/mg/

[Anonymous No.12668218]

Math, generally
>analog machines edition
Talk maths!

Früher: >>12657631

[Anonymous No.12668236]

Fuck niggers addition

[Anonymous No.12668240]

Do all well ordered sets greater than (0,1)w have anuncountable section?

[Anonymous No.12668257]

>>12668236
Enjoy your ban.

[Multimorph No.12668265]

>>12668257
Do not reddit post on 4chan

[Anonymous No.12668280]

>>12668257
I'm behind 72 proxies kiddo.

[Anonymous No.12668283]

>>12668218
I have a certain functor. I would like to show that it preserves products. How exactly do I go about doing this?

[Anonymous No.12668286]

I've just started my math degree

[Anonymous No.12668292]

>>12668283
>>12668286
don't end up like the category tranny.

[Anonymous No.12668303]

>>12668265
>trying to achieve fame in an anonymous site through namefagging
>calling anyone reddit

[Anonymous No.12668356]

>>12668240
What is (0,1)w? Well-orderings are linearly ordered by embeddability. If the well-ordering is greater than the first uncountable ordinal then the first uncountable ordinal embeds into it, and so it has an uncountable section.

[Anonymous No.12668411]

>>12668292
she's hot though

[Anonymous No.12668452]

>>12668411
Fine become a category tranny more boy pussy for me.

[Anonymous No.12668535]

>>12668283
>preserves products
All products, or just small products, or just finite products?
If the distinction isn't salient to you, then you should probably ignore the categorial/functorial structure is a red herring, and simply translate the diagrams into equations and solve algebraically.

[Anonymous No.12668543]

>>12668283
>preserves products
All products, or just small products, or just finite products?
If the distinction isn't salient to you, then you should probably ignore the categorial/functorial structure, and simply translate the diagrams into equations and solve algebraically.

[Anonymous No.12668552]

You guys know any working memory exercises?

[Anonymous No.12668563]

Is there a closed form formula for
[eqn]\sum_{i=0}^a \sum_{j=0}^b j[/eqn]

I figure its been done before and maybe even shows up in some textbooks but I don't know what name you would call this or have a textbook with it and I'm too lazy to derive it myself.

[Anonymous No.12668565]

>>12668563
messed it up, it should be
[eqn]\sum_{i=1}^a \sum_{j=1}^i j[/eqn]

[Anonymous No.12668583]

>>12668563
>too lazy to derive it myself
But not too lazy to typeset the formula? I don't believe you.

[Anonymous No.12668594]

>>12668583
thats not hard to typeset. i've started deriving it myself anyways because i figured itd take to long to get a response from all you posers here and I realized that its less tedious than i first thought because the 1/2 factors out

[Anonymous No.12668607]

>>12668565
Isn't it just triangular numbers i.e.
[eqn] \frac{n(n+1)}{2} [/eqn]

[Anonymous No.12668615]

>>12668563
>>12668565
Take a look at Pascals triangle. The answer is hiding there.

[Anonymous No.12668990]

>>12666569
Lack of exercise.
>>12666666
test

[Anonymous No.12669037]

>>12668615
actually thanks for this comment, it made me immediately reconsider my problem as just combinations and realize that what I was trying to solve was exactly the same as the number of combinations, just expressed in a more convoluted way. was cool to rediscover this connection between repeated summation and combinations anyways.

[Anonymous No.12669180]

Are the naturals primitives in set theory? I know 3 constructions for the naturals but it seems like they're already baked in before that and the constructions just make them visible (a cope). You can't have notions of surjections without the concept of quantity.

[Anonymous No.12669425]

are there any good lectures based on baby rudin I can watch? trying to self study it but itd be nice to see a professor talk about it to make sure I am seeing the bigger picture correctly.

[Anonymous No.12669730]

>>12669180
Axiom of infinity postulates one of the constructions.

[Multimorph No.12670051]

>>12669669
What do you mean by sine comes from exponentiation? Also nice digits

>>12668356
Yes
(0,1)w is the countable cartesian product of 0s and 1s, infinite boolean strings which actually take the form of an infinite 2 pronged tree branch, hyperbolic space as opposed to euclidean

[Anonymous No.12670458]

there are circle theorems
are there any related sphere theorems?

[Anonymous No.12670467]

>>12669180
>You can't have notions of surjections without the concept of quantity.
Not sure how this "quantity" requires naturals.

Surjectivity is just some forall-there-exists statement about some sets (the functions, which are just graphs, which are just sets of pairs, which are just small nested sets)

[Multimorph No.12670525]

>>12670458
https://en.wikipedia.org/wiki/Soddy%27s_hexlet
https://en.wikipedia.org/wiki/Steiner_chain

[Anonymous No.12670535]

>>12670458

[Anonymous No.12670563]

>>12668286
Stay away from philosophy of mathematics. Just do your homework and you will be fine

[Anonymous No.12670589]

>>12668286

[Multimorph No.12670720]

>>12670535
Holy shit anon is a genius

[Anonymous No.12670765]

>>12670535
this is just an cirlce with the taxicab metric

[Anonymous No.12670874]

Are there non-semigroup gradings on simple Lie algebras?

[Anonymous No.12670903]

Question is How many 5 digit numbers contain either a three, or a five?
The prof later told us she accidentally worde it wrong to look like the exclusive or when she didnt mean it, so its 3 and/or 5, not either or.
I sent in what i had to someone else who took the class before me, he said he cant remember shit, so thats a dead end.
I think my logic is sound here, but i feel like something is wrong and i cant quite place it.
Need help, dont even care about the marks now, just want to know how to solve this proper.

[Anonymous No.12670939]

Consider the collection of all 5 digit numbers with 3s in one of the digits, and then collection of all 5 digit numbers with 5s in one of the digits.
Note that a 5 digit number could have 3s and 5s. Given that the question says EITHER a three or a five, I would assume it means exclusively a 3 or a 5.
You can count all three cases.
Also
>well, even if you get it wrong, rest assured that you'll never have to do math like this irl
what a faggot.

[Anonymous No.12670971]

>>12668286
my condolences

[Multimorph No.12670973]

Satz: Die Will ist Frei

Beweis:
>Die Will kommt aus Neuronen
>Neuronen sind atomisch
>Ganze atomen sind Quanten
>Es gibt kein Regierung fur Quanten atomen
>Es gibt kein Regierung fur Will
>Die Will ist Frei

Die Einzige Regierung ist von Existenz an sich, und das ist Quanten auch. Nur reines Sein gebraucht.

>>12670903
Hmm I got 67k but Idk if my method was right, what I did was 20 percent of 100k plus 20 percent of 80k plus 20 percent of 64k etc

[Multimorph No.12671101]

Do you like this drawing of a parabola and hyperbola and circle

[Anonymous No.12671193]

the progress in mathematics is slow because of the widespread racism and prejudice in the community
women and people of color bring to mathematics unique insights, unattainable for white heterosexual males
Consider, for example, category theory - this has been a niche field for a long time, and only recently sprouted into greatness, (mostly) thanks to the ideas of transsexual category theorists

[Anonymous No.12671212]

>>12671193
i'd chalk it up to the ideas being more and more complex and dependent on other things and as a result being less accessible to the new mathematician regardless of what you are. you need like 5-7 years post-undergrad just to get up to date let alone understand all that shit.
people aren't into math because it's hell on earth. anyone who studys it will tell you their suffering over abstract symbols on a page that are supposed to make sense. nobody wants to suffer except us for some reason.
cat theory is an exception because somehow it ties into programming, and programming is already filled with trannies.

[Anonymous No.12671233]

>>12671193
Kill yourself (by choking to death on my cock).

[Anonymous No.12671251]

>>12671233
yes daddy uwu

[Anonymous No.12671318]

>>12671193
Give up your feelings of inferiority, tranny

[Anonymous No.12671379]

>>12670458
same thing bro

[Anonymous No.12671746]

I'm going to take some caffeine and study some maths.

[Anonymous No.12671750]

>>12671318
used to feel inferior and weak as a male. Now I am an empowered, beatiful woman!

[Anonymous No.12671887]

>>12670051
>What do you mean by sine comes from exponentiation
[math]cos(x) = \frac{exp(ix)+exp(-ix)}{2}\\sin(x) = \frac{exp(ix)-exp(-ix)}{2i}[/math]

[Anonymous No.12671989]

>>12668218
given some line in red.
What are the characteristics of the set of functions that when recursively applied to those set of points in red covers at least the area in green?
What field of math studies this?

[Anonymous No.12672132]

>>12671379
>projecting

[Anonymous No.12672240]

>>12668218
I don't understand this picture. Is it a joke? How is a cat on a blanket upsetting quantums?

[Anonymous No.12672451]

>>12672240
Literally billions of people have heard about Schrödinger cat

[Anonymous No.12672483]

>>12672451
and billions have no actual idea about what it entails, and why Schrodinger brought it up as a thought experiment in the first place
popsci was a mistake

[Anonymous No.12672507]

>>12668218
Hey anons, here's a more substantional math question.
Lets say I want to plot a curve with 3 data points.
The curve should have the formula of:
y=a*exp(b/x)+c
All 3 data points have x and y deviations.
How do I receive the deviation of each curve variable (a,b,c) using those 3 datapoints?

Or lets say I got the curve and want to insert a different x value and receive y. What will the deviation be?

[Anonymous No.12672510]

>>12672483
People explaining that Schrodingers cat was meant to be ridiculous is like the new version of people explaining what Schrodingers cat is

[Anonymous No.12672516]

Is it okay if i am infinitist-tard but wildberger-tards make me feel suspicion about math?

[Anonymous No.12672702]

Do you ever wonder if there's a higher kind of mathematics that explains mathematics themselves and shows its existence but that is also faraway from our understanding?

[Anonymous No.12672729]

>>12672702
It is called metamathematics, plenty of literature on the subject

[Anonymous No.12673099]

Anyone get the joke?

[Anonymous No.12673122]

>>12673099
heh, classic.

[Anonymous No.12673244]

>>12668218

Jesus Christ, those online """exams""", please do not ban me

[Anonymous No.12673252]

>>12673099

in infinite dimensional cube the diagonal is perpendicular to the edge

[Anonymous No.12673263]

>>12672729

it is probably called category theory as it explains everything

[Anonymous No.12673414]

How do you collaborate with others during lockdown? University won't provide me with a tablet, should I just buy one myself? We're stuck in different regions and can't meet, what the fuck

[Anonymous No.12673502]

>>12673414
>How do you collaborate with others
i don't...

[Anonymous No.12673528]

>>12673502
bro... you need to talk to people, get out there and write papers with the big boys, you're never going to get tenured otherwise...

[Anonymous No.12673864]

>>12673414
Just buy a portable board.

[Anonymous No.12673877]

>>12673414
I talk to my sugardaddy once a week. It's enough to drain my social energy.

[Anonymous No.12673884]

>>12668286
3 years into math degree here. Don't do it.

[Anonymous No.12673905]

>>12668565
[math]\frac{1}{2}(\frac{a(a+1)(2a+1)}{6} + \frac{a(a+1)}{2})[/math]

[Anonymous No.12673924]

If i want to specialize myself in cryptography do i NEED to take courses in quantum computing (and/or some quantum physics)?
Also how well is the cryptography field doing overall and is it as much number theory as i think it is?
Currently my plan is to take some courses in algebraic geometry, elliptic curve and algebraic number theory.

[Anonymous No.12673932]

>>12673924
you don't need to take quantum computing
and even if you want to learn about quantum computing, most people do that without knowing any physics

[Anonymous No.12673943]

>>12673932
That's reassuring
I had this idea that the field cares mostly about cryptography in the context of quantum computers.

[Anonymous No.12674125]

>>12670563
Why?

[Anonymous No.12674131]

>>12673884
Why?

[Anonymous No.12674355]

>>12672510
>>12672483
Schrodinger was fucking a whore free of charge when he thought about the equation

[Anonymous No.12674480]

is it just me or lately we're having anons impersonating anime tranny ?
or maybe they cloned themselves and now /mg/ is full of anime tranny clones, like rei clones going all around trying to figure their mathematical identity

[Anonymous No.12674751]

>>12674480
who wouldn't like to be an anime tranny?

[Anonymous No.12674767]

>>12674751
This. Estrogen makes you do math better.

[Anonymous No.12674847]

is it possible to get an inverse for the middle regions of y=x^3-x? the one inverse I get only works for |x|>some c. for the inverse of x^2 you can just change the sign to get the inverse for the left or right branch, but changing the signs in the inverse for y=x^3-x doesn't seem to do anything.

[Anonymous No.12674857]

>>12674847
yes, but the formula will not be beautiful
find another way

[Anonymous No.12674887]

>>12674857
well what if I want to know the formula? I don't understand why the inverse seems to have values for regions that fail the vertical line test and I want to know how to get the inverse for every invertible region.

[Anonymous No.12675255]

[math]\int_{a}^{b} f(x)dx[/math]
test

[Anonymous No.12675458]

>>12674887
if you want a formula, you'll need to use cubic equations formulas. Cardano & co
it's going to look way uglier than the equation itself, usually there's not much reason to go there and you find better ways for whatever you're trying to accomplish

[Anonymous No.12675489]

>>12675458
i did use the equation for roots of a cubic, and no combination of signs produced a function defined in the region around 0.

[Anonymous No.12675593]

[math]\int_{\int_{\int}^{\int}}^{\int_{\int}^{\int}}[/math]
test, also does this to any level of nesting have a name?

[Anonymous No.12675596]

>>12675593
death by a thousand integrals

[Anonymous No.12675610]

[math]\int^{\int^{\int^{\int^{1}_{0}x}_{\int^{1}_{0}x}x}_{\int^{\int^{1}_{0}x}_{\int^{1}_{0}x}x}x}_{\int^{\int^{\int^{1}_{0}x}_{\int^{1}_{0}x}x}_{\int^{\int^{1}_{0}x}_{\int^{1}_{0}x}x}x}x[/math]

[Anonymous No.12675616]

>>12675610
Idiot

[Anonymous No.12675629]

>>12675610
fix your notation

[Anonymous No.12675642]

>>12675610

[Anonymous No.12676073]

>>12675610
pretty!

[Anonymous No.12676081]

>>12674480
I didn't expect to miss him but I do. He linked good shit.

[Anonymous No.12676121]

>>12668218
Distributed division

1234/2


0112
0505

0617

.....

[Anonymous No.12676398]

>>12675489
then you must have made an error in your calcs
from someone who's whole fucking research is centered on cubic forms, let me give you the following tip: ALWAYS tripple check your calculations, like
>cubics: tripple check
>quartics: check four times
>quintics: nope

[Anonymous No.12676445]

I'm going over the proof that the infinite union of countable sets is countable (under axiom of choice); however, I am missing the nuance of using the diagonal mapping to prove this. What does the diagonal mapping achieve?

[Anonymous No.12676467]

>>12676445
nevermind it clicked, it allows one to march through each element in the set

[Anonymous No.12676499]

>>12676445
depends one "which" infinite unions, countable infinite unions yes, uncountable unions no

[Anonymous No.12676578]

>>12676081
He's still here. I just didn't have anything to post.

[Anonymous No.12676641]

>>12676578
should i transition

[Anonymous No.12676668]

>>12676641
No. You would never be a real woman, only a freak who is no longer a man. Do not let a mental illness dictate what you do. It is OK to be a feminine man. You don't need to do hormones. Instead, you should focus on things you enjoy and on things that allow you to feel even a little bit of self worth through achieving something. With that said, grab your textbook or open up the paper you were planning to read and start working. It's better to read a book saying "Lie" on the cover than live in a lie.

[Anonymous No.12676680]

>>12676668
why do they call you anime tranny then? are you not really a tranny
thank you for the advice
do you have dysphoria

[Anonymous No.12676729]

>>12676680
>why do they call you anime tranny then? are you not really a tranny
I am, yes. I am a mentally ill guy pretending to be a girl by dressing up as one and taking hormones. It will never make it real, I will always be fake. Even if I got surgery, I would still be fake. Unless it is really the only choice other than to an hero, I would never recommend transitioning to anyone. It will not change your skeleton, you can't be a bio mom, you will still hate your body and feel pain because of the damage done on it by puberty. But this is not science or maths. Please do remember that in the complexities of life, some things are purely imaginary and can't change those that are real.

[Anonymous No.12676738]

>>12676729
what you basically said is why I'm repressing
always wanted to be a mom but I can't
would rather die than be a cheap imitation of a woman with a manly skeleton
I hope your interests and mathematics help you keep your mind off dysphoria anon

[Anonymous No.12676747]

>>12676729
Damn dude I honestly thought you were deluded but you seem to know the reality of your situation. I guess the hundreds of posts calling you an anime tranny did have some effect.

[Anonymous No.12676803]

>>12676738
>what you basically said is why I'm repressing
I'm sorry to hear that, anon. Nobody should live with such feelings, Not you, not your noisy neighbour, not even the bullies at school who beat you up, threw stuff at you and called you names for "being a faggot". Nobody.
>I hope your interests and mathematics help you keep your mind off dysphoria anon
Thank you. The same to you. May you find your peace somehow somewhere some day. How far are you in your studies?

>>12676747
I may be mentally ill and not too smart either, but I'm not dumb enough to exclude physiological realities from consideration. I am a stupid attention whore and I'm sorry for consistently ruining these threads.

[Anonymous No.12676810]

>>12676803
>I am a stupid attention whore and I'm sorry for consistently ruining these threads.
You're probably going through a bipolar episode or something and you'll go right back to the usual but at least you had a moment of clarity, I respect that.

[Anonymous No.12676865]

>>12671989
please define these functions

[Anonymous No.12676927]

>>12676729
>>12676803
please never cut off your dick i want to suck it

[Anonymous No.12677499]

hey guys
i cant seem to understand what limsup and liminf mean.
i know a suprimum is the absolute maximum value a series' element can achieve, and it is called maximum if its part of the series. same about inf, as minimum. but what is limit of these? what does it mean?

[Anonymous No.12677652]

My best friend got in Stanford, MIT, Berkeley, and UChicago for graduate school. I'm happy for him, but he can also go fuck himself.

[Anonymous No.12677916]

>>12668563
Look up hilbert polynomial, these are the number of distinct homogenous polynomials of degree a in 3 variables or something, as it is the number of different ordered sums of 3 integers to get a.
It's fun to derive it on your own though
You ever heard about the sum of the first n integers is n(n+1)/2? Well you can prove it with a nice trick of adjoining two appropriate triangles and noting you get a rectangle of sides n and n+1. Like the other anon suggested this time it's tetrahedra, and it's not two, but six.
Sorry if something is imprecise, that's the idea.

[Anonymous No.12677932]

is there anyone knowledgeable in borel equivalence relation stuff?

[Anonymous No.12677986]

I haven't been doing jack during lockdown, I'm sick of being a NEET, and I decided I'd spend the rest of my time studying Ramsey theory and trying to find R(5, 5) to become famous. Any textbook recommendations?

[Anonymous No.12678023]

This is really confusing me. Where is x^2 coming from? What does "missing in the order" mean?
It's supposed to be describing a leading coefficient

[Anonymous No.12678056]

>>12678023
It's just saying that f(x) = 2x^4 - 7x^3 + 0x^2 + 3x - 1, but we don't write the 0x^2 since it's 0.
You need to be 18 to post here.

[Anonymous No.12678070]

any good sources for graspig linear algebra? the coursematerial is pretty subpar

[Anonymous No.12678072]

>>12678056
I'm 20, just retarded and regretting skipping classes when I was in school.
Thank you, that's what I thought it was saying.

[Anonymous No.12678075]

>>12678023
as said, theyre in order, but since its 0*x^2, it doesnt show up, because its zero
put it this way:

[math]f(x)=2x^4-7x^3+0x^2+3x+0x^0[/math]
[math]f(x)=2x^4-7x^3+0+3x+0[/math]
[math]f(x)=2x^4-7x^3+3x[/math]

and yes, x^0 is also a thing

[Anonymous No.12678077]

>>12678075
not sure how i fucked the lines with the commands
tex is absolute dogshit HIROYUKI

[Anonymous No.12678080]

>>12678023
0x^2 = 0.
1+0 = 1
basically, whetherb you write 0x^2 or not is irrelevant, but won't change the order.

[Anonymous No.12678087]

>>12678075
Thanks, that really helped once I figured out the formatting. I feel stupid learning the basics and getting confused. I think the coursework was just written in a way I didn't understand easily.
>>12678080
So if one of the values in an equation is equal to zero, then I just omit it correct? Thank you for the help

[Anonymous No.12678223]

>>12678070
>>12677986
https://4chan-science.fandom.com/wiki/Mathematics

[Anonymous No.12678231]

>>12678070
https://4chan-science.fandom.com/wiki/Mathematics#Linear_Algebra

[Anonymous No.12678242]

>>12668218
Hello dear math giga chads.
Can you please lend a hand with this problem/question?

The question is as follows:
>You'd be hard pressed to find a function [math]f:\mathbb{R} \rightarrow \mathbb{R}[/math] such that [math]f[/math] is everywhere continuos but nowhere differentiable, however, the "majority" of continuous functions are like this. Do you believe this also happens with complex valued functions? Justify your thoughts with either a counterexample or a theorem

Now, we know that the majority of real valued functions are everywhere continuos and nowhere differentiable because the set of all such functions is of
the first category whilst the set of all functions differentiable in at least a single point is of the first category.

What the fuck can I say for complex functions? Intuitively the same holds as in R but I don't know how the hell I would go about proving this

[Anonymous No.12678246]

>>12678242
Fuck, I meant to say that the set of nowhere differentiable continuous functions is of the second category, not of the first

[Anonymous No.12678257]

>>12678070
terrence tao notes

[Anonymous No.12678258]

>>12668565
a(a+1)(a+2)/6

[Anonymous No.12678259]

>>12678242
use an everywhere continuos but nowhere differentiable real function to make a complex function with the same property

[Anonymous No.12678283]

>>12678259
A complex function with the same property is actually much easier to find. For example [math]f(z) = Re(z)[/math] works but I don't anything with that, I need to make an statement on the set of functions not on a single function

[Anonymous No.12678294]

>>12678283
>I need to make an statement on the set of functions not on a single function
>Justify your thoughts with either a counterexample or a theorem

[Anonymous No.12678310]

>>12678242
do you know the proof for real case?

[Anonymous No.12678317]

>>12678294
The thing is I don't get what would constitute a counterexample, finding a single function doesn't tell me anything about the set itself

[Anonymous No.12678322]

>>12678310
It's outlined in Abbott's understanding analysis section 8.2

[Anonymous No.12678341]

>>12678322
i mean, i think a similar proof works for the complex case

[Anonymous No.12678885]

>>12678077
You should spam space everywhere you can to avoid line changes. It works somewhat like this: you write your tex thing and it is texed only after you send it, so if there would be some forced line break coming from the board itself somewhere because you wrote everything together, then that can totally ruin your pretexed tex. That's why you should hit the space bar like a pimp hits his girls.

[Anonymous No.12678892]

>>12678885
>texed only after you send it
I mean the post is first like any other post, and only then it gets the tex stuff. You can see this when you open a long /mg/ thread with lots of texing. Sorry I haven't slept.

[Anonymous No.12679084]

>>12678885
>>12678892
dumb tranny you need to sleep

[Anonymous No.12679253]

>>12679084
Not yet, darling. There is work to be done.

[Anonymous No.12679261]

>>12668565
It's the number of triples of numbers (i,j,k) such that i+j+k=a

[Anonymous No.12679296]

>>12669730
>>12669180
I absolutely love the ridiculous definition of naturals in set theory as "the unique standard natural numbers" pretending like this makes any sense at all. Hmm, to figure out whether 3 is or isn't a natural number, we just need to go through ALL the sets (cardinality issues aside), for each subset check whether or not it's inductive (that is, check if it contains the empty set and then go through ALL the elements of that set x, and check if {x} is in the set), and then check whether 3 is in that set. If it's true for ALL such subsets, then you can say that 3 is in the set. Be careful not to miss any sets, because you might think you have a number, but it could turn out that it's a nonstandard number, that there is an inductive set which doesn't have that number in it. To figure out how to go through ALL the sets, well here buddy you're on your own, since ZFC only tells you that some things are sets but does not tell you what isn't a set.

[Anonymous No.12679354]

>>12679296
i don't know bro i feel like i'm able to iterate over "subsets of 3" pretty well cause there are like 2 or 3 of them

[Anonymous No.12679474]

I'm trying to prove that the scalar multiplication map [math] \mu: K\times X \to X[/math] is a linear map in order to prove that it is continuous. However, I'm running into trouble because it clearly is not linear since [math] \mu(\alpha(c_1, x_1) + \beta(c_2, x_2)\neq \alpha c_1x_1 + \beta c_2x_2 = \alpha\mu(c_1, x_1) + \beta\mu(c_2,x_2)[/math]. Am I retarded or is this actually true that it is not a linear map and I need to approach the problem another way?

[Anonymous No.12679502]

>>12679474
I have no idea why you think it works like that. You see, for any pair [math](a, x) \in K\times X[/math], you have [math]\mu(a, x) = ax[/math], so the thing you probably are after is [math]\mu(ab, x) = (ab)x = a(bx) =a\mu(b, x)[/math] and [math]\mu(a, x+y) = a(x+y) =ax + ay =\mu(a, x) + \mu(a, y)[/math]. What is your X?

[Anonymous No.12679514]

I know I'm retarded, and you have every right to just tell me to fuck off, but would anyone be willing to describe to me how pic related is different from any other derivative problem where you're just finding f prime of x?

[Anonymous No.12679577]

>>12677499
liminf(x_n)_{n>0} := lim_{k->infinty} inf(x_n)_{n>k} = sup_k inf(x_n)_{k>n}

[Anonymous No.12679583]

>>12679577
swap k and n in last subscript

[Anonymous No.12679611]

>>12679502
And [math]\mu(a+b, x) = (a+b)x = ax +bx = \mu(a, x) + \mu(b, x)[/math]. Brain malfunction.

>>12679514
Maybe the idea is to show that there are cases in which the derivative does not depend on x. No idea.

[Anonymous No.12679636]

>>12679514
find f'
plug in -3 for x
thats all they want you to do. don't feel bad about it being literal high school calc, the vast majority of this general is not at a high level of math study and most are pseuds.

[Anonymous No.12679639]

>>12679514
if the domain has no -3 i guess

[Anonymous No.12679644]

>>12679636
t. Seething midwit

[Anonymous No.12679658]

>>12679636
So the answer would just be 3?

[Anonymous No.12679664]

>>12679514
It's 3

[Anonymous No.12679665]

>>12679658
what's the derivative of x
what's the derivative of x+C
it's the same thing
and it's not 3

[Anonymous No.12679677]

>>12676803
>I'm sorry for consistently ruining these threads.
Oh no, you aren't ruining anything, these threads are just bad.

[Anonymous No.12679689]

>>12679658
1

[Anonymous No.12679955]

This whole universe was created for the sole purpose of God watching you struggle with math problems and laughing at you.

[Anonymous No.12679992]

>>12668218
If the speed of sound was infinite, what would you hear?

[Anonymous No.12680025]

[Anonymous No.12680376]

My life is terrible, hopefully my love of mathematics will help me improve it.

[Anonymous No.12680385]

Is there anything that makes differential equations a less shittier time to learn? I got the math textbook pack from /t/, but the books I've looked through aren't doing it so far

[Anonymous No.12680391]

>>12680376
It won't. I'm sorry anon, but math will only make your life worse

[Anonymous No.12680393]

>>12680391
Hopefully it will make me money, that's what I meant.

[Anonymous No.12680395]

>>12680385
How can you not like DEs?

[Anonymous No.12680401]

>>12680393
Hahahahha oh no oh no oh no

[Anonymous No.12680420]

>>12680401
Mathematicians can get well paying jobs in many fields, I'm particularly interested in finance and data science.

[Anonymous No.12680444]

>>12669425
https://www.youtube.com/watch?v=8hJYD_NcOGQ&list=PLun8-Z_lTkC5HAjzXCLEx0gQkJZD4uCtJ

[Anonymous No.12680456]

>>12680420
>Mathematicians can get well paying jobs in many fields

[Anonymous No.12680460]

>>12680456
Are you in high school? I'm in uni and that's not a secret to anyone?

[Anonymous No.12680483]

>>12680395
....fair point. Maybe it might just be that my calculus is rusty, which is why I could be struggling

[Anonymous No.12680491]

Why isn't there an f''(c)?

[Anonymous No.12680492]

>>12680491
?
who says there isnt

[Anonymous No.12680504]

>>12680492
The TA

[Anonymous No.12681508]

Is Lang's Algebra a good first book for Abstract Algebra? I never studied any Algebra up until now, and was wondering how it compares to D&F. I've self studied real analysis, manifolds, and mathematical logic btw.

[Anonymous No.12681550]

>>12681508
Oh yeah, absolutely. Lang's Algebra is a top tier introductory book used all over the world for freshman algebra courses. Lang himself says in the preface that the work is meant for a gentle first contact with algebra and higher mathematics.

[Anonymous No.12681602]

>>12681550
I can't if you're being sarcastic, but thank you anyway! I just want to know if I'm doing it right since I'm not gonna study textbooks for brainlets like Fraleigh or Gallian.

[Anonymous No.12681659]

>>12681602
Go download the book and read the preface.
>I just want to know if I'm doing it right since I'm not gonna study textbooks for brainlets like Fraleigh or Gallian.
Grillet's Abstract Algebra is actually self-contained and a brick textbook intended for grad students, go read that one.

[Anonymous No.12681888]

>>12677499
Conside the sequence (-1)^n. This does not have a limit. It has subsequences which do have limits though, like a subsequence of only 1's and a subsequence of only -1's. These are the limsup and liminf respectively.

[Anonymous No.12682096]

Which Finnish university should I do my PhD in if I want to become an algebraist?

[Anonymous No.12682144]

>>12682096
finns are the cancer of the internet

[Anonymous No.12682228]

>>12668286
Get out while you can. Learn a trade

[Anonymous No.12682244]

>>12682096
you should piss off, Finland is analytic territory

[Anonymous No.12682484]

>>12682096
I thought he was abroad. No need to correct my language. See >>12676578

[Anonymous No.12682574]

>>12682484
Or maybe I'm just a neet trying to cheer people up and push them to try make their dreams come true. Nothing in my life is real. I don't even exist.

[Anonymous No.12682623]

>>12682574
Dumb tranny you are just trying to make everyone hate you and tell you to fuck off. Your larp would have been too good for a NEET. Take your meds and girl pills. Get some sleep. You're just letting dysphoria control your mind now. I used to know a tranny who was like you now every time dysphoria hit. Rest and return when you feel like a "she" again.

[Anonymous No.12682645]

Has anyone actually seen the evidence for circles? Where’s the so-called proof? Where’s the proof that a triangle has sides and a rectangle has corners? Where’s the proof that a triangle has radii equal to the hypotenuse of a rectangle? Where’s the proof that a rectangle has corners? Where’s the proof that a triangle has sides? Where’s the proof that a triangle has radii equal to the hypotenuse of a circle? Where is the proof that a circle has corners? All of these things are being proven by Euclid. And people aren’t even talking about them. Because it doesn’t fit the narrative.

[Anonymous No.12682663]

>>12682623
Maybe.

[Anonymous No.12682691]

>>12673099
Lmao

[Anonymous No.12682718]

>>12682623
shut up dude, you're fixating on picking on the open wounds of someone who goes out of her way to say things she doesn't believe 100% just to be more amicable and pleasing to others

[Anonymous No.12682750]

>>12682645
>Wheres the proof that a triangle has sides?
The definition of triangle is a shape with three sides and three corners. It's like asking "Where is the proof that bipedal animals have two legs?".

[Anonymous No.12682769]

>>12682718
I know she's not a NEET. She's just trying to do a character assassination on herself so people would call her shit.

[Anonymous No.12682780]

>>12682574
You need real friends.
Or at the absolute least friends with names.

[Anonymous No.12682817]

>>12682780
Agreed. They should add me on discord and talk to me everyday instead of making so many blog posts here

[Anonymous No.12682819]

>>12682817
Agreed.
Post your discord so he can add you.

[Anonymous No.12682889]

>>12682769
hmm I guess I see what you're saying, it's a self-defeating speech coming from excessive frustration and pessimism. Dysphoria isn't the root, it's just another bridge.
But enough talking about our dear mascot

[Anonymous No.12683004]

Are the reals the only useful 1-dimensional extension of the rationals?

[Anonymous No.12683413]

Another thread says that all one variable polynomials have either zero or uncountably many solutions over the quaternions. How far up the Cayley-Dickinson construction do you have to go for polynomials to be completely meaningless?

[Anonymous No.12683456]

>>12683004
the reals aren't useful. all useful numbers can be expressed as rationals.

[Anonymous No.12683485]

>>12683413
You can define and study polynomials over any algebra. Is that meaningful enough for you?

[Anonymous No.12683507]

>>12683456
>the reals aren't useful

[Anonymous No.12683518]

>>12683507
If you think that claim was false, then answer this one. Who uses numbers outside of school? NO ONE!

[Anonymous No.12683527]

>>12683518
>NO ONE
>ONE
One is a number

[Anonymous No.12683537]

>>12683527
You got me.

[Anonymous No.12683562]

Is Vladimir Arnold's ODE book a good introduction to DE?

[Anonymous No.12683666]

>>12677499
Think of it like this:
Many sequences are bounded above. Of these, there are some that only exceed certain values a finite number of times: e.g. x_n = 1/n is bounded above by 1 but only x_1, x_2, and x_3 are greater than 1/4. Therefore, 1/4 is a supremum of the series for n > 3. The lim sup is the limit of the suprema as we cut off more and more of the early terms. In the example I give it's obvious that as we exclude more and more of the early terms, our supremum approaches zero; therefore, limsup x_n = 0. From this definition, it's clear to see that the limsup is simply the greatest accumulation point of a series, and likewise with liminf. Since we know a series converges if it has only one accumulation point (under some conditions of course), a series converges iff limsup = liminf.
See picrel for a more complex example; since limsup =/ liminf it does not converge.

[Anonymous No.12683873]

On the binomial distribution:
Why to get the probability of K successes you have to multiply by the probability of getting K and of not getting K?

[Anonymous No.12683910]

>>12681508
It's fine, but you'd be better off starting with dummit and foote.

[Anonymous No.12683921]

>>12683562
yes

[Anonymous No.12683950]

>>12683873
That's the probability of getting *exactly* k successes. The idea is you need to get k successes (each w/ probability p) and the rest (n-k) failures (each w/ probability of 1-p). The successes can occur in nCk ways, but you can also look at it as the failures occurring kC(n-k) ways, since kC(n-k) = kCn. Easy visual proof in pascal's triangle.

[Anonymous No.12683994]

If [math] F: Top \to HoTop[/math] is the canonical functor, I want to prove that given topological spaces X,Y, [math] F(X)\times F(Y)\cong F(X\times Y)[/math]. I'm having trouble proving this. I'm not even particularly sure what I'm supposed to be proving. I've tried constructing an explicit isomorphism but can't seem to get it to work. Pls help.

[Anonymous No.12684001]

>>12683950
I thought this was the case but I can't see it in pascal's triangle.
I can't see it in any way for that matter.

[Anonymous No.12684029]

>>12683950
The multiplication part specifically: I can see why multiplying by p^k gives you the probability of at most k successes but I can't see how (1-p)^(n-k) solves the problem.
Oh no wait, I saw it while writing.

[Anonymous No.12684032]

>>12683994
Assuming your functor is the one that takes a space to itself and a map to its homotopy class, then you want to show that whenever you have some spaces [math]X, Y[/math] and you take the projections [math]p_Z\colon X\times Y\to Z[/math] where [math]Z = X, Y[/math], the homotopy classes (i.e. the morphisms in the homotopy category) represented by those projections satisfy the universal property of a product: Given any [math][f]\colon W\to X, [g]\colon W\to Y[/math], there is a [math][h]\colon W\to X\times Y[/math] satisfying [math][p_X]\circ [h] = [f], [p_Y]\circ [h] = [g][/math], and that this class is unique. Should those be the case, then you have what you want. The reason why you are so unsure is that there isn't actually anything to prove.

[Anonymous No.12684034]

>>12683950
Thanks anon, have one more (You).

[Anonymous No.12684094]

>>12668218

[Anonymous No.12684095]

>>12684001
This is the proof I learned a couple years (sorry for long, I just want it to be really clear; Reddit spacing for clarity):
Imagine you're a teacher managing a kindergarten with n kids. You want to send the kids on a school bus, but it only has k seats. You could do this by picking your k favorite kids, leaving n-k behind, or you could just pick your n-k least favorites and get the rest to go on the bus. But it's clear that either method you use, you'll have assign the kids into two categories: the ones you like more and the ones you like less--in other words, picking your favorite k out of n has the same effect as picking your least favorite n-k out of k, and vice versa. Therefore, for each assignment you get from the first method, you could have gotten it from the second.

An example: say the bus has n-1 seats.
> I rank the kids in order of my preference and I pick out the top n-1 and let them go on the bus.
> I rank the kids in order of my preference and I pick out the kid on the bottom and make them stay home.
It should be clear that both these methods are basically doing the same thing.

The reason it's present in pascal's triangle is because nCk = (n-1)Ck + (n-1)C(k-1). You can see that as follows:
>If I need to pick k out of n kids to go on the bus, I either let Billy get on or I don't. If Billy's not going, I need to choose k from the remaining n-1 (now excluding Billy). If Billy's going, I need to choose k-1 (since Billy's already taking up a seat) from the remaining n-1.

[Anonymous No.12684106]

>>12684095
*send the kids on a [field trip, but the school bus] only has k seats.

[Anonymous No.12684260]

I was thinking, does every compact set in [math]\mathbb{R}^{2}[/math] has a copy of the unit circle or is it homeomorphic to it?
Then I realized, no. A point is compact and doesn't satisfy any of those. What about a set with more than one compact? Still no, the product of the Cantor set with itself is still compact and again, it doesn't satisfy those.

[Anonymous No.12684271]

>>12684260
What about a compact and connected set with more than one point? If yes, prove it. If no, give a counter-example.

[Anonymous No.12684349]

>>12684271
I don't think so, I think Sierpinski Carpet may work as a counterexample. I don't think it's "fat" enough" to have a copy of the unit circle.

[Anonymous No.12684373]

>>12684349
Or even simpler, [math][0, 1]\times \{0\}[/math]. Compact, connected, iinfinitely many points and no circles. I'm not sure about Sierpinski. Could you not just use the boundary of the first removed square? That would be homeomorphic to [math]S^1[/math].

[Anonymous No.12684452]

>>12684373
yeah, you are right
It usually takes me time to formulate stuff.

[Anonymous No.12684488]

>>12673099
Is the joke basically the same as the pi = 4 meme but true?

[Anonymous No.12684550]

>>12684452
No worries, it's not a speed contest.

[Anonymous No.12684583]

>>12672702
model theory and metamathematics, as anon here >>12672729 suggests. It is not category theory tho, as anon here claims >>12673263

>>12673502
This

>>12679296
The adequate way would be to define the natural numbers as any Peano system, where the latter is an infinite set that satisfies the Peano axioms. It is easy to prove that any two Peano systems are "equivalent". Then the naturals are just a way to build a Peano system, which actually does make sense if you look up what the ordinals are.

This is the thing, we really don't care we build the numbers, no one uses the set form of the numbers, it is just like making a model, no one cares which material did you use, just that it serves its purpose. Moreover no one "checks" if a set is a number since quickly we replace all set notions for arithmetic ones.

Finally if you have more doubts about the whole "iterative set" thing, I recommend you to read about the foundation and constructibility axioms

[Anonymous No.12684619]

>>12680395
>tfw filtered by phase portraits

[Anonymous No.12684634]

>>12680385
use tools online to visualize all of the slope fields and solutions its fun
try to think about other uses for the differential equations like figuring out for what initial conditions your solution has certain behaviors and things like that

[Anonymous No.12684637]

>>12684488
in your head, keep subdividing the circle. You end up with a rhombus. So.. no

[Multimorph No.12684728]

Are there any series with discontinuities at the limit? Such as, for all finite terms the answer is 0 but at infinity its 1, something akin to that.

[Anonymous No.12684754]

>>12684728
Not really. For a sequence to have a limit L, by definition there must be infinitely many terms in the sequence that are arbitrarily close to L. But what I think you're getting at is if there are things that behave differently in the limit than they do in the finite case, of which there are many examples:
>the set of roots of finite degree polynomials with integer coefficients is countable--for polynomials of infinite degree, it is uncountable
>some 1-d fractal-esque objects have, in some senses area (see space filling curve)
>some curves (defined as the limit of some process) are everywhere continuous but nowhere differentiable
>some uncountable sets have zero Lebesgue measure
etc. You might enjoy Analysis.

[Anonymous No.12684856]

>>12684728
In the sense, is there a sequence \{a_n\} so that a_n = 0 for n finite but \lim a_n = 1, then no (exactly by the definition of limit of a sequence we have \lim a_n = 0).

But of course we can have a map F and a sequence \{a_n\} so that F(a_n) = 0 for n finite and F(\lim a_n) = 1. e.g. the geometric series 1/2^n (n>0) is less than 1 for all n, but equals 1 in the limit. so let F be the indicator that the partial sum is >= 1.

[Anonymous No.12684863]

>>12668286
Enjoy your 300k starting B^)

[Anonymous No.12685321]

so why aren't orbifolds just called hypermanifolds or something like that

[Anonymous No.12685575]

Anyone here use uppers? Did it help you become a more effective mathematician?

[Anonymous No.12685576]

>>12684583
>The adequate way would be to define the natural numbers as any Peano system, where the latter is an infinite set that satisfies the Peano axioms
Are you not aware that there are "nonstandard" Peano systems? Just imposing the Peano axioms will not pin down the set. In fact, imposing any recursive axiom system will not be enough to pin down the set.

[Anonymous No.12685615]

>>12685575
A friend in college used weed and it helped her to "visualize" stuff more clearly, but she eventually got addicted to it.

[Anonymous No.12685840]

Let [math]S = \{(u,v) | u,v \in \mathbb{R}^3, |u| = 1, \left< u,v \right> =0 \} [/math]. I want to show that this [math]S[/math] is an embedded submanifold of [math]\mathbb{R}^6.[/math]

The definition of submanifold I am using is in pic related.

Is [math]S[/math] a 6-dimensional submanifold? or is it lower dimension?
I am also struggling to understand how to apply this "flattens out locally" idea to this problem.

[Anonymous No.12686024]

>>12685840
>embedded submanifold
It clearly has a cusp at [math]v = 0[/math] tho.

[Anonymous No.12686104]

>>12685576
What do you define by "nonstandard" in this sense?

[Anonymous No.12686215]

This board really got flooded with retards since covid, and it was not great before.
Mg is the only reason I still come here, thanks frens.

[Anonymous No.12686354]

>>12685575
Fuck off pathetic druggie. You will never make it.

[Anonymous No.12686363]

>>12686354
> YWNMI
> excuse me?

[Anonymous No.12686493]

>>12670973
even google translate would come up with a better translation than this
how did german become a meme in these threads anyways

[Anonymous No.12686693]

>>12686493
Garbage begets garbage, and God knows these threads have been on a downward spiral for a long time.

[Anonymous No.12686754]

I hate online classes because I feel them uninspiring but I like not having to leave my room.

[Anonymous No.12686771]

>>12686754
do you watch pre recorded ones, or are yours live? Nothing more comfy than setting playback to 2x and blasting through.

[Anonymous No.12686790]

>>12686493
Zey want to restore ze Empire. https://www.youtube.com/watch?v=w81MS8qDb80

>>12686754
It also really sucks to be stuck at home without an access to your office. Or printers. I want to read on paper, not on a screen.

[Anonymous No.12686799]

>>12686771
They are live.
Things work different from how they do in america. I only have three courses and one classmate in two of those, so I kinda have to pay attention in case the teacher asks anything.

[Anonymous No.12686823]

>>12686790
>Or printers. I want to read on paper, not on a screen.
I too have a violent distaste for trees and like to print everything I'll read, including articles, entire books and 4chan threads.

[Anonymous No.12686956]

>>12686754
I havent attended a class since August, I just read the textbook and do the assignments.

[Anonymous No.12687855]

Any good resources for abstract algebra? I feel like a smoothbrain in this class

[Multimorph No.12688056]

>>12684856
And for the space filler the F can be indcating if there is area r not

Hmm...I was thinking of a physical problem. A elastic catenary. Pull it down and for all n it wouldnt touch the poles but at infinity it would touch all points of the poles.. I think...

[Multimorph No.12688058]

>>12686493
Das ist nicht freundlich.

[Multimorph No.12688061]

>>12686790
Wow ich verstehe die Wort in das Lied.

[Anonymous No.12688102]

>>12687855
I liked Herstein's book. Topics in Algebra, I think, is the name.

>>12688061
Yes. It has the lyrics in German and English.

[Anonymous No.12688755]

>>12685840

I'm fairly certain this is exactly the tangent bundle of the two sphere S^2 \subset R^3 , considered as a subset of R^6. In particular it would be 4-dimensional. A chart on S^2 induces a chart on T(S^2): I'm a bit tired but hopefully that should be coherent enough to help.

For another approach, this lemma might help: If f: M -> N is a smooth map between manifolds, y = f(x) is a regular value, and d_x f has rank k, then f^-1 (y) is a codimension k submanifold. I can't think of a good map for f however.

Practically, we get a lot of information about manifolds from maps and vice versa; historically a map f had "k-manifoldness" if it mapped k points to a single regular value. I don't know if the "flattens out S locally" bit is super helpful for solving problems, but it does help to visualize things.

[Anonymous No.12689525]

Is 20 pages of a math textbook a good goal to aim for to complete in a day? Undergrad btw

[Anonymous No.12689541]

>>12689525
Depends on the topic, for a lot of undergrad I'd say yes.
Some subjects (and textbooks for that matter) are a little more dense than others so necessarily will take longer.

For example, most intro to Graph Theory books you could blast through 50 pages in a sitting, but I couldn't imagine doing that for Baby Rudin

[Anonymous No.12689548]

>>12689541
Ok cool. I think for baby rudin most class sites I've seen keep a 1 chapter per 2 weeks which is averages to around 20 pages per 2 weeks, so maybe this reflects both the difficulty of rudin and also the laziness of undergrads

[Anonymous No.12689563]

>>12689548
I think the key is to avoid forcing through pages when you don't understand. That is, if you don't get it you should wait and think until you do and not try and grind to get to the page count.

[Multimorph No.12689688]

>>12689525
How the fuck are you capable of that? You cant just build intuitions in an instant, or are you a genius?

[Anonymous No.12689695]

>>12668565
This should get you started. Now use the properties of series and known series to calculate the final sum
[math] \sum_{i=0}^{a}\sum_{j=0}^b j =\sum_{i=0}^{a} \frac{b(b+1)}{2} [/math]

[Anonymous No.12689697]

>>12689695
sorry, replace b with i

[Anonymous No.12689798]

>>12685840
Use the inverse function theorem.

[Anonymous No.12689881]

show me a picture of an orbifold

[Anonymous No.12689909]

>>12674125
So many speculations and complaining of proofs and applicability of mathematics. It is a waste of time unless you have finished the "front end" of mathematics being your homework and wanted to understand the "back end" of it, the metamathematics.

[Anonymous No.12689939]

>>12689881
Draw a circle, have the trivial group act on it, quotient the action away.

[Anonymous No.12689974]

>>12689939
I’m in despair! People on the internet who use my favorite anime to shitpost have left me in despair!

[Anonymous No.12690032]

>>12670903
total count of five digit numbers : 9*10^4
total number of five digit numbers not containing either 5 or 3 : (9-2)*(10-2)^4 = 7*8^4
totak number of five-digit numbers containing at least a 3 or 5 : the difference of the above two, 61328

[Anonymous No.12690057]

>>12689525
If you're going to treat studying math like taking vitamins you won't learn anything

[Anonymous No.12690071]

>>12688061
you also mangled the article cases beyond repair.

[Anonymous No.12690107]

>>12683910
They're both thick, but what's the difference?

[Anonymous No.12690189]

>>12689939
something more interesting PLEASE

[Anonymous No.12690426]

>0=0

[Anonymous No.12690430]

>>12684550
>it's not a speed contest
It actually is.

[Anonymous No.12690435]

>>12689881
Imagine a point, but with automorphisms

[Anonymous No.12690505]

I understand that in Z/4Z 3+1 = 4 or 2+3 = 1 but why does 2 = 4 = 0? I don't understand.

[Anonymous No.12690515]

>>12690505
Nevermind it was a mistake in my lesson.

[Anonymous No.12690516]

>>12690505
>2=4=0?
I'm confused too. Is there a mistake? In mod 4, 2(4)=0. Maybe that's what's meant.

[Anonymous No.12690530]

>>12690516
Yep t'was a mistake. My teacher is a hack.

[Anonymous No.12690534]

>>12684094
BASED

[Anonymous No.12690542]

>>12680460
how important is GPA?

[Anonymous No.12690551]

>>12684094
Damn bros

[Anonymous No.12690588]

>>12690189
Upper half plane and Fuchsian groups, I think, was somewhat cool. It's been 5-6 years since I did anything with those, so maybe I'm remembering wrong things.

>>12690430
Maybe.

[Anonymous No.12690604]

>>12690430
prove it

[Anonymous No.12690615]

>>12668218
Bros I have differential forms question. Let [math]U \subset \mathbb{R}^n[/math], then [math]\Omega^k(U)[/math] denotes the vector space of [math]k[/math]-forms on [math]U[/math]. What is the dimension of this space? Since the underlying field of [math]\Omega^k(U)[/math] is [math]\mathbb{R}[/math], then the set of smooth functions times increasing k multi-indices is a basis. This means that the space is infinite dimensional. But I read all over that the dimension of this space is n choose k. This seems to me only to make sense when we restrict to constant coefficients on the basis consisting of increasing k multi-indices. Also do we ever think about [math]\Omega^k(U)[/math] as a [math]C^{\infty}(U)[/math]-module?

[Anonymous No.12690618]

[Anonymous No.12690720]

>>12690615
>actually getting confused by that abuse of notation
Weird, don't think I'd ever seen it before.
Anyhow, [math]\Omega ^k(U)[/math] has infinite dimension, but it admits a frame with n choose k elements, which is, in a sense, the correct dimension.

[Anonymous No.12690867]

>>12690542
if it starts with 3.7 or more, I don't think most employers give a damn about it being much higher.
I've even seen job app forms from companies where you fill in one of
>3.75-4
>3.25-3.75
>2.5-3.25
> <2.5
or something to that effect

[Anonymous No.12690961]

>>12690604
I don't wanna.

[Anonymous No.12690998]

>>12690615
Depends if you mean differential form as a single tensor at a fixed point or as a tensor field on the whole manifold (or its open subset). First case it's finite dimensional over R, second case it's infinite dimensional over R.

[Anonymous No.12691004]

>>12690720
And yes, thinking about the space of sections of a vector bundle as a C^inf(M)-module is definitely a thing.

[Anonymous No.12691202]

what are schauder bases used for outside functional analysis

[Anonymous No.12691220]

>>12690618
Topos theory is a thing of the past, comrade. It's the retarded cousin of type theory designed by people that were worshiping Set as if it were the right place to do maths.

[Anonymous No.12691246]

>>12691202
usage of schauder bases IS usage of functional analysis

[Anonymous No.12691278]

>>12691202
Fourier series

[Anonymous No.12691404]

Bought a used copy of baby Rudin. Previous owner wrote a poem in the back, what a wanker.
Anyways, wish me luck.

[Anonymous No.12691473]

>>12691404
>Anyways, wish me luck.
Best I can do is comedic misfortune.

[Anonymous No.12691498]

>>12691278
so id have to go down the mathematical phsyics/engineering route

>>12691404
tipex over it and write peepeepoopoo over and over to cover it

[Anonymous No.12691534]

What is the current state of research in stochastic partial differential equations? Can anyone point me in the right direction? Have recently become interested in the subject.

[Anonymous No.12691586]

>>12691404
wtf that's my copy

[Anonymous No.12691589]

>>12691534
I think I remember one of my professors talking about his work on the KPZ universality class years ago
https://en.wikipedia.org/wiki/Kardar%E2%80%93Parisi%E2%80%93Zhang_equation

[Anonymous No.12691620]

>>12691498
fourier analysis is pure math

[Anonymous No.12691634]

>>12675610
I laughed
Up there with the most convoluted ways of writing 0

[Anonymous No.12691665]

>>12691589
Interesting, thanks.

[Anonymous No.12691690]

Is there any cool resource I can read for exterior derivatives?

[Anonymous No.12691698]

>>12691620
fourier analysis is a part of functional analysis
however there are applications of fourier series

[Anonymous No.12691701]

Are there any Rings where:
there's one or two units
there's a finite amount of elements
there are no zero-divisors
Essentially like [math](\mathbb{Z},+,\cdot)[/math] but with a finite amount of elements

[Anonymous No.12691707]

>>12691701
What have you tried?

[Anonymous No.12691713]

>>12691707
I tried asking /mg/
this isn't a homework problem, dog
I'm in a lecture right now learning about units and I was wondering about this

[Anonymous No.12691716]

>>12691690
books

[Anonymous No.12691719]

>>12691716
thanks

[Anonymous No.12691720]

>>12691719
anytime fren

[Anonymous No.12691721]

>>12691720
take care fren

[Anonymous No.12691722]

>>12691713
>I tried asking /mg/
Did you try asking your stupid question in the thread for stupid questions?

[Anonymous No.12691726]

>>12691713
Try [math] \mathbb{Z} / p \mathbb{Z} [/math] where p is a prime.

[Anonymous No.12691728]

>>12691722
is it a stupid question?
>>12691726
Isn't everything a unit there? (other than 0)

[Anonymous No.12691732]

>>12691701
try looking in the mirror haha

[Anonymous No.12691734]

>>12691732
fug

[Anonymous No.12691737]

>>12691728
This is for grads only

[Anonymous No.12691747]

>>12691728
Yeah, there's a flowchart for this stuff.

[Anonymous No.12691749]

>>12691737
on my way to that soon enough. i'm a last semester undergrad mathlad
taking 2 grad classes right now in fact.

[Anonymous No.12691753]

>>12691749
>last semester
>basic ring theory
That's even worse.

[Anonymous No.12691754]

>>12691747
thanks dog

[Anonymous No.12691758]

>>12691753
I took abstract algebra a year ago, this is the second week of this course and we're reviewing shit

[Anonymous No.12691765]

>>12691220
This absolute genius disagrees.
She's going to revolutionize mathematics and people will only get it decades later, like Cantor, Abel or Galois but with way more depth and far reaching consequences.

[Anonymous No.12691769]

>>12691765
looks like a downy
godspeed

[Anonymous No.12691775]

>>12691758
Ah, I see.
Thank God, I was really concerned there.
Anyhow, >>12691726

[Anonymous No.12691780]

>>12691775
again, isn't everything that isn't 0 a unit there since [math]\gcd(n,p)=1[/math]

[Anonymous No.12691786]

>>12691780
Why yes, that's correct.
Consider p=2, 3 tho.

[Anonymous No.12691791]

>>12691786
fug, I guess that works

[Anonymous No.12691794]

>>12691780
It works for two primes m8

[Anonymous No.12691797]

>>12691791
Those are actually provably the only examples.
Proof left to you.

No one else do it, he needs to figure the issue out on his own.

[Anonymous No.12691798]

>>12691797
lmao, will do when I get a chance

[Anonymous No.12691825]

>>12691797
wait hold up
does this just come down to something necessarily either being a zero-divisor or a unit
now i feel like a brainlet for not realizing those were the only ones sooner.

[Anonymous No.12691826]

>>12691825
>does this just come down to something necessarily either being a zero-divisor or a unit
Bingo.

[Anonymous No.12691853]

>>12673099
Rofl. Only a true brainlet would not get this

[Anonymous No.12691856]

>>12675610
Based as fuck

[Anonymous No.12691886]

>>12684488
No.
When you increase the radius of an n-dimensional ball, the volume increases like [math]x^n[/math].
This means that, as n goes to infinity, all of a ball's volume is concentrated on the border.

[Anonymous No.12691914]

>>12691825
The finiteness of the ring is important, if you lift this hypothesis you can find lots of other examples other than the ring of integers.

[Multimorph No.12692236]

>>12692234