/mg/ - Math General

[Anonymous No.9642860]

>What is a Zhu algebra?
>What is a Kähler manifold?
>What is the Lewis Carroll Identity?
You may find the answers to these beautiful questions in this thread, as well as:

>What are you studying?
>What are your vocational plans?
>How do I kill myself?
>Am I going to make it?

(There is literally nothing wrong with being autistic.)

[Anonymous No.9642912]

Any intuition on how to build a cryptosystem based on the fact that some surjective functions do not have a right inverse?

[Anonymous No.9642915]

Can someone explain to me what the hell Sheaf Theory is?

[Anonymous No.9642919]

>>9642915
>Sheaf Theory
not math

[Anonymous No.9642928]

>What are you studying?
Recapping spectral sequences at the moment.
>What are your vocational plans?
Researcher or unemployed.
>How do I kill myself?
I'll probably use a belt and a door handle.
>Am I going to make it?
No.

[Anonymous No.9642947]

What are /mg/'s thoughts on the "What is..." series?

http://arminstraub.com/math/what-is-column

[Anonymous No.9642952]

Notice how /mg/ discussion quality plummeted when ponyless bronies started using it to beg for attention?

[Anonymous No.9642956]

>>9642952
>ponyless bronies
huh?

[Anonymous No.9642958]

>>9642952
>ponyless bronies
?

[Anonymous No.9642959]

>>9642947
Looks good. I love pretty pictures.

[Anonymous No.9642960]

>>9642952
Excuse me?

[Anonymous No.9642964]

TIL lewis carrol wrote one of the most famous novels of all time and also contributed to algebra

[Anonymous No.9642967]

>>9642964
The queen liked his book so much she ordered all of his works, but most of them were mathematical so she was disappointed.

[Anonymous No.9642968]

>>9642912
>>9642915
Proper etiquette is to narrow your question down to something more specific. For overly general ones there's always various search engines available. Use those as a starting point.

[Anonymous No.9643010]

>>9642860
>>What is a Zhu algebra?
Zulu mode
>>What is a Kähler manifold?
Facism
>>What is the Lewis Carroll Identity?
Queen's boytoy
>What are you studying?
gömblex numbers :DDDDD
>What are your vocational plans?
become a stripper so I can afford math books
>How do I kill myself?
Jumping off a tall building
>Am I going to make it?
no lol
>(There is literally nothing wrong with being autistic.)
There absolutely is

[Anonymous No.9643025]

>>9642928

[Anonymous No.9643033]

i want to check out some obscure references to an article I'm reading, but I can't find them
how to search for math articles? are there any sites worth knowing, besides scihub and libgen?

[Anonymous No.9643036]

>>9642952
Wtf are ypu talking about?

[Anonymous No.9643061]

>What are you studying?
Nothing, I'm just reading Emergence of the Theory of Lie Groups by Thomas Hawkins.

>What are your vocational plans?
Unemployment.

>How do I kill myself?
I'll follow zü's orders.

>Am I going to make it?
No.

[Anonymous No.9643063]

>>9643025
I'm not dead yet.

>>9642947
I checked this out and it seems quite nice. Thanks for the share.

>>9642915
Start with a topological space. First, find out what a presheaf is, then how presheaves turn into sheaves, and then what kind of relationships various sheaves over the space can have. Then generalize the space to a site. I can give you a hint: ordered sets can be considered categories, so you can take a contravariant functor from your space's topology to the category of sets, abelian groups, modules, etc. Start with that.

[Anonymous No.9643067]

>>9643061
>zü

[Anonymous No.9643069]

>>9643033
You could check if where you live has any kind of interlibrary loan system.
I don't know how it works elsewhere, but here in Ontario students can get books and/or photocopies of articles sent to your library free of charge from any academic library in the province.

[Anonymous No.9643108]

>>9642912
this meme is among my favourites

[Anonymous No.9643125]

>>9642860
Daily reminder that while Cirno a cute, Cirno is also for bulli.

Not gonna make it.
Reason: Baka Baka

[Anonymous No.9643131]

>What are you studying?
H-high school math to get myself back in the flow.
>What are your vocational plans?
I don't know.
>How do I kill myself?
Self immolation.
>Am I going to make it?
We all are.

[Anonymous No.9643139]

>>9643131
>Team Creme
>Literal brainlets

Not gonna make it.

[Anonymous No.9643141]

>>9643131
>We all are.
We don't deserve someone motivational in here, stop being cute and leave us depressed

[Anonymous No.9643151]

>>9643141
Hourly reminder that entropy and chronology will eat you all slowly and surely and your waifus are not real. Your "friends" probably don't like you and are just using you for your brain and when you become obsolete they will cast you aside. You will probably all die forgotten. Nobody loves you.

:D

Did I miss anything?

[Anonymous No.9643177]

>>9643139
It has been a long time. I am also learning intro calculus. I will fulfil my dreams and creme is the the best team and we love all. When I succeed and they interview me why I did it I will tell them:
>For Team Creme
>For the anime poster
>For that nay sayer. What a total Phaaaaaag

[Anonymous No.9643224]

>>9642915
Without going into deep algebraic geometry (which I still don't know), they have some use in algebraic topology, for example in (co)homology: one nice application is a proof of De Rham theorem, which links De Rham cohomology, a widely known differential invariant of differential manifolds, to Cech cohomology, a topological invariant defined in the sheaf language, therefore you have that De Rham cohomology is also a topological invariant (this is actually an incomplete version of the theorem).
Also they are used (and maybe they were introduced in this context) for Riemann surfaces, Forster introduces them early in his book 'Riemann surfaces'. Essentially the geometrical structure that you describe with charts is equivalent to say which functions are holomorphic(differentiable, etc.), hence the notion of sheaf.

[Anonymous No.9643231]

>>9643177
Brainlet anime posters like you will never understand.
The price of true knowledge...

[Anonymous No.9643244]

>>9643231
>Brainlet anime posters
No such thing.

[Anonymous No.9643262]

>>9643244
>says The Cirno poster.
*bulli*

[Anonymous No.9643265]

>>9643262
>>says The Cirno poster.
Who are you quoting?

[Anonymous No.9643390]

ITT: Post hacks

[Anonymous No.9643396]

>>9643390

[Anonymous No.9643399]

>>9636995
>>9637002
That sounds nice. I've made an account, you can send me an invite.

[Anonymous No.9643403]

>>9643390

[Anonymous No.9643488]

>>9643399
2nd.

[Anonymous No.9643578]

more like Anime general

[Anonymous No.9643587]

>>9643578
>more like Anime general
and that's a good thing

[Anonymous No.9643622]

>>9643587
kill yourself weeb

[Anonymous No.9643625]

>>9643622
>kill yourself weeb
Why the cyberbullying?

[Anonymous No.9643679]

Is ZF(C) dense in the category of axioms?

[Anonymous No.9643694]

>>9642947
Based.
https://arxiv.org/abs/1305.4293

[Anonymous No.9643787]

>>9643679
What are the morphisms in the category of axioms?

[Anonymous No.9643815]

>>9643787
>What are the morphisms in the category of axioms?
I follow the canonical structure

[Anonymous No.9643842]

>>9643679
not as dense as you lmao

[Anonymous No.9643857]

>>9643679
>category of axioms
That is not a thing.

[Anonymous No.9643870]

>>9642919
I have no idea, but if you mention it in your grant you get funded instantly

[Anonymous No.9643898]

>>9643787
>What are the morphisms in the category of axioms?
I have no idea, but if you mention it in your grant you get funded instantly

[Anonymous No.9644277]

Friends, can you help me with this?

Can someone tell me what maths this is? I'm a non-stem who wants to study a sound course and I need to know at least this to make it in.

And if anyone could offer some basic textbooks to start learning maths after finishing high school 7 years ago.

https://www.koncon.nl/storage/documents/example-Math-test-Sonology-2009.pdf

[Anonymous No.9644285]

>>9644277
So algebra, converting units, linear functions and equations, second degree functions...

[Anonymous No.9644286]

>>9644277
>>9644285

[Anonymous No.9644289]

>>9644277
>>9644285
>>9644286

[Anonymous No.9644297]

>>9644277
>>9644285
>>9644286
>>9644289
It's middle-school algebra. These are the sort of exercise we did in 5th or 6th grade here (Romania).

[Anonymous No.9644299]

>>9644277
>>9644285
>>9644286
>>9644289

[Anonymous No.9644300]

>>9644297
Thank you. So I just need to go back and learn basic algebra? What else can you recommend? T

[Anonymous No.9644304]

>>9644300
>What else can you recommend?
If these are the sort of exercises you're having problems with, nothing. (No offence meant.)

[Anonymous No.9644314]

>>9644304
There is no problem. I've just forgotten the methods or there is new info I don't yet know and want to learn.

I know you're suggesting my brain isn't for maths, but I would still like a suggestion as to how to progress.

[Anonymous No.9644331]

>>9644314
>I would still like a suggestion as to how to progress.
Hit Khan Academy or something.

[Anonymous No.9644336]

>>9644331
>>9644314
To be honest with you, I really have no idea what to suggest.

[Anonymous No.9644344]

>>9644331
Thanks

[Anonymous No.9644345]

>>9644300
basic mathematics by serge lang. take your time and do every problem.

[Anonymous No.9644349]

>>9644345
That book is too difficult for the level he is at.

[Anonymous No.9644371]

>>9644345
Thanks

>>9644349
Really? Do you have another suggestion?

[Anonymous No.9644420]

Brainlet here, is there a fun/illustrated glossary of math for the terms: functors, abelian groups, rings, axioms, some-latinsounding shit, tensors, without requiring a recursive search of the definition of the words

say I don't know what is a tensor, then I have to recursively search many seemingly unrelated terms until I have an abstract and probably false idea of what a tensor is, but I could still have known the idea if the idea was explained with toy pictures or something like that, specially because many of these definitions may possibly lead to ambiguities so even if you memorize the definition you're prone to fuck up and have no idea what you're talking about.

I find that math is not really hard, what its hard it's the retarded literature that appears to obsessively encrypt it with words that I don't understand, when explained with basic concepts and logic, I can seem to understand everything but the wall of language fucks my shit up

[Anonymous No.9644447]

>>9644420
> fun/illustrated glossary of all math
> recursively search many seemingly unrelated terms
> if you memorize the definition you're prone to fuck up
> obsessively encrypt it with words that I don't understand

Welcome to math, there is no such thing as you claim.
If you are not a really hard worker, in which case you should have not those problems, I suggest you to enroll at a university with decent teachers.
Also, for some basic topics try to lurk in https://unapologetic.wordpress.com/ , select subject and read. Don't expect to understand everything there, only books and hard work will get you into the heights.

[Anonymous No.9644455]

>>9644447
>there is no such thing as you claim.
Time to start

[Anonymous No.9644467]

>>9644455
How about no. Math is not for lazy brainlets. We shall keep it that way.

[Anonymous No.9644473]

>>9644455
Also, state your background and what you want to learn, or better search the infinite topics on stackexchange. You cannot learn math by memorizing definitions(or by tumblr images), it is freaking useless. So many times you will understand the definitions after pages and pages of nonsense, and will say at the end 'well, maybe it is no so unreasonable', or will cry and decide it is finally time to accept it and go on.
For tensors and multilinear algebra try to read also the free book 'linear algebra via exterior products - winitzki', and other literature, and search or ask if you don't understand something in particular. I would not suggest you to get into category theory stuff if you don't have even a basic understanding of algebra.

>>9644467
Nailed it.

[Anonymous No.9644487]

>>9644420
>say I don't know what is a tensor, then I have to recursively search many seemingly unrelated terms until I have an abstract and probably false idea of what a tensor is
yes, this is exactly how math works. there are no shortcuts.

[Anonymous No.9644531]

>>9644473
>I would not suggest you to get into category theory stuff if you don't have even a basic understanding of algebra.
You can't have a non-trivial understanding of algebra if you don't even know what a functor is.

[Anonymous No.9644626]

>>9642860

Can one of you tell me a good intro to set theory? I NEED IT

[Anonymous No.9644643]

>>9644345
>basic mathematics by serge lang
Lang is a meme.

[Anonymous No.9644646]

>>9644531
>You can't have a non-trivial understanding of algebra if you don't even know what a functor is.
Actually, category theory is irrelevant to most of mathematics

[Anonymous No.9644703]

>>9644643
Why is Lang a meme? What?

[Anonymous No.9644720]

too much anime, not enough math.

[Anonymous No.9644765]

>>9644626
what level?
>basic: naive set theory, halmos
>intermediate: introduction to set theory, hrbacek + jech
>advanced: set theory, jech

[Anonymous No.9644779]

>>9643399
>>9643488
Feel free to join anytime :3 We need to verify you though so we don't get any of those brainlets, hope you understand https://discord.gg/eT8p9p

[Anonymous No.9644875]

>>9644626
Start with model theory

[Anonymous No.9644961]

>>9644779
btw was in that chat romm and these guys are looking for a french guy who works in a tomato market lmao. what the fuck does farming have to do with math?

[Anonymous No.9644985]

>>9644961
Are you a newfag or something? Read through threads and connect the dots lol
And who said french?

[Anonymous No.9645058]

Finishing up a (very barebones) elementary number theory course atm. We covered divisibility, distribution of primes, reciprocity, primitive roots, and rational points on conic sections. Honestly we didn't go very deep into any of these areas though. We're using Hardy-Wright and only read selected sections. Should I finish reading Hardy-Wright or move on to something more advanced in number theory?

[Anonymous No.9645063]

>>9645058
>Should I finish reading Hardy-Wright or move on to something more advanced in number theory?
Whichever you want.

[Anonymous No.9645066]

>>9645063
So basically having the topics I mentioned under my belt I'm prepared enough to move forward?

[Anonymous No.9645074]

>>9645066
No. Number theory is an ass of a domain. It is full of traps which require ad-hoc, particular arguments. It is one of the few domains in math where you simply can't develop an intuition for because every new aspect seems to come out of left field every time.

[Anonymous No.9645078]

>>9645066
>So basically having the topics I mentioned under my belt I'm prepared enough to move forward?
If you have some abstract algebra knowledge you can pick up an introductory algebraic number theory text, if you have some analysis knowledge you can pick up an introductory analytic number theory text. You could try learning about p-adic numbers, continued fractions, the list goes on

[Anonymous No.9645182]

>>9644961
yea it has nothing to do with math

[Anonymous No.9645185]

>>9644985
>who said french
you did. one of you I mean. I read the chat pretty fast so I don't remember exactly.

[Anonymous No.9645193]

>>9645182
Well, there's that Pareto guy

[Anonymous No.9645211]

Guys I just learned about the chain rule, math is fun haha.

[Anonymous No.9645214]

how about we start a real discord in which we actually talk about math and keep these depressive weebs out?

[Anonymous No.9645216]

>>9645193
wow, o p t i m a l comment fren.
Epic 4chan (you) coming at cha'.
Haha, cool and nice.

[Anonymous No.9645218]

>>9645211
Yay. :O

[Anonymous No.9645219]

>>9645211
Its not a rule. Its a theorem.
>>9645214
I hate weebs, but fuck off reddit.

[Anonymous No.9645236]

>>9645219
it's not the fact that they're weebs that's bothering me man but the fact that they're all depressed as shit. hanging out with morose people ain't healthy. shit's contagious.

[Anonymous No.9645261]

>>9645214
if you do that, i'd join, though it would have to be math centered

[Anonymous No.9645265]

>>9645214
that exists already

[Anonymous No.9645267]

>>9645265
what is it called

[Anonymous No.9645281]

>>9645267
Proper Mathematics

[Anonymous No.9645284]

>>9645267
>what is it called
r/Math

[Anonymous No.9645286]

>>9642912
Any "cryptosystem" implementation will only ever implement functions on finite domain and codomain, so the idea of literally using such a function is ruled out. (You're restricted to systems that represent logical constructions themselves, i.e. use the computer bits to represent syntax)

[Anonymous No.9645307]

>>9645284
>hurr durr muh reddit

[Anonymous No.9645314]

https://discord.me/maths

[Anonymous No.9645361]

>>9645074
Thought that might be what you were getting at. I did have the feeling that as we moved from one topic to the next they weren't as solidly connected as other areas in math.

>>9645078
I'm patching up my seriously bad analysis foundation, but I've been doing group theory and have wondered about the connection between number theory and algebra. There's tonnes of number theory in abstract algebra, and a lot of number theory results seem to be proven using group theory. I think getting into algebraic number theory would be a good next step. Do you have a book recommendation?

[Anonymous No.9645424]

>>9645314
It ain't working.

[Anonymous No.9645439]

>What are you studying?
Calc 2
>What are your vocational plans?
Blasting people with radiation
>How do I kill myself?
Jesus loves you
>Am I going to make it?
Believe in the me that believes in you

[Anonymous No.9645446]

>>9645361
>Thought that might be what you were getting at.
I'm not the guy you were talking with. I chipped in because number theory is an ass of a subject. Every bit of number theory has been developed in a very disjointed/haphazard manner. More than any other field in math it is the outcome of an accretion of results that came about due to work on very specific problems/puzzles. To use an analogy, number theory is more like an archipelago than a continent, and most of the islands in it are isolated.

[Anonymous No.9645480]

Why do physicists abuse mathematical notation so much? A lecture I had to slog through wrote the integral of dm*r where r is after the differential but then they integrated as if r was a function of m and not a constant. It fucked me up for a second. Before anyone calls me a freshman I'm a third year math student, I've just avoided physics like the plague. I would use LaTeX but I'm a dirty phoneposter atm.

[Anonymous No.9645530]

>>9645480
Lebesgue integration is a bounded linear functional on the algebraic closure of the space of measurable functions, and for more general domains it can induce a left action, which makes the space into a left [math]C^1[/math]-module. The notation of writing the differential to the left of the integrand is suggestive of this universal property of integration.
Since you don't seem to even understand the most basic of Lebesgue theory I suggest you think twice (or perhaps thrice) before opening your mouth again in the future.

[Anonymous No.9645531]

>>9642860
xcvcv

[Anonymous No.9645561]

>>9645530
This was a Riemann integral in an intro class and by convention the differential is to the right. Yes I know the Riemann integrals are a subset of Lebesgue integrals you autistic anime poster. The domain was R^3 and that way of writing affects clarity, as evidenced by my confusion. These brainlets weren't thinking of the nuances of Lebesgue theory when they did this, they were just being flippant.

[Anonymous No.9645573]

>>9645530
>>9645561
Also for all other integrals they put the differential on the right, so they even violated their own convention. Whether or not you're right you can't be arguing against consistency.

[Anonymous No.9645613]

>>9645561
But the fact is that the notation you were shitting on in fact reflects deep, essential properties of integration in a context more general than you know.
>by convention
So if the convention was to throw shit out the window (such as in 17th century France) it's automatically right?
I expected no more from an engineer who only knows how to crank the machinery. When some notation slightly changes (with good, deep reasons) they start freaking out.
>subset
I assume you mean that the space of Riemann integrable functions are a closed subspace of the Lebesgue integrator functions, though your attempt at wording that was extremely and laughably stupid, which isn't surprising for a brainless enginqueer.
>that way affect clarity
For whom? Certainly not anyone other than yourself.
>as evidenced by my confusion
See above. The confusion of a a completely braindead rote-memorizing engineer is excusable.
>these brainlets weren't thinking of the nuances of Lebesgue theory
Certainly you weren't either, for if that were the case then you wouldn't have complained, or used hilariously egregious language when describing precise mathematical objects. The fact that this simple contradiction arises in your attempt at basic rational thinking is very telling.
>they
Who is this "they"?
>for all other cases
How is this relevant?
>they
Again, who is this "they"?
>argue against inconsistency
I'm arguing against shitting on one of the rare instances where the physicists get their maths right. Where's the inconsistency? It seems that notation is the only thing you barely understand enough to complain about.

[Anonymous No.9645635]

>>9645613
Learn to read, I'm a math major. "They" are the individuals responsible for preparing the lecture, it was an online video. They literally defined this integral as a limit of a sum, so the differential term commutes of course. So your fundamental property is illustrative of nothing in this case. They broke their own convention which is bad math, consistency is important. Even if they miraculously weren't wrong.

[Anonymous No.9645640]

>>9645613
Also allow me to turn your argument around. If they were correct about this case, then they were incorrect with respect to the dozen other integrals they defined.

[Anonymous No.9645646]

Does anyone here do math as a hobby? Is it a satisfying one?

[Anonymous No.9645658]

>>9645635
>learn to read
I can read perfectly, which I can hardly say for yourself.
>I'm a math major
What it says on a piece of paper that you will pay upwards of 50k for in 5 years (or presumably more, judging by your mental deficiency) has no bearing on what title your low IQ lands you.
>they
How exactly is the mentioning of this "they" relevant at all to this discussion of you being painfully and embarrassingly wrong on all accounts? No one aside from yourself has made any reference at all to this "they" that you seem to spout so zealously at every turn.
>illustrative of nothing
In the narrow, basic case that "they" are considering, which you seem to have a tenuous grasp already. Though the questions remains: why is this "they" at all relevant to my argument? Perhaps you need to redo your grade 8 English too.
>breaking conventions is bad math
Ah so you're a retarded redditor. The low IQ possessed by your kind is highly contagious, so kindly never reply to me anymore.

[Anonymous No.9645661]

The anime posters one /sci/ are a double edged sword. I don't care for wether or not they post anime, that's just how they identify themselves.
The good part is that the content they post is mostly good and holds up a standard. The bad part is their ideological dissing and unfounded hostility for the lulz. Makes one hard to side with.

[Anonymous No.9645664]

>>9645658
Who hurt you?

[Anonymous No.9645677]

>>9645664
>Who hurt you?
No one, I'm doin quite well today actually.

[Anonymous No.9645679]

>>9645573
>so they even violated their own convention
Why do you conclude they take it to be on either side in the first place?

It's against your convention, not more, not less.

[Anonymous No.9645685]

I came to the conclusion that /mg/ suffers with the battered wife syndrome.

Some nigga writes up gibberish, skips proofs, tell the reader to "fuck off and think" but /mg/ is aways like "i-it's m-my fault for being a brainlet, please spare me, I-I will do my best next t-time".

Moving on:
I fucking hate Topology

[Anonymous No.9645687]

>>9645661
You have to understand, the source of that vitriol is self-hate. At least it is in my case. I've called people brainlets here before. In retrospect, it wasn't always warranted. I often fear I am a brainlet myself. (I'm not the guy above by the way).

[Anonymous No.9645689]

>>9645685
>those tits
I want to pet her pussy.

[Anonymous No.9645693]

>>9645658
This is why you don't have any friends. You even pick fights with your fellow math people (not saying mathematician because I'm hardly a mathematician yet). I'm sorry pronouns confuse you, living with autism must be tough. Allow me to spell this out to you. This set of instructive videos does not exist in isolation. The convention used both in elementary calculus classes and in elementary physics classes is to have the differential delimit the integrand. Without this convention, it is difficult to discern a constant from a function. This convention is not my own but rather is defined in the textbook, so the dumb physicists flippantly disregarded their own convention. Your point about Lebesgue integrals is correct but tangential to mine. These videos defined multiple Riemann integrals over real valued functions using this convention and then violated it.

[Anonymous No.9645697]

>>9645685
That's actually a pretty good analogy.

[Anonymous No.9645702]

>>9645693
>this much projection
Sort yourself out. If me speaking facts and educated guesses is enough to send you on this (admittedly hilarious) diatribe then I truly feel sorry for you.

[Anonymous No.9645707]

>>9645693
>fellow math people
You seem to be more of an engineer. Why do you think that any mathematician would consider your kind to be "fellows"?

[Anonymous No.9645714]

>>9645702
Projection? Did you read about that in a popsci news article?
>>9645707
Engineers don't think about notation. Even if I'm wrong at least I'm asking questions.

[Anonymous No.9645723]

>>9645646
I have never understood the meaning of the word "hobby". I do mathematics out of love. Well, did. I am materially unable to pursue the love of my life at the moment.

[Anonymous No.9645725]

>>9645702
By the way, thank you for the information. I learned more from this than I ever did in that shit class. No need to be so hostile though. Can we just agree that engineers and physicists are reprehensible? Also this same class has set vectors to be equal to that scalar 0 multiple times. Is there an obscure reason that's correct?

[Anonymous No.9645727]

>>9645714
>Engineers don't think about notation.
You seem to know an awful lot about what engineers think. Where does this in-depth knowledge of their behavior come from?

[Anonymous No.9645731]

>>9645727
From being trapped in classes with them during my early undergrad.

[Anonymous No.9645733]

>>9645689
Saratoga is not for lewd, fellow math nigga.

[Anonymous No.9645738]

>>9645727
Unlike you, some of us interact with people outside our field of study.

[Anonymous No.9645740]

>>9645725
This is the first ever smart post you've written in this thread. Learn from your mistakes and maybe you'll be able to carry yourself like a mathematician on the far future.
Now if you will excuse me I'm going to print a 100pg paper from the department printer.

[Anonymous No.9645741]

>>9645725
>Also this same class has set vectors to be equal to that scalar 0 multiple times.
This question is unreadable by non-engineers. Please translate it into appropriate language so that the people here can understand.
>>9645731
Like it or not, they have rubbed off on you.

[Anonymous No.9645742]

>>9645741
Maybe, I sure hope not. Also none of you would argue that a 3x1 matrix can be set equal to a scalar, right?

[Anonymous No.9645743]

>>9645738
As a general rule, I don't consider brief encounters with barely sentient beings to be "interaction".

[Anonymous No.9645744]

Why do you guys hate engineers? I do my best to understand math but you guys keep bullying us.

[Anonymous No.9645749]

>>9645744
Because your existence threatens our secret club.

[Anonymous No.9645750]

>>9645742
>3x1 matrix
>scalar
I wouldn't know what those are, sorry.

[Anonymous No.9645757]

>>9645750
lol
Can a member of R be set equal to a member of R^3?

[Anonymous No.9645764]

>>9645757
>set equal
This is a meaningless thing to consider in general.

[Anonymous No.9645774]

>>9645764
Oh so you're just trolling, good talk.
Can a dimension 1 quantity be equal to a dimension 3 quantity in this respect?

[Anonymous No.9645779]

>>9645750
>>9645764
By the way, nobody is going to be impressed by your lack of knowledge. Brush up on your linear algebra.

[Anonymous No.9645794]

>>9645774
>quantity
This isn't standard terminology. What exactly is a "quantity"?
>>9645779
>linear algebra
I don't see it posted anywhere within this thread. Are you sure you're talking about linear algebra?

[Anonymous No.9645805]

>>9645757
As sets, yes there are one to one mappings between R and R^n for any n.

In the standard set theories, it's merely not possible to find a bijection between R and the subsets of R, as that would be a bigger set than R.

[Anonymous No.9645814]

Since we're talking about integrals, how many of you tried to redefine what an integral is or generalise received definitions? This little tirade reminded me of an episode from back when I was still an undergrad. I used to spend a lot of time rewriting all my notes by replacing all the received standard definitions with my (at the time naive idea of) "generalised" definitions. One of my few successes was when I ended up properly generalising the Riemann integral. Sure, it turned out to be yet another reformulation of the definition of the Lebesgue integral but that was one of the things that nudged my interest in the direction of foundational mathematics.

(The most time I've ever spent on trying to "generalise" something are periodic functions.)

>>9645733
Who? (You're wrong by the way. She was born to be placed on the mating press.)

>>9645757
Yes, actually. It depends on what exactly "set equal" means though.

[Anonymous No.9645817]

>>9645814
>Who?
Saratoga is the girl's name, dummy

[Anonymous No.9645825]

>>9645794
Consider two objects [math]v_1,v_2[/math] where [math]v_1 \in \mathbb{R}[/math] and [math]v_2 \in \mathbb{R}^3[/math]. Can these two objects be equal in the sense that they refer to the same object? My physics class says yes.

[Anonymous No.9645833]

>>9645817
I figured that one out myself. (As well as the fact that she's a shipgirl from Kantai Collection.)
I forgot to rewrite the 'who' as a 'why'. Please excuse me, I am drunk at the moment.

[Anonymous No.9645838]

>>9645825
Also note that I am referring to the identity relation, not some other equivalence relation.

[Anonymous No.9645849]

>>9645744
Because I'm gelous of the fame and concrete results you achieve. You use little math, sometime you use right results with uncomplete mathematical proofs, maybe complain about the difficulty of mathematics or that your teachers are no good, while you could (maybe) just selflearn. You steal our PUSSY, MOCK US, and deal with engines and cool shit. Most of engineers I know are very rude and have an enormous ego.That's why sometime is funny take a little revenge. No hard feelings.

t. my brother is one of them

[Anonymous No.9645859]

>>9644961
>>9645185
They probably meant "Tamako Market" you dyslexic shithead.

[Anonymous No.9645861]

>>9645825
Let P be the proposition that [math]v_1 \in \mathbb{R}[/math], the set of all real numbers. Let Q be the proposition that [math]v_2 \in \mathbb{R}^3[/math], the set of all ordered triples of real numbers.
Is the following statement true?
[math]\exists_{v_1}\exists_{v_2}(v_1 = v_2)[/math] where = is the identity relation.

[Anonymous No.9645864]

>>9645859
Who is one of the "regular" animeposters. (Although I haven't seen him for weeks.)

[Anonymous No.9645866]

>>9645861
Shit I meant [math]\exists_{v_1}\exists_{v_2}(P\land Q \land (v_1 = v_2))[/math]

[Anonymous No.9645867]

>>9645861
Your question is not well-posed, and unlike that other guy, I am not saying this to bust your balls.

[Anonymous No.9645870]

>>9645867
You're right, I corrected it

[Anonymous No.9645872]

>>9645861
>the set of all real numbers
There are non-standard models of set theory where the "set of real numbers" is not well-defined. You need to make your assumptions more explicit.

[Anonymous No.9645874]

>>9645866
Yes, there exists such a model. Hint: canonical embedding.

[Anonymous No.9645876]

>>9645685
>I fucking hate Topology
And here I thought every math student loved its glory. Mind to elaborate, if not cringe?

[Anonymous No.9645877]

>>9645872
In Zermelo-Fraenkel set theory.

[Anonymous No.9645881]

>>9645874
Is that a different equivalence relation though?

[Anonymous No.9645885]

>>9645881
How do you mean "different"? There is no one equivalence relation. What '=' means is model-dependent.

[Anonymous No.9645897]

>>9645885
In the Zermelo-Fraenkel set theory (with the axiom of choice if necessary), is my statement ever true. "=" refers to the identity relation on two objects in any set, i.e. 1 + 1 = 2. My physics class implicitly asserts that it is true by setting an ordered triple equal to the scalar real number 0, which I believe to be incorrect.

[Anonymous No.9645900]

>>9645897
>ever true
What do you mean precisely by "ever"?

[Anonymous No.9645901]

>>9645897
>In the Zermelo-Fraenkel set theory (with the axiom of choice if necessary), is my statement ever true.
Yes.

[Anonymous No.9645904]

>>9645897
>setting an X to equal Y
Can you elaborate? This doesn't seem to make sense.

[Anonymous No.9645908]

>>9645900
Stop it faggot. This is not funny.

[Anonymous No.9645910]

>>9645900
Is it a logically consistent statement?
>>9645901
How so? A proof or counterexample would be appreciated.
Here is the equivalence relation I refer to, as characterized by Leibniz.
"Given any x and y, x = y if and only if, given any predicate P, P(x) if and only if P(y)."

[Anonymous No.9645918]

>>9645904
Setting two objects equal is the same statement as my question, just less formal. Disregard it and address my actual question.

[Anonymous No.9645921]

>>9645861
>>9645866
>>9645867
>>9645870
>>9645872
>>9645874
>>9645877
>>9645881
>>9645885
>>9645897
>>9645900
>>9645901
>>9645904
>>9645910
>>9645918
STOP NOW.

[Anonymous No.9645925]

>>9645910
>Is it a logically consistent statement?
This is model-dependent. There are models of ZF where every statement is logically consistent.

[Anonymous No.9645934]

>>9645910
>as characterized by Leibniz
This has nothing to do with '=' in ZFC, which denotes equality/identity between sets (and in which your [math] v [/math]s are also sets).

>How so?
I already told you: you can (canonically) embed [math] \mathbb{R} [/math] into [math] \mathbb{R}^3 [/math]. Think about it yourself.

>My physics class implicitly asserts that
I don't care.

[Anonymous No.9645937]

>>9645925
This splitting hairs meme has never been funny and will never be funny.

[Anonymous No.9645938]

>>9645934
>canonically
What do you mean exactly?

[Anonymous No.9645943]

so what happens in the last month of calculus 3? am i going to be sodomized with endless, tedious arithmetic? i hate partial derivatives

[Anonymous No.9645944]

>>9645910
For [math]v_1 \in \mathbb{R}[/math] and [math]v_2 \in \mathbb{R}^3[/math], under the Zermelo-Fraenkel set theory framework, where the only axioms are those described in this framework (i.e. no adopting an axiom that turns every statement vacuously true) where [math]\mathbb{R}[/math] is the set of all real numbers, and [math]\mathbb{R}^3[/math] is the set of all ordered triples of real numbers. Define "x = y" by the following statement: [math]\forall_{x}\forall_{y}((x=y)\iff (P(x) = P(y))[/math] where P is any predicate. Is the following statement logically consistent given only the above? [math]\exists_{v_1} \exists_{v_2} (v_1 = v_2)[\math]. I hate you for making me type this, please tell me I haven't missed anything.

[Anonymous No.9645945]

>>9645938
See
>>9645937

[Anonymous No.9645948]

>>9645944
FUCK
Correction: [math]\exists_{v_1} \exists_{v_2} (v_1 = v_2)[/math]

[Anonymous No.9645950]

>>9645945
That's a genuine question. Please answer it or fuck off if you are unable to.

[Anonymous No.9645953]

>>9645910
If you model the ordered pair of two things x and y, i.e. (x,y), via
(x,y) := {{x}, {x,y}}
(this is Hausdorff's definition, the standard one)
and if you model the natural numbers via
0 := {}
1 := {0}
2 := {0,1}
3 := {0,1,2}
etc.
(Neumann ordinals, the standard one)
then, evidently, the number 1 is in the set (0,7).

If you only got sets, then you use models to talk about stuff and then you introduce those "auxilliary theorems", stuff you weren't able to prove in raw category theory, for example.

>>9645814
Sounds interesting, be a bit more concrete with your integral and periodic function definitions.

I'm a fan of creatures such as
https://en.wikipedia.org/wiki/Generalized_mean
https://en.wikipedia.org/wiki/Product_integral
or q-analogs such as
https://en.wikipedia.org/wiki/Jackson_integral

but those games can lead to endless seas. Like the whole branch of fuzzy so and so's. Or parametrized so and so's. I suppose sheaves are a good example for where it worked.

Similar to "fuzzifications", I'm a bit sad when I see people lose themselves in some generalizations, like e.g. the manifold generalizations, or breaking up topology axioms in this and that subject to play with a bit more general objects. Good if it works and you can tackle some tanglibe or at least popular problem, but often it doesn't work.

[Anonymous No.9645956]

>>9645944
You're talking to two different persons. One of them is just trying to bust your balls. I already gave you the answer. The rest is details and clerical work. (That is not how you define '=' in ZFC. You're confusing '=' as used in logic and '=' as used with sets.)

[Anonymous No.9645957]

>>9645944
Assuming the sets in question exist, yes and no.

[Anonymous No.9645958]

>>9643399
>>9644961
Are you unironically: >>9636320 HTT? If so I apologize i didn't realize this at the time. I was referring to your posts on bible, donating money, tamako market, k-on and such. But when I asked this you somehow mistook it for "French tamako market poster", if you come back i'll add you in
>>9645864
He was in the previous thread and I really like him so trying to get him in :c

[Anonymous No.9645959]

>>9645956
I'm using the logic definition deliberately. This is the definition used in my class.

[Anonymous No.9645963]

>>9645957
go home wildburger

[Anonymous No.9645964]

>>9645959
That definition is well-defined if and only if a very strong form of the axiom of choice holds.

[Anonymous No.9645967]

>>9645953
What is meant by a ``tangible" problem?

[Anonymous No.9645968]

>>9645964
Then it is certainly well-defined, since every form of the axiom of choice holds trivially.

[Anonymous No.9645969]

>>9645968
Haven't heard of this. Reference?

[Anonymous No.9645971]

>>9645964
My question doesn't have to be so strong anyway. Assuming you aren't the memeing pedant guy, they keep saying the scalar [math]0[/math] is equal to the vector [math]\textbf{0}[/math], in the typical sense. This is obviously wrong.

[Anonymous No.9645973]

>>9645959
>This is the definition used in my class.
I doubt that.

>>9645950
>That's a genuine question.
I doubt that.

[Anonymous No.9645974]

>>9645969
Please see any serious undergraduate text on set theory.

[Anonymous No.9645977]

>>9645971
They are provably equal assuming the consistency of very strong forms of transfinite induction. The converse also holds assuming strong AC for universes.

[Anonymous No.9645979]

>>9645968
>since every form of the axiom of choice holds trivially.

[Anonymous No.9645982]

>>9645977
Sure, whatever, I'm not assuming that. They're asserting that an element of one dimensional euclidean space can refer to an element of three dimensional euclidean space, which is obviously false.

[Anonymous No.9645987]

>>9645971
They keep saying that an element in the field subjacent to the vector space is equal to an element in the vector space itself? I find this hard to believe. Unless they're considering the field as a linear space over itself.
Maybe it's just an abuse of notation (they denote both elements by '0' letting you figure out from context which '0' they mean.)

[Anonymous No.9645988]

>>9645982
The consistency of strong forms of transfinite induction is provable in ZF with universes, which you have implicitly assumed by requiring that the reals form a small set.

[Anonymous No.9645991]

>>9645982
You're being trolled. You're pretty much in a newfag trap right now. That's the guy who's busting your balls.

[Anonymous No.9645992]

>>9645987
They're literally asserting that the 0 vector of 1 dimensional euclidean space is equal to the 0 vector of three dimensional euclidean space. It is an abuse of notation which was my issue in the first place. Why do physics assholes always abuse notation?

[Anonymous No.9645998]

>>9644297
> Romania
Go back to your stain on this planet you filthy Romani.

[Anonymous No.9646006]

>>9645998
>confusing romanians and romani
>thinking that poster isn't just an amerimutt

[Anonymous No.9646012]

>>9645992
>They're literally asserting that the 0 vector of 1 dimensional euclidean space is equal to the 0 vector of three dimensional euclidean space.
This is not a problem. Once again: embeddings.
We call a "scalar" an element of the field subjacent to a linear space. (The fact that you can view the field itself as a 1-dimensional linear space over itself is neither here nor there.)

[Anonymous No.9646018]

>>9646012
Yes it is a problem, they're not referring to an embedding you autistic fuck. This is equivalence in the elementary sense.

[Anonymous No.9646020]

>>9645959
The standard set theory axiom that enables you to prove equality of sets is

∀x,y. ( ∀z. (z∈x ⇔ z∈y) ⇒ x=y )

i.e. two sets x and y are equal if any set x that is in one is also in the other. I.e. if x and y have the same elements.
In logic you say things about "=", e.g. x=y => y=x, and not how you can generally prove equality of two terms in a theory. Such axioms are instead to be taken as axioms of the theory (not of the logic).
Generally adopting the Leibniz principle which involves "any P" forces you to have infinite axioms or choose a higher order logic.
However, not that since set theories (e.g. Fraenkels) merely fix axioms to use "is element of" and all statements come down to sentences involving this notion, the axiom I wrote above is also a kind of specialized instantiation of the Leibniz axiom.

Notions of equalities like in Martin-Löf type theory are also related to that, except the rules there (some super induction rules about how to prove equality) are more involved.

>>9645967
Let's say something people in other fields could know about too. Might be a bad restriction, though. Let's come from the other side: What motivates you for the generalization quest?

>>9645971
You guys discussion is a bit moot. In any case, you can put R and R^3 in bijection, but of course if you model triples as some kind of contrainer, and you got a model for 0 as number in R, then the zero vector (0,0,0) in R^3 can't be equal to 0 (in that model) as then you had the expression for 0 nested in itself. That's not a formal argument, but I suppose you can formalize this. For set theories which break with that, however, see e.g.
https://en.wikipedia.org/wiki/Non-well-founded_set_theory
There are many ways to play those things.

[Anonymous No.9646023]

>>9646020
IS THAT A-

[Anonymous No.9646028]

>>9646020
It's just physics brainlets calling vectors and scalars equal, it's indefensible.

[Anonymous No.9646031]

>>9646006
I know what I said.

[Anonymous No.9646036]

>>9645992
Buddy, it is not really an abuse of notation. In first place everybody uses 0 for the zero vector, because you understand from the context. But then it is also not an abuse of notation, because a vector space V and every subspace and scalars are part of one structure, exterior algebra / Grassmanian or whatever the hell you want. It is like considering Z and 2Z, you do not distinguisg between 0 in the first rng or in the second. Now please stop the cringe.

[Anonymous No.9646038]

>>9646036
The only cringe here is you, avatar fagging animeposter

[Anonymous No.9646043]

>>9645998
My country may not be the best place on the planet, but one of the few good things about it (similarly to many other countries ex-commie countries) is excellent math education (or was, at least while I was still in school, since the situation seems to have degraded recently, ironically because the politicians in charge decided to copy the American model).
I have family members who emigrated to the US and all their children skipped grades there (none of which are mathematically adept, not by Romanian standards anyway).

[Anonymous No.9646044]

Here's an abuse that'll trigger you guys. "Let f(t) be a function"

[Anonymous No.9646045]

>>9646038
Actually he should stop posting new game. It's /u/ trash, literally

[Anonymous No.9646046]

>>9645943
do i need to attach a pixiv anime girl to my post to get attention in this thread

[Anonymous No.9646047]

>>9646044
[math]\delta \in \mathcal{S}[/math]

[Anonymous No.9646048]

>>9646046
You'll have to do line and surface integrals, they can be tedious

[Anonymous No.9646051]

>>9646018
>This is equivalence in the elementary sense.
No, it most likely isn't. I hate to adopt that other guy's tune but you really are a brainlet.

[Anonymous No.9646054]

>>9646051
Whatever, it doesn't matter, focus on this
>>9646044

[Anonymous No.9646057]

>>9646051
I've become so frustrated I'm incoherent, you're right.

[Anonymous No.9646059]

>>9646031
So you are assuming a gypsy would be able to operate a computer. That is a very strong assumption.

[Anonymous No.9646064]

>>9646036
If we talk logic here, I'd definitely consider the zero in two non-isomorphic groups as different object, even if one embeds in the other.
If they are isomorphic, but you still speak about models in set theory, then they will generally also not be equal. In that case you can at least as the question, even if it's evil (TM).

Probably worth mentioning that R and R^3, both considered as R-vector spaces, don't permit an isomorphism in any case, afaik.

[Anonymous No.9646068]

>>9646064
Thank you for saying what I'm thinking but less retarded.

[Anonymous No.9646077]

>>9646043
At least Americans have souls. Most of the top Romani I know often learned through rote memorization and had little emotional output. Romani are specialized at such a young age that they do not even learn high school history. Romania is a third world country that dedicates all of their recourses to young aspies to win the international competitions.

[Anonymous No.9646078]

>>9646064
> I'd definitely consider the zero in two non-isomorphic groups as different object, even if one embeds in the other.
You're an idiot then. Not all subgroups are isomorphic to the whole group, yet all a group's subgroups share their 0s.

[Anonymous No.9646083]

>>9646077
I doubt you know any "top Romani".

[Anonymous No.9646086]

>>9646078
A vector in R^2 has dimension 2 so it is not equivalent to a vector in R^3

[Anonymous No.9646088]

>>9646086
>dimension
Irrelevant.

[Anonymous No.9646091]

>>9646088
Wrong

[Anonymous No.9646093]

>>9646064
> never heard of monster model
You talk about logic, but the only thing I read is blablabla. I feel sorry for myself for being baited, I'm done.

[Anonymous No.9646098]

>>9645953
I think I'm one of those people who make you sad anon.

[Anonymous No.9646103]

>>9646091
No. Because embeddings.

[Anonymous No.9646110]

>taking a linear algebra test
>getting tripped up on a question asking if my previous Matrix was invertible based on it's determinant
>can't remember if det A = 0 means A it's invertible or not
>have a brain blast and remember determinants are just the fucking area of a parallelogram
>and if det A = 0 obviously there'd be no area, making the the vectors linearly dependent
>and therefore not invertible per the Invertible Matrix Theorem.

>tfw utilized different theorems and the geometric translations of all this shit to intuitively figure out a problem.
Is this where Math becomes fun? I know this is probably basic-bitch shit, but intuitively figuring out this problem was pretty satisfying.

[Anonymous No.9646111]

>>9646078
For a group considered as a concrete set with a binary function to model their binary operations, and the isomorphism considered as a function into intself, then yes, you're right in that regard.
No reason to through around insults, though. Sometimes I feel like people feel some sort of general stress release when they can attack someone online. Is that it?

Coming back, however, for a vector space over a field, to say that an element of the field IS also an element of the vector space sure is a stretch. Even if plain text notation might use one symbol for two object in the respective structure.

[Anonymous No.9646112]

>>9646103
Wrong

[Anonymous No.9646122]

>>9646111
> to say that an element of the field IS also an element of the vector space sure is a stretch.
I agree. Refer back to >>9645987 and >>9646012

>>9646112
See
>>9646103

[Anonymous No.9646128]

>>9646098
Well, elaborate on your quests.

I was thinking more about nLab people which you can watch get on academic tangents for 2 year before coming back to writing papers about the problems they started out with, and also my own old Prof who ended up in a shit branch which only finds interest in some other lonely Profs somewhere on the other end of the globe in Japan.

To put this on a related tangent: I think getting kids isn't really helping with any academic persuit (by which I mean a family can mean the effective end of a good mans output). Thoughts?

[Anonymous No.9646130]

>>9646122
Wrong

[Anonymous No.9646144]

>>9646048
thanks i guess. also reeee

[Anonymous No.9646155]

>>9646110
inb4 someone tries to argue that the determinant is not the area parallelogram

[Anonymous No.9646168]

PS OP you tricked me into thinking I'll find out what a Zhu algebra is here. So tell.

Googling brings up W-algebras. is this related to W-types? Probably not, because Kac was involved and he seems too old and so I conclude it's closer to Lie-Algebras.

On that note, what's your favorite book on algebraic groups?

>>9646110
Yes, I think that's a quite good example to that effect.

As an aside, you could also have come up with the right conclusion by consider any matrix whatsoever. E.g. "The unit matrix is invertible, and the unit matrix has determinant one, so the invertible ones are the ones with nonzero determinant".

[Anonymous No.9646174]

>>9646168
There's so many different statements equivalent to det A = 0 so your statement is kind of vacuous.

[Anonymous No.9646192]

>>9645361
Stewart-Tall is good for ANT, although A classical introduction to modern number theory is a GOAT book to delve into number theory

[Anonymous No.9646196]

>>9646128
>Well, elaborate on your quests.
My main idea was to "split" a periodic function into a pair of (multi-)functions: a "base" (naively, the starting function on a fundamental interval of choice) and a "transport" function, whereby the periodic function was the composition of these two.
And then I started to fiddle with each independently and tried to recover as much information about the starting "generalised"-periodic function from this pair. (Which ended with me re-discovering... fractals.)

>Thoughts?
I'm a NEET who dropped out of grad school a little less than a year ago. So I don't even want to think about such things.

[Anonymous No.9646203]

>>9646196
>I'm a neet
lmao at your life
Not good enough at math to work in academia? Don't worry buddy, you'll get there eventually.

[Anonymous No.9646204]

>>9645613
holy shit /r/murderedbywords

[Anonymous No.9646212]

>>9646204
You have to go back

[Anonymous No.9646218]

>>9646110
could you have just seen that the 0 matrix has determinant zero and is obviously not invertible you dipshit

[Anonymous No.9646221]

>>9646212
>You have to go back
Go back where?

[Anonymous No.9646224]

>>9646212
brb posting on /r/4chan

[Anonymous No.9646225]

>>9646196
>My main idea was to "split" a periodic function into a pair of (multi-)functions: a "base" (naively, the starting function on a fundamental interval of choice) and a "transport" function, whereby the periodic function was the composition of these two.
>And then I started to fiddle with each independently and tried to recover as much information about the starting "generalised"-periodic function from this pair. (Which ended with me re-discovering... fractals.)

[Anonymous No.9646233]

>>9646218
I had to prove the opposite.

[Anonymous No.9646234]

>>9646233
>I had to prove the opposite.
Mathematicians use "we", not "I".

[Anonymous No.9646238]

>>9646233
then use the identity you fucking retard

[Anonymous No.9646241]

>>9646234

[Anonymous No.9646242]

>>9646234
>Mathematicians use "we", not "I".

[Anonymous No.9646246]

>>9646238
>retard
Why the ableism?

[Anonymous No.9646249]

>>9646168
>PS OP you tricked me into thinking I'll find out what a Zhu algebra is here. So tell.
https://arxiv.org/abs/1804.00020

[Anonymous No.9646252]

>>9646238
I did though

[Anonymous No.9646256]

>>9646225
S-shut up.

[Anonymous No.9646257]

>>9646234
>>9646196
>>9646241
>>9646242
>it's another "neet larps as a mathematician" episode

[Anonymous No.9646260]

>>9646256
>stuttering over text

[Anonymous No.9646261]

>>9646257
I never said I'm a mathematician.

[Anonymous No.9646262]

>>9646257
>it's another "neet larps as a mathematician" episode
But that's the entire general.

[Anonymous No.9646269]

>>9646260
D-deal with it.

[Anonymous No.9646270]

>>9646261
>I never said I'm a mathematician.
>>9646262
I'm so tired

[Anonymous No.9646271]

>>9646260
>>stuttering over text
Who are you quoting?

[Anonymous No.9646274]

>>9646271
(You)

[Anonymous No.9646284]

>>9646270
Please stop making fun of me. It hurts.

[Anonymous No.9646288]

>>9646284
Come here.

[Anonymous No.9646290]

>>9646284
>Please stop making fun of me. It hurts.
good, you need to be humbled

[Anonymous No.9646308]

What are some topics that will appear in the next /mg/?

[Anonymous No.9646312]

>>9646308
>What hormones should I buy?
>Look at this cartoon girl.
>Are my socks cute?
>How do I kill myself?
>Can NEETs be mathematicians too?

[Anonymous No.9646313]

>>9646288
You are a kind anon. I wish I could repay you somehow.

>>9646290
This is too much humiliation for today. I'm going to sleep now.
(Fuck you too buddy.)

[Anonymous No.9646317]

>>9646308
>This is not well-defined.
>Please refer to the physics thread >>>/toy/physics
>There exists sets which cannot be a given a group structure
etc.

[Anonymous No.9646319]

>>9646313
I hope you don't wake up

[Anonymous No.9646332]

>>9646317
>>There exists sets which cannot be a given a group structure
This is true, and in fact, cryptosystems based on this are what keep your online banking secure.

[Anonymous No.9646337]

>>9646313
>(Fuck you too buddy.)
Do you need to swear?

[Anonymous No.9646339]

>>9646313
I'm far from kind. I just believe in the solidarity of troubled souls. Sleep tight.

[Anonymous No.9646347]

>>9646339
>I just believe in the solidarity of troubled souls.

[Anonymous No.9646369]

>>9646288
this is the sweetest thing I've ever seen on 4chan

[Anonymous No.9646375]

>>9646369
>this is the sweetest thing I've ever seen on 4chan

[Anonymous No.9646395]

[math]P \vee \neg P [/math]

Prove me wrong.

[Anonymous No.9646398]

>>9646395
>Prove me wrong.
The burden of proof is on you.

[Anonymous No.9646401]

>>9646395
>Prove me wrong.
The burden of proof is on you.

[Anonymous No.9646407]

>>9646398
>>9646401
no u samefag

[Anonymous No.9646409]

>>9646398
>The burden of proof is on you.

[Anonymous No.9646410]

>>9646196
You know that Cantor was working on periodic function when he derailed math forever

>... Heine proposed that Cantor solve an open problem that had eluded Peter Gustav Lejeune Dirichlet, Rudolf Lipschitz, Bernhard Riemann, and Heine himself: the uniqueness of the representation of a function by trigonometric series. Cantor solved this difficult problem in 1869. It was while working on this problem that he discovered transfinite ordinals, which occurred as indices n in the nth derived set Sn of a set S of zeros of a trigonometric series. Given a trigonometric series f(x) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series
>...and then he noticed that Sω would also have to have a set of limit points Sω+1, and so on. He had examples that went on forever, and so here was a naturally occurring infinite sequence of infinite numbers ω, ω + 1, ω + 2, ...[37]
>Between 1870 and 1872, Cantor published more papers on trigonometric series, and also a paper defining irrational numbers as convergent sequences of rational numbers. Dedekind, whom Cantor befriended in 1872, cited this paper later that year, in the paper where he first set out his celebrated definition of real numbers by Dedekind cuts. While extending the notion of number by means of his revolutionary concept of infinite cardinality, Cantor was paradoxically opposed to theories of infinitesimals of his contemporaries Otto Stolz and Paul du Bois-Reymond, describing them as both "an abomination" and "a cholera bacillus of mathematics".[38] Cantor also published an erroneous "proof" of the inconsistency of infinitesimals.[39]

>>9646249
Ah, looks very QFT motivated. How or why does the Weierstrass elliptic function enter the frame?

[Anonymous No.9646417]

>>9646410
ω looks like a ballsack lol

[Anonymous No.9646425]

>>9646407
>samefag
>20 seconds apart

[Anonymous No.9646428]

>>9646395
>Prove me wrong.
We use single-valued logic as the standard here, where statements can only be proven to be true, not false.

[Anonymous No.9646430]

>>9646428
>We use single-valued logic as the standard here, where statements can only be proven to be true, not false.

[Anonymous No.9646477]

>>9646417
>ω
(ง○ω○)ง I'm going to beat you up anon

[Anonymous No.9646541]

>>9646083
> my opponent said something logical so I will attack their character
I know so many top Romani that I would be doxxed if I listed them all.

[Anonymous No.9646552]

>>9646541
To be clear, I know 5 IMO Gold medalists from Romania.

[Anonymous No.9646610]

All I want is to git gud enough to understand topological data analysis

The prospect of mapping any real world statistical relationship you can think of to topological structures is just ultra cool to me

[Anonymous No.9646613]

>>9646610
pic related

[Anonymous No.9646692]

>>9646410
>looks very QFT motivated
Yes because everything with "quantum" in its name is motivated by physics.
>this fucking stupid

[Anonymous No.9646710]

>>9646692
Yeah, my bad. It's clearly motivated by empirical AQFT and empirical/concrete string theory. We have actually read this paper with my TQFT group yesterday. Didn't understand much though....
*posts some 3 dimensional whore*

[Anonymous No.9646843]

hank is gay

[Anonymous No.9646948]

If I master these three books, will I have a solid undergraduate understanding of Geometry?

[Anonymous No.9646950]

>>9646948
>geometry
>2018
lol

[Anonymous No.9646963]

>>9642912
Do you mean surjective linear functions?

[Anonymous No.9646965]

>>9646948
>https://www.maa.org/press/maa-reviews/an-axiomatic-approach-to-geometry-geometric-trilogy-i
>This is the first in a trilogy, all three volumes of which are now available. The two other books are entitled, respectively, An Algebraic Approach to Geometry and A Differential Approach to Geometry. Algebraic Approach primarily covers affine, Euclidean and projective geometry from the perspective of linear algebra, and then culminates in a chapter introducing the basics of algebraic geometry. Differential Approach covers classical differential geometry of curves and surfaces, and shows how the power of calculus can be used to shed light on geometric ideas. Together with the book now under review, these books do an excellent job of conveying the broad sweep of geometry, and give considerable insight into the various ways in which one can approach the subject.

Skip axiomatic and read the algebraic and differential books.

[Anonymous No.9646966]

>>9646710
>Yeah, my bad. It's clearly motivated by empirical AQFT and empirical/concrete string theory. We have actually read this paper with my TQFT group yesterday. Didn't understand much though....

[Anonymous No.9646973]

>>9646966
Empirical mathematics with strong physical intuition, like TQFT and string theory, is the only kind which is rigorous and well-defined. The school of Grothendieck/Serre needs to be destroyed and forgotten with all its meaningless abstractions.

[Anonymous No.9646975]

>>9646973
>Empirical mathematics with strong physical intuition, like TQFT and string theory, is the only kind which is rigorous and well-defined. The school of Grothendieck/Serre needs to be destroyed and forgotten with all its meaningless abstractions.

[Anonymous No.9646976]

>>9646950
I guess we know which subject you got a bad grade in.

[Anonymous No.9646977]

>>9644420
Just study linear algebra, abstract algebra, and matrix groups for most of that shit. Entry-level brainlet cuck

[Anonymous No.9646984]

>>9646950
>>9646977
Why are you so angry, anon? People are trying to learn something. That's a good thing.

[Anonymous No.9647232]

>>9646541
>>9646552
>idiotic /pol/ memes
>logical
Whatever floats your boat.
>I know 5 IMO Gold medalists from Romania.
Does it matter? After all, Romanians don't have souls.

[Anonymous No.9647237]

>>9646843
Literally who?

[Anonymous No.9647242]

New thread when?

[Anonymous No.9647265]

>>9646260
N-n-newfag

[Anonymous No.9647325]

Are the people who make this threads the same pathologically bitter people that destroy them? If so, why?
You ruin the place for everything when every second post is an angry insult. Just don't get emotionally involved with peoples positions that you happen to disagree with.

[Anonymous No.9647365]

>>9647362