/mg/ - Math general - Perfectoid edition

TalkBomber
TalkBomber

What are you studying, /mg/?

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All urls found in this thread:

veekyforums.com/thread/9609872/science
veekyforums.com/thread/9616470/science
proofwiki.org/wiki/Vector_Space_has_Basis
en.wikipedia.org/wiki/Hilbert_space#Orthonormal_bases
youtube.com/watch?v=sD0NjbwqlYw
mathoverflow.net/questions/43690/whats-a-mathematician-to-do/44213
en.wikipedia.org/wiki/Mathematical_beauty
math.ucla.edu/ugrad/courses
en.wikipedia.org/wiki/Dual_number
ncatlab.org/nlab/show/Kock-Lawvere axiom
math.cornell.edu/~oconnor/sia.pdf
veekyforums.com/thread/9622175/science

TurtleCat
TurtleCat

Check the catalog, nerd

StonedTime
StonedTime

There is no /mg/ thread there. Only some reddit trash.

VisualMaster
VisualMaster

Physics major here trying to count all groups of order 3 (up to an isomorphism). It's hard as fuck.

AwesomeTucker
AwesomeTucker

There's only one you moron.

GoogleCat
GoogleCat

It's hard as fuck.
Do you need to swear?

Fuzzy_Logic
Fuzzy_Logic

mega brainlet

New_Cliche
New_Cliche

Hint: 3 is prime.

Illusionz
Illusionz

wrong since 3*19=57
you must be grothendieck

MPmaster
MPmaster

so this is the level of conversation from math majors with their 300k starting

New_Cliche
New_Cliche

veekyforums.com/thread/9609872/science
what are you talking about?

cum2soon
cum2soon

Actual /mg/ thread here veekyforums.com/thread/9616470/science

Dreamworx
Dreamworx

But /mg/ isn't a reddit thread? So this seems to be the legitimate one.

Playboyize
Playboyize

Who ENS here?

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Methshot
Methshot

But /mg/ isn't a reddit thread? So this seems to be the legitimate one.
Scholze is the personification of redd*t

Methnerd
Methnerd

You.

BinaryMan
BinaryMan

It doesn't matter what you think. Reddit threads encouraging off-topic discussion and redditry such as despising the anime culture of this website will not be tolerated.

JunkTop
JunkTop

What are some applications of vector spaces which do not have a basis?

PurpleCharger
PurpleCharger

Please be my friend.

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Ignoramus
Ignoramus

vector spaces which do not have a basis
There is no such thing silly user.

Need_TLC
Need_TLC

Appart from the memes, functional analysis deals with this shit, i.e. linear spaces with eveb an ubcoubtable basis such as function spaces. It's used in fourier analysis and harmonic analysis which is useful for PDE, but yea
All vector spaces have a basis no matter how much the retards here yell.

cum2soon
cum2soon

My answer will depend on what exactly you study.

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likme
likme

Don't listen to that physicist

Playboyize
Playboyize

You seem to know what he's talking about. Can you share this information with me?

VisualMaster
VisualMaster

Appart from the memes, functional analysis deals with this shit, i.e. linear spaces with eveb an ubcoubtable basis such as function spaces.
I said no basis, not uncountable basis.

JunkTop
JunkTop

No such thing sweetie

Skullbone
Skullbone

Most vector spaces do not have a basis unless you assume it does

Firespawn
Firespawn

Most
What do you mean by this? Can you provide one example?

BlogWobbles
BlogWobbles

What do you mean by this? Can you provide one example?
The real vector space of functions [math] \mathbb{R} \to \mathbb{R} [/math]

ZeroReborn
ZeroReborn

He's just some retarded troll ignore him.

BunnyJinx
BunnyJinx

He's just some retarded troll ignore him.
I'm not a "he".

Harmless_Venom
Harmless_Venom

Yea, you are just a faggot

King_Martha
King_Martha

Prove that it doesn't have a basis.

takes2long
takes2long

It definitely has a generator set

hairygrape
hairygrape

It definitely has a generator set
That is not a basis.

Gigastrength
Gigastrength

faggot
Why the homophobia?

Deadlyinx
Deadlyinx

Prove that it doesn't have a basis.
The burden of proof is on you.

Carnalpleasure
Carnalpleasure

It has a subset that is linearly inependent and that spans the whole space.

Emberburn
Emberburn

It has a subset that is linearly inependent and that spans the whole space.
The burden of proof is on you.

Flameblow
Flameblow

isnt (1) the basis??

SniperWish
SniperWish

Reminder to report and ignore the retard.

BlogWobbles
BlogWobbles

isnt (1) the basis??
What function "(1)" is meant to denote? And why does it generate the whole space?

LuckyDusty
LuckyDusty

proofwiki.org/wiki/Vector_Space_has_Basis yea I know, it's a "popsci" link, hilarious, but just to prevent any newb falling for you bullshit.

StonedTime
StonedTime

see

VisualMaster
VisualMaster

And why does it generate the whole space?
hmm because you can multiply 1 for every number and you get the whole R

eGremlin
eGremlin

You are also retarded my dude. The space is all the functions, not all the real numbers.

FastChef
FastChef

[math]\forall x\in \mathbb{R}[/math] let [math]V_x: \mathbb{R}\rightarrow \mathbb{R}, V_x(y)=\chi _{\{ x\} }(\{y\})[/math], these functions are clearly linearly independent, and [math]\forall f:\mathbb{R}\rightarrow\mathbb{R}, f=\int_{\mathbb{R}}f(x)\cdot V_x(x)dx[/math]

Fuzzy_Logic
Fuzzy_Logic

The space is all the functions, not all the real numbers.
They are isomorphic vector spaces.

Stupidasole
Stupidasole

Not in any way or form.

Illusionz
Illusionz

Sorry, there isn't supposed to be an (x) after V_x at the end there.

Nude_Bikergirl
Nude_Bikergirl

Commit sudoku

Garbage Can Lid
Garbage Can Lid

Alright, I'll look for my puzzle magazine first thing in the morning.

Sir_Gallonhead
Sir_Gallonhead

interval calculus :$

King_Martha
King_Martha

They are isomorphic vector spaces.
The burden of proof is on you.

girlDog
girlDog

∀x∈R let Vx:R→R,Vx(y)=χ{x}({y}), these functions are clearly linearly independent, and ∀f:R→R,f=∫Rf(x)⋅Vx(x)dx
That's not necessarily a linear combination.

Next?

haveahappyday
haveahappyday

The space is all the functions
uhm... so if we multiply every function by the costant function 1 we will get all the space

massdebater
massdebater

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idontknow
idontknow

explain to me what i did wrong

lostmypassword
lostmypassword

explain to me what i did wrong
Everything.

Poker_Star
Poker_Star

ok, so you have no argument lmao

Deadlyinx
Deadlyinx

ok, so you have no argument lmao
There is no notion of multiplying functions in this vector space.

PackManBrainlure
PackManBrainlure

then how the fuck are you supposed to generate the space if you can't have a linear comb

Snarelure
Snarelure

The field are the reals, multiplying by the identity function is not a fucking linear combination, is a whole new operation.
By reading definitions carefuly

Skullbone
Skullbone

Which one? T'es un feuj ?

StonedTime
StonedTime

then how the fuck are you supposed to generate the space if you can't have a linear comb
You can have linear combinations.

ZeroReborn
ZeroReborn

multiplying by the identity function is not a fucking linear combination
multiplication is not linear
Are we reaching new level of retardness or what?

JunkTop
JunkTop

"the identity function" is not a scalar in the vector space.

BunnyJinx
BunnyJinx

so what is a scalar in that vector space?

GoogleCat
GoogleCat

But the space of functions doesn't form a field you inbred retard, so you cannot form a vector space of the space of those functions over itself.
The real, as the set of real numbers which are not the same as the spacw of real valued functions.

StrangeWizard
StrangeWizard

so what is a scalar in that vector space?
Any real number.

Fried_Sushi
Fried_Sushi

[eqn]
x^2 - 5 = 2\\
\frac{d(x^2 - 5)}{dx} = \frac{d2}{dx}\\
2x = 0\\
x = 0
[/eqn]

Need_TLC
Need_TLC

infinitely many summands
linear combination

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Lunatick
Lunatick

real not reddit thread here veekyforums.com/thread/9616470/science

Garbage Can Lid
Garbage Can Lid

en.wikipedia.org/wiki/Hilbert_space#Orthonormal_bases
In the infinite-dimensional case, an orthonormal basis will not be a basis in the sense of linear algebra; to distinguish the two, the latter basis is also called a Hamel basis. That the span of the basis vectors is dense implies that every vector in the space can be written as the sum of an infinite series, and the orthogonality implies that this decomposition is unique.

Booteefool
Booteefool

an orthonormal basis will not be a basis

girlDog
girlDog

I'm not , but perhaps you should've clarified ahead of time that you meant a basis in the general sense and not in the specialized sense that "basis" is often used to mean in the context of discussing a Hilbert space like R → R

farquit
farquit

I said "vector space" and "basis", not "Hilbert space" and "orthonormal basis".

Bidwell
Bidwell

well, ok

idontknow
idontknow

Is he actually this stupid, or is he just doing it for attention?

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likme
likme

well, ok
Which inner product can you put on this space of functions to get a Hilbert space?

Playboyize
Playboyize

oh right, oops

Snarelure
Snarelure

He's a pretty decent researcher apparently.
Just very autistic about foundational stuff I guess.

RavySnake
RavySnake

to be fair the rise of set theory in mathematics is basically an endorsement of autism

TurtleCat
TurtleCat

"Autistic" is a bizarre way of describing it, given that being literally autistic myself has probably been one of the biggest factors in me actually learning & understanding foundations

kizzmybutt
kizzmybutt

Recapping some basic alg topo as a bedtime book.

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Soft_member
Soft_member

FRUMP

cum2soon
cum2soon

may your dream sequences be exact

Gigastrength
Gigastrength

how hard would it be to learn multivariable calc on my own? ive just finished integration at uni.

TalkBomber
TalkBomber

How much linear algebra do you know?

CouchChiller
CouchChiller

not much. should i learn that first? is there anything i should look into before starting linear algebra/multi-variable calculus

DeathDog
DeathDog

*anything else?

PurpleCharger
PurpleCharger

Intro-level multivariable calculus is like 80% calculus + linear algebra. I may be forgetting something, but I think you should be able to at least learn some important basics as long as you're comfortable with single-variable derivatives and with vectors and linear transformations.

BunnyJinx
BunnyJinx

Hmm, you don't really did that much libear algebra, or you can learn it as you need it, also what is your goal? I.e. are you a mathematician?

Stark_Naked
Stark_Naked

What bedtime book are you using?

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5mileys
5mileys

How does this impact anything? You're a single autist.

hairygrape
hairygrape

cool! not really sure what linear transformations are either yet. i probably know them, just not by name.

i hope to be one! im a first year math major

Snarelure
Snarelure

im a first year math major
not really sure what linear transformations are
How does this even happen?

CouchChiller
CouchChiller

A linear transformation is something that maps vectors to other vectors and which is "linear", which has several equivalent definitions. The standard one in the context of formal math—albeit maybe not the most enlightening one—is that a function [math]f[/math] from one vector space to another is called "linear" if
1. for any vectors [math]v, w[/math] in the source space, [math]f(v + w) = f(v) + f(w)[/math], and
2. for any vector [math]v[/math] in the source space and scalar [math]a[/math], [math]f(av) = af(v)[/math].

There are better explanations, but it'd take a while to explain, and a proper source would probably do it better than me anyway.

JunkTop
JunkTop

A few simple examples—rotations about the origin are linear, as are reflections through lines/planes that pass through the origin. Uniform stretching along one or more axes is also linear.

Nojokur
Nojokur

?
that's so cute

likme
likme

i’m kind of behind on my Math knowledge. also, just finished my second quarter: haven’t done much at uni yet.

so, like a function but for vectors instead of numbers? thanks, I’ll look into it!

Poker_Star
Poker_Star

fuck is ens

Sharpcharm
Sharpcharm

it *is* a function! a function is just an association of inputs to outputs, no matter what kind of thing you're working with. also, to be clear, linear functions are a *specific kind* of functions between vectors, just like how continuous functions are a specific kind of function.

Soft_member
Soft_member

Embarrassed Nude Shitposter

haveahappyday
haveahappyday

Can't you define for non orientable manifolds if you consider the boundry of your manifold not just the geometric boundry, but the the induced boundry sent from the domain of parametrization? Maybe not differential forms, but other types of integrals on your manifold.

lostmypassword
lostmypassword

manifolds are not intrinsically parameterized

Techpill
Techpill

I know, but obviouslly to extend these concepts and theorems, you will lose the intrinsic setting, but some theorems giving intrisinct information may still work, like the gauss bonnett theorem, or maybe I'm confusing shit, but I belive this may be related to surgery theory. I suppose a more concrete question is could I get somethibg like stokes theorem with integretion defined from an integral defined with just the metric tensor?

Sharpcharm
Sharpcharm

Zorn's Lemma.

Burnblaze
Burnblaze

see

Emberfire
Emberfire

Please refrain from spamming.

Evilember
Evilember

Zorn's Lemma.
So you can not prove every vector space has a basis unless you assume every vector space has a basis.

Firespawn
Firespawn

Basic Mathematics by Lang. Living in a third world country only teaches you how to plug and chug equations

SniperGod
SniperGod

Basic Mathematics by Lang.
Lang is a meme.

TalkBomber
TalkBomber

Integration on a Riemannian manifold is done w.r.t. the volume form defined by the metric.

The existence of a non-zero volume form is the same thing as the existence of an orientation.

TurtleCat
TurtleCat

You can use Riesz representation theorem to show a measure can be defined and that it's a volume form iff it's orientable.

Sir_Gallonhead
Sir_Gallonhead

Got it! Thanks, user!

King_Martha
King_Martha

It may be a meme, but it sure is quite helpful. What textbooks can you suggest apart from him and Gelfand?

Firespawn
Firespawn

Thanks. I guess they were.

This one.

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cum2soon
cum2soon

S

w8t4u
w8t4u

A

askme
askme

G

Bidwell
Bidwell

E

iluvmen
iluvmen

T

idontknow
idontknow

I

hairygrape
hairygrape

H

Playboyize
Playboyize

S

Gigastrength
Gigastrength

S

Techpill
Techpill

H

Methshot
Methshot

I

Methnerd
Methnerd

T

PackManBrainlure
PackManBrainlure

T

Carnalpleasure
Carnalpleasure

O

Sharpcharm
Sharpcharm

O

Snarelure
Snarelure

B

Emberburn
Emberburn

L

Emberfire
Emberfire

I

Burnblaze
Burnblaze

combo!

LuckyDusty
LuckyDusty

What are some advanced calculus topics after multivariate/vector calculus?

Nojokur
Nojokur

Axler

StrangeWizard
StrangeWizard

[eqn]\int_{0}^{\infty}dR \int_{0}^{\pi}d\lambda \int_{0}^{2 \pi} \frac{8 \thinspace \text{sin}(\lambda)}{(2 - \text{cos}(R - \lambda + \phi) + \text{cos}(R + \lambda + \phi))^{3}} d\phi[/eqn]

Any suggestions on how to prove that this integral converges? Numerical integration seems to suggest that it does, but that's not a proof.

Fried_Sushi
Fried_Sushi

Okay, I don't know why they thought this shit converges numerically, because it fucking doesn't. Any hints on how to prove it diverges at the origin, for example?

BlogWobbles
BlogWobbles

a bunch of academic thieves/embezzlers/jews

CouchChiller
CouchChiller

Someone wasn't accepted to the ENS.

ZeroReborn
ZeroReborn

differential geometry
although you'll need to learn some topology first
Lee's topological manifolds is good, and it's written with preparation for his smooth manifolds book in mind, which I haven't read but have heard good things about

whereismyname
whereismyname

No shit. I didn't sit the entrance exam yet. But I'll be there in a year. I still despise the ENS and everyone involved in it (except for me). I'll just pretend to be friends for a while until the day of the rope comes about and the fourth reich is set up

Illusionz
Illusionz

Lee's topological manifolds is good, and it's written with preparation for his smooth manifolds book in mind, which I haven't read but have heard good things about
I vouch for both of them, and recommend the interested user to do all the exercises and problems.

Dreamworx
Dreamworx

Could you explain yourself without using those ebin maymays? Also, why do you want to go if you hate the place so much? Don't you have principles?

Lord_Tryzalot
Lord_Tryzalot

Numerical integration seems to suggest that it does
Are you sure about that?

King_Martha
King_Martha

People at the ENS get the opportunity to obtain the few PhDs that are actually worth it, i.e. PhDs that are not just some glorified technician degree. Those who get glorified technician degrees are usually foolish outsiders hired by the ENS to do menial tasks. They're essential cheap manual labor. Cattle. They do not produce research because they don't have time to do this. They are merely tasked to help with technical problems, teaching, or code-monkeying for the jews, while the jews have enough free time to actually think about problems related to the field. This ends up with jews getting glowing research and others getting nothing, because they were too busy being cattle and not doing actual research. And this cycle goes on and on. Cattle get no acknowledgements and are deemed not adept enough. The thing is, research ain't easy when you have no teaching to do and no technical problems to solve. But it is really hard when you have to teach and spend the remaining time fixing stupid shit, especially when you are directly competing with the dirty jews with zero teaching load and zero code-monkeying to do. I'm not even gonna comment on the blatant (((nepotism))).
Only people from the ENS get tenure, the others are just weeded out with a useless "PhD" which isn't even a real PhD.

I don't want to be cattle, so the only way is to join this thief organization. (Also, it is state-sponsored, students get paid by us, taxpayers, simply to study and steal other people's work).

I have principles, but sometimes you've got to do what you gotta do to survive when the population is so brainwashed as to believe that jews have France's best interest in mind.

The world has become a joke. I love maths and science, but hate those involved in it.

farquit
farquit

Why do you care about this integral?

viagrandad
viagrandad

sounds like you're just salty that jews are smarter than you

cum2soon
cum2soon

I was told that was the case, but I've been trying to get approximate results with Mathematica and it gives huge answers with almost as big error estimations. I'm starting to think it diverges, but I don't know.

A proffessor of the Physics Department at the university I study is developing a physical theory for the kinematics of elementary particles with spin, and this integral appears somewhere in there. My friends told me about it and I decided to give it a try.

massdebater
massdebater

we'll see in a year, nigger-lover

idontknow
idontknow

Where have you heard all of this if you're not inside? The chans? I remember people talking about the ENS, but didn't pay much attention (and was in French, which I'm not that familiar with). Also, why do you say that the PhDs they give to outsiders are worthless? And why not go to some other country?

Techpill
Techpill

I know it by looking at what people become when they don't get in an ENS.

Why should I have to leave my home country to the jews? I am French and white, this is my country, not Israel's. They can fuck off (and they should before shit hits the fan). In my country, there's free healthcare. This is not common at all, and my parents paid for it through their hard work (and I will for forty years too soon enough), so I should be able to benefit from it. I could go to some other country and get a PhD, but it will be much harder to get a job in academia either from said country (because I'll be an outsider and no country is dumber than France when it comes to immigrants/traitors) or from France (because I'll be "gone" in the eyes of the jews. Some nigger or jew will take my job instead)

Snarelure
Snarelure

I know it by looking at what people become when they don't get in an ENS.
What do they become?
Why should I have to leave my home country to the jews?
Why shouldn't you?

Evilember
Evilember

They become high school teachers.

Because I'm not a cuck, they are a mere percent of the total population. If the average person weren't so dumb they'd invest in ovens. Also, it's a matter of principles, you can't just let people steal everything from you, including your past. I've never been abroad and lived my whole life in France. Everyone I know is French and France is my culture (except for the cuckoldry fetish which seems to have cut a wide swath in there, I wonder why)

WebTool
WebTool

being cucked by ideology so hard that you become convinced you're not a cuck

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ZeroReborn
ZeroReborn

The reason we're cucked is the shared stupidity of average people, which is helped by waves of migrants diluting the average iq and jews controlling media, not because of my mediocrity as an individual. Also, I'm pretty sure I'd beat this 112 iq if I took a real iq test.

AwesomeTucker
AwesomeTucker

/pol/

Illusionz
Illusionz

I visited my granny today. She was too tired to discuss category theory with me this time. Sad times.

Preach, sister!

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Lord_Tryzalot
Lord_Tryzalot

motivate me to do maths please

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King_Martha
King_Martha

come up with your own topic of study and motivate yourself you lazy piece of shit

SomethingNew
SomethingNew

Let [math]\mathbf F[/math] be a subfield of [math]\mathbf C[/math]. If [math]\mathrm{Vect}_\mathbf F\,B[/math] is dense in [math]\mathbf H[/math] for its euclidean norm, then for all [math]\mathbf x\,\in\,\mathbf H[/math], [math]\left( \left\langle \mathbf b \mid \mathbf x\right\rangle\,\mathbf b \right)_{\mathbf b\,\in\,B}[/math] is summable and [math]x\ =\ \sum_{\mathbf b\,\in\,B} \left\langle \mathbf b \mid \mathbf x\right\rangle\,\mathbf b[/math]
What do I do next? Only a finite number of coordinates of [math]y[/math] are non-null btw, that's why I can use the inner product like that.

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5mileys
5mileys

Study or you will never understand Fomenko's mathematical works.

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Lunatick
Lunatick

fug :DDDD ok dad

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hairygrape
hairygrape

tfw you realize that semantics is left-adjoint to syntax

Show me your comfiest adjunctions, /mg/

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Poker_Star
Poker_Star

That's not true

Emberfire
Emberfire

Prove it

PurpleCharger
PurpleCharger

Is it possible to study maths after university? I mean, just out of interest

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CodeBuns
CodeBuns

No, jewish people suck out your math skills after graduation.

BunnyJinx
BunnyJinx

not him, but the burden is on you really

Stark_Naked
Stark_Naked

they do it well before graduation though, right at birth due to race mixing

Spamalot
Spamalot

I am in Calc 1 and getting shit on by integrals. At what point did it "click" for you guys? I have the exam in ~1 month and really want to get 100 on it

LuckyDusty
LuckyDusty

I never got it until calc3 where my Prof was more proof bases. So maybe look into "why" you're doing the integral?

happy_sad
happy_sad

ENS poster, are you still here ? I'll be moving from Canada all the way to France to try and study there, got any tips to share ?

lostmypassword
lostmypassword

Former Lyon reporting

Gigastrength
Gigastrength

Brainlet here, why does the Riemann Zeta function converge for negative integers ?

Lord_Tryzalot
Lord_Tryzalot

Check this one out
youtube.com/watch?v=sD0NjbwqlYw

Evilember
Evilember

Thanks

Dreamworx
Dreamworx

hey /mg/ do you have any hobbies outside math?

university math takes all my time so all I do is math with the occasionnal procastination when I'm tired, like right now.

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Boy_vs_Girl
Boy_vs_Girl

Yes. I go for walks, play board games with my family when I visit them, shitpost, listen to music, etc. Those and math are my hobbies.

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CodeBuns
CodeBuns

sweet. I was hoping to hear more "serious" hobbies from math-anons, like music creation, drawing, programming, etc.

but your hobbies sound comfy, I like you.

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MPmaster
MPmaster

I'm incapable of anything important, so I just do the comfy stuff. Nevertheless, good night to you, poster of nice animals.

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TalkBomber
TalkBomber

d-does vidya games count

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whereismyname
whereismyname

mostly read some shit (old school scifi, sometimes elements, sometimes principia) talk shit with my electrical eng bud (poor ol shit) and procrastinate actually doing math despite it being my favorite shit baka

Methshot
Methshot

do you read greg egan? I just started dichronaut and it's amazing

you too!

vidya is the activity that makes me the most relaxed.
I get way too autistic with books and end up excited instead of calm.

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Garbage Can Lid
Garbage Can Lid

product-hom adjunction is basic but extremely comfy

Illusionz
Illusionz

I'm too fucking stupid for this shit. There is really no point in studying mathematics unless you have mathematical talent in the top 0.25%. I used to think I was smart but now I realise that I'm nothing at all, it's just that everyone else is even more stupid.

CouchChiller
CouchChiller

mathoverflow.net/questions/43690/whats-a-mathematician-to-do/44213

William Thurston was an inhuman genius, so really think about his response.

Ignoramus
Ignoramus

I find that mathematics is made by people like Gauss and Euler

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King_Martha
King_Martha

Good answer, I didn't like how he got too philosophical at the end but his initial statements give us brainlets hope and motivation to do more math.

takes2long
takes2long

I still despise the ENS and everyone involved in it (except for me).
so this is the power of critical thinking...

w8t4u
w8t4u

Why not take uncountable summations over the set of kronecker deltas?

askme
askme

Why not take uncountable summations over the set of kronecker deltas?
Linear combinations in vector spaces are finite sums.

iluvmen
iluvmen

Do okay in math, definitely not a strong suit
Love Econ
Major in it
Meet advisor
So how good are you with math?
Fuck guys, I just want to learn about the economy.

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idontknow
idontknow

I'm not the person you are replying to, but what is meant by "Zorn's Lemma" as a response is presumably that if you assume AoC, then we can use that axiom to "find" a basis in the existential sense.

This string of though is slightly different from assuming the existence of a basis outright. Mostly because a mathematician may find it more plausible to assume AoC than existence basis as an axiom. In the end though, this is essentially philosophy. If you don't like it, then there are a lot more concrete areas of math. (I don't mean that as an insult. Mathematics is a large subject, I think there is room for many different research perspectives.)

hairygrape
hairygrape

Everything practical is modeled by math because math is only thing simple enough for human beings to understand unambiguously. You're just going to have to grow to deal with that fact.

(I am not saying math is simple, I am saying that everything is very complicated and math is the simplest thing which is still complicated.)

Snarelure
Snarelure

Most students at the ENS aren't jews, you stupid algerian.

Burnblaze
Burnblaze

I'm not the person you are replying to, but what is meant by "Zorn's Lemma" as a response is presumably that if you assume AoC, then we can use that axiom to "find" a basis in the existential sense.
This string of though is slightly different from assuming the existence of a basis outright. Mostly because a mathematician may find it more plausible to assume AoC than existence basis as an axiom.
It is circular reasoning to assume what you are meant to prove. There is an absence of evidence regarding the existence of a proof that every vector space has a basis without assuming every vector space has a basis (but this is not evidence of absence).

TalkBomber
TalkBomber

Actual brainlet tier comment. Empty logic is what all axiomatic mathematics boils down to. The logical formalism is just a means to a way of understanding; human intuition is prime.

LuckyDusty
LuckyDusty

absence of evidence
circular reasoning
evidence of absence
Refer to /lit/ if you wish to discuss such topics.

StonedTime
StonedTime

axiomatic mathematics
As opposed to what?

DeathDog
DeathDog

absence of evidence
circular reasoning
evidence of absence
Refer to /lit/ if you wish to discuss such topics.

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AwesomeTucker
AwesomeTucker

Ontologically speaking, you should refer to the deep board known as /lit/ if you wish to discuss "evidence" and "circular reasoning".

JunkTop
JunkTop

Ontologically speaking
We only speak mathematically here.

BunnyJinx
BunnyJinx

/lgbt/

Fuzzy_Logic
Fuzzy_Logic

/lgbt/
Why the homophobia?

Nude_Bikergirl
Nude_Bikergirl

What's with the "why the _____?" meme?
I swear I only see it on this board

Lunatick
Lunatick

en.wikipedia.org/wiki/Mathematical_beauty

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Harmless_Venom
Harmless_Venom

Just report the retard. All of these are his posts, you can check the archive to see the full extent of this mental illness.

Lord_Tryzalot
Lord_Tryzalot

One of those posts is about correcting some retard who thought a vector space of functions was 1 dimensional.

Sir_Gallonhead
Sir_Gallonhead

All of these are his posts
This is false, and I'm not a "his".

Spamalot
Spamalot

One of those posts is about correcting some retard who thought a vector space of functions was 1 dimensional.
Which is of course a mathematical absurdity, since every vector space is infinite dimensional.

Evil_kitten
Evil_kitten

What does /mg/ feel about Platonism?

TalkBomber
TalkBomber

Define "platonism".

RumChicken
RumChicken

Define "platonism".
I'm not looking for answers from the uninformed.

Nojokur
Nojokur

see

Raving_Cute
Raving_Cute

Got an A- in Real Analysis and a B in probability theory

Will I ever go to Grad school, /mg/?

Booteefool
Booteefool

Your grades in engineering don't really matter in grad school unless you mean engineering grad school, in which case you should ask in a more appropriate place.

Lord_Tryzalot
Lord_Tryzalot

Engineering? What
Obviously, I mean maths

Sir_Gallonhead
Sir_Gallonhead

Why would you mention real analysis and probability theory if you meant math?

Boy_vs_Girl
Boy_vs_Girl

What is a "mathematics course" if those are "engineering"?

King_Martha
King_Martha

mathematics
This is not well-defined.

farquit
farquit

Check any mathematics department.

haveahappyday
haveahappyday

one algebraic dimension you brainlet

Bidwell
Bidwell

math.ucla.edu/ugrad/courses
Math 131AH: Analysis (Honors)
Math 170A: Probability Theory
UCLA department of Mathematics. What are you trying to do

Inmate
Inmate

one algebraic dimension you brainlet
This does not contradict what I wrote.

idontknow
idontknow

Seems like mathematics departments also teach engineering in your country and are thus not mathematics departments. That's pretty sad.

hairygrape
hairygrape

Can you provide an example of a mathematics department in your country?

Methshot
Methshot

Try asking on /int/ if you want to discuss what countries people are from. It's a board created precisely for that purpose.

Methnerd
Methnerd

unsurprising non-answer

Snarelure
Snarelure

So you can't. I see.

Skullbone
Skullbone

you can check the archive to see the full extent of this mental illness.
Imagine the kind of person who reads an archive of Veeky Forums

Emberfire
Emberfire

Off-topic discussion is not encouraged. Try making a thread on /int/ and linking it here.

Raving_Cute
Raving_Cute

lift and play lacrosse

Nude_Bikergirl
Nude_Bikergirl

Anything with the prefix "algebraic" or suffix "algebra" and every subfield. This includes tautological cases like "algebraic commutative algebra" and so on.

Lunatick
Lunatick

What is this physishit leaf/chink's problem? This general has been abolutely dog shit these last few months. Even by Veeky Forums standards.

happy_sad
happy_sad

What is this physishit leaf/chink's problem?
You just listed them.
This general has been abolutely dog shit these last few months.
And that's probably going to continue if the poor creature doesn't take its medication.

farquit
farquit

Because in Mathematics you're pretty much limited to becoming a professor or a researcher where both are extremely hard to aquire. To have a sort of back up for your future it's good they have engineering stuff in case you are unable to find job in previously mentioned areas or if you just want a more well-paying job.

kizzmybutt
kizzmybutt

Having "back up" for people who make choices which aren't the best in their particular circumstances isn't an excuse to try and shit up math departments with unrelated stuff like "real analysis" and "probability theory". You do realize that actual engineering schools exist, right? Just go to those if you want a more well-paying job.

Techpill
Techpill

You seem pretty retarded. Mathematics major is a very risky one, you have no idea how hard it is to get admitted to researching or compete to become a professor with hundreds of other applicants in very limited amount of universities. Getting some engineering knowledge could give you a stable job to occupy you while you keep applying to research or something so you don't become homeless and regret your degree decision right after. I know quiet a few mathematicians who didn't get their positions as researchers when first applying but kept applying for 2-3 years postdoc and worked as programmers/engineers in meanwhile. Now they're researchers and left their engineer/programming jobs.

Evilember
Evilember

Mathematics major is a very risky one
Every non-retard who signs up for one knows that. How does this imply that your risky choices are somehow not your responsibility?
Getting some engineering knowledge
Do that elsewhere. You wouldn't study chemistry in a philosophy department. Similar reasoning applies to any two distinct fields.
I know quiet a few mathematicians who didn't get their positions as researchers
I'm not surprised that you know quite a few people who aren't smart since you seem to be like that yourself. Now fuck off to some other board if you wish to discuss off-topic trash such as your low intelligence and inability to be a researcher, i.e. a mathematician. I suggest trying out /adv/.

Firespawn
Firespawn

I just looked that up, screw my rapidly deteriorating funds I have a book to read, I usually read zany scifi (Brian Aldiss) but Greg Egan looks like some good stuff.

Know what you mean with the book 'tisms, I get so into a book I end up taking long to read good ones cause I keep getting so exited I just pace round the place for like hours. :^)

RavySnake
RavySnake

Must be hard not having any friends

WebTool
WebTool

Every non-retard who signs up for one knows that.
Where did I imply that they don't know? It is their responsibility, but that doesn't mean it's wrong to give them good credit.
Do that elsewhere. You wouldn't study chemistry in a philosophy department. Similar reasoning applies to any two distinct fields.
No. It's good to be competent in other areas too. And that's a very retarded counter-argument, chemistry won't give you nearly as a wide range of job fields to apply to as engineering, and chem is more irrelevant to philosophy than engineering is to math.
I'm not surprised that you know quite a few people who aren't smart since you seem to be like that yourself. Now fuck off to some other board if you wish to discuss off-topic trash such as your low intelligence and inability to be a researcher, i.e. a mathematician.
If you think it's about being "smart" then you are completely fucking retarded, you should kill yourself for that. It's the industry's fault, there's no high demand for mathematicians they have to compensate for the lack of positions in some way, and having a stable job until you can start your math career is a very good one. There are people way smarter than you'll ever be (honestly you seem pretty retarded so I assume it's a lot) but struggle to find a position because of the lack of demand, but eventually they'll get in and do some research. Having a job on the side so you don't become a hobo or have to do some other major isn't a bad backup plan.

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TurtleCat
TurtleCat

Listening to music, singing, reading

Boy_vs_Girl
Boy_vs_Girl

Yeah. It seems like the guy is having a pretty rough time. Maybe someday he will learn to accept himself and his engineering passion without trying to shit up other fields.

chemistry won't give you nearly as a wide range of job fields to apply to as engineering
That's beside the point. Chemistry and philosophy are merely placeholders for any two distinct fields (which engineering and mathematics are, regardless of what you and other engineering filth tries to claim). You seem to be incapable of tackling basic abstractions. No wonder you can't get a job as a researcher.
No.
So you think that math departments are an appropriate place for engineering merely because retards like you can't make proper life choices such as going to engineering school or learning engineering on the side (outside of math departments) if they can't handle the risks involved with majoring in mathematics? I don't think someone who really believes that everyone has to accommodate his poor decisions can be reasoned with.
chem is more irrelevant to philosophy than engineering is to math
In what way precisely is engineering (something which isn't used in math) "relevant" to math?
If you think it's about being "smart" then you are completely fucking retarded
Not having extremely low intelligence is a prerequisite which clearly neither you nor your friends possess.
Having a job on the side so you don't become a hobo or have to do some other major isn't a bad backup plan.
Try actually reading my posts before replying to them. I never claimed that having a job on the side is a bad backup plan for those who aren't in any way mathematically exceptional. But having a side job is clearly possible without trying to poison math departments with engineering. That should be obvious even to someone like you.

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MPmaster
MPmaster

fucking same, are you me?

anyway I'm glad I made you discover something!

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idontknow
idontknow

I can't even. It's so sad to see how stupid you are, yet ironically act smart.
Just go back to memeddit please and be the person everyone dislikes because of how autistic he is irl, you aren't worthy of anything

kizzmybutt
kizzmybutt

Yeah. It seems like the guy is having a pretty rough time. Maybe someday he will learn to accept himself and his engineering passion without trying to shit up other fields.
It was directed towards you

Emberfire
Emberfire

I might be stupid, but I'm clearly above your level of mental retardation since I can understand simple things such as the distinction between engineering and math.
you aren't worthy of anything
Says someone who has deep and unresolved personal issues regarding not being able to get the job he initially wanted.

DeathDog
DeathDog

Is stochastic processes more maths or stats related? I see it being offered in 4th year by my university without any stats prerequisite whatsoever.

girlDog
girlDog

I have a lot of that in my comp sci program and we only get one or two stats course before

likme
likme

I pissed in my beer and drank it. Couldn't tell the difference in taste. Give me a formula for this feel.

whereismyname
whereismyname

Ham radio and watches if these even count.

MPmaster
MPmaster

Why does linear algebra feel so boring

Emberburn
Emberburn

How the fuck is Real Analysis and Probability Theory not math? They're crucial stepping stones to learning Measure Theoretic Probability, which is what you're going to need to know if you want to do any deep work in probability or stochastic processes. NB: the shit without any applications

What do you consider to be maths? Algebra? Topology? There's more out there than just abstract shit that no one cares about

SniperWish
SniperWish

Depending on how it's done, it could be one of the more pure math courses you ever take. It's not stats related, it is its own field, but the theory gets used sometimes in stats.

It's pretty cool stuff. Take it if you're not scared of potentially writing proofs

WebTool
WebTool

Because linear algebra is boring

StonedTime
StonedTime

Don't reply to the spammer.

PurpleCharger
PurpleCharger

They're crucial stepping stones to learning Measure Theoretic Probability
It's not surprising that engineering topics would be a stepping stone to learning more engineering topics.
What do you consider to be maths? Algebra? Topology?
Those and their subfields would be almost the entirety of math. Correct.
There's more out there than just abstract shit that no one cares about
Yes, clearly there is non-abstract stuff outside of mathematics. Why did you feel the need to mention this?

GoogleCat
GoogleCat

see

Fuzzy_Logic
Fuzzy_Logic

Falling for the bait.
They the same stuff every thread. Ignore it and move on.

Dreamworx
Dreamworx

They the same stuff every thread.
Truth doesn't really change from thread to thread so I wouldn't expect anything else.

takes2long
takes2long

tfw your name will never be remembered for anything significant
you will never contribute anything to modern mathematics

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TreeEater
TreeEater

Oh boohoo, crybaby. Instead of crying you should be trying or simply as a quitter dying!

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Carnalpleasure
Carnalpleasure

cheers
at least we can enjoy it

Lord_Tryzalot
Lord_Tryzalot

the only things I have to my name are two lame ass articles that are so mediocre no one has referenced them and I am embarrassed of telling anyone I wrote them
failed postdoc after only 4 months
back to being a neet
my money will run out in 2 months tops
can't seem to find the will to get a job
have no idea what I even want to do at this point

Is suicide such a cowardly option ?

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Spamalot
Spamalot

In certain situations I wouldn't consider it to be cowardly but in yours I would.

cum2soon
cum2soon

watches
what, collect watches?

massdebater
massdebater

Why ? I am nothing more than an alcohol consumption machine at this point. I pissed my bed yesterday. From where I'm standing, it takes a lot of courage to just end it all. I keep fantasising about suicide but I don't even seem to be capable of jumping off a roof or tying a rope around my neck and jumping off a tree.

Methnerd
Methnerd

try actually killing yourself it's not that easy

Spazyfool
Spazyfool

I loved your proof of how the Riemann hypothesis is false, especially the choice of basing it on the clever method of proof by tautology.

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Crazy_Nice
Crazy_Nice

Yeah, I also masturbate to them.

hairygrape
hairygrape

Do you still like mathematics though?

Methnerd
Methnerd

If a book mentions a tensor product of commutative rings but doesn't mention over which ring the tensor is being taken of, can I assume it's the integers?

TalkBomber
TalkBomber

Yes.

TechHater
TechHater

Is it a tensor product of their additive groups? Do you know if there is a ring homomorphism from one ring to the other? In the first case you can use integers and in the second one use the domain of the homomorphism, as that turns the other ring into a module over itself.

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Nude_Bikergirl
Nude_Bikergirl

No mention at all, so I'm going to assume integers

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Snarelure
Snarelure

Oh, you are just using the rings' internal structures there! No idea what it is over, but I'm not sure if that's even relevant. Just go with integers.

Attached: )).jpg (40 KB, 500x349)

Emberfire
Emberfire

Anything with the prefix "algebraic" or suffix "algebra" and every subfield.
The burden of proof is on you to show that those are mathematics courses.

TurtleCat
TurtleCat

tensor product of commutative rings
This is a mathematics thread.

LuckyDusty
LuckyDusty

/lgbt/

VisualMaster
VisualMaster

/lgbt/
Why the homophobia?

Nojokur
Nojokur

Don't reply to the spammer.

Lunatick
Lunatick

Ca traine sur Veeky Forums a l'ENS ?

Crazy_Nice
Crazy_Nice

see

whereismyname
whereismyname

What's the name for how (1-x)^2 = (x-1)^2 ?

Illusionz
Illusionz

That (-1)^2=1?

Garbage Can Lid
Garbage Can Lid

No, just how to equations that are seemingly opposite have the same result
Or is this only the case for this one example and not a rule of sorts?

Sir_Gallonhead
Sir_Gallonhead

if (a/b)^n = 1 then a^n=b^n
since ([x-1]/[1-x])^2=(-[1-x]/[1-x])^2=(-1)^2=1, you have (x-1)^2=(1-x)^2

King_Martha
King_Martha

Maybe symmetry, which is something all metrics share, but in itself it's too week of a property to study symmetric Operations alone.
wuts a metric
wuts an operation
Google it nigger

girlDog
girlDog

A function f:R -> R is said to be even if f(-x)=f(x) for all x in R. This in particular implies that f(1-x)=f(-(1-x))=f(x-1) and is a property of the squaring function.

Evil_kitten
Evil_kitten

Oh yes, this.

CouchChiller
CouchChiller

Isn't the integrand periodic in the variable R?

Emberburn
Emberburn

Thanks

SniperGod
SniperGod

I HATE LINEAR ALGEBRA
AAAAAAAAAAAAAAAAAAAAAAAAAAA

LuckyDusty
LuckyDusty

why, user? It's fairly comfy, if a little dry

RumChicken
RumChicken

Brainlet detected.

farquit
farquit

Which of these are mathematics, and which are not?

Algebraic Geometry; Algebraic Topology; Analysis of PDEs; Category Theory; Classical Analysis and ODEs; Combinatorics; Commutative Algebra; Complex Variables; Differential Geometry; Dynamical Systems; Functional Analysis; General Mathematics; General Topology; Geometric Topology; Group Theory; History and Overview; Information Theory; K-Theory and Homology; Logic; Mathematical Physics; Metric Geometry; Number Theory; Numerical Analysis; Operator Algebras; Optimization and Control; Probability; Quantum Algebra; Representation Theory; Rings and Algebras; Spectral Theory; Statistics Theory; Symplectic Geometry

SniperGod
SniperGod

all of them since technically everything can be expressed in mathematics

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RavySnake
RavySnake

everything can be expressed in mathematics
Why is that true?

RumChicken
RumChicken

Why
Please refer to /x/ and /lit/ for discussing such topics.

DeathDog
DeathDog

Please refer to /x/ and /lit/ for discussing such topics.
The burden of proof is on you.

Fried_Sushi
Fried_Sushi

Words can be described using formal languages, a subset of mathematics.

Logic is a subset of mathematics.

All known disciplines of science can be described using words and logic (as far as I know).

Therefore all of those are mathematics.

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Garbage Can Lid
Garbage Can Lid

i hate this meme

Lord_Tryzalot
Lord_Tryzalot

Logic is a subset of mathematics.
Wrong. Only some subsets of logic are subsets of mathematics.

King_Martha
King_Martha

subcategories*

Soft_member
Soft_member

Provide a counterexample.

girlDog
girlDog

A set is by definition a certain kind of category.

w8t4u
w8t4u

Take the complement of the class "categorical logic".

massdebater
massdebater

logic
mathematics
Neither of these are sets, and so the "subsets" you speak of do not exist.

hairygrape
hairygrape

sometimes I like to imagine what it would be like to see a good-faith discussion here

Techpill
Techpill

How can one introduce an "imaginary" number [math]e \in \mathbb{R}^{\mathbf{im}}[/math] (where [math]\mathbb{R}^{\mathbf{im}}[/math] stands for some "imaginary" version of [math]\mathbb{R}[/math] ) such that [math]e>0[/math] and [math]e^n = 0[/math] for some [math]n[/math] in the standard non-imaginary naturals?

TreeEater
TreeEater

trying real hard to find a difference between these posts other than the ) having a space before it in the second one

Carnalpleasure
Carnalpleasure

Something like this?
en.wikipedia.org/wiki/Dual_number

RumChicken
RumChicken

But [math]\mathbb{R} \lbrack x \rbrack / (x^2)[/math] won't be a field. I guess I would have to introduce the notion of an "imaginary" field which is probably worth doing in and of itself.

AwesomeTucker
AwesomeTucker

It's a pretty elementary result that fields do not have nonzero nilpotent elements in classical mathematics. You might be interested in this, though ncatlab.org/nlab/show/Kock-Lawvere axiom

PurpleCharger
PurpleCharger

good-faith discussion
What do you mean?

StrangeWizard
StrangeWizard

to begin with, it might involve not saying things like
A set is by definition a certain kind of category.
which are clearly only intended to provoke a reaction
hopefully it should be clear that i'm referring to the form and subtext of that quote, not to its semantic content (not that there is much)

Ignoramus
Ignoramus

I don't mind assuming classically false axioms. The link seems pretty cool. I will look into it.

Illusionz
Illusionz

Why should people not say that?

Garbage Can Lid
Garbage Can Lid

ysk that this theory does not actually posit the existence of any nilpotent elements. it just lets you deduce things from statements about nilpotent elements that are classically just vacuously true. Here's a friendly-ish intro: math.cornell.edu/~oconnor/sia.pdf

askme
askme

It's fairly comfy
how so?

Poker_Star
Poker_Star

"Presenting something as an undeniable fact which your interlocutor presumably will not think is an undeniable fact" is a classic smugness tactic

Deadlyinx
Deadlyinx

not the person you're replying to, but most things in linear algebra are really well-behaved and tractable compared to lots of places

Techpill
Techpill

Sup you brainlets

Methshot
Methshot

hey /math/

how do you guys see yourselves being born smarter than others?

Do you think, like : "heh, it's me it had to happen, I wouldn't know how being a brainlet feels like, must suck" ?

you guys are fucking lucky.

I enjoy reading about science and trying to understand some mathematical topics with channles like 3blue1brown.

Anyway I love you guys. I wish I would be able to study maths but I simply am not.

Don't forget you're kinda lucky. I'll go back to lurking and pretend I'm a mathfag.

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PackManBrainlure
PackManBrainlure

tractable
Can you elaborate? As in tractable for brainlets?

Snarelure
Snarelure

sad_pepe_with_gun.png

Flameblow
Flameblow

tractable for brainlets is tractable for everyone..?..?

LuckyDusty
LuckyDusty

Sure, but it being tractable for brainlets doesn't necessarily make it comfy for non-brainlets.

StonedTime
StonedTime

completely unrelated
fucking brainlet

DeathDog
DeathDog

New thread. veekyforums.com/thread/9622175/science

Illusionz
Illusionz

As in, specific classes of problem in linear algebra tend to be very solvable (well, for finite-dimensional stuff)—most things are very finitary, or algorithmically approachable, or easy to find classifications for. By contrast, there tend not to be broad classifications or algorithmic approaches to things like solutions of differential equations or homotopy groups of spheres, even in finite dimensions.

Nude_Bikergirl
Nude_Bikergirl

Have you tried sitting down and working through actual material? Browsing wiki pages is generally incomprehensible if you aren't already familiar with the relevant topics, and pop-math content is generally not even *supposed* to give actual understanding.

RavySnake
RavySnake

you guys are fucking lucky.
must be why people here talk about killing themselves so often huh

Sharpcharm
Sharpcharm

functions

Evilember
Evilember

embarrassment

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