first for symplectic geometry

hi can you guys help me, someone told me that 10 + 10 = 20 and 11 + 11 = 20 too and I don't get it

>>16432396
The wikipedia page for q-analogs doesn't make any sense, what are they really?

>>16432427
>11+11=20
It's pretty fucking obvious you just factor out the one here:
1(10+10)=10+10=20

Since I first learned of it the multi-armed bandit model seems to apply to every aspect of human life. Shouldn't it be more widely taught?

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Does this pattern have a name? I made it as a basis for an hexagonal maze, but I don't think I've seen this before.

>>16432926
It's fundamentally a triangular tiling of the Euclidean plane, just with thick black outlines on the triangles in question

>>16432933
Thanks

>>16432396
Why is he sitting in that chair backwards?

>>16432427
Maybe he meant in base 11

>>16432427
Did you hear about the race between nineteen and twenty? 21

Any tensor algebra and calculus textbook that isn't proof based, I'm just a simple engineer

>>16433130
A brief on tensor analysis , Simmonds. Best of bests

>>16433097
That’s amazing, can’t believe I’ve never heard this one before

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https://www.quantamagazine.org/big-advance-on-simple-sounding-math-problem-was-a-century-in-the-making-20241014/

>>16431947 simple counterexample, let A be the y axis with the origin deleted, and let the image of f be the x axis, say f(t)=(t,0)

>>16433786
I didn’t see A has to be closed.
How about A is the y axis with (-1,1) removed, and f(t)=(0,sin(t)-1/t)

>>16433824
sin(t)-1/(t+2), rather

>>16433650
why do you fuckers keep posting this meme list even though not one of you actually ever read a book from it? it just seems like heavy cool math words that make you sooooo cool among the other kids

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need to find the derivative of this, I did it but got a huge gigantic almost unreadable function

I got: 10(U)^9 * (e^pix + pie^pixcosx+2x+2cosx+x^2-sinx) / (1+cosx)^2

Is this answer even close to being right? mathway can't figure it out and neither can my calculator

>>16433933
it's not too hard to do by hand but wolframalpha was able to do it no problem

>>16433936
is my answer even close

>>16433940
I don't really feel like looking at your non-latex answer, try using wolfram alpha

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>>16433940
here

>>16433940
have you considered asking wolframalpha if the answer you got is equal to the answer it got?

>>16433942
>>16433952

I tried wolframalpha but it doesn't explain a lot. So, I take the chain rule twice here right?

>>16433979
fine, i'll do it by hand for you
>>16433933
first, take the chain rule, yielding
[eqn]
10\left(\frac{e^{\pi x}+x^2}{1+\cos(x)}\right)^9\cdot\frac{d}{dx}\left(\frac{e^{\pi x}+x^2}{1+\cos(x)}\right)
[/eqn]
then the inner derivative is (by the quotient rule)
[eqn]
\frac{(1+\cos(x))\cdot(e^{\pi x}+x^2)' - (e^{\pi x}+x^2)\cdot(1+\cos(x))'}{(1+\cos(x))^2}
[/eqn]
the derivative of [math]e^{\pi x}+x^2[/math] is [math]\pi e^{\pi x} + 2x[/math]
the derivative of [math]1+\cos(x)[/math] is [math]-\sin(x)[/math]

now stop being a fucking faggot and do your homework properly and actually read the textbook

I studied Munkres up to compact spaces, should I keep going with Munkres or go back and learn analysis? Currently I only know basic analysis.

>>16434363
The first part of munkres is basic analysis, so I would keep going.

what books filtered you? chang's continuous model theory is mogging me brutally as we speak

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>>16435062

>>16435062
Haven't gotten filtered yet but I've just started researching like a grown up. I'm excited to see what kind of knowledge can burden me to such a degree.

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>>16435062
continuous model theory is hard; most brutal book for me was picrel

Let [math] A [/math] be a nonempty closed subset of [math] \mathbb{R}^n [/math].

Let [math] f : [0,\infty) \rightarrow \mathbb{R}^n [/math] be an injective continuous function.

Suppose [math] A \cap \mathrm{image}(f) = \emptyset [/math], and also suppose [math] \mathrm{lim}_{t\to\infty} f(t) [/math] does not exist.

Then is [math] A \cup \mathrm{image}(f) [/math] necessarily non-path-connected?


We note [math] A \cup \mathrm{image}(f) [/math] can be connected but non-path-connected; the topologists' sine curve is such an example.

>>16435798
I tried to outline a proof

Consider a path [math]g(s)[/math] which connects a point [math]a[/math] in [math]A[/math] to [math]f(0)[/math]. The curve must intersect the boundary of [math]A[/math] at some point [math]g(s_0)[/math].
Consider a small neighborhood [math]N_\epsilon(g(s_0))[/math]. The set [math]B_\epsilon=\{t:f(t)\in N_\epsilon(g(s_0))\}[/math] must be unbounded, or else by continuity there exists a number M such that [math]\sqrt{f(t)-g(s_0)}>M\ \forall t\in B[/math], in which case [math]N_M(g(s_0))\cap image(f)=\emptyset[/math]. Therefore there is a subsequence [math]t_1,t_2...[/math] such that [math]t_n\rightarrow\infty[/math] as [math]n\rightarrow\infty[/math] and [math]\lim_{n\rightarrow\infty}f(t_n)=g(s_0)[/math]. Importantly, such a subsequence must diverge to infinity if the function is to converge to [math]g(s_0)[/math].
Observe that [math]g(s)[/math] can be assumed injective on the image of [math]f[/math] WLOG because for every curve [math]g'[/math] there is a curve [math]g[/math] with the same image which is injective on the image of [math]f[/math] by deleting overlapping path components (image[math]f[/math] is in bijection with the nonnegative real line so it plays nicely). Then [math]g(s)[/math] restricted to image[math]f[/math] is equal to [math]f[/math] up to a change of variables.Then [math]\lim_{s\rightarrow s_0^+}g(s)=g(s_0)\implies\lim_{t\rightarrow\infty}f(t)=g(s_0)[/math] which contradicts the assumption.

>>16433650
is mastering all this even realistic

>>16436748
It's a good start

>>16432529
kek

captcha 0MG4H0

The proof of Fubini's Theorem is 5 pages in my textbook. And I really don't like the presentation (have not defined product measures, or even what the [math]dx, dy[/math] mean (entire time we've been working on [math]f:\mathbb{R}^d \to \mathbb{R} [/math]. Tempted to just skip the proof and move on.

good resources on logic and discrete math?

>>16439376
The proof should be quite standard "approximate, approximate, approximate".
You have sigma-finite measures, so you first show the result for finite measures and take a limit later. You have integrable functions, so you first show it for simple functions and take limits later. You have an indicator of a set in the product sigma algebra, so you first take an indicator of a measurable rectangle (which generates that sigma algebra). For these indicators it's obvious, so you're done.

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>>16439461
Yeah, after staring at it and rewriting as I go for some time I almost have it through. So far everything in the text justifies it. I suppose I was just annoyed by what to me seemed like a lack of rigor for example in pic rel where we still don't have a precise definition of what [math]dx[/math] and [math]dy[/math] mean (I know they mean the respective measures, but not rigorously) so that just reads as nonsense and should instead be, based on what we have done and only what we have done
[math]\lim_{k \to \infty} \int_{\mathbb{R}^d} f_k = \int_{\mathbb{R}^d} \lim_{k\to\infty} f_k = \int_{\mathbb{R}^d} f[/math].
The text has not introduced the ideas of sigma-finite measure, or like I said a product measure. That is covered in the Abstract Measure Theory chapter much further along.
Nevertheless I am now able to follow the proof (almost done now), and like you said the strategy is just to show it is the case with indicator functions on measurable sets (starting with cubes/rectangles etc.), as then you can extend that to [math]L^1(\mathbb{R})[/math] and be finished. It's quite neat.

>>16439472
[math]L^1(\mathbb{R}^d)[/math]*

I don't need homework help, but I am legitimately curious.
I'll even change the equation from what I was given so you can't say I'm asking for answers:
Why does an equation like:
Solve this by grouping and factoring do this:
(y^3-whocares*y)=0
Become
y(y^2-whocares)=0
And then, for whatever reason,
y=0 is one of the answers before we solve for the other two with the y^2-whocares =0.
I don't understand the leap of logic that makes us split up the equation.

>>16439774
Mathematics is a lot like making love to a beautiful woman. When you see an equation you have to caress her, gently manipulating her parts until you have her in the correct position.

I hope this helped.

>>16439785
Is this Barron Trump? Only HE knows what a beautiful woman is

>>16439774
That just follows from the distributive laws
[math]y(y^2 - Gy) = y*y^2 - y*Gy = y^3 - Gy^2[/math]

>>16439807
This follows from the fagittutive laws, that the post this links to is a fag, oh so help me god.

I'm reading the mcat preparation book next month when I get it and am reading some of them now that aren't math related
If it's maths (and physics!) that I get then I'm really worried. I'm bad with numbers
Have any of you read thr maths and physics mcat book? What's in it? How do I force myself to learn these subjects for the first time in my life (not even high school education)?

>>16439785
How does this metaphor extend to those equations where you can't solve for a given variable?
e.g. [math]z=we^w[/math]
How do I get a woman to give me a w

>>16440000
You use something that's made just for
her...in your example, it's the W function.
Then, she'll turn around and say "nice quads"
and "that was wonderful, babe".

Which book is best if I want to learn the mathematics behind AI?
Deep Learning by Ian Goodfellow, Yoshua Bengion, Aaron Courville
or
Mathematics for Machine Learning by Marc Peter Deisenroth, Aldo Faisal, Chen Soon Ong

any good book on elliptic functions that dont go yeah this function is defined as this theta ratio now deal with this hundred addition formulas (like whittaker watson or lawden)? a book that has great intuition and applications would be great

When you cut a polyhedron into a 2-dimensional net, the edges that are cut along always form a spanning tree of the graph of the polyhedron.
4D polytopes have 3D nets which are made by cutting along faces of the polytope. Is there a way to make some kind of higher-dimensional analog to graphs that follows this? I looked at the wikipedia page for hypergraphs and it isn't what I have in mind.

Posted this on /sqt/ with no response still, hope you guys can help me out. Any help is appreciated. Also, I lost pretty much 2 weeks worth of differential geometry class, so I gotta catch up on a lot of things. With that said, I could use some good extra references (textbooks, lecture notes, etc). Thanks in advance.
What really is the distribution of vector fields?
I thought it was just the span of the vector fields but apparently that definition if only locally correct (whatever that means).
And also, the definition I'm using for vector field is that a vector field on a manifold [math]M[/math] is a linear map [math]X:C^\infty(M)\to C^\infty(M)[/math] that is also a derivation. Following from this definition, how can I define a covector field? A covector field is supposed to be a differential form, right?

There's only so much bits and bobs to discover in all-tech before you know how to create any tech gayly. I am masterful in all-tech.

>>16442372
You DO overflow, same with art, similar with chemicals.

>>16442365
Covector field maps from the vector field to the base field

>>16436720
Thank you for your help anon. Sorry I didn't respond earlier, I was meeting some relatives

What is the point of regurgitating all of the theorems I learnt in real analysis in terms of exact sequences? Sure, fine, there's a kind of isomorphism between some theorems, what makes this particular kind of isomorphism so great?

>>16432396
Tell me about trigonometry /sci/ What exactly is it? What can I use it for? Can I create an LLM with it? Can I make Skynet with it? Can I make a Quantum Computer with it?

>>16443150
im sorry but i doubt you are gonna be able to do any of those if you dont know what trigonometry is anon

I read something about logic years ago and that said that all definable parts of third-order, fourth-order etc logic can be represented with arbitrarily long formulas in second-order logic. Is this true?

How sophisticated were you in your freshman year of uni? im a few months into the program and prior to that I pretty much know undergraduate real analysis in my 12th grade of highschool. Im also studying complex analysis on my own.

>>16444119
I knew pretty much nothing when I started. Only the abc-formula and stuff like that.

The infinitists got Wildberger
https://njwildberger.com/2024/10/22/n-j-wildberger-youtube-videos-currently-unavailable/
https://www.youtube.com/@njwildberger

>>16444482
I stick every maths youtuber I actually enjoy on archive.org. It's only Eugene Khutoryansky and Taylor Dupuy so far but that's because everybody else is shit-tier.

>>16433130
You will do ze proofs and you will like it

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>your answer is correct but its not in the correct form so you are wrong

Geometry bros: Lee or do Carmo?

>>16447912
EGA

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>>16435062
I doubt there even exists one person (excluding Gromov) who really "got it".

Is there any way I can approach analysis by an abstract algebra standpoint? I mean, I take an analysis problem and solve it using abstract algebra techniques and concepts, and reformulate any analysis theorem and definition with an algebra based definition?
If so, do you guys know any textbook that go for this approach?

>>16447912
Not Lee, at least not as your first book. It's terrible for learning as motivation is basically void in his Manifolds and Differential Geometry book, he even admits it and points to his later works. Don't really recall much from do Carmo, though I used his books for some of my lectures. If you're new to DG, try O'Neill's Semi-Riemannian Geometry With Applications to Relativity instead. Sharpe, Lee, Brédon, etc. are for when you know the basics imo. Also check out the various different lecture notes that are floating on the web, some are really good.

>>16448057
The intersection of algebra and analysis is not simple. What you are describing can only happen in certain situations. Take algebraic topology or lie groups for example

>>16448057
ww.math.uni-bonn.de/people/scholze/Analytic.pdf

>>16447912
Uhhhhh, i don't love do Carmo. But i don't have a recommendation, sorry. So go with the other guy's rec

>>16448287
shieet i didn't know scholze posts on mg

Why can't progress be made on Navier-Stokes by just mapping it's phase space?

>>16448287
Hey anon, thanks.
The link's not working for me, could you provide another link or the textbook name?

>>16448853
www.math.uni-bonn.de/people/scholze/Analytic.pdf
w was missing.
It was a joke anyway.

>>16448861
>w was missing.
lol, now I'm feeling dumb.
>It was a joke anyway.
That's alright. I appreciate it anyway, seems like a nice text. Thanks.

Is it weird to have math dreams? I just woke up in the middle of the night and my brain was trying to solve some equations or some shit, I was still like half-asleep,but I clearly remember like my brain was still active in that way, has happened to me a few times now, especially when I'm thinking about some concepts in detail and trying to visualize them

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What is [math]A^{(M\times N)}[/math] supposed to mean?

>>16448989
[math]A^{(X)}[/math] is the set of maps [math]f:X\to A[/math] for which there is a finite subset [math]X_0[/math] such that f is 0 outside of [math]X_0[/math]. It is "the free A-module with basis X". More precisely, if [math]x\in X[/math], denote [math]e_x\in A^{(X)}[/math] the function which is 1 in x and 0 elsewhere, then [math]\{e_x: x\in X\}[/math] is a basis for the A-module [math]A^{(X)}[/math].

>>16449022
In this case, can't I just write [math]\langle X\rangle[/math] or [math]\langle e_x\rangle_{x\in X}[/math] instead? What are the advantages of such convoluted and obnoxious notation that the author is using?

>>16449045
Where is the ring A in that notation?

>>16449118
Well, I could define e_x beforehand and use the second notation I presented. That way it's clear what ring I'm considering.

>>16449123
The notation is fine, I have no idea why you're being a baby about it lmao

>>16449126
Ok, I'll decide on the notation later.
Anyway, do I have to make any assumptions about [math]X[/math]? I mean, does it have to be finite, infinite and/or countable, must it have some algebraic structure, etc? Or any set will do?

>>16440956
Start by not reading a book about the mathematics surrounding machine learning. They're overcomplicated, meant to confuse you, and you will only find yourself increasingly more confused.
I'd highly encourage you to start by doing some linear algebra and Calculus III. My old university had all of the calculus texts avaliable online for free and you can find them here:
https://arts-sciences.und.edu/academics/math/calc-1-texts.html
Once you feel pretty comfortable with that, move into some differential equations and linear algebra. Focus on the matrix multiplication in linear and learn DE to enhance your problem-solving ability.

>>16435090
I like you. Researching like an adult but with the wonderment of a child.

>>16433130
>Proofs
Engineer here as well. I'm getting my ass mogged right now in linear algebra cause it's so theory heavy. Nevertheless, I feel like it will enhance my ability in the field to solve problems in some way. It might just be in our best interest to do the proofs and get 'em over with so if they come up in the future we'll know how to deal with 'em.

If any anons have some suggestions for writing proofs/getting good at them, I'd appreciate it

>>16449160
>Suggestions for getting good at proofs
Learn from the masters! Read Euclid, Dedekind, Edmund Landau and André Weil. Alternatively, i find it easier to grasp the proof concept following a good book/course on proof-based elementary linear algebra rather than any of those Transition books/courses

what's the difference between top unis and like low top 500 unis for undergrad and up

>>16449700
For undergrad it matters diddly squat, top unis are top because they have the best researches. They will look good in your CV though. After that it starts mattering more.

>>16449700
Mostly social. You develop a much better network of talented people at top unis because almost all the most talented people are clustered there. The courses are "the same" at McUniversities in the sense that they use mostly the same books with mostly the same syllabi but there are a lot of things you can't get from just reading a textbook that you need real people for

What is the most elementary solution to Basel problem? (The only one I know involves Fourier series.)

>>16450279
i think cauchy has one only using basic trigonometry and squeeze theorem

>>16450279
>>16450298
https://en.wikipedia.org/wiki/Basel_problem#Cauchy's_proof

I'm trying to use the first isomorphism theorem to prove that there is a canonical isomorphism between [math]\mathcal{A}^k(V)[/math] and [math]\bigwedge^kV[/math], where [math]V[/math] is a vector space (over some field [math]K[/math]) and by [math]\mathcal{A}^k(V)[/math] I mean the subspace of [math]\bigotimes^kV[/math] consisting of skew-symmetric tensors.
First I'm defining [math]\bigwedge^kV[/math] by
[eqn]
\mathop{\bigwedge{}^k}V := \mathop{\bigotimes{}^k}V/J^k(V)
[/eqn]
where I define [math]J^k(V)\leq \bigotimes^kV[/math] to be the subspace spanned by all tensor products [math]\bigotimes_jv_j[/math] s.t. for at least two different indices [math]\lambda,\rho[/math] I have [math]v_\lambda = v_\rho[/math].
If I consider the map
[eqn]
\begin{align*}
\pi : \mathop{\bigotimes{}^k}V &\to \mathop{\bigotimes{}^k}V/J^k(V)\\
\tau &\mapsto \tau + J^k(V)
\end{align*}
[/eqn]
then I just need to find a suitable [math]\varphi \in \mathrm{Hom}(\bigotimes^kV,\mathcal{A}^k(V))[/math] s.t. [math]\ker(\varphi) = J^k(V)[/math], and then by the first isomorphism theorem I'll have an induced isomorphism [math]\psi : \bigotimes^kV/J^k(V) \overset{\sim}{\to} \mathcal{A}^k(V)[/math] given by [math]\psi\circ\pi = \varphi[/math].
As an additional question, in my definition of [math]J^k(V)[/math], is it equivalent to my definition to say that [math]J^k(V)[/math] is spanned by all tensor products [math]\bigotimes_jv_j[/math] s.t. [math]\{v_j\}_j[/math] is a linearly dependent collection of vectors? And how would this definition and possible proof of canonical isomorphism hold for modules instead of vector spaces?
Any help is appreciated, thanks in advance.

>>16450279
[math]sin(\pi x)= \sum\limits_{n=0}^{\infty}{(\pi x)^{2n+1}(-1)^{n}\over (2n+1)!} =(\pi x)\prod\limits_{n=1}^{\infty}(1-{x^2 \over n^2}).\\
Equate\ x^3\ terms.[/math]
Idk who first did it (probably euler).

>>16450902
Isn't phi the map that sends [math]v_1\otimes \cdots\otimes v_n\mapsto \frac{1}{n!}\sum_{\sigma \in S_n}(\text{sign}\sigma)v_{\sigma(1)}\otimes\cdots\otimes v_{\sigma(n)}.[/math]
Then psi is just what sends the wedge product the summation on the right? I'm retarded though is my excuse if this completely wrong. I vaguely remember doing this. I think Kieth Conrad goes over this construction is his expository paper on Exterior Powers. He does it for modules, but if he does have some examples that cover the specific case of vector spaces.

Would you agree that calculus is the branch of mathematics that deals with limits?

>>16451321
Analysis is the study of continuous functions on the real numbers in the standard topology. Calculus is a compilation of the most useful techniques from analysis. It could be said that calculus is the study of limits insofar as every real number is the limit of a Cauchy sequence, however this seems too narrow since it doesn't yet mention functions.

>>16451321
I believe you're thinking of category theory.

I should have majored in physics or computer science, but now it’s too late to go back.

>>16451321
More precisely, calculus is the branch of mathematics that deals with the order topology of [math]\mathbb{R}[/math]

>>16451339
>Analysis is the study of continuous functions on the real numbers
How do you define your precious continuous functions without limits? How do you define derivative and definite integral without limits?
>>16451815
Nice.

>>16451691
Why would you think that? Flipping to physics might be a challenge but I know plenty of people who did physics or math that ended up in highly paid CS careers.

>>16451823
More gemerally, a function is said to be continuous if and only if the inverse image of any open set is open. The meaning of "open" is provided by the topology itself. The "limit definition" of continuity follows as a consequence

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>>16451339
>>16451815
>>16451823

>>16432926
What software is this?

What metric on rationals, when completed gives a non-Archimedean field?

>>16452471
A metric induced by a non-Archimdean absolute value.

It is in the name anon.

>>16452471
p-adic metrics

My professor is having a complex analysis midterm on a Sunday evening. Do you think I should send him this email?

Dear Prof M,
Sunday is the sacred holy day of our lord and savior Jesus Christ. I consider complex analysis the work of the devil, and I am deeply offended by the insensitive timing of this midterm exam.

Best,
A

>>16452845
He will call you a heathen for not capitalizing Lord.

How do I show that in ZFC there is no S such that S = { {S} }? I can't just apply Russell's paradox here because of the nested membership.

>>16453170
Use Foundation

>>16448057
You might be interested in synthetic differential geometry, smooth loci, or non-standard analysis

I'm at a loss here, I've got [math] C([0,1])[/math] of continuous maps from [math] [0,1][/math] to [math] \mathbb{R}[/math] with the norm defined by [math] ||f||_{1}=\int_{0}^{1}|f(t)|dt[/math]. I need to determine whether the function [math] F:C([0,1])\rightarrow \mathbb{R}, f\mapsto ||f||_{1}[/math] is differentiable at the zero map.
I have F as the composite of [math] k:C([0,1])\rightarrow \mathbb{R}, f\mapsto \int_{0}^{1}f(t)dt [/math] and [math] p:C([0,1])\rightarrow C([0,1]), f\mapsto |f|[/math]. [math] k [/math] is differentiable everywhere, but I'm having a hard time with the differentiability of [math] p [/math] which is continuous at the zero function but my intuition tells me it shouldn't be differentiable at that point. Any ideas?

>>16453597
F(f)=F(-f) would imply that the derivative is 0, but F(f) is of the order of f so it has no zero derivative.

What's the latest/largest found prime number in an unbroken prime sequence 2, 3, 5, 7, 11, 13, 17, 19... Both value and index
(I'm not talking about Mersenne prime)

>>16453632
Largest I can find doing an exhaustive check is: https://sweet.ua.pt/tos/goldbach.html ~ 4x10^18

But as that site and sites like https://t5k.org/lists/small/millions/ will tell you, the limiting factor for the algorithms they use (sieves) is memory. For that reason no one really stores or generates these super long lists since for such "small" numbers it is quicker to simply perform a primality test on the number you're interested in.

>>16436748
Of course not, this post you referenced was written by a literal schizo 100%

>>16453776
>this post you referenced was written by a literal schizo 100%
http://verbit.ru/

>>16453807
He вoзмoжнo вoт вce этo выyчить зa нecкoлькo лeт

>>16452007
I made it myself, I call it the image calculator. I haven't released it yet but I did release the similar "drawing calculator"
https://github.com/Photosounder/drawing-calculator

What's an example of a non-measurable function? Say from the real line to itself

>>16454223
Take the characteristic function of a non-measurable set. (Example of non-measurable set: Take one point in [0,1] in each equivalent class in (R,+)/(Q,+), it is non-measurable because a union of countable translates cover R)

>>16454223
The indicator function of a non-measurable subset of the real line.

Can someone be smart without understanding math beyond hs level + statistics? You need statistics for academia and business so thats a given. Some of my professors are math idiots.

>>16454322
If they're getting money who's the idiot after all?

>>16454336
Lots of retards make money. It's called being a manager and having your parents pay for college. Or being a welder.

>>16451997
What does the "l" mean? I get it up to the sigma algebra part.

>>16454611
Lebesgue measure.

>>16454620
How do you pronounce Lebesgue? (Apparently it's [le-BEG] but I need a second opinion.)

>>16454636
I say lehbek

>>16440000
She is out of your league

badum tsss!

>>16454636
isnt it like lebeyg where bey is same as baby

>>16454636
https://voca.ro/1idgmywHBlgk

if [math]a=o(\rho^{n-1})[/math] where [math]\rho=\sqrt{h_1^2+h_2^2+\dots+h_m^2}[/math] how is it that [math]a\cdot h_i=o(\rho)[/math]

>>16455116
[math]|h_i|\leq \rho[/math]

Are there transformations of some vector or covector, or tensor that preserve entropy, i.e stretching, shrinking, or padding an image while having the relative/entropy btn the original and new unchanged?

Is it possible to prove 'the complement of a set is a proper class' constructively and just using separation?

I can think of ways to prove it constructively using either (binary) union + separation or just induction (to use that \in is asymmetric).
I've also managed to prove it just using separation but relying on classical logic.

Are there any non-trivial solutions to [math]\int f = f'[/math]?

>>16455498
f = f'' ?

>>16455498
f=e^x

>>16455498
f(x)=cosh(x)

how do I learn boolean logic very well? any good books

>>16456114
Halmos

File: 1730339639268723.png (175 KB, 400x531)

175 KB PNG

Just flunked a math test. It only dropped my overall grade by 2% though. I'll still pass. I've been in a mental health spiral for the last 2-3 weeks. Totally incapacitated. I feel like I might be coming out of it though. I have another one in 2 days for a different class. Please pray for me.

>>16456647
god luck dawg it's not big deal don't stress it so much school is not the only important thing

>>16456647
>tfw no dumb cat-twink bf to teach math