/sci/ - Science & Math

>>9505121
Did you just copy the tags from arxiv? top kek.

>>9505121
And yet you are here, waiting for pity replies on your 4/10 bait

>>9505121

>>9505121
>faggots
Why the homophobia?

>>9505121
Good thing we can still talk about harmonic analysis, boys. Singular integrals arouse me to no end.

Guys, if I have two vectors (u, and v) orthogonal to another vector (a), is the sum of u and v also orthogonal to that vector (a) ?

>>9505269
yes, this should be clear and i recommend you prove it to yourself if it's not, both with a picture and with direct computation

>>9505273
Is it because summing u and v with regards to their orthogonality on a yields

a1(u1+v1) + a2(u2+v2)+...+a3(uk+vk), which must be zero?

>>9505269
<u,a> = 0
<v,a> = 0

<u+v,a> = <u,a> + <v,a> = 0 + 0 = 0

>>9505279
(i assume you mean ak(uk+vk) for the last term.)
apply the distributive law:
[eqn]\sum_{i=1}^k a_i(u_i + v_i) = \sum_{i=1}^k a_iu_i + a_iv_i = \left(\sum_{i=1}^k a_iu_i\right) + \left(\sum_{i=1}^k a_iv_i\right) = 0 + 0 = 0[/eqn]
see where i apply the orthogonality of u and v to a here? this is the method of direct computation; draw pictures in [math]\mathbb{R}^2[/math] and [math]\mathbb{R}^3[/math] to get the proper intuition for why this is true.

>>9505290
>>9505293

Gotcha, thanks for the help guys

>>9505293
>>9505279
>assuming finite-dimensionality

>>9505316
>assuming my teacher assumed an infinite dimensionality when she gave me this problem.

>>9505121
What the fuck do you want to talk about then?

>>9505322
>>assuming my teacher assumed an infinite dimensionality when she gave me this problem.
Not assuming finite-dimensionality doesn't mean assuming infinite-dimensionality.

>>9505323
>What the fuck do you want to talk about then?
Do you need to swear?

>>9505331
What does it mean then?

>>9505316
i think i was reasonably smart to assume that anyone asking on /sci/ "is the sum of two vectors, each of which is orthogonal to a, again orthogonal to a?" is only concerned about the finite case. if you want to share any details about the infinite-dimensionality case, i'm sure some people here would be interested, so i'll encourage you to do so.

>>9505335
your teacher may not have made any assumptions at all, in which case you way want to separate your proof into two cases: finite-dimensions and infinite-dimension. not assuming one doesn't imply the assumption of the other - it's possible that neither were assumed.

>>9505347
>i think i was reasonably smart to assume that anyone asking on /sci/ "is the sum of two vectors, each of which is orthogonal to a, again orthogonal to a?" is only concerned about the finite case.
That's not smart at all.

>>9505121
Does anyone know of a proof of the Excision Theorem (for singular homology) that doesn't make you want to kill yourself?

>>9505335
>What does it mean then?
It's true for all vector spaces.

>>9505348
if my objective is helping the poster as quickly as possible, taking the time to write out a proof for every possible case they might be concerned with would be inefficient if they were only concerned with a subset of those cases. it is smart, but there is a risk that i will not actually address the poster's issue.
that being said, i don't think it matters whether or not the vector space is infinite-dimensional for the poster's question. however, again, the vast majority of people asking that question are not concerned with the infinite dimensionality case (there is no proof of that proportion, obviously, but i think you'll find any polls of that population will corroborate my claim) so it makes no difference.
i get the feeling you've never actually taught anyone before.

>>9505365
> the vast majority of people asking that question are not concerned with the infinite dimensionality case (there is no proof of that proportion
see >>9505290

>>9505365
>taking the time to write out a proof for every possible case they might be concerned with would be inefficient if they were only concerned with a subset of those cases.
The general proof is shorter than what you wrote.

>>9505375
i think might have quoted a bit more than necessary.
>>9505384
the general "proof" follows directly from the definition of inner product, as the other anon gave, so i took a wild guess that isn't based whatsoever on my experience in helping undergraduates with these things that perhaps the poster was not familiar with the more general notion of inner products.

>>9505391
>so i took a wild guess that isn't based whatsoever on my experience in helping undergraduates with these things that perhaps the poster was not familiar with the more general notion of inner products.
I would suggest taking guesses actually based on experience then so that you don't make unnecessary assumptions.

>>9505365
Your "proof" might have been useful if was generalizable to the infinite-dimensional case, but it does not since it relies on the existence of a basis.

>>9505121
Yeah this place is shit but where should I go for math discussion? I don't like reddit or physicsforums. Is there some decent math forum?

>>9505421
if you have a specific question, then use math.stackexchange or mathoverflow

>>9505421
ideally, you'll have colleagues and coworkers to discuss things with, which is a lot of fun
>this place is shit
i haven't been here too long, but i agree - having to wade through posts like >>9505420 who fail to understand that what is useful to one may not be useful to another must be suffering

>>9505257
(You)

>>9505436
Yep, but I'm looking for just general math talk, nothing specific.

Nietzsche looks like the cop on Stranger Things

>>9505269
Think about it geometrically. Any two non parallel vectors span a plane. If another vector is perpendicular to each of these vectors, then it is necessarily perpendicular to the plane. The vector u+v is clearly in this plane, and hence it is orthogonal to the plane normal vector

>>9505489
something I should have put in my book but it slipped my mind. Once you add a third orthogonal vector all the no-chaos-in-the-plane theorems become irrelevant

Anyone here taking applied math? I'm switching from chemistry because there are no jobs, and I think I would like to do something which intersects math, medicine, tech, and sales.

>>9505545
Applied math is a meme.
You can take pretty much any of the courses offered in an applied math department in a normal math department.

>>9505574
>You can take pretty much any of the courses offered in an applied math department in a normal math department.
Where are applied math courses not offered by the math department?

>>9505576
Sorry, I don't understand what you are asking.

>>9505574
where is the applied math department different from the pure math department? there's generally only a single math department with a pool of courses, some of which are prescribed to applied math majors (e.g. numerical analysis) and others are prescribed to pure math majors (e.g. topology) but they share most courses

>>9505594
Oh I get it now.
There are many. Just googling it shows you some of them:
https://www.google.com/search?q=applied+mathematics+department

>>9505585
>Sorry, I don't understand what you are asking.
I.e. where does there exist an "applied math department" that is separate from the "normal math" department?

>>9505121
Can someone recommend a book to practise topology/metric spaces tasks(thus it should include answers).

>>9505545
>applied math
No such thing.

>>9505121
I'm new to set theory. Is this piece of reasoning correct (*Especially* the step where I let X=A)?

I haven't worked with proofs that involve the knowledge of a conditional as part of the proof, normally I just prove conditionals. I guess a more general question would be, if I know some conditional to be true in a proof, if I manage to manipulate the antecedent to a tautology and the consequent to what I'm trying to prove, would that be a correct proof?

Suppose [math]\mathscr{P}(A) \subseteq\mathscr{P}(B)[/math]. This means that [math]X\in\mathscr{P}(A)\rightarrow X\in\mathscr{P}(B)[/math] for some set [math]X[/math]. Thus [math]X\subseteq A\rightarrow X\subseteq B[/math]. Let [math]X = A[/math]. Then [math]A\subseteq A\rightarrow A\subseteq B[/math]. Hence [math]A\subseteq B[/math] (Since [math]A \subseteq A[/math] is always true).

>>9506416
>This means that X∈P(A)→X∈P(B) for some set X.
You don't want the "for some set X" here.

The rest is fine, but the faster way to do it is: assume P(A) is a subset of P(B). since A is an element of P(A), A is an element of P(B), so A is a subset of B.

>>9506416
for every set X, not for some set.

>>9506426
>>9506437
Ah shit, meant "for an arbitrary set X" or "for every set X".

Thanks! What about this part, though?
>if I know some conditional to be true in a proof, if I manage to manipulate the antecedent to a tautology and the consequent to what I'm trying to prove, would that be a correct proof?

Also, that faster way was really clever, how did you come up with it? Was it just seeing that A is an element of P(A)? If you notice my way is more "mechanical", just working from the definitions and seeing where I land.

Its possible to learn vector calculus with just a week?

>>9506471
I think he's saying that you should put the description before you use the symbol so, instead of saying

This means that X∈P(A)→X∈P(B) for some set X.


You would say:

This means that for some set X X∈P(A)→X∈P(B)

This would make your proof easier to read :DD

A topologic space can be defined by requiring closure under arbitrary unions and finite intersections. Members of this space are called open sets.

Then wtf are measurable sets, since they are just define to belong to a [math]\sigma[/math]-algebra?

>>9506858
https://en.wikipedia.org/wiki/Sigma-algebra#Definition

>>9506863
what i meant was that if members of a topological space generalize the notion of open sets, the what do [math]\sigma[/math]-algebras generalize the notion of? i.e. what is the intuition behind calling members of a [math]\sigma[/math]-algebra measurable (other than we can define a measure on it).

>>9506471
>>if I know some conditional to be true in a proof, if I manage to manipulate the antecedent to a tautology and the consequent to what I'm trying to prove, would that be a correct proof?
Yes,
https://en.wikipedia.org/wiki/Modus_ponens

>>9506515
If it's just differentiation, sure.
If it's just integration, probably.
If it's both, no way.

>>9506956
I don't think sigma-algebras really generalize anything the way topologies do. I'll try to give you my idea of why their axioms make sense. It's not a perfect motivation but here goes

I like to think of sigma algebras in terms of "if I know how to measure some sets, what other sets can I measure?". To be more precise:
Suppose we have some space [math] X [/math], some collection [math] \mathcal{F} [/math] of subsets of [math] X [/math] we can measure, and a measure [math] \mu [/math]. For this to make sense I will assume that the measure is finite i.e. [math] \mu(X) < \infty [/math]. This of course means that [math] X \in \mathcal{F} [/math] as well.

If [math] A \in \mathcal{F} [/math] then we can measure its complement: [eqn] \mu(A^c) = \mu(X) - \mu(A) [/eqn] and so our collection of measuralbe sets must be closed under taking complements.

If [math] A_1, A_2, \ldots \in \mathcal{F} [/math] are disjoint then we can measure their union as well: [eqn] \mu(\bigcup_i A_i) = \sum_i \mu(A_i) [/eqn] so [math] \mathcal{F} [/math] must be closed under countable disjoint unions. One can check that any collection of sets which is closed under disjoint unions and complements is closed under taking unions so [math] \mathcal{F} [/math] must be closed under general countable unions.

So what we get is that [math] \mathcal{F} [/math] contains [math] X [/math], is closed under complementation, and is closed under countable unions - that is, it is a sigma-algebra.
So this is one way to motivate the definition. It's also worth trying to think of it in terms of events in probability, and to look into the pi-lambda theorem.

>>9507292
Forgot to say: We can of course not do the complement step if [math] \mu [/math] is not finite, but as just motivation I think this works anyway.

>>9507292
>[math]``<" ``\infty"[/math]
What do you mean by this?

>>9507313
Its an ice cream cone with two scoops stacked on top of each other, laid down sideways, ain't that obvious?

>>9506956
>>9507292
>I don't think sigma-algebras really generalize anything the way topologies do.
It's technically true to say topologies are "generalizing" open sets from R^n but I think it's not very good to think about it that way.
Nobody really tried to generalize openness; what happened is that people wanted to generalize _convergence_ to places where metrics could not handle it (e.g. pointwise convergence of real functions), and it turns out that abstract neighbourhoods (or open sets) are the machinery you need to get this to work properly.

Similarly measures are trying to generalize the concept of size or volume to things where usual ways of measuring that don't work, and sigma-algebras are essentially what you are forced into if you insist that a volume function behave at all reasonably.

The other poster is right, probability is definitely the easiest way to understand why the sigma-algebra properties are sensible.

>>9507319
Yeah I agree that it's not really the right way to tink about topologies either. It works decently as a crutch at first, and when you work with nice enough spaces like manifolds or such. When you start looking at anything more weird, non-Hausdorf things and the Zariski topology and such, it really just gets in the way to think of R^n.

I was reading about weaker forms of finitism and started to wonder. Can one actually prove the existence of ``infinite" sets or are they merely play pretend?

>>9507347
the existence of infinite sets follows trivially from the axiom of infinity

>>9507349
So it's just play pretend? Is there no real justification for their existence then?

>>9507363
I suppose one could say that the Reals are a justification of the existence of infinite sets since they themselves are infinite

>>9507366
How does an even more bogus concept than infinite sets justify their existence?

>>9507347
Show me a mathematical framework with only finite sets that is used to do all sorts of math (from differential equations to elliptic curves) and then maybe finitism will have some sort of merit.
Also, the existence of mathematical objects, even finite ones, is debatable, they're all in our heads.
What are you reading, anyway?

>>9507388
>Show me a mathematical framework with only finite sets
What about objects which are only locally (or internally) finite? Or is that cheating?
>differential equations
>math
What's the name for this kind of mental illness?
>the existence of mathematical objects, even finite ones, is debatable, they're all in our heads.
In some sense this is true, but clearly the ``existence" of finite objects is less debatable. And are you trying to imply that our heads do not exist?
>What are you reading, anyway?
It's something I'm writing.

>>9507414
>>differential equations
>>math
do you even complex nonlinear stochastic dynamical feedback systems brah?

>>9507414
>What about objects which are only locally (or internally) finite? Or is that cheating?
There is a bunch of theory of finite sets, but you should be able to do maths internally (more than basic combinatorics, e.g., differential equations), and that I haven't seen yet.

>the ``existence" of finite objects is less debatable.
Not really. Both only exists in the sense that we imagine a mathematical universe that respects some basic rules, intuitionistic finite set theory, for example, but they don't really exist in any physical sense. The association we make between physical objects and mathematical objects is a social construct, it's all in your head, man.

>>9507414
>>differential equations
>>math
Oh, I get it, since anything is not math, all you need is the empty set.

>>9507438
>don't really exist in any physical sense
>it's all in your head
Pick one.

>>9507446
Go to /lit/ and ask them about ontology and epistemology. Math threads and /sci/ in general isn't a good starting place for this kind of discussion since we don't study these subjects seriously.

>>9507461
I don't know what that is nor do I really care. My post is pretty physical in nature.

Given a subspace of dimension n (V), how would one find the dimension of the subspace which consists of all vectors orthogonal to those in V?

>>9507490
If V is a subspace of W with dim(W) = m, then the subspace of vectors orthogonal to V (which btw is known as the orthogonal complement of V) is m - n.

>>9507313
This, kids, is what rigor mortis looks like. This shitposter is probably a masters student or a smug undergraduate who has already taken the course functional analysis and all potential as a successful mathematician has been dashed.He may overcome it in approximately 10 years if he's lucky, although most never recover. Their concept of beauty is whatever results in a textbook they've read about, likely mostly based off of definitions that they will claim require no motivation.

>>9507547
That guy is just retarded, the first thing you do in any measure theory course is to define the extended real numbers.

>>9507500
>the subspace of vectors orthogonal to V (which btw is known as the orthogonal complement of V) is m - n.
This is a meaningless notion.

>>9507572
>That guy is just retarded, the first thing you do in any measure theory course is to define the extended real numbers.
I'm not a "guy".

>>9507490
>Given a subspace of dimension n
Why restrict to finite dimension?

>>9507774
you still have an asshole don't you?

>>9507774
yeah, not with that attitude

What is the most counter-cultural subfield of mathematics?

What's some stuff that's inspired you to work harder on mathematics?
I'm early in it and I think I enjoy it and that it's suitable for me but going deep into mathematics would be very different from just doing the lowest university algebra and calculus that I have so far.

I'm at a bit of a crossroads now when I can choose to go wholeheartedly into mathematics, I'd focus on it as hard as possible and I think I could git pretty gud but I'm not sure if it's really a good choice.
I'm not some genius so while I think that busting my ass for a very long time would make me really good at mathematics, I don't know if that would mean that I would still be mediocre compared to all the really good mathematicians.

>>9507830
>What is the most counter-cultural subfield of mathematics?
IUT

how much of set theory do you really need for topology? shit like cardinals and ordinals seems specialized to set theory, and nothing else

>>9507846
Ruined by little kids and the normie media.
>hey guys abc right kappa lmao? xD

>>9507852
Munkres topology starts with almost everything you'll need.
What's missing is a discussion on order/pre-order and filters which a prerequisites for nets and filters in topological spaces.

>>9507830
Rational trigonometry

>>9507871
>developing new and exciting math
>"counter-cultural"
hmmmmmmmmm

>>9507871
This sounds better already. Would you recommend this?

>>9507873
He is anti-mainstream, though. I'm just not sure if he's radical enough for me.

>>9506416
Hey, I'm studying set theory too. Basically your argument is
[math]p \ \land (p\longrightarrow q) \iff q[/math]

and it's called modus ponendo ponens. You may want to reread some logic.

are projective points that are corresponding to linearly independent vectors non-collinear?

Guys what function is this?
Define clearly pls.

>>9507913
>Guys what function is this?
It's not.

>>9507913
Which line shows the value of the function?

>>9507913
Fermat's zigzag function.

>>9507919
>>9507915
Are u retarded?
It's x = f(t)

>>9507924
>Are u retarded?
> It's x = f(t)
What you've drawn is not a function, only a relation.

>>9507913
even better : [math]f(x) = \displaystyle \sum_{n=0}^{\infty} \frac{1}{2^{n}}h(2^{n}x) [/math] for [math]h(x)=|x|[/math], [math]|x|\leq 1[/math] and [math]h(x+2)=h(x)[/math].

>>9507924
If the vertical axis is x and the horizontal axis is t then that wasn't obvious

>>9507915
>>9507919
>>9507920
>>9507937
I m the one who asked this question.
This is simple function
f(t) = { x , when t reaches odd number
-x, when t reaches even number }

I was asking for mathematical notation.
How are we having 12 yo wannabe noobs in here?

>>9507942
Oh spoonfed braindead

>>9507913
it's not a function
it's a correspondence

>>9507950
>I was asking for mathematical notation.
[math]\varphi\colon[0, 2]\to\mathbb{R}[/math]

>>9507950
>f(t) = { x , when t reaches odd number
>-x, when t reaches even number }
This isn't what's in your picture.

>>9507961
Yes realized. May be you be less of a facebook chatter and reply and explain in one post?

>>9507972
>Yes realized. May be you be less of a facebook chatter and reply and explain in one post?
see >>9507915

>>9507913
x = 0.5 - abs(-(t - floor(t)) + 0.5) works.

>>9508017
any projective geometry people in?

>>9508030
>projective geometry
not science or math

>>9508031
nice meme, mind if I share it with reddit?

>>9505121
oh boy

>>9508034
It's not a "meme".

Euclidean geometry is math, but once you projectivize, your space is no longer mathematical.

>>9508046
huh, linear algebra isn't math now? woah...

>>9508059
>huh, linear algebra isn't math now?
What do you mean?

>>9508065
clearly you haven't studied anything related to projective geometry, because if you did you'd realize linear algebra is the power house behind a lot of proofs.

>>9507951
Learn charts instead, freshman. Your chart implied that t was a value (0.5), not the axis.

>>9508072
>clearly you haven't studied anything related to projective geometry, because if you did you'd realize linear algebra is the power house behind a lot of proofs.
I'm still not sure what you mean, of course linear algebra is math.

>>9508082
linear algebra is the language of projective geometry.

>>9508089
>linear algebra is the language of projective geometry.
This is simply false.

>>9507773
>>9507500
Oh shit, it should be has dimension m - n of course... or is this some new infinity dont real meme Ive missed?

>>9508096
cool, so you don't actually have anything to add. nice chatting with you.

>>9508089
>linear algebra is the language of projective geometry.
[citation needed]

>>9508116
>All math is just linear algebra
>Projective geometry is math
QED

>>9508116
take a course in it, get back to us.

>>9508122
>>All math is just linear algebra
[citation needed]

>>9508122
>>Projective geometry is math
[citation needed]

>>9508128
>take a course in it, get back to us.
I only take math courses.

>>9508139
define math

>>9507852
none

>>9508139
Well, how is it not math? Can you give an example of something that is math and what makes it math?

What's the argument for logic not being math?

>>9508141
>define math
There is no viable definition.

>>9508196
well, answer this then >>9508155

>>9508268
>well, answer this then >>9508155
I don't see why you expect an example of something which is undefined.

>>9508196
I don't know if there is a "viable" definition. The dictionary, however, defines mathematics as
>the abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics ).

Also, it's possible to give examples of math such as

[eqn] \frac{\big( 2\pi \big)^3}{\pi^2}=8\pi [/eqn]

and

[eqn] \big( \Phi\pi \big)^3+2\times\left(\frac{\pi}{2}+\frac{\pi}{2} \right)\approx137 [/eqn]

or even

[eqn] 2+2=2\times2 [/eqn]

>>9508321
Well, if it's undefined, how can you know that something is not math?

>>9508321
so first it was
>projective geometry is not math!
now its
>math isn't even defined! don't look at me for answers
grow up. maybe go outside for some fresh air for once.

>>9508344
Is [math] 1=2[/math] math?
Is [math] 1 [/math] math?
Is [math] + [/math] math?

>>9508349
>Well, if it's undefined, how can you know that something is not math?
Nothing is math since math is undefined, look at the OP.

>>9508355
all of those things can be defined mathematically

>>9508361
>defined mathematically
What do you mean?

>>9508355
I think the critical thing about what is or is not math comes down to whether you are going to keep waiting for my enemy to kill himself or if you are going to help me kill him and his people

>>9508367
Yes.

>>9508373
I don't think he's planning on killing himself.

>>9505121
of course someone as butthurt and delusional as OP would like Nietzche

>>9505121
>Nietzsche
not science or math

>>9507856
Normalfag*

>>9508684
any analysts in?

>>9507292
>>9507319
I see. thanks familia

>>9508549
>fag
Why the homophobia?

>>9508802
np m8

>>9508771
Nope, try searching for them in >>>/toy/. This is the math general.

Suppose I have a low-dimensional space with an explicit cellular decomposition

What is the best way to compute the homology of that space minus a point.?

>>9508803
That's a cute girl, anon.

Wish I could spend all day in /mg/ stroking my arrogant elitist ego, but unfortunately got work to do.

>>9507427
Wouldn't any one of those adjectives imply the others?

>>9508847
Yes. Almost makes me a lesbian.

>>9508928
too bad you're nothing but a mentally ill cross-dressing faggot who'll never be a real girl.

OwO why'd you delete your post?!

>>9509074
>faggot
Why the homophobia?

>>9509079
It's the mods again.

It's your fault for ever taking /mg/ seriously. This is the thread where failed mathematicians come to whine, and real mathematicians come to vent and shitpost. It's bound to be shit.

>>9509101
Please don't trivialize my quality posts by comparing them to faecal matter.

>>9509083
good, 'bout time they cleaned up.

>>9509170
Yeah, perhaps. But now you know I didn't delete it.

>>9509180
Doesn't change my original statement whatsoever. Get help.

>>9509186
I'm beyond helping. Besides, my mind is the last bit of privacy I have. They can track me, they can follow me, and they can predict me up to a certain level, but they can't read my mind. Talking to a """""""""""""""""""""""""professional helper""""""""""""""""""""""""" would make me open up my gate to the system's agents (not in the 007 sense), and then I would be stripped naked in front of the society I will never really be a functional part of. I would have nothing left to fight it with, so I would lose my personal war. I won't get help.

>>9509200
>I'm beyond helping. Besides, my mind is the last bit of privacy I have. They can track me, they can follow me, and they can predict me up to a certain level, but they can't read my mind. Talking to a """""""""""""""""""""""""professional helper""""""""""""""""""""""""" would make me open up my gate to the system's agents (not in the 007 sense), and then I would be stripped naked in front of the society I will never really be a functional part of. I would have nothing left to fight it with, so I would lose my personal war. I won't get help.
cringe

>>9509212
Cringe or not, that is a reason for me not to get help.

i want to study graphics engineering (by myself,not in school)

it involves vectors,points and variables. what type of math should i practice? and where

brainlet here

i have 15 objects of which there are 3 types
there are 8 of type A, 3 of type B, 4 of type C

how many ways can i pick k of the 13 objects?

i cant figure out the binomial coefficient -

i can do it for regular shit but i dont understand how to account for different object types.

>>9509200
cool blog, where's the subscribe button?

>>9509340
Just add 4chan to your favourites.

>>9505121
lol

How do you actually prove whether a set is well-defined?

For example [math]\{2,3,4\}[/math] is 'naively' well-defined but [math]R=\{S \mid S \not \in S\}[/math] isn't but to show this you need to check whether [math] R\in R[/math].

Is there a general algorithm or method by which this is done?

>>9509360
Pick some axiomatization of set theory, check if the set satisfies them all, and make a conclusion based on what you see.

>>9509360
>"general" "algorithm"
Fuck off right back into your cave. >>>/g/

>>9509360
>isn't but to show this you need to check whether [math]R \in R[/math]
This always (trivially) holds classically.

>>9509364
>>9509399
smug anime posters are even more cancerous than /g/ retards

>>9509408
Oh please. I'm the Tito of Smugoslavia, I can't be cancer.

>>9509408
Do you have a mental disability? In what way is the image attached to >>9509399 "smug"?
Also, fuck off to some other website if you dislike anime.

>>9509290
feelsbadman

Topological Hochschild homology and integral p-adic Hodge theory
Bhargav Bhatt, Matthew Morrow, Peter Scholze
https://arxiv.org/abs/1802.03261

>In mixed characteristic and in equal characteristic [math]p[/math] we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic [math]K[/math]-theory by motivic cohomology. Its graded pieces are related in mixed characteristic to the complex [math]A\Omega[/math] constructed in our previous work, and in equal characteristic [math]p[/math] to crystalline cohomology. Our construction of the filtration on [math]\mathrm{THH}[/math] is via flat descent to semiperfectoid rings.
>As one application, we refine the construction of the [math]A\Omega[/math]-complex by giving a cohomological construction of Breuil--Kisin modules for proper smooth formal schemes over [math]\mathscr{O}_K[/math], where [math]K[/math] is a discretely valued extension of [math]\mathbb{Q}_p[/math] with perfect residue field. As another application, we define syntomic sheaves [math]\mathbb{Z}_p(n)[/math] for all [math]n\geq0[/math] on a large class of [math]\mathbb{Z}_p[/math]-algebras, and identify them in terms of [math]p[/math]-adic nearby cycles in mixed characteristic, and in terms of logarithmic de~Rham-Witt sheaves in equal characteristic [math]p[/math].

>>9509449
>Topological Hochschild homology and integral p-adic Hodge theory
Not science or math.

>>9508900
like checking facebook and bullshitting in pointless meetings?

Are "proofs" that are not done in Coq really proofs?

Math ? Feh! All things are nothing to me.

>>9509604
>>9509633
Proceed to >>>/lit/ for discussion of such topics.

How can I learn how to do proofs involving family of sets? I perfectly manage to do every proof/exercise involving sets operations, cartesian product or relations, but I feel like a complete brainlet at the topic of family of sets. Any tip pls? (tips, books, youtube vids, anything can be useful)

I'm using Enderton's and baby Jech's to learn set theory.

>>9509633
Math is my property t b h

>>9509782
>How can I learn how to do proofs involving family of sets?
Example of a question you're having trouble with?

>>9508771
You need to prove that the partial sum converges uniformly, not just the terms in the sum lmfao.
Also this is high school calculus, not analysis. Actual analysis involves sheaves.
>>9508843
Meyer-Vietoris sequence.
>>9509546
Except Hoschchild cohomology groups are used in geometric quantization and construction of Yang-Mills theory on deformed principal [math]G[/math]-bundles where [math]G[/math] is a semisimple Lie group.

>>9509787
Prove that for any sets A and B, the following holds [math]\bigcup (A \cup B) = (\bigcup A) \cup (\bigcup B) [/math]

Rather than reading someone else's whole proof (as I can browse infinite examples of these on the internet), I'd like to know the process behind the proof. How can I use the definitions to prove that?

From Enderton, I recall that the definition of the union of a set A is the set S such that [math]S = \{x\,:\,\exists b \,(b \in A\, \land\, x \in A \} [/math], but I don't know how that can help

>>9509806
>How can I use the definitions to prove that?
Prove left inclusion and right inclusion. First of all you need to be taking the union over some index set, so for example if [math] x \in \cup_{i\in I} (A_i\cup B_i)[/math] then [math]x \in A_j\cup B_j [/math] for some [math] j\in I[/math]. So [math] x\in A_j [/math] or [math] x\in B_j [/math] for some [math]j\in I[/math]. So [math] x\in \cup_{i\in I} A_i [/math] or [math] x\in \cup_{i\in I} B_i [/math]. So [math] x\in (\cup_{i\in I} A_i) \cup (\cup_{i\in I} B_i) [/math]. Therefore [math] \cup_{i\in I} (A_i\cup B_i) \subset (\cup_{i\in I} A_i) \cup (\cup_{i\in I} B_i) [/math]. And you similarly prove [math] \cup_{i\in I} (A_i\cup B_i) \supset (\cup_{i\in I} A_i) \cup (\cup_{i\in I} B_i) [/math] to prove that [math] \cup_{i\in I} (A_i\cup B_i) = (\cup_{i\in I} A_i) \cup (\cup_{i\in I} B_i) [/math]

>the definition of the union of a set A
This is a meaningless notion.

can someone give me a closed form solution for the fibonacci sequence?

thanks in advance

>>9509875
>can someone give me a closed form solution for the fibonacci sequence?
https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression

>>9509819
I never thought of inclusion that way, and your proof was very insightful, never thought of using an instance of indexed set. Thanks, I hope to keep that in mind.

Have you read this? I'm considering it.
Do you know any books on mathematics that you would call entertaining?

>>9507347
>>9507388
You can reduce calculus from its infinite version commonly taught at university to a finite difference version:
https://en.wikipedia.org/wiki/Finite_difference

In fact, the above is what is actually used in computer science when discretizing a differential equation.

Elliptic curves and circles both require some concept of infinity, although it is possible to simply define them algebraicly.

>>9509360
In axiomatic set theory, there is no notion of "well-defined" sets. Objects are either sets or not sets, which is determined by whether or not the object follows from the axioms of set theory.

R =: { S ( S ∉ S ) } is not a set because of the axiom of regularity prevents sets from being elements of themselves and a trivial corollary prevents the existence of a set containing all sets.

>>9509819
>>9509806

The arbitrary union of a set M ( ∪M ) is defined by :

x∈∪M ⇔ ∃A∈M ∧ x∈A .

The existence of ∪M is guaranteed by the union axiom. The notion of arbitrary union is used often in set theory for the constructions of towers, chains, etc.

I need help designing an algorithm to tessellate the surface of an ellipsoid into planks of lengths roughly equivalent to it's radius along various points from one end to another.

I can get the radius at any point. I can get the length (it is symmetrical about the midpoint, and the centroid). Brain kind of shut down though, and I need some advice or direction.

>>9510167
Scratch some of that.

The planks span from radius n to radius n+1. The planks are are 1/30th of the radius n, and 1/30th of radius n+1, so they get larger until they reach the midpoint, then they start getting smaller, until they reach the end.

>>9510167
>I need help designing an algorithm
You might want to ask in the >>>/g/hetto/ then.

>>9510188
i would have asked for a formula but that's probably too hard for /sci/ to do in the time allotted

Wot so what is real math

>>9510193
At least that would be somewhat more on topic.

>>9508089
>fixing coordinates

everyone point and laugh

>>9509360
You prove that it exists using the axioms, and prove that it doesn't exist by finding a contradiction with the axioms.

>>9509360
[math]\{x \in E \mid \phi(x)\}[/math] is only allowed when E is a previously well-defined set.

To build bigger sets, you are allowed a few operations: cartesian product, function space, power set.

To start off you are allowed the empty set and the set of natural numbers. Then apply the operations above till you reach the desired set.

>>9506471
>Also, that faster way was really clever, how did you come up with it? Was it just seeing that A is an element of P(A)? If you notice my way is more "mechanical", just working from the definitions and seeing where I land.
Not the anon whomst responded to you, but the difference is you are not experienced enough yet tohave a strong intuition of what the symbols mean. Being member of a powerset means that you are part of the set (kinda like [math]\in[/math] but for subsets instead of elements. When you understand this his way of proving your thing becomes the first thing you think of. but it agree it's very clever. props anon!

hermès link could feed a village in liberia!

>>9507879
>I'm just not sure if he's radical enough for me.
No such thing as a radical :^)

>>9510660
I knew someone would post this. Will he help me fight the degeneracy of mainstream mathematics ridden with results by (((them)))?

>>9510665
Of coursh. Wildberger is striving to bring geometric intuition back to the field of mathematics so plagued by the devil of abstract algebra, and his pristine framework serves as a great reminder not to get caught up on layers and layers of abstraction that cannot be represented physically.

>>9510679
To take a step closer to physics is to take a step closer to (((Witten))) and (((Einstein))). You won't fool me, semitic snake.

How do invert this tridiagonal nxn matrix?

>>9505121
Nietzsche is just anti-science sophistry.

>>9510681
>(((Witten))) and (((Einstein)))
Whose theories have little connection to common sense and intuition either. Rather it would be a step closer to Euclid, Archimedes, Newton and Gauss.

>>9510707
Special relativity is probably the most common sense thing to happen in physics during the 20th century

>>9505673
Pls help.

Why is this wrong?

Consider the sequence [math]f_n:=f\chi_{[-n,n]}[/math], where [math]\chi_{A}[/math] is the indicator function on the set [math]A[/math]. Then (clearly?) [math]\lim \int f_n=\int f[/math]. Since for each [math]n[/math], the set [math][-n,n][/math] is compact, using the definition of the limit, this is our compact set

>>9509788
How do I use the mayer-vietoris here?

If X is the space, should I like cut out a small disc around some point and then use A=X\pt B=disc ?

>>9508771
use Weierstrass M-test

>>9508843
Take X without the point and the point as your spaces A, B. Then if you know the homology of X and of the point (trivial), the intersection is also trivial, then you're left with an exact sequence that tells you about the direct sum of the homologies of the two spaces A,B

>>9511476
It's not wrong, just incomplete.
It's not so clear why the limit converges, can you explain?

>>9511636
Well, [math]\lim f_n = f[/math] clearly, then using Lebesgue dominated convergence with our dominating function being [math]|f|[/math], then the limit is exactly that

>>9511644
Yeah, and who said that's wrong?

>>9511654
then why the FUCK is question 2 to prove exactly that

>>9511613
That seems too easy. I was under the impression you can't just take {pt} as one of the sets, you need to take a small nbhd of that point.

>>9511662
yeah but using excision you are done

I hate algebraists so much.

>>9512277
>I hate algebraists so much.
Tell me more.

>>9512277
It's rude to pick on the autistic, anon.

>>9512277
They didn't let you in the cool girls' club? Instead of hating them, ask what you could do better yourself.

>>9512277
t. can't into algebra

>>9512342
functional analysis is objectively better than ANY algebra.

>>9512344
Functional analysis is infinite dimensional linear algebra.

>>9512373
And it makes pussy's drenched, unlike whatever bullshit algebraist study. The minute you say Hopf algebra or any shit like that, every cunny without a 200km radius dries into sand.

>>9509819
Why is that definition meaningless? Now I have to prove that the union of the power set of A is equal to A. How can I do it? It hurts being a family-let

>>9510042
Is that notion useful when I have to prove theorems like the one I mentioned above? Or do I have to use other definitions (such as index)

>>9512449
When you prove set equalities show that one is a subset of the other and vice versa. A is trivially a subset of the union, what about the other way around?

>>9512489
>A is trivially a subset of the union
Why? I know A belongs to P(A) because of the definition of the power set. But how can I *prove* that it is also a member of the union? (I know it's obvious at an intuitive level)

>what about the other way around?
I don't know how to prove it, that's why I asked

Everytime I scroll by this thread I feel bad about something I said about Nietzsche on time. I was thinking about the nihilist in the Big Lebowski when I said it. Don't weep Nietzsche, it will be ok.

t. the guy who has never read the work of even one famous philosopher

>>9505121
>I leave to you cretins the immortal words of my man Nietzsche, please think about these hard and maybe you will learn to resent this ugly place too:
>>There exists no more repulsive and desolate creature in the world than the man who has evaded his genius and who now looks furtively to left and right, behind him and all about him. In the end such a man becomes impossible to get hold of, since he is wholly exterior, without kernel: a tattered, painted bag of clothes.
Is philosophy dead?

What work being done by living philosophers matters?

>>9512499
For any a in A then {a} is in the powerset so a will be in the union, if you really want to murder it.
Oh wait, A is not a member of the union, it's a subset of the union, important distinction.

>>9512529
I think I solved the [math] \bigcup P(A) \subseteq A[/math] part

The union of P(A) is defined to be [math]\bigcup P(A) = \{x: \exists b\,(b \in P(A)\,\land x\in b)[/math]
Since [math]b \in P(A) \iff b \subseteq A[/math] (I don't know how to prove this)
[math] x\in b \land b\subseteq A \iff x \in A[/math] (given that b is a subset of A, every element belonging to b is an element belonging to A, so if x belongs to b, then x belongs to A)

Therefore, for any x belonging in the union of P(A), x belongs in A. Or in other words, the union of P(A) is a subset of A.

is this enough?

>>9512589
The definition of the power set of A is that every element of it is a subset of A, so if b is an element of the power set of A, then it is a subset of A. I get it now.

>>9512449
>Why is that definition meaningless?

It's not meaningless, I think the person replying to you is probably used to different terminology. There is an error in the definition you wrote for the union of a set though - the final "A" should be "b" instead.

>>9512589
Yes, this plenty.

>>9512341
Yep. We didn't invite you either because we were doing topology.

If I have random variables X and Y with pdfs f and g (resp.), how do I compute the pdf for h(X,Y) where h is a given function?

If you have to prove that two sets are equal, are these two arguments equally correct? Is one better than the other?

1) Double Inclusion
[math](A=B) \iff (A \subseteq B \land B\subseteq A )[/math]

2) uhhhh this one
[math]\{x: p(x)\} = \{x: q(x)\} \iff (p(x) \iff q(x))[/math]

2) is the one that suits me the most as you can use direct definitions and the rest is logically proving p(x) <=> q(x), but >>9509819 suggested proving double inclusion for that problem

so is it a thing of 'use the one that suits you the most' or (1) is more correct/rigorous?

>>9512935
>more correct/rigorous
These are meaningless notions. Rigor and correctness are binary, while "more correct" and "more rigorous" imply some sort of spectrum.

Polymath15, third thread: computing and approximating [math]H_t[/math]
https://terrytao.wordpress.com/2018/02/12/polymath15-third-thread-computing-and-approximating-h_t/#comments
>This is the third “research” thread of the Polymath15 project to upper bound the de Bruijn-Newman constant [math]\Lambda[/math], continuing this previous thread. Discussion of the project of a non-research nature can continue for now in the existing proposal thread. Progress will be summarised at this Polymath wiki page.

> We are making progress on the following test problem: can one show that [math]H_t(x+iy) \neq 0[/math] whenever [math]t = 0.4[/math], [math]x \geq 0[/math], and [math]y \geq 0.4[/math]? This would imply that [math]\Lambda \leq 0.4 + \frac{1}{2} (0.4)^2 = 0.48[/math] which would be the first quantitative improvement over the de Bruijn bound of [math]\Lambda \leq 1/2[/math] (or the Ki-Kim-Lee refinement of [math]\Lambda < 1/2[/math]). Of course we can try to lower the two parameters of [math]0.4[/math] later on in the project, but this seems as good a place to start as any. One could also potentially try to use finer analysis of dynamics of zeroes to improve the bound [math]\Lambda \leq 0.48[/math] further, but this seems to be a less urgent task.

>>9512935
I usually use 1) because it is actually less convoluted (in the regular sense) than 2).

>>9512935
Two sets are equal if and only if they have the same elements, so 1) and 2) are equivalent.

I fucking hate differential geometry.
Fucking notational clusterfuck.

>>9513262
>fucking
>Fucking
>clusterfuck
Do you need to swear?

>>9513262
you're right. you need to develop your own notation to make sense of it.

>>9512935
those are the same fucking thing

>>9513271
Yes, because reading it makes me mad.

>>9513014
god analysis is gross

>>9513323
PDEs are gross.
Abstract analysis is nice.

>>9512706
>doing anything but shitposting
Pleb.

>>9513401
>Abstract analysis is nice.
Can you show some examples of how "nice" it is?

>>9512706 >>9513432 >>9513401

2016's nobel prize was given to one of the 1st application of Topology to practical problems in Electrical Engineering
https://en.wikipedia.org/wiki/Topological_order#Applications

This probably caused a lot of Butthurt in Pure Mathematicians, who in general hate when their math is applied to anything useful

>>9513603
>Electrical Engineering
Not science or math. Proceed to >>>/toy/ to discuss this further.

I did it

>>9513640
Did what?

I'm learning the feistel cipher and XOR at the same time. Is it possible to have a long string of XORs? L0 ⊕ R0 ⊕ L0 ⊕ R0 ⊕ R0 ⊕ L0

What is the limit of [math] 1^x [/math] when x go to infinity ? My teacher said it's not 1/but it's really strange, am I being memed?

>>9513640
Nice pirate hat, donut dude.

>>9514212
>What is the limit of 1x when x go to infinity ? My teacher said it's not 1/but it's really strange, am I being memed?
draw a picture

>>9513643
Replicated those gifs that one guy made.

>ask algebra proff a question during lecture
>he spergs out, goes red in the face, glues his eye to his lecture notes and tries to comprehend an original thought for once
>stumbles on every word, get's completely derailed
>whole lecture he's pissed off, literal autistic rage
>ask analysis proff a question during lecture
>with class and suaveness he not only answers my question in a manner that even the most low IQ in the class can understand but also develops new insight
>is able to transition into his lecture material from the question with finesse and coolness, literally Chad of the math department
haha, oh wow. Quite the observation I'm seeing here. Embarrassing!

>>9505149
Quantum Algebra is characteristic of arxiv, haha.

How the fuck are we suppose to truly talk about mathematics when we dont have access to fucking LaTeX in other boards

>>9514462
Even if this is a shitpost this exact thing happened to me literally yesterday

>>9514485
I speak from many years experience, it's a startling correlation.

>>9514462
>ask analysis proff
Are you double-majoring in engineering and mathematics?

>>9514479
TeX in other boards would be 99% used to shitpost with the funny rainbow text

>>9514526
Please show me how to shitpost with funny rainbow text :)

>>9514462
>with class and suaveness he not only answers my question in a manner that even the most low IQ in the class can understand but also develops new insight
It's because low IQ people understand each other better than high IQ people can ever do. That he is low IQ follows from the fact that he is an analcyst.

>>9514514
Well said, sister.

>>9514212
>My teacher said it's not 1
Your teacher is either retarded or he actually told you that if f(x) Tends to 1 when x tends to infinity, then you can't deduce what the limit of f(x)^x is.
For example, consider (1+1/x)^x. Base goes to 1, exponent to infinity, but the limit is e.

>>9514526
True, brainlets cant use LaTeX..

define "mathematics"

>>9505121
Hi brainlet here, how do I learn category theory? I'm new to this whole advanced math thing.

>>9514817
By studying.

>>9514817
>Hi brainlet here, how do I learn category theory?
Take your pick:
>Category Theory in Context by Emily Riehl
>Basic Category Theory by Tom Leinster

Just stay away from the flaming pile of garbage known as "mac lane"

>>9514514
Did you fail analysis or something? Point on the doll for me where Rudin touched you.

>>9514567
truth hurts, I'm sorry it has to be like this. Autistic little cretin.

>>9514853
I will never forgive you.

>>9514824
what should I study to do this? I've tried Spivak, but I keep getting stuck.

>>9514856
Living in your mind, rent free.

>>9514860
I suggest Hardy's book on calculus. It is a good introduction to category theory, which is just a debate on how to interpret Baire's theorem.

>>9514861
I must free my brain then. With a precise shot, piercing my cranium. Too long has my brain been restricted to a dark cave.

>>9505121
If you embed the hyperreals in the surreals, what are the simplest surreals not in the hyperreal?

>>9514875
>surrealism
>>>/ic/

>>9514876
Wasn't funny the first time you did this. Why are you not allowing the discussion of math in the math general?

>>9514879
Numbers aren't math. Only arrows are.

>>9514880
Prove it.

>>9514880
>Numbers aren't math.
Nothing is math since "math" is not well-defined.

>>9514882
You are asking me to prove a definition?

>>9514883
Don't talk to me.

>>9514885
I'm asking you to show that numbers aren't math and that only arrows are. Evidently, you can't do this and are condemned to forever just be a IQ-let shitposter in /mg/

>>9514887
>a IQ-let
I know I am right because that is the definition I gave, and definitions can only be proven to be nor not be equivalent, but never be proven true.

>>9514893
Your definition is inconsistent. Also, you haven't even defined math. Would expect no less from a category theorist.

>>9514896
Okay, let me phrase it so that you will understand it: math is the class of all arrows in the category of diagrams. This definition can be found as an object in the category of axioms.

>>9514902
Inconsistent drivel.

>>9514920
Grumpy analcyst getting buttblasted after his surreal numbers were refuted with precise argumentation. Would you like to get a more analytical explanation? Your feelings < my claim = truth, as your kind seems to like estimating upwards. No reason to try be the Salvador Dali of mathematics.

>>9514920
>Inconsistent drivel.
not science or math

>>9514924
>>9514939
No one cares.

>>9514941
>No one cares.
How can these posts be real if caring isn't real?
>>9514879
>>9514882
>>9514887
>>9514896
>>9514920

>>9514817
>new to advanced math
>better learn category theory before I know any categories other than Set
you're going to fit in perfectly in this general anon

>>9514870
>Baire's theorem.
I'm a pretty big brainlet here, what's a Braire's theorem?

>>9515041
https://en.wikipedia.org/wiki/Baire_category_theorem

>>9515033
my boss says I have to learn category theory by next month. Where learn is defined as not sounding like a complete idiot to someone who actually knows something.

I'm an engineer btw, so basically a complete idiot. We tried to hire a mathematician who actually had expertise in this and failed. Which is actually sort of sad, because if we actually did we're pretty sure they could solve this entire field of engineering we're in, greatly reducing the need for peons like us.

need to learn all of symplectic geometry by tomorrow and all i know is remedial college algebra
any quick guides?

>>9515149
Just be yourself and smile.

>>9507388
Elliptic curves over finite fields.
Discrete differential geometry.
Calculus of finite variation.
Finite difference calculus.
Finite algebras.
You can turn any math into non-trivial finite case.
I study finite topology