What are you studying, /mg/?

# /mg/ - Math general - Perfectoid edition

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

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

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

Scholze is the personification of redd*t

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

Appart from the memes, functional analysis deals with this shit, i.e. linear spaces with eveb an ubcoubtable basis such as function spaces. It's used in fourier analysis and harmonic analysis which is useful for PDE, but yea

All vector spaces have a basis no matter how much the retards here yell.

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

Appart from the memes, functional analysis deals with this shit, i.e. linear spaces with eveb an ubcoubtable basis such as function spaces.

I said no basis, not uncountable basis.

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

The real vector space of functions [math] \mathbb{R} \to \mathbb{R} [/math]

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

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

The burden of proof is on you.

isnt (1) the basis??

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

**proofwiki.org**

And why does it generate the whole space?

hmm because you can multiply 1 for every number and you get the whole R

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

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

The space is all the functions, not all the real numbers.

They are isomorphic vector spaces.

∀x∈R let Vx:R→R,Vx(y)=χ{x}({y}), these functions are clearly linearly independent, and ∀f:R→R,f=∫Rf(x)⋅Vx(x)dx

That's not necessarily a linear combination.

Next?

The space is all the functions

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

ok, so you have no argument lmao

There is no notion of multiplying functions in this vector space.

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

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

By reading definitions carefuly

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

You can have linear combinations.

multiplying by the identity function is not a fucking linear combination

multiplication is not linear

Are we reaching new level of retardness or what?

But the space of functions doesn't form a field you inbred retard, so you cannot form a vector space of the space of those functions over itself.

The real, as the set of real numbers which are not the same as the spacw of real valued functions.

[eqn]

x^2 - 5 = 2\\

\frac{d(x^2 - 5)}{dx} = \frac{d2}{dx}\\

2x = 0\\

x = 0

[/eqn]

**en.wikipedia.org**

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

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

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

well, ok

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

He's a pretty decent researcher apparently.

Just very autistic about foundational stuff I guess.

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

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

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

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

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

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

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

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

im a first year math major

not really sure what linear transformations are

How does this even happen?

A linear transformation is something that maps vectors to other vectors and which is "linear", which has several equivalent definitions. The standard one in the context of formal math—albeit maybe not the most enlightening one—is that a function [math]f[/math] from one vector space to another is called "linear" if

1. for any vectors [math]v, w[/math] in the source space, [math]f(v + w) = f(v) + f(w)[/math], and

2. for any vector [math]v[/math] in the source space and scalar [math]a[/math], [math]f(av) = af(v)[/math].

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

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

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

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

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

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

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

Zorn's Lemma.

So you can not prove every vector space has a basis unless you assume every vector space has a basis.

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

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

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

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

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

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

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

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

differential geometry

although you'll need to learn some topology first

Lee's topological manifolds is good, and it's written with preparation for his smooth manifolds book in mind, which I haven't read but have heard good things about

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

Lee's topological manifolds is good, and it's written with preparation for his smooth manifolds book in mind, which I haven't read but have heard good things about

I vouch for both of them, and recommend the interested user to do all the exercises and problems.

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

Numerical integration seems to suggest that it does

Are you sure about that?

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

Only people from the ENS get tenure, the others are just weeded out with a useless "PhD" which isn't even a real PhD.

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

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

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

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

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

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

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

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

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

What do they become?

Why should I have to leave my home country to the jews?

Why shouldn't you?

They become high school teachers.

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

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

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

Preach, sister!

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

Let [math]\mathbf F[/math] be a subfield of [math]\mathbf C[/math]. If [math]\mathrm{Vect}_\mathbf F\,B[/math] is dense in [math]\mathbf H[/math] for its euclidean norm, then for all [math]\mathbf x\,\in\,\mathbf H[/math], [math]\left( \left\langle \mathbf b \mid \mathbf x\right\rangle\,\mathbf b \right)_{\mathbf b\,\in\,B}[/math] is summable and [math]x\ =\ \sum_{\mathbf b\,\in\,B} \left\langle \mathbf b \mid \mathbf x\right\rangle\,\mathbf b[/math]

What do I do next? Only a finite number of coordinates of [math]y[/math] are non-null btw, that's why I can use the inner product like that.

tfw you realize that semantics is left-adjoint to syntax

Show me your comfiest adjunctions, /mg/

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

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

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

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

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

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

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

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

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

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

but your hobbies sound comfy, I like you.

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

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

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

you too!

vidya is the activity that makes me the most relaxed.

I get way too autistic with books and end up excited instead of calm.

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

**mathoverflow.net**

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

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

I still despise the ENS and everyone involved in it (except for me).

so this is the power of critical thinking...

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

Linear combinations in vector spaces are finite sums.

Do okay in math, definitely not a strong suit

Love Econ

Major in it

Meet advisor

So how good are you with math?

Fuck guys, I just want to learn about the economy.

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

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

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

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

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

This string of though is slightly different from assuming the existence of a basis outright. Mostly because a mathematician may find it more plausible to assume AoC than existence basis as an axiom.

It is circular reasoning to assume what you are meant to prove. There is an absence of evidence regarding the existence of a proof that every vector space has a basis without assuming every vector space has a basis (but this is not evidence of absence).

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

absence of evidence

circular reasoning

evidence of absence

Refer to /lit/ if you wish to discuss such topics.

absence of evidence

circular reasoning

evidence of absence

Refer to /lit/ if you wish to discuss such topics.

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

What's with the "why the _____?" meme?

I swear I only see it on this board

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

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

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

Which is of course a mathematical absurdity, since every vector space is infinite dimensional.

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

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

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

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

**math.ucla.edu**

Math 131AH: Analysis (Honors)

Math 170A: Probability Theory

UCLA department of Mathematics. What are you trying to do

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

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

you can check the archive to see the full extent of this mental illness.

Imagine the kind of person who reads an archive of Veeky Forums

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

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

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

What is this physishit leaf/chink's problem?

You just listed them.

This general has been abolutely dog shit these last few months.

And that's probably going to continue if the poor creature doesn't take its medication.

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

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

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

Mathematics major is a very risky one

Every non-retard who signs up for one knows that. How does this imply that your risky choices are somehow not your responsibility?

Getting some engineering knowledge

Do that elsewhere. You wouldn't study chemistry in a philosophy department. Similar reasoning applies to any two distinct fields.

I know quiet a few mathematicians who didn't get their positions as researchers

I'm not surprised that you know quite a few people who aren't smart since you seem to be like that yourself. Now fuck off to some other board if you wish to discuss off-topic trash such as your low intelligence and inability to be a researcher, i.e. a mathematician. I suggest trying out /adv/.

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

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

Every non-retard who signs up for one knows that.

Where did I imply that they don't know? It is their responsibility, but that doesn't mean it's wrong to give them good credit.

Do that elsewhere. You wouldn't study chemistry in a philosophy department. Similar reasoning applies to any two distinct fields.

No. It's good to be competent in other areas too. And that's a very retarded counter-argument, chemistry won't give you nearly as a wide range of job fields to apply to as engineering, and chem is more irrelevant to philosophy than engineering is to math.

I'm not surprised that you know quite a few people who aren't smart since you seem to be like that yourself. Now fuck off to some other board if you wish to discuss off-topic trash such as your low intelligence and inability to be a researcher, i.e. a mathematician.

If you think it's about being "smart" then you are completely fucking retarded, you should kill yourself for that. It's the industry's fault, there's no high demand for mathematicians they have to compensate for the lack of positions in some way, and having a stable job until you can start your math career is a very good one. There are people way smarter than you'll ever be (honestly you seem pretty retarded so I assume it's a lot) but struggle to find a position because of the lack of demand, but eventually they'll get in and do some research. Having a job on the side so you don't become a hobo or have to do some other major isn't a bad backup plan.

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

chemistry won't give you nearly as a wide range of job fields to apply to as engineering

That's beside the point. Chemistry and philosophy are merely placeholders for any two distinct fields (which engineering and mathematics are, regardless of what you and other engineering filth tries to claim). You seem to be incapable of tackling basic abstractions. No wonder you can't get a job as a researcher.

No.

So you think that math departments are an appropriate place for engineering merely because retards like you can't make proper life choices such as going to engineering school or learning engineering on the side (outside of math departments) if they can't handle the risks involved with majoring in mathematics? I don't think someone who really believes that everyone has to accommodate his poor decisions can be reasoned with.

chem is more irrelevant to philosophy than engineering is to math

In what way precisely is engineering (something which isn't used in math) "relevant" to math?

If you think it's about being "smart" then you are completely fucking retarded

Not having extremely low intelligence is a prerequisite which clearly neither you nor your friends possess.

Having a job on the side so you don't become a hobo or have to do some other major isn't a bad backup plan.

Try actually reading my posts before replying to them. I never claimed that having a job on the side is a bad backup plan for those who aren't in any way mathematically exceptional. But having a side job is clearly possible without trying to poison math departments with engineering. That should be obvious even to someone like you.

I can't even. It's so sad to see how stupid you are, yet ironically act smart.

Just go back to memeddit please and be the person everyone dislikes because of how autistic he is irl, you aren't worthy of anything

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

It was directed towards you

I might be stupid, but I'm clearly above your level of mental retardation since I can understand simple things such as the distinction between engineering and math.

you aren't worthy of anything

Says someone who has deep and unresolved personal issues regarding not being able to get the job he initially wanted.

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

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

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

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

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

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

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

They're crucial stepping stones to learning Measure Theoretic Probability

It's not surprising that engineering topics would be a stepping stone to learning more engineering topics.

What do you consider to be maths? Algebra? Topology?

Those and their subfields would be almost the entirety of math. Correct.

There's more out there than just abstract shit that no one cares about

Yes, clearly there is non-abstract stuff outside of mathematics. Why did you feel the need to mention this?

Falling for the bait.

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

They the same stuff every thread.

Truth doesn't really change from thread to thread so I wouldn't expect anything else.

tfw your name will never be remembered for anything significant

you will never contribute anything to modern mathematics

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

the only things I have to my name are two lame ass articles that are so mediocre no one has referenced them and I am embarrassed of telling anyone I wrote them

failed postdoc after only 4 months

back to being a neet

my money will run out in 2 months tops

can't seem to find the will to get a job

have no idea what I even want to do at this point

Is suicide such a cowardly option ?

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

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

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

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

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

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

Anything with the prefix "algebraic" or suffix "algebra" and every subfield.

The burden of proof is on you to show that those are mathematics courses.

No, just how to equations that are seemingly opposite have the same result

Or is this only the case for this one example and not a rule of sorts?

if (a/b)^n = 1 then a^n=b^n

since ([x-1]/[1-x])^2=(-[1-x]/[1-x])^2=(-1)^2=1, you have (x-1)^2=(1-x)^2

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

wuts a metric

wuts an operation

Google it nigger

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

Which of these are mathematics, and which are not?

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

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

The burden of proof is on you.

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

Logic is a subset of mathematics.

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

Therefore all of those are mathematics.

Logic is a subset of mathematics.

Wrong. Only some subsets of logic are subsets of mathematics.

logic

mathematics

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

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

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

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

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

It's a pretty elementary result that fields do not have nonzero nilpotent elements in classical mathematics. You might be interested in this, though **ncatlab.org**

to begin with, it might involve not saying things like

A set is by definition a certain kind of category.

which are clearly only intended to provoke a reaction

hopefully it should be clear that i'm referring to the form and subtext of that quote, not to its semantic content (not that there is much)

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

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

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

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

hey /math/

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

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

you guys are fucking lucky.

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

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

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

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

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

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

you guys are fucking lucky.

must be why people here talk about killing themselves so often huh