/mg/

[Anonymous No.12157556]

Math, generally
>ancient wisdom edition
Talks Math

[Anonymous No.12157571]

i've never seen a visual notation for vectors. anyone aware of any? like, having different style arrows to indicate position vectors, difference vectors, unit vectors, basis vectors, etc.

[Anonymous No.12157580]

Previously >>12147606

[Anonymous No.12157608]

Please help.

If the hypotenus is 22 and |x|=|z/2| then what is the sides then. I am certain Z is a negative Please provide an answer with 2 or 1 decimals.

[Anonymous No.12157710]

>>12157608
How is someone so confuesed they type shit like this and think it makes sense?

[Anonymous No.12157715]

>>12157608
>>12157571
we have a brainlet problem

[Anonymous No.12157721]

>>12157608
>hypotenus
Sounds like the official medical term for when you push your dick back into its socket and it gets stuck

[Anonymous No.12157764]

>>12157710
>>12157715
>>12157721
Hypotenuse*
So you guys don't know the answer?

[Anonymous No.12157789]

>>12157764
What the fuck are x and z? Why can z be negative?

[Anonymous No.12157795]

>>12157764
>So you guys don't know the answer?
I can't make any sense of the question

[Anonymous No.12157800]

>A binary relation [math]R[/math] between sets [math]M[/math] and [math]N[/math] is defined as a set [eqn]R=\{(m,n)\in M\times N:\varphi{(m,n)}\}[/eqn] such that [math]mRn[/math] is syntactic sugar for [math](m,n)\in R[/math]
>A function [math]f\colon X\to Y[/math] is defined as a binary relation [eqn]f=\{(x,y)\in X\times Y:\varphi{(x,y)}\}[/eqn] such that [math]y=f(x)[/math] is syntactic sugar for [math](x,y)\in f[/math]
>The graph of the function [math]f[/math] is defined as the set
[eqn]\textrm{graph of }f=\{(x,y)\in X\times Y:y=f(x)\}[/eqn] such that [math]y=f(x)[/math] is equivalent to [math](x,y)\in\textrm{graph of }f[/math]
Is it just me or are a function and its graph the exact same object? As in, by definition they're the same thing. They're both subsets of [math]X\times Y[/math] such that if [math](x,y)[/math] is a member then [math]y=f(x)[/math].

[Anonymous No.12157813]

>>12157789
>>12157795
Mb not good at english.

There is a triangle, the hypotenuse is 22
The two other sides are x and z
x=z/2
How do I find the sides.
t. brainlet .

[Anonymous No.12157821]

>>12157800
>Is it just me or are a function and its graph the exact same object?
You need to into Hilberts nullstellensatz

[Anonymous No.12157830]

>>12157813
x^2+z^2=22^2
x^2+(x/2)^2=22^2
Now finish it. Also, how's high school?

[Anonymous No.12157832]

>>12157813
22^2=x^2+z^2=x^2+(2x)^2=5x^2 so solving for x=sqrt((22^2)/5) and then z=2x

[Anonymous No.12157838]

>>12157832
>>12157830
Yeh sorry correction (2x)^2 not (x/2)^2
Now I'm the brainlet

[Anonymous No.12157844]

>>12157800
I don't see a problem with this. I believe those are standard ways of defining relation, function and graph of function.
Just keep in mind that relation is function only if [math]\forall x \in X \exists ! y \in Y (x,y) \in f[/math].

[Anonymous No.12157903]

>>12157800
yes, but no one thinks of a function as the same as its graph unless they are a set theorist or something
functions act on things. relations don't
functions and graphs have different vocabularies associated with them, which separate them.

[Anonymous No.12157909]

>>12157800
>>12157844
>are a function and its graph the exact same object

"Yes."
But the issue with the question is that you're presuming set theoretical foundations apriori.
In that context, a function (or any other "object" for that matter) will be some set.

Two notes:
Firstly, By Extensionality, your function notion will forget about it's codomain.
E.g. let P(x,y) be y=x^3, let X=Y=N and let Y' be the union of N and the comlpex numbers.
Then with P, X,Y define the same function as X,Y'. That is to say, your notion of function e.g. has no inherent concept of surjection.
(Along the same line, there's then also a whole array of category theoretical notions that do the same job as epimorphisms, in Set)

You say
>a function f:XY is defined as
but "f:XY" here, if you play the set theory game in first order logic, is just some proposition about f.

Secondly (but that's just fyi), I just want to point out that while the definition is perfectly fine, there's the notion of class function that's not captured if, as you seem to do there, you require Y to be a set. E.g. ZF (unlike Z) has Replacement which enables you to map, via a predicate P, far out of the "comfort zone". E.g. you may want to "apply the powerset operation |N| times", and form the union of those sets, to get from the empty set to the infinite set of (hereditarily) finite sets. The function involved there isn't even a set but ZF don' care.

[Anonymous No.12157912]

f : X -> Y

[Anonymous No.12157930]

Stupid question, but is there some sort of 'roadmap' or checklist I could follow for learning college-level math and above? I'm learning most things in isolation and it's getting a little too dissonant and freeform for my taste.

[Anonymous No.12157935]

>>12157909
f : X -> Y, the arrow got lost
Also, Replacement and union itself is what then makes the result of the procedure a set, so that example then is a set function a fortiori. But the point is that in set theory, there's no problem of taking a set X and mapping into the universe of all set - even if that mapping is not a set. You can get far with just the predicate P. tl;dr set codomains are a tad overrated

[Anonymous No.12157938]

>>12157912
>f : X -> Y
based notation

[Anonymous No.12157956]

>>12157938
Lately I actually go with \colon, as in
[math]f\colon X\to Y[/math]
That moves the colon closer to the f. Not entirely sure how I feel about this.

My point about "let f : X -> Y" be a function however is that while this is common language, it barely translates as a formal declaration (in the context where "function" means graph of function). Pic related is one catalog of definitions to go by. This probably amounts to just treating it as sugar for [math]f \in Y^X[/math].

[Anonymous No.12157967]

>>12157938
Lately I actually go with \colon, as in
[math]f\colon X\to Y[/math]
That moves the colon closer to the f. Not entirely sure how I feel about this.

My point about "let f : X -> Y" be a function however is that while this is common language, it barely translates as a formal declaration (in the context where "function" means graph of function). Pic related is one catalog of definitions to go by.

[Anonymous No.12157988]

>>12157930

[Anonymous No.12157989]

My brain is not working. For f = u + iv, don't we have [math]\Delta f = \Delta u + i\Delta v [/math]? With delta the Laplace operator.

[Anonymous No.12158001]

>>12157989
duh

[Anonymous No.12158009]

>>12158001
thank christ. came across some stack exchange thing where instead of using basic linearity he did all of these extra steps without reason. guess we're both retarded.

[Anonymous No.12158040]

>>12157967
>That moves the colon closer to the f. Not entirely sure how I feel about this.
Feel good that you're doing the right thing. The plain : has binary operator spacing, the same spacing LaTeX uses for + and - and = and so on. It can make sense if you use it to mean "such that" (so I would use plain : for set building), but for [math]f\colon X\to Y[/math] I don't really see the colon as having the same purpose.

[Anonymous No.12158106]

>>12157930

[Anonymous No.12158261]

plz help me brianlent. Given an irrational x>0 and ε>0, is there a nice way to find naturals p,q that minimize p*q subject to the restraint |p/q - x| < ε?

[Anonymous No.12158292]

>>12158261
https://en.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations

[Anonymous No.12158351]

>>12158292
That minimizes |p/q - x| subject to q<N, it seems reasonable that those are equivalent, but I wasn't able to prove it.

[Anonymous No.12158620]

>>12157800
>(x,y)\in\textrm{graph of }f
>Is it just me or are a function and its graph the exact same object?
yes and it very important to remember this in non ZFC undergraduate maths

[Anonymous No.12158621]

>>12157800
>(x,y)\in\textrm{graph of }f
>Is it just me or are a function and its graph the exact same object?
yes and it very important to remember this in non undergraduate maths

[Anonymous No.12158657]

I feel like I no longer like math. What do I do bros?

[Anonymous No.12158716]

>>12158657
don't do any math for a few weeks

[Anonymous No.12158758]

>>12158657
get a real hobby, nerd

[Anonymous No.12158818]

>>12158351
Given a positive rational number [math]q[/math], there are infinitely many ways to write it as fraction [math]q = \frac{m}{n}[/math] where [math]m, n \in \mathbb{N}$. Thus, there is a representation of rational number s.t. product m*n is minimal.
We also have standard way of writing rational numbers (... =30/40 = 15/20 = 6/8 = 3/4). I think that you should be able to prove that minimal element (in the sense of minimizing m*n) is unique (up to a sign).

[Anonymous No.12158821]

>>12158621
>yes and it very important to remember this in non undergraduate maths
lol why

[Anonymous No.12158870]

>>12158821
Not him but the open graph theorem maybe?

[Anonymous No.12158892]

>>12158870
this has nothing to do with it

[Anonymous No.12158897]

Good proofs have low complexity.
Dip a nut in water until it's easy to break.
A long chain of simple links could still be complex retarded garbage when viewed from afar. Theories need to be simple as well, not just proofs. It's not OK to hide the complexity of a proof in the unintuitive intricacies of your theories.
Formless mathematical ideas are stirred in the mind until they suddenly arise in your consciousness and then you pick one. Poincaré.
Personal observation: when you force yourself to think in words math comes more easily. Purely symbolic thought is not very conducive for mathematical thought. Also linguistic thought is more easily remembered. Most of my previous thoughts that I remember have been linguistic.

[Anonymous No.12158905]

Puzzle:
Find polynomials f(x), g(x), h(x) such that the set {(f(n), g(n), h(n)) : n natural} contains infinitely many primitive pythagorean triples.

[Anonymous No.12158926]

>>12158905
sorry i dont reply to anime posters

[Anonymous No.12158928]

>>12158926
Really getting Alice in Wonderland vibes from this response

[Anonymous No.12158931]

>>12158926
Understandable. Have a nice day.

[Anonymous No.12158936]

>>12158905
excuse me sir, this is /sqt/ level question
4x^2 - 1, 4x, 4x^2 + 1

[Anonymous No.12158940]

>>12158936
The funny thing about the "level" of the question is that it's not really a feat of the question as a math question, but just a matter if one has seen the question or related exhibition before.

[Anonymous No.12158982]

What field in mathematics just allows me to laze around and do nothing?

[Anonymous No.12158999]

>>12158982
Which doesn't, I mean it depends on your advisor.

[Anonymous No.12159086]

>>12158982
You need to actually do things, bro... You're never going to make it with that attitude

[Anonymous No.12159104]

Does anyone have the brainlet topologist wojak saying "which hole?"?

[Anonymous No.12159152]

Dumping

1/3

[Anonymous No.12159158]

>>12159152
delete it, rotate the picture and post again

[Anonymous No.12159162]

>>12159152

[Anonymous No.12159173]

>>12159162
Buy the book or support your local library/university if you enjoy these dumps.

[Anonymous No.12159421]

>>12157571
Penrose diagramatic notation

[Anonymous No.12159584]

>>12157800
>syntactic sugar
Like, HFCS?

[Anonymous No.12159726]

>>12159104

[Anonymous No.12159750]

>>12159726
Please pour some water into the cavity

[Anonymous No.12159760]

>>12159158
>Can't read sideways

[Anonymous No.12159761]

A sheaf of rings on a topological space gives you a ringed space. Is there an equivalent for sheaves of groups/abelian groups/modules/...?

[Anonymous No.12159766]

>>12159158
>>12159760
(forgot to attach image)

[Anonymous No.12159769]

>>12159761
Are you asking what a sheaf of groups is or?

[Anonymous No.12159786]

>>12159761
Grouped, abelianly grouped, moduled space. Vector spaced space.

[Anonymous No.12159788]

>>12159761
LOL how scattered must your brain be to ask such a question.

[Anonymous No.12159791]

>>12158936
i also have a file called 1 (16).jpg (from a "4chan folder" torrent on /t/) . . . what is the origin of this naming convention

also i came up with 2x-1, 2x^2 -2n, 2x^2-2n+1 , does this work???

[Anonymous No.12159793]

>>12159786
Stop.

[Anonymous No.12159796]

>>12158936
No prove there's no polynomial that goes through ALL the triples.

[Anonymous No.12159798]

Hello friends!

Someone might find this interesting:
https://topology.ima.umn.edu/
>The Applied Algebraic Topology Research Network promotes and enables collaboration in algebraic topology applied to the sciences and engineering by connecting researchers through a virtual institute. Be part of this community and help us grow this network. Our goal is to help bring people together so that they can collaborate.
https://www.youtube.com/c/AppliedAlgebraicTopologyNetwork

>>12159793
How about sheaf of ringsed space?

[Anonymous No.12159807]

>>12159152
>>12159162
>>12159173
>dumping intro algorithms book
>not even saying which book it is
?? wtf

[Anonymous No.12159814]

>>12159769
>>12159788
What's wrong with my question?

[Anonymous No.12159816]

>>12159814
Because the construction of a ringed space is so simple that it should be completely obvious that the rings could be replaced with nearly any other algebraic structure you want.

[Anonymous No.12159823]

>>12159814
What is your question? Are you asking whether such a thing as a sheaf of groups exists, what to call a space equipped with such a sheaf, or what the definition of a sheaf of groups is?

[Anonymous No.12159825]

>>12159816
Then why does the term ringed space always appear and not for other types of sheaves?

[Anonymous No.12159827]

>>12159823
>what to call a space equipped with such a sheaf
This one.

[Anonymous No.12159834]

>>12159816
More than that, you can use objects from any concrete category. So you can have sheaves of spaces, sheaves of graphs, etc.

[Anonymous No.12159835]

>>12159825
Cultural reasons. Ringed spaces were where the concept first appeared.

[Anonymous No.12159837]

>>12159834
>>12159825

[Anonymous No.12159844]

>>12159814
I was gonna answer "Anons lack reading comprehension and can't tell that you're asking if there's a name for "space with a sheaf of groups/abelian groups/modules".", but this >>12159825 post completely threw me off.

[Anonymous No.12159846]

>>12159835
So if I have a topological space with a sheaf of abelian groups on it, how do I call the resulting space?

[Anonymous No.12159848]

>>12159844
What threw you off?

[Anonymous No.12159856]

>>12159848
Because if that was the question, I'd have replied to >>12159816 with something like "Yes, is there a name for it tho?".

[Anonymous No.12159859]

>>12158716
This. Took a semester off of undergrad and when I came back suddenly I loved my studies again. Also unironically stuff like numberphile is a good way to zoom out and remember why you liked math in the first place.

[Anonymous No.12159905]

>>12158758
What hobbies do you have? Pls don't say "having sex".

[Anonymous No.12159906]

>>12159859
Learning about beeg numbahs on my ipod, those were the days

[Anonymous No.12160038]

>>12159846
Why even talk about the space like that? Just refer to the sheaf since it has the information about the space it's on already.

[Anonymous No.12160138]

>>12160038
>Why even talk about the space like that?
Why talk about ringed spaces?

[Anonymous No.12160179]

Are there any actual uses of these or is just algebraic masturbation?
https://en.wikipedia.org/wiki/Wheel_theory

[Anonymous No.12160193]

>>12160179
wheels man, they keep on rollin'

[Anonymous No.12160207]

>>12158982
Algebra

Real chads study analysis.

[Anonymous No.12160220]

>>12160207
You have that backwards.

[Anonymous No.12160226]

>>12160207
This, no one has ever computed anything using algebra. They just make up gay names for things no one cares about.

[Anonymous No.12160252]

>>12160226
>They just make up gay names
Please don't bully homological algebra.

[Anonymous No.12160288]

>>12160226
>no one has ever computed anything using algebra
?????

[Anonymous No.12160313]

>>12160288
It's not a computation if you don't even use Hölder, the Fourier transform, or dominated convergence.

[Anonymous No.12160315]

>>12160252
Okay, I’ll bully you instead. *unzips*

[Anonymous No.12160385]

>>12160138
I wouldn't, I'd just talk about the sheaf itself.

[Anonymous No.12160412]

>>12160313
What about Lebesgue measures?

[Anonymous No.12160494]

>>12160288
>Tomasz Kaczynski
lel

[Anonymous No.12160499]

Anyone have any good resources on calculus of variations that are short? I need to move quickly on a project, so I can't read a whole book or anything (I need to learn how variational inference works). For reference, I have basic math training in applied math (baby Rudin analysis, intro probability, linear algebra, first course in odes).

[Anonymous No.12160510]

>>12160220
analysis is a masculine, active, domineering mentality. algebra is receptive, feminine, passive in mentality. analysis is for chads, for men.

[Anonymous No.12160520]

>>12160499
Gelfand & Fomin
It's Dover, so it's super cheap ($12 on Amazon).

[Anonymous No.12160613]

>>12160510
Is topology like genderqueer or something?

[Anonymous No.12160619]

>>12159421
interesting...

[Anonymous No.12160643]

>>12157930
Mate just learn analysis/calculus and pick up whatever else you want to

[Anonymous No.12160655]

>>12160643
And linear algebra.

[Anonymous No.12160757]

>>12159791
i don't know
i just downloaded a folder full of anime girls from somewhere, and that's how they were named
>>12159796
assume all primitive triples were given by some [math]f(n)^2 + g(n)^2 = h(n)^2[/math]
h is a polynomial, so h(n) can attain the same value at most [math]\textrm{deg} h[/math] times
so we would have: for any natural c, there are at most [math]\textrm{deg} h[/math] primitive triples [math]a^2 + b^2 = c^2 [/math]
From gaussian integer stuff we know that for primes [math]p_1, \dots p_k[/math] of the form 4m+1, there are exactly 2^k ways to write [math]n = p_1 \cdots p_k[/math] as a sum of two squares. Each of those ways give rise to a primitive solution: if [math]n=a^2 + b^2[/math] wasn't primitive then some q divides both a and b, but then q^2 would divide n, which is not the case.
So overall it's a contradiction because you can take k as big as you wish.

[Anonymous No.12160883]

>>12160385
>I wouldn't
Algebraic geometers do.
>inb4 akshually I'm an analyst
Opinion discarded.

[Anonymous No.12160917]

>>12160613
topologists are literally female souls trapped in male bodies, they are what trannies claim to be. geometers are spiritual eunuchs

[Anonymous No.12160997]

>>12160520
thanks! Looks like a good book.

[Anonymous No.12161102]

Do you own any springer yellow books?
I ordered one for myself a few days ago - on the order page, it said it's "print on-demand". I've heard books made this way are often of poor quality (smudged ink, bad binding etc). Do you have any bad experiences?

[Anonymous No.12161172]

https://en.wikipedia.org/wiki/Bloch_sphere
What's mathematically interesting about this construct?

[Anonymous No.12161211]

>>12161102
I have Galois and Field Theory by Morandi and it's fine.

[Anonymous No.12161226]

>>12160757
>i just downloaded a folder full of anime girls from somewhere, and that's how they were named
Sad.
But if you're going to post batch downloaded anime girls, you might as well post cute Remilias.
https://mega.nz/folder/gxNgHTKT#qJWC08Jf4O15-nYFSLSF3g

[Anonymous No.12161265]

>>12157830
More like middle school.

[Anonymous No.12161278]

>>12161226
i mean i watched the shows and i know the characters i post
it's just that i didn't save the images one by one, i got them from a .zip file instead or some imgur gallery

[Anonymous No.12161295]

Why is it than when an innocent undergrad wants to learn what dx dy means, retarded geometers start talking about differential forms? Differential forms and their integration make no fucking sense if you don't understand the basic analytical definitions and theorems needed in calculus. That they can be used to abuse notation completely hides the real meaning of objects like dx, and if you actually understand what is to integrate and differentiate you see why differentials work. Jesus christ why is that people who have taken analysis still don't know how to prove separation of variables method for ODEs lmao.

[Anonymous No.12161327]

>>12161295
>start talking about differential forms?
Because that's where the answer to their question lies.

[Anonymous No.12161345]

>>12161327
No you retard, just because dx is used as notation in differential forms, that means this is what is meant when you solve differential equations.

[Anonymous No.12161369]

Is [math] G_1 * G_2 / (H_1 * H_2) \cong G_1/H_1 * G_2\H_2[/math] where * is the free product and [math]H_1,H_2[/math] is a norma normal subgroup of [math]G_1, G_2[/math] respectively? I'm thinking yes but I'm having trouble proving it.

[Anonymous No.12161387]

>>12161369
Use the universal property of the coproduct.

[Anonymous No.12161388]

>>12160854
Do you know why /mg/?

[Anonymous No.12161432]

>>12161387
So I have my diagram for the universal property of the coproduct in the context of this problem (which is basically just the universal property diagram for the product with all the arrows reversed). My main question is if I have [math]\pi_1: G_1\to G_1/H_1[/math] and [math]\pi_2: G_2 \to G_2/H_2[/math], do I have the morphisms [math]\pi^{-1}_i: G_i/H_i \to G_i[/math]. If that is the case, then I think it pretty much follows immediately that there is a unique morphism from [math]G_1/H_1 * G_2/H_2 \to G_1*G_2[/math], right?

[Anonymous No.12161441]

>>12161432
No, the coproduct has inclusions. Each of the groups G_1 and G_2 have a specified embedding in their coproduct. It is with respect to these maps that you have a universal morphism. They're not just the inverse maps of the projections, which typically don't exist anyway since the projection usually has a kernel.

[Anonymous No.12161444]

>>12159761
No, you just talk about a sheaf of blah on X.

[Anonymous No.12161449]

So nobody can tell me why the analogue of ringed space for sheaves of groups doesn't exist?

[Anonymous No.12161450]

>>12161388
I can make a system that's incomplete and inconsistent easily.
Take zfc which is incomplete, and also have an axiom that says there exists X such that X is an element of X.
You now have a system that's incomplete and inconsistent

[Anonymous No.12161459]

>>12161449
We told you already, it's just a quirk of language due to the circumstances in which sheaves were first studied. Do you have some other issue or do you not understand that?

[Anonymous No.12161461]

>>12161449
Because abelianed/grouped/moduled space sounds funny.

[Anonymous No.12161464]

>>12161388
Gödel assumes Con(ZFC) for this reason.

[Anonymous No.12161465]

>>12161450
>You now have a system that's incomplete
Why is it incomplete? It's clearly inconsistent, but I don't see why it's incomplete.

[Anonymous No.12161492]

>>12161465
Continuum hypothesis for example

[Anonymous No.12161497]

>>12161492
>what is ekusplojon

[Anonymous No.12161499]

>>12161464
That notation means ZFC is consisten?

[Anonymous No.12161508]

>>12161499
yah

[Anonymous No.12161521]

>>12161497
Good question.

[Anonymous No.12161522]

>>12161497
As people with intuition on what's true and false in a system it would seem like we have a falsehood being taken as true, and thus you can use implications to prove anything. But within the actual system itself, it sees the statement only as true

[Anonymous No.12161539]

>>12161441
Yes I get that there are inclusions in the diagram but I believe you need to use the fact that the inclusion composed with the inverse projection gives us the conditions necessary to use the universal property of the coproduct.

[Anonymous No.12161550]

>>12161539
You don't use the inverse of the projection. It's not even a function, much less a homomorphism.

[Anonymous No.12161553]

>>12161522
I typed this like a retard.
So explosion happens if you prove a single proposition to be both true and false. If A is that statement then obviously A=>B is true for any B because A is false, and obviously that would mean B is true cause A is also true.
I'll admit that I've been retarded and it doesn't quite work in ZFC but it's possible to have a system where for example A and ~A are both true, but not have it be the case that A is both true and false.
I think the only thing you'd need to reach this point is to reject LEM

[Anonymous No.12161660]

Der Grund fur die leere Energie

Annehmen, es gibt eine Box um die Welte zur Zeit des Urknalls. Die Box ist undurchlassig. So, die Welte konnte nicht entfalten, es wurde keine Planeten, Sterne, Menschen geben.

Energie bewegt energie. Das Proto-Universum enthielt alle Energie. Wann das Proto-Universum explodierte, ein Teil der Energie wurde Bewegung, der andere Teil wurde Materie. Die undurchlassig Box hat genug potenzielle Energie, um die kinetische Energie des Universums aufzeheben.
Leere rettet das Universum! Wenn leere ware nicht vorhanden, das Universum wurde kein Leere haben, also eine Box oder ein Energiesegen. Seit die Leere logisch negiert/ersetzt ein negatives Feld oder ein positives Feld, wir *konnten* annehmen die Leere physisch negiert die Felder, mit gleich Energie. Seit es ist ungewiss welche Feld is negiert, es ist ungewiss ob die Leere hat positiv oder negativ Energie, also es schwankt (wie Quanten).

Die prinzip ideen sind dass logisch negiert physich negiert gleich, die Erganzung die Leere enthalt alles (enthalt Gegensatz), und logisch Gegensatz Quantenfluktuationen gleich.

[Anonymous No.12161666]

>>12161508
Wait so if ZFC is inconsistent does that mean Gödel's theorems are wrong?

[Anonymous No.12161690]

For n-vectors u and v, why is it that uv*uv* = v*uuv*?

[Anonymous No.12161740]

>>12161660
Typing in languages other than English outside of /int/ is a bannable offense.

[Anonymous No.12161872]

>>12161740
>burgers seeth this much when someone doesn't speak their shitty languange
kys

[Anonymous No.12161946]

Please help me.

If the size of set A is |A| = n, then

[math]|\{x \epsilon P(A): |X| \leq 1\}| = n + 1[/math]

This is my solution so far:

[math]
|x \epsilon P(A)| = | \{ \emptyset, \{\emptyset\}, \{ A_1, A_2, ..., A_n \} \}| = | \{ \emptyset, \{ \emptyset \} \} | + n = 0 + 1 + n = n + 1
[/math]

I'm not sure if I'm right, so it would be great if someone could correct me.

[Anonymous No.12161954]

>>12161946
The set containing all the A_i doesn't have size ≤1...

[Anonymous No.12161964]

>>12157813
Go back to Khan Academy

[Anonymous No.12161969]

>>12161954
This question was from a textbook and the answer happens to be that. I'm just wondering if that was correct, so I tried to prove it (which is the solution I posted above). I do get where you are coming from, so if the textbook is incorrect, what is the right answer? Would it just be 1? What if set A contains other elements (excluding the empty sets) whose size is less than or equal to 1? How else would I show that?

[Anonymous No.12161988]

>>12161969
Throw that book out and get a new one, everything so far has been fucked. Do you know what the powerset of a set is?

[Anonymous No.12162017]

>>12161954
That's not what it says brainlet. It's the set of the subsets that are less than or equal to one, in other words, the set of singletons and the empty set

[Anonymous No.12162018]

>>12161872
>posting on an international forum in a thread which needs understanding the others in order to be effective using a language that is not the #1 used language on such forum is peak cringe, you kys

[Anonymous No.12162067]

Would you guys say this is in the top 10 theorems of all time?
https://en.wikipedia.org/wiki/Heine%E2%80%93Borel_theorem

[Anonymous No.12162124]

>>12162067
Not even close, all it does is show that compactness is a valid generalization of closed and bounded sets, which isn't too crazy since that's the whole point of the definition to begin with

[Anonymous No.12162165]

>>12161295
>>12161327
>>12161345
great point. it's also a terrible fucking answer because the way one defines integration of forms is by pulling back in coordinates and integrating as usual on R^n, then summing with a partition of unity. so it literally doesn't answer the question at all. it's complete and utter horseshit.
the answer should always be motivated by measure theory.

[Anonymous No.12162168]

>>12161690
it's clearly true

[Anonymous No.12162170]

>>12161539
there is no projection from a free product onto one of the factors. what the fuck are you talking about? are you like removing all the terms from the other factor and then multiplying what remains or something? is that even a homomorphism? i think it is. no one does that.

[Anonymous No.12162178]

>>12161690
because u(v*u) = (v*u)u since the thing in parenthesis is 1x1

[Anonymous No.12162187]

>>12162067
it's a very nice proof but like other anon said it's not surprising
one of the nicest proofs though for sure

[Anonymous No.12162188]

I'm trying to show that a simple function is Lebesgue integrable using measurable partitions. I picked the partition used in a canonical representation, but I can't see who [math]M_i[/math] and [math]m_i[/math] for [math]U[f,P][/math] and [math]L[f,P][/math] should be. I think they have to be [math]a_k[/math], but I'm not sure if this correct.

[Anonymous No.12162246]

>>12162188
are M_i and m_i meant to be the sup and inf of the function over each partition? then yes, they'd be the value of the function on that set since it's constant there.
I mean you should probably tell us what your notation means instead of just writing letters and expecting people to figure them out.

[Anonymous No.12162273]

>>12162246
Yeah. I chose [math]P=\{E_i\}^{n}_{i=1}[/math] and
[eqn]M_i=\sup_{x\in E_i} f(x)[/eqn][eqn]m_i=\inf_{x\in E_i} f(x)[/eqn]
Sorry, I thought it was standard notation.

[Anonymous No.12162302]

Is the set [math]\mathcal{A} = \{\frac{1}{n} + \frac{1}{m} : n,m \in \mathbb{N}, n \neq m \} \cup \{0\}[/math] compact?

[Anonymous No.12162304]

>>12162302
What have you tried?

[Anonymous No.12162306]

>>12162273
Perhaps it's standard notation for Riemann integration. Pretty sure the way most people define Lebesgue integration is by defining what the Lebesgue integral of such a simple function is (simply sum of a_i * measure of E_i) and then taking Cauchy sequences of simple functions for the L^1 norm. These Cauchy sequences may be represented by functions which are the pointwise almost everywhere limits. then you prove many such reasonable functions are limits of Cauchy sequences of simple functions.

[Anonymous No.12162309]

>>12162302
Do you think it's closed? It is a subset of [0, 2], which is compact, so it is itself compact iff closed.

[Anonymous No.12162313]

>>12162302
Is 1 a limit point of the set?
Is 1 in the set?

[Anonymous No.12162368]

>>12162313
Based hand holder

[Anonymous No.12162373]

>>12162306
The book I'm using first uses a definition similar to Riemman integral, but instead of partitioning an interval in subintervals it partitions the interval in Lebesgue measurable subsets and for the sums it uses the measure of each subset. Right now I'm reaching the part that shows both definitions are equivalent soon.

[Anonymous No.12162464]

>ctrl+f "indeed,"
>482 results

[Anonymous No.12162569]

>>12162018
Lmao shut up amerifat, monolingual brainlet fuck

[Anonymous No.12162581]

>>12162569
Cope.

[Anonymous No.12162587]

>>12162464
Insneed

[Anonymous No.12162605]

>>12162587
[math]\varsigma \eta \epsilon \epsilon \delta[/math]

[Anonymous No.12162606]

>>12157556
How do you ask for an infinite series for a closed form expression? For example, you can ask for the closed form of an infinite series, but how about the converse?

[Anonymous No.12162607]

>>12162606
wut

[Anonymous No.12162676]

My uni doesnt even have a real or complex analysis course.
Am I fucked?

[Anonymous No.12162684]

>>12162676
yes

[Anonymous No.12162689]

Is it normal to forget things you studied after a few months?

[Anonymous No.12162696]

>>12162676
Yes.

[Anonymous No.12162697]

>>12162689
Yeah it's like speaking a language. You don't use it you lose it. Or the more complicated parts anyway. Talk to an emeritus professor some time. They can tell you all about the state of their field 30 years ago, but many of the details are lost to them.

[Anonymous No.12162709]

>>12162697
>Raised bilingual
>Don't remember the language anymore
Feels bad.

[Anonymous No.12162710]

>>12162689
no, you are weird and dumb

[Anonymous No.12162740]

>>12162684
>>12162696
Is there anything I can do?

[Anonymous No.12162742]

>>12162740
What are you studying?

[Anonymous No.12162744]

>>12162740
What are your goals? I find it borderline impossible to believe that a university offering a degree in mathematics (pure or applied) doesn't offer classes in analysis.

[Anonymous No.12162843]

>>12161172
literally anything about spin 2

[Anonymous No.12162853]

>>12162740
>>12162744
this. are you at a 2 year school or something? if so, just take as much math as you can this semester and look to transfer for next fall (meaning, apply now -- the deadlines are soon as hell iirc).

[Anonymous No.12162957]

>>12162569
>implying
I'm from Hungary you utter disgrace

[Anonymous No.12162962]

>>12162957
How hard was it to learn English? The only reason I asked is because all of the Uralic languages are ranked as level 4 (with 5 being the hardest) for difficulty of native English speakers learning.

[Anonymous No.12163011]

>>12162962
English is super easy to learn. It's such a simple language.
t. another Uralic

[Anonymous No.12163051]

>>12163011
Based and Finnpilled.

[Anonymous No.12163066]

>>12163051
Yes.

[Anonymous No.12163090]

>>12163066

[Anonymous No.12163104]

>>12163090
what math do I need to study before learning Finnish?

[Anonymous No.12163118]

>nonassociative algebras can be associative, but nonnegative integers cannot be negative
Increasingly tempted to ditch English and do math in a language with better support for agglutinative definitions...

[Anonymous No.12163136]

>>12163090
Just imagine having to write essays with a minimum word count back in school with a huge load of information packed into one word like for example
>koirastanikokaan
>even out of my dog?
500 words was like half of the Bible.

>>12163104
Lindelöf spaces.

[Anonymous No.12163454]

>>12161295
>>12162165
pretend I'm an innocent undergrad and tell me what does the dx and dy mean in integration and ODE. I'm very curious about your answer.

[Anonymous No.12163571]

>>12157556
Since Sines and Cosines come form the idea, that Homoticies conserve ratios, sholdn't there be generalize formula of sine for any two arbitrary angles?

[Anonymous No.12163577]

>>12162373
I see. That seems like it works completely the same as the typical way of defining the Lebesgue integral, and it probably illuminates a lot more clearly why continuous functions have the same result when you integrate with one or the other on compact sets. But it's also nice to define it the other way because in the process you prove that the space L^1 is complete (as an abstract metric space completion of the simple functions) and that the simple functions are a dense subspace (this is extremely useful for many many proofs where it's essentially obvious for simple functions and then you can take limits).

[Anonymous No.12163593]

>>12163571
*Homotheties

[Anonymous No.12163602]

>>12161690
uwu

[Anonymous No.12163606]

>>12162962
>>12162957
100% agreed, especially consuming English media through one's childhood makes it easy.

[Anonymous No.12163612]

>>12163454
Hmmm, okay. I wasn't thinking about ODE and obviously measures have nothing to do with ODE (unless we want to start talking Radon Nikodym theorem, which I don't). So here's an attempt:

The dx in integration and the dx in differentiation sound like they mean the same thing, an infinitessimal change in x. But there isn't any such thing as an infinitessimal change in x, that's just a useful way to think about it.
In both of these cases, the dx is just notation. There's no such thing as dx outside of d/dx, or dx outside of integral dx. It would be like you writing a left parenthesis without a right parenthesis, or a fraction with nothing in the numerator. The dx doesn't stand on it's own, it's just part of the notation. Why is it there? Because it fills in the spot of a Delta x, which does stand on its own but goes away after we take a limit.

So when people think of derivatives like a ratio of a small chance in f over a small change in x, they're thinking about derivatives in a useful way but not in a perfectly true way. Similarly, when they think of integrals as a sum of quantities f(x) dx, they're thinking about integrals in a useful way but not in a true way. Sometimes in math, it's fine to think about things in not quite the exact way you're supposed to think about them (as long as you prove that the changes in your perspective are justified.)

Let's do that now in a really important case, separation of variables for ODE. Why is it that people can just "multiply both sides by dx" in an ODE, when I just said that dx isn't actually a thing, it's just part of two pieces of notation? This is called an "abuse of notation." It's abuse because it doesn't really make any sense from a mathematical perspective. But it still works as long as we integrate afterwards. Let's see why.
(Cont)

[Anonymous No.12163628]

>>12163454
>>12163612
Say you have an ODE [math] \frac{dy}{dx} = f(y)g(x) [/math]. This is the sort of ODE where we want to use seperation of variables.
Here's what you would do if you were using the abuse of notation and you treated dx and dy like they're actually things, and not just symbols in the notation for a derivative.
[eqn] \frac{1}{f(y)} \, dy = g(x) \, dx \quad \implies \quad \int \frac{1}{f(y)} \, dy = \int g(x) \, dx [/eqn]
Here's what you're actually allowed to do, if we make use of the substitution [math] u = y(x) [/math]:
[eqn] \frac{1}{f(y(x))} \frac{dy}{dx} = g(x) \quad \implies \quad \int \frac{1}{f(y(x))} \frac{dy}{dx} \, dx = \int g(x) \, dx \quad \implies \quad \int \frac{1}{f(u)} \, du = \int g(x) \, dx [/eqn]
After we integrate and change back from u to y, we get the same thing as we did when we abused notation.
So the abuse of notation hides that we need to do a substitution in our integral. But it still "works" even though it doesn't make mathematical sense. So people do it.
You might notice we did a substitution, where people usually also abuse notation and write something like [math] du = \frac{dy}{dx} dx [/math]. This is another thing that you can justify, just by checking what substitution actually does and that it's the same as what you get from pretending du and dx are anything but meaningless notational symbols.

[Anonymous No.12163642]

>>12163612
>>12163628
You know after I wrote this I'm thinking about how I used a similar argument to explain what dx and dy were to a physicist a week or so back and he just kept saying the same "I think it's just an infinitessimal change in x" bullshit over and over again to me. Why is it that when a mathematician explains something to a physics undergrad, the physics undergrad takes it upon himself to talk back and tell the mathematician what he thinks it REALLY is? Math undergrads don't talk like that and take the time to think through why their preconceptions might be built on shoddy foundations. I certainly do not mind being corrected if it's for a legitimate reason, especially because the correction is often warranted, but even if the correction is misguided. But when someone can't get out of their extremely warped perspective of how mathematics works and acts like you're stupid for caring about this stuff, it's so fucking annoying.

[Anonymous No.12163722]


vec3 mathMarch(vec3 startPos; vec3 dir)
{
vec3 pos = startPos;
for (int i = 0; i < MAX_STEPS; i++)
{
float dist = sdf_sphere(pos);
pos += dist*dir;
}
}


Hi /sci/ dying in the ass here trying to notate this mathematically. Not sure how to throw it in a sigma and can't think of way to re-write it recursively. Any tips?

[Anonymous No.12163730]

>>12163722
Sorry I'm a /g/ brainlet, here it is formatted.

[Anonymous No.12163739]

>>12163612
differential forms give meaning to dx outside of integration, they make dy/dx into a true ratio. and they do it in a way which corresponds to the original intuition. so why is this worse answer than "it's just notation"?

[Anonymous No.12163743]

>>12162464
I love using indeed, why the face?

[Anonymous No.12163747]

>>12163571
>generalize formula of sine for any two arbitrary angles

You mean the Law of sines and cosines? loom it up retard.

[Anonymous No.12163792]

>>12163730
I'd think

>>12163730
[math] f^{\sf MAXSTEPS}({\sf startPose}) [/math]

where
[math] f^k({\sf pos}) := {\sf pos} + {\sf dir}\cdot {\sf sdfSphere}\left(f^{k-1}({\sf pos}) \right) [/math]
and
[math] f^0({\sf pos}) := {\sf pos} [/math]

but do a quick implementation like that to confirm

[Anonymous No.12163796]

Suppose you have a graded ring [math]B[/math]. Is it required that the ring is non-empty in every degree?

For example, can I assume there exists an element [math]f\in B_1[/math]?

I'm asking because I'm reading this book that does not make any assumptions on the graded ring (other than it is an algebra over a field, but I don't think it's relevant here) and he's picking some element from [math]B_1[/math] for an argument. When reading Hartshorne, I think he always used to make some extra strong assumption like the irrelevant ideal [math]B_+[/math] is generated by [math]B_1[/math] so it wasn't be ambiguous, but he also used that property for other things (like finding an open cover with certain properties)

[Anonymous No.12163813]

actually, maybe better to write

[math] f({\sf MAXSTEPS}, {\sf startPose}) [/math]

where

[math] f(k, {\sf pos}) := {\sf pos} + {\sf {min}}(k, 1) \cdot {\sf dir}\cdot {\sf sdfSphere}\left(f(k-1, {\sf pos}) \right) [/math]

[Anonymous No.12163816]

>>12157556
To those who know about it, what does /mg/ think about open individualism?
Pic Unrelated

[Anonymous No.12163832]

>>12163796
>Is it required that the ring is non-empty in every degree?
Non-empty, yes, but not non-trivial. Take the cohomology ring [math]H^*(\mathbb{Z} /p\mathbb{Z}; \mathbb{Z})[/math] for your favourite prime [math]p[/math]. Here, [math]H^n(\mathbb{Z} /p\mathbb{Z}; \mathbb{Z})=0[/math] for [math]n[/math] odd, [math]H^n(\mathbb{Z} /p\mathbb{Z}; \mathbb{Z}) \cong \mathbb{Z}/p \mathbb{Z}[/math] for [math]n>0[/math], and [math]H^0(\mathbb{Z} /p\mathbb{Z}; \mathbb{Z}) \cong \mathbb{Z}[/math]. It is a graded ring.

[Anonymous No.12163842]

>>12163832
Right, I forgot about 0. Does that mean the book is actually needs a stronger assumption?

[El Arcón No.12163846]

>>12163792
>>12163813
sf looks hot there

[Anonymous No.12163849]

>>12163796
>>12163842
IIRC for a homogenous algebra you insist that the zero component of the gradation be just the base ring.

[Anonymous No.12163858]

>>12163849
Aaaaaaand I was completely wrong.
https://perso.univ-st-etienne.fr/rberger/homog.pdf

[Anonymous No.12163870]

>>12163849
>>12163858
Well in the case of a graded algebra over a field, you're going to want the field to have degree 0, otherwise the gradation will be trivial

[Anonymous No.12163879]

>>12163870
Yes, but there's a difference between asking for the field to have degree zero and asking for the degree zero component to be just the field (as in i.e. [math]k[x][/math]).

[Anonymous No.12163886]

>>12163879
Ah I thought you meant more like [math]A\subseteq B_0[/math] for some graded ring [math]B[/math] over [math]A[/math]

[Anonymous No.12163899]

>>12163792
Thank you so much based Emma poster, this looks perfect

[Anonymous No.12163914]

>>12163849
>>12163858
From Liu hisself.
Either the homogeneous algebra has non-trivial grade one elements, or it's a field.
If it's a field, Spec and Proj are empty and have minus infinite dimension, I think, so the formula still works.

[Anonymous No.12164041]

>>12158905
Have to agree with >>12158936 on this, the two parameter parametrisation of the primitive triples is well known, just fix one of the parameters

[Anonymous No.12164082]

>>12162676
yes

[Anonymous No.12164255]

>>12163612
>>12163628
Good posts. Thanks.

[Anonymous No.12164263]

When [math]\mu[/math] is a distribution function for random variable X, what do we mean by [math]Ef(X)=\int f(y)\mu(dy)[/math] when f measurable? I really don't understand this notation [math]\mu(dy)[/math]. Anybody here know?

[Anonymous No.12164278]

>>12164263
it means the same thing as [math]d \mu[/math]

[Anonymous No.12164279]

What is the endgame of probability theory? I don't know of any prized open problems...

[Anonymous No.12164288]

>>12164278
Ah okay thank you <3

[Anonymous No.12164353]

>>12164279
most every mathematician is just trying to advance the field they're interested in; not everyone has to be working on the hottest shit . . .

[Anonymous No.12164583]

>>12164353
yea but I feel like algebra and topology have so many great ideas and unifying programs going on.

[Anonymous No.12164640]

>>12163739
It doesn't, it just borrows notation.

[Anonymous No.12164687]

>>12161102
I do. It's orange and the ink is a bit smudgy.

[Anonymous No.12164751]

N E W
N I K O L A J
V I D E O

[Anonymous No.12164788]

>>12162689
Yes, but at the same time remember that your next exposure to the material will stick a lot quicker/hard.
Look up the book "make it stick". It's about teaching and learning and it's very good.

[Anonymous No.12164861]

>>12164751
hello nikolaj when are you going to have cute grills in your videos like in your python videos

[¬ ∃x. ∀y. (y ∈ x) No.12164916]

>>12164861
That wasn't me. I can invite her back on, but I haven't done anything related to mathematical finance in a while.

>>12164751
Annoying. But this was more fun than expected
https://youtu.be/yo1uj9a-Ig8

[Anonymous No.12165050]

>>12164916
make a video on internal set theory.

[Anonymous No.12165079]

>>12164916
who is nikolaj is just a fancy 4chan memer on youtube? (ye, i don't want to spend 1h on a video)

[Anonymous No.12165113]

>>12164916
You seem to have lost weight. Good job.

[Anonymous No.12165116]

>>12164916
Nice video, Bogulyubov.
>if the power set of the set of all sets were equal to the set of all sets
Can you actually prove it like that in ZFC?
As far as I know (not far at all), ZFC doesn't actually rule out urelements, so if we had one like [math]a[/math], then [math]\{ a \}[/math] would be in the set of all sets, but I can't see a reason for it to be in the power set (since [math]a[/math] isn't a set, and thus not a subset of the set of all sets).

[Anonymous No.12165117]

Which are some mathematical branches with interesting notation?

[Anonymous No.12165121]

>>12165117
Planar algebra

[Anonymous No.12165128]

>>12165116
Never mind, I'm wrong, Extensionality screws it up.

[Anonymous No.12165149]

>>12165079
Yeah it looks like he's basically some fag who spams his videos in every thread.

[Anonymous No.12165178]

>>12157556
Nice ive made molecules in the shape of 14 for research project. Theyre called rotaxanes and are pretty nifty things.

[Anonymous No.12165200]

So any continuos compact curve can be uniformly approximated by polygonal. What are the typical generalizations of this theorem to higher dimensions?

[Anonymous No.12165215]

How many people in this general are published

[Anonymous No.12165249]

>>12165116
What I had in mind is that if [math] {\mathcal P}V \subseteq V [/math], then the map given by just identity on [math]{\mathcal P}V[/math] while mapping the rest to e.g. the empty set would be a surjection.

>>12165117
I think I've only ever seen varpi [math] \varpi [/math] in plain number theory.

[Anonymous No.12165261]

A surjection [math]V\to {\mathcal P}V[/math], that is.
So we find [math]V[/math] has a new set (whatever that new set may hold).

[Anonymous No.12165264]

A surjection [math]V\to {\mathcal P}V[/math], that is.
So we find [math]{\mathcal P}V[/math] holds some set that wasn't in [math]V[/math] (whatever that new set may hold).

[Anonymous No.12165341]

>>12164640
>It doesn't
???

[Anonymous No.12165345]

>>12165200
any smooth manifold can be triangulated

[Anonymous No.12165399]

>>12165249
Ah, I see. That works.

[Anonymous No.12165414]

What do you guys think of the idea of "logical independence"? Basically, you can say that
>(x implies y) is false and
>(not x implies y) is false and
>(x implies not y) is false and
>(not x implies not y) is false
Then x and y are independent. You may note the fact that whether or not x is true, there are cases where y is true and cases where y is false. From this we see that x is never capable of determining y's truth value, all combinations of their truth values are possible, and one can be varied freely without contradicting the other.

However, this doesn't hold the same sort of independence as a universe such as one equipped solely with one ordered pair (x,y) where x and y are independent, because the former contains the restriction that even if all possible combinations of x and y's truth value are possible, one truth value of x may correspond with a amount of states where y can have a given truth value, meanwhile, in the ordered pair universe, x and y have equivalent cardinality of free states (R^1).

[Anonymous No.12165431]

>>12165414
I can't interpret either of this sentences.
Are you defining a new logic
If "implies" is material implication, then "not x implies y" is equivalent to "x or y", so if this is false, both are already false.
There's logics that avoid the so called paradoxes of material implication, see e.g.
https://en.wikipedia.org/wiki/Relevance_logic

It should be clear to you that nobdy but possibly you could understand the part where you start speaking of
>cardinality of free states (R^1).
Also, I'd not pull an Immanuel Kant and write a paragraph long sentence.

[Anonymous No.12165457]

>>12165414
I mean it's possible if they're predicates dependent on x for example and each statement is quantified over all of x but it's really not that special

[Anonymous No.12165479]

>>12165431
>not x implies y
I take this to mean that there are cases where x is true and y is false
>cardinality of free states (R^1)
I just meant that x and y can both vary freely over the reals, they have the same range or cardinality if you want to think in terms of alephs

[Anonymous No.12165484]

I was reading a complex functions book and the author said (in context of the riemann sphere) that points with norm |1/e| are in the e neighborhood of infinity. Is this motivated or convention?

[Anonymous No.12165533]

>>12165484
The motivation is that it's analogous to the relationship between neighborhoods of 0 or 1 in [0,1] and neighborhoods of positive and negative infinity in the extended reals. It just extends the analogy to complex

[Anonymous No.12165593]

I never thought I would become interested in science or maths and here I am so I looked up lectures on youtube on
So I watched an intro to linear algebra and I had to pause some 6 minutes into it for like 10 minutes to understand what was said and rewatch it several times and from there I could follow for another 10 minutes when I could not follow anymore at all
Is this normal or am I already a lost cause?

[Anonymous No.12165609]

>>12165593
Just give up now. There is no happiness for midwits in mathematics.

[Anonymous No.12165610]

>>12165533
From proofwikie:
>A neighborhood of +∞ is a subset of the set of real numbers R wich contains an interval (a,+∞) for some a∈R.
Wouldn't the proper analogy be then that the point with norm 1/e is in the 1/e neighborhood -- isn't calling it an "e" neighborhood a weird convention? Or does it relate to the fact that 1/e has a close position to the origin along the sphere and plane

[Anonymous No.12165611]

>>12165593
ANon. You are learning a brand new thing. Just be patient. How long did it take you to learn to potty train? To learn English as a baby? Years.

>>12165609
Weakling

[Anonymous No.12165621]

>>12165593
It might be a shit video. Or you're bad at math. Or somewhere in between. (Or you'd learn better from text than videos; not everyone's visual. Also, what is your notetaking methodology? You're not just sitting there listening, are you?)
Try some more videos. On the one hand, incompetence in math won't get you far; on the other hand, math is hard and I have a low opinion of most youtube tutorial content creators.

[Anonymous No.12165625]

Are French, English, and German the only languages you need to know for math?

[Anonymous No.12165638]

>>12165621
It was an actual university lecture and I was taking notes until the point where I did not understand anymore, I tried writing down what I did not understand but the further I got the less I knew what I did not even understand
I don't know if I am bad at maths, in school I never learned for it and passed anyway albeit with mediocre grades and now I haven't taken a maths class in five years and only suddenly now I got an interest in science and wanted to dig deeper

>>12165611
Well, the question is should I keep trying? After just one lecture I feel incredibly stupid for not understanding almost anything

[Anonymous No.12165639]

Let X_1, ..., X_n be iid random variables with common distribution exp(t). Let m_n = min{X_1,..,X_n} and let w_f = inf {x: F(x)>0}, how do I show that m_n converges to w_f in L_p for all p>0? I've already found the distribution of the minimum and I know that it converges almost surely

[Anonymous No.12165663]

>>12165625
Russian. You would be better served by just learning German and Russian if you're a native English speaker.

[Anonymous No.12165685]

Can someone review this proof of the Cantor set having measure zero for me?

Consider the sets $C_n$ used in the construction of the Cantor set $C$. We choose some $\epsilon > 0$ and construct open sets $O_n$ s.t. if $x \in C_n$, then $(x - \epsilon/n, x + \epsilon/n) \in O_n$. Note that $\forall n, C \subseteq O_n$. Since $\lim_{n \rightarrow \infty} |O_n| = 0$, we have that the Cantor set has measure zero.

[Anonymous No.12165697]

>>12165685
Fuck, here's a better one:

Consider the sets [math]C_n[/math] used in the construction of the Cantor set [math]C[/math]. We choose some [math]\epsilon > 0[/math] and construct open sets [math]O_n[/math] s.t. if [math]x \in C_n[/math], then [math](x - \epsilon/n, x + \epsilon/n) \in O_n[/math]. Note that [math]\forall n, C \subseteq O_n[/math]. Since [math]\lim_{n \rightarrow \infty} |O_n| = 0[/math], we have that the Cantor set has measure zero.

[Anonymous No.12165699]

>>12165697
That doesn't look inline to me, what did I do wrong?

Does the proof read well? Is it right? Does it miss anything important?

[Anonymous No.12165724]

>>12165611
Midwit coper.

[Anonymous No.12165729]

>>12165699
>doesn't look inline to me
What do you mean? It's displaying normally and not line breaking.

[Anonymous No.12165739]

>>12165638
It's a part of learning to not understand, try using a couple different resources for a topic or just ask questions here

[Anonymous No.12165745]

>>12165729
For me it is. Weird.

[Anonymous No.12165751]

>>12165745
Check your adblocker and make sure you aren't posting from meme apps like Kuroba.
>do adblockers really
Adblockers really. uMatrix in particular.

[Anonymous No.12165786]

>>12165663
How hard is German to learn as a native English speaker?

[Anonymous No.12165792]

>>12165786
meh, it's not bad

[Anonymous No.12165953]

>>12165345
But can it be approximated uniformly by such triangulation?

[Anonymous No.12165993]

>>12165751
Nah, I'm using Safari with no adblocks.

>>12165685
>>12165697
Bump.

[Anonymous No.12166013]

>>12165993
Looks inline to me and I'm using safari but I haven't updated yet

[Anonymous No.12166067]

>really bad at analysis

Please help. What am I missing? The proofs are nothing like what I've done before.

[Anonymous No.12166074]

>>12166067
Post examples.

[Anonymous No.12166084]

>>12165993
>>12166013
go back
>>12166067
>proof class didn't prepare brainlet for analysis
>w-what do i do!????
you hate to see it

[Anonymous No.12166092]

>>12166084
>go back
To?

[Anonymous No.12166165]

>>12166074
Proving the universal property of Cantor sets. I can get by in class just fine, but the method of proofs isn't something that's coming to me through independent thought like with other math classes. I feel like I'm missing some key ingredient to help me think in terms of analysis.

[Anonymous No.12166200]

>>12163743
Your pic but unironically

[Anonymous No.12166240]

>>12166200
same

[Anonymous No.12166427]

What's the highest IQ group?

[Anonymous No.12166455]

>>12166427
Integers mod 2, no question about it

[Anonymous No.12166471]

>>12166455
This.

[Anonymous No.12166490]

>>12166427
lie groups

[Anonymous No.12166491]

>>12166067
Read book of proof

[Anonymous No.12166492]

>>12164353
Don't post nigger garbage like that ever again.

[Anonymous No.12166495]

>>12164751
Nikolaj deserves to die in agony

[Anonymous No.12166497]

>>12163104
combinatorics

[Anonymous No.12166501]

>>12157988
Horrible list

[Anonymous No.12166506]

>>12160207
True

[Anonymous No.12166507]

>>12160315
kys

[Anonymous No.12166508]

>>12165639
Go back to the textbook retard

[Anonymous No.12166522]

>>12166495
Why?

[Anonymous No.12166594]

I don't know if anybody will actually read through pic related but why can you assert that there are q and r such that r is less than |c|/2.
I thought Euclidean division could only show that it's less than |c|

[Anonymous No.12166595]

>>12163104
Function theory.

[Anonymous No.12166600]

>>12166594
Also the bottom half is just case work for different values of c so you don't have to read that I just included the whole proof in the pic

[Anonymous No.12166618]

>>12157800
Functions as a concept are older than sets. Also, keep in mind that in some contexts it is often convenient to call the "same"(in the sense that f(x)=g(x) when ever f and g are both defined at x) functions the same name even if their domains or targets are different

[Anonymous No.12166658]

>>12163739
it's a worse answer for an undergrad in a calculus course 100%.
most of them haven't even taken linear algebra so how is the concept of a differential form even supposed to be coherent to them?
not to mention the concept of a tangent space is something they only develop in calculus truly
so I would say for most undergrads there's no reason to bring the full wait of differential forms to bear on this question unless they have a serious interest in mathematics

[Anonymous No.12166691]

>>12166658
>unless they have a serious interest in mathematics
You and I both know 90% of students in Calc I have no interest in math and are just there out of obligation to a degree plan.

[Anonymous No.12166704]

>>12157930
Follow a schools schedule dumb ass find their catalog moron

[Anonymous No.12166708]

>>12158897
Can you give an example of thinking in words how else does one think?

[Anonymous No.12166714]

>>12166594
(ay - 19bx)/c is just a real number
you can always write a real number as [math]q + r[/math] where q is integer, and [math]|r| \leq 1/2[/math]

[Anonymous No.12166716]

>>12161102
Buy it from the German website

[Anonymous No.12166751]

Anyone read this? Worth a read for somebody looking to get into higher mathematics with a highschool level education?

[Anonymous No.12166768]

>>12166708
You think in words when you consciously vocalize your thoughts.
Most of the thoughts I have are not in words, they come in symbols, shapes and vague notions that are hard to describe. In order for me to convert them to words it takes conscious effort and energy.
Imagine thinking about going to the kitchen to eat. For me, just thinking about it is very different than forming the sentence in my mind "I want to go to the kitchen to eat".
Isn't it the same for you?

[Anonymous No.12166778]

>>12166751
Yes it's the first book any math major should read. You can't understand proofs without formal logic.

[Anonymous No.12166782]

>>12166751
Also remember to do all of the exercises.

[Anonymous No.12166791]

>>12165685
>>12165697
Wtf Mathbros, how do you understand this shit? Looks like a magic spell ya fookin wizards.

[Anonymous No.12166797]

>>12166791
>how do you understand this shit?
By reading it.

[Anonymous No.12166831]

>>12166797
C-m v2 56 x 69 mmm 69 `;-9999'-86555, take a trip to the cum zone, 974 lim ∞ = 0

SOLVE FOR?

[Anonymous No.12166836]

>>12166067
>Please help. What am I missing? The proofs are nothing like what I've done before.
do constructive analysis, instead of the crap à la bourbaki where they pull existence out of their excluded middle ass.

[Anonymous No.12166846]

New!!!
>>12166845

[Anonymous No.12166852]

New thread:
>>12166538

[Anonymous No.12166856]

>>12166852
No, psycho

[Anonymous No.12167016]

>>12166856
No, normalfag

[Anonymous No.12167022]

>>12167016
>No
Glad we agree.

[Anonymous No.12167065]

>>12166507
Don’t get jealous slut there’s enough cock to go around.

[Anonymous No.12168017]

Is there any way to improve the op? I was thinking why don't we put fields and then popular readings of them on it, something like:

>Analysis
Rudin
Tao
Etc.

[Anonymous No.12168456]

why are there 3 /mg/'s

get your shit together

[Anonymous No.12168647]

>>12162853
Spherical and bezelless LED monitors when?