Actually, for every splitting field G of an irreducible polynomial P over field F also an extension of F[X]/<P(X)>
Can I ask thermodynamics or mechanics of materials here
@plucky zodiac see physics server in #old-network
Thanks
bro now everything from calc 3 is clicking
the exterior derivative on a 1-form in R³ precisely gives curl

using the metric tensor on R^3 you identify vector fields with 1-forms
take the exterior derivative for a 2-form
do some more geometry ("hodge star") to get a (3 - 2 = 1)-form
and then use the metric tensor again to get a vector field back
the result is curl
idk what metric tensors are
also hodge star is coming soon but not yet
but like did I say smth incorrect or no
replace metric tensor by "inner product" or "dot product" even
oh ok
i'm just clarifying on "precisely"
get an isomorphism between and apply it
oh ok
in R^3 it's just (P, Q, R) -> P dx + Q dy + R dz
yeah
this is defined in terms of the coordinates on R^3, but you may give a coordinate-free definition of this. good to keep in mind if you're interested in generalizing this to other situations
makes sense
yeah im basically going through that michael penn playlist and getting the general ideas
once im done with this I will formally learn it through a book
holy shit grad curl and div are just exterior derivatives
damn
alright that's enough for today
💤
the differential forms playlist?
yes
it really is
Oooo
teach me
dont u dare
shyshu my name is more accurate now
no smh
No its not!
then teaching me is ensuring that u are learning it all
explaining to others is the best proof that u have learnt something
you know what they say teaching is the best way to learn
no worries
just tell me what u think it is
u dont need to do it rn lol
go sleep
LMAO
i will ping u later
when you're sleeping 
LOL



Hi,
Is there anyone from India who wanna be in a team with me for an online maths competition in November. I need 5 people.
Please hit me up.
@spiral escarp do I need to be indian or can I also just act indian
Its a country based competition.
So you need to be in India
However, I think u can join it from ur own country
The competition is wmtc
Its a little like arml
Are there any good math study abroad programs in France?
hello world
Gonst to be a bizbiz major right?
yessss
Buy me some food 
my roommate will be a biomedical engineering major LOL
lmao
;-;
and we probably will make comparable salaries

lol
LOL
he's taking calc 3 first semester
he's gonna be like "wtf are these triple integrals" and ill be like "oh small child"

Yeah you show him how to swindle those integrals out of their money
Do you know what your courses will be?
uhhhh did u know u can do all this with differential forms?? 🤓
LMAOOOOO
gmod is about to make this guy's life a living hell
Hola rycie bycie
low key probably will say that
thats my goal!!!
Illegal until the age of 21 federally
Yes
oh
It's probably not too dumb for weed
it?
What’s dumb is that that shit is legalized at all
oh yeah
I will not do drugs or alcohol
I don't drink coffee anyway
I do do time unfortunately
Time reeeeaaaaallly changes your brain while developing
Coffee is a special treat
HAHA LOZSER
o
It is not to be had most days
yeah
I have large amounts of caffeine every day
It also just makes me feel worse
Monster energy iced coffees are not coffee
Every day is special to me because I don’t have favorites
I had a legit coffee yesterday it was good but 1 buck
I usually have instant coffee mixed in a mermalade jar
Sometimes I get a croissant or something at a bakery and I get a latte with it
Disgusting
slorpy u die 30
is the julia set the "boundary" of something like a mandelbrot set?
bruh
mcdonalds in spain is so bad 😦
Chocolate milkshakes way better than coffee
No not really?
whats the span of mcdonalds
what is it?
Unlike America, it actually gets HOT here. I don’t want a hot drink
but they're not the boundary of something else nice
julia sets are made by a similar slightly shifted iteration scheme to the mandelbrot set
hm i see
i don't remember it
ICED coffee is delicious
I guess i can just do $\partial M$ where M is the mandelbrot set
Neamesis (Neamesis for honorabl)
can i?
sure
niceee
dunkin frozen coffee is good af
you are welcome to do as you please
can you integrate over that?
dunkin donuts coffee is dirty sock water
:/
probably not, i doubt it's rectifiable. idk
yk the contour integral
what is iced coffee sir moderator
rectifiable?
No
what is iced coffee?
modinator
yes
coffee with ice
it's coffee with ice in it to make it cold
bozo
Yea I'm a university student.
oh ok
yeah, that's the condition for being able to do contour integrals on a curve
there is the method of doing pour over coffee onto ice
When I got iced coffee they like filled it with cream and put a shot of espresso or whatever and it was bland af
I think they call it japanese iced coffee
Made me nauseous
and they lie and say it's better
This is my preferred way of doing iced coffee
oh so you can only do contour integrals on a curve of finite length?
It's so much better what
I want CAFFEINE
I love it
I want SUGAR
Cold brew is also good
you are tasteless
oh my god do you put sugar in your coffee
disgusting
No?
yeah good
Milk >> cream
I can make the best coffee but I do instant coffee instead
milk is delicious
That was my argument for energy drinks ofc ryc
because I don't deserve the good one
imagine drinking coffee 
???
i want a fucking latte
My internship has a full coffee bar
I've had so many macciatos
It's so bad but I love them
I love machetes
jealous
They’re fun to swallow
we might be getting an espresso machine in the math department lounge this year
hopefully
Lol
rips your guts as it goes down
I bet the engineering department has a coffee machine already ryc
Don’t you feel under appreciated?
Maybe it’s because you DONT DO SHIT
You lazy mathematician
yes, that's why i joined people in complaining about the lack of a well equipped student faculty lounge last may
every math department I have been in has had an espresso machine worth more than a year of phd funding
and now it is happening
the big ones with a bunch of hoses and steel levers
They should divert that money to the CS dept
that's the IDEA
look like an engine block almost
why would i give them more than they give me?
Because
i'm trying to EARN here
TFW the student doesn't want to be exploited by the university 
Why would someone pay you?
absolutely not. i am a modern man in a modern world
I'll provide them in a little trickle
And thus a drag
plink pink plink
Mathematics is a disservice
Both monetarily and in every other way
plink plink plink



