/mg/

[Anonymous No.12030264]

Math, generally
>sets provide a non linear way of viewing reality
edition
Talks maths

[Anonymous No.12030413]

>>12030264
You are supposed to link to the previous thread. It's literally the supermarket trolley ethics scenario applied to internet forums. The point of studying math, is to improve so by not doing this you are sabotaging yourself.
I'll do it for you though: >>12025349

[Anonymous No.12030430]

>>12030413
Isometric embeddings of the flat torus in [math]\mathbb{R}^3[/math]

[Anonymous No.12030458]

>>12030430
This is it: I'm building an onahole from that

[Anonymous No.12030463]

>>12030430
Can this be continued fractally? What is the resulting dimension?

[Anonymous No.12030493]

>>12030264
The better venn diagram

[Anonymous No.12030499]

Threadly reminder to fall in love with physicists

[Anonymous No.12030524]

Math is inconsistent.

[Anonymous No.12030539]

>>12030458
based coomer

[Anonymous No.12030548]

>>12030524
yes and?

[Anonymous No.12030560]

whats the best example of duality in math?

[Anonymous No.12030567]

Why is integrating the intersections of different solids so difficult? There's no general way to solve sphere/torus intersections analytically.

[Anonymous No.12030571]

Help me out here. I remember reading about some guy who purported to solve one of the millenial problems, but his proof was so dense, with so much new math invented, that nobody could be bothered to check it. Do you recognize this story and have some details?

[Anonymous No.12030580]

>>12030571
mochizuki?

[Anonymous No.12030585]

>>12030571
Sounds like Mochizuki and the abc conjecture.

[Anonymous No.12030604]

>>12030560
Stone. Priestley if you wanna be fancy.

[Anonymous No.12030608]

>>12030463
>Our program generates pictures of the isometric embedding of the square flat torus that reveal some kind of self-similarity in the infinite succession of corrugations. This strongly suggests a fractal structure. This seems even more surprising because the fractal nature is incompatible with the presence of tangent planes. This seeming paradox is resolved when we look more specifically at the behavior of the corrugations at different scales. At each stage, the amplitude of oscillations decreases too quickly to ensure a perfect self-similarity. As a consequence, the limit surface is not as rough as a fractal. Since the limit surface is C1 regular, we call it a C1 fractal . The pictures below show the differences of roughness between a fractal curve and a C1 fractal.

[Anonymous No.12030614]

>>12030580
Looks like it, though I've read it so long ago I can't be sure. There is also this polish NEET who has been working on a P =! NP proof for sixteen years, trying to show that a certain permutation function is one-way only. I've been reading his blog, it's fascinating, he reports his progress making vague references to some lemmas and definitions that only he knows what they contain. He claims he's almost finished. The guy is either a genius or a severely deluded sad fuck. Hard to tell, he's too coherent to be schizophrenic though.

[Anonymous No.12030651]

Stupid person here. I'm trying to move the edges of a polygon so that at least one vertex of the polygon matches at least one vertex of the rectangle. I thought just scaling up the polygon at its centroid would be enough, but clearly it's not. I also thought of projecting the vertices to the nearest side, but again, that probably does not work (unless it does, at infinity?).

How should I do something like this?

[Anonymous No.12030663]

>>12030651
This doesn't seem possible at all.

[Anonymous No.12030672]

>>12030651
> at least one vertex of the polygon matches at least one vertex of the rectangle
What? You just need to translate it until one of the vertices meet. Unless there are other conditions on “moving” the polygon that I don’t understand

[Anonymous No.12030673]

>>12030651
>I'm trying to move the edges of a polygon so that at least one vertex of the polygon matches at least one vertex of the rectangle.
at least one to at least one? you're trying to do this for a general case of any polygon at all? what exactly is the problem here?

[Anonymous No.12030678]

>>12030651
>at least one vertex of the polygon matches at least one vertex of the rectangle
easy

[Anonymous No.12030684]

>>12030672
>>12030673
Shit, I only realized I described it horribly too late. What I want to do is have any polygon with at least 4 or more vertices to be "projected" onto a rectangle, but making it so that at least each of the rectangle's vertices has one vertex from that polygon.

Sort of like inflating a balloon inside of a box, but in 2D.

[Anonymous No.12030692]

>>12030684
>What I want to do is have any polygon with at least 4 or more vertices to be "projected" onto a rectangle, but making it so that at least each of the rectangle's vertices has one vertex from that polygon.
yeah it's easy to imagine a polygon for which this is impossible, this is not going to happen for any polygon with at least 4 or more vertices (unless you do unspeakable transformations to them)

[Anonymous No.12030706]

>>12030684
Choose four vertexes on your polygon and map them to your corners.
Then just map any other point to the line between the two points it is between, based on the distance between the two vertices (along the path which is the polygon's boundary).

[Anonymous No.12030709]

>>12030684
so you want a formula for the largest rectangle that a polygon can fit in itself? but also have 1 common vertex? just pick one vertex and project the sides until you hit the outer polygon, you can even try to project a rectangle from every vertex and compare which one is the largest

[Anonymous No.12030720]

>>12030684
In that case I think it’s impossible, but it may be that you’re able to get creative with the way you project it. For instance, maybe you pick a different point than the center to draw your projection lines to

[Anonymous No.12030748]

>>12030692
I would not mind those unspeakable transformations. The balloon inflation example allows it even. I just wouldn't want for one vertex of the polygon to be projected onto a side of the rectangle it shouldn't, like the topmost vertex of the star going to the edges, even though there are other vertices that would "minimize" the distortion.

>>12030706
>>12030709
>>12030720
Will consider these, Thanks anons. Honestly I'm not even sure why I suddenly thought about this problem. Ah well.

[Anonymous No.12030770]

> watch new 3blue1brown video
> it has the meme fruit problem in it
> close the video

[Anonymous No.12030779]

Why all the five Platonic solids exist (I'm NOT asking why there cannot be more of them, as hexagons would make a flat object and 6 regular triangles forms an hexagon)? How come one can glue three regular triangles together at their edges so a fourth one matches perfectly? How can eleven pentagons form a object that twelveth pentagon finishes perfectly?

Funny how I am able to derive volumes of all these objects given edge length and make a computer script drawing these objects as 3D projection from any viewing angle, yet I cannot proof they exist (except cube and perhaps tetrahedron if I really think about it a few hours).

Also why there are exactly 13 Archimedean solids and why they exist? Please answer the Platonic question first and this in another post if you will.

[Anonymous No.12030808]

>>12030779
>why all the
>why there are
>why they exist
holy fuck learn to speak english, retard

[Anonymous No.12030873]

>>12030808
Thank you for correcting my spelling mistakes, fuckwit. Now I had to delete my post and the question bothers me forever as I cannot find the answer otherwise. Bet you are a fat american virgin who can't speak any other language yet cry about minor mistakes of foreign speakers.

[Anonymous No.12030883]

>>12030205
https://www.youtube.com/c/NikolajKuntner/videos

This nibba?

[Anonymous No.12030888]

>watching 3B1B over the age of 15
ishygddt

[Anonymous No.12031030]

>>12030888
YouTube was new when I was 15, and it contained no popular math videos.

[Anonymous No.12031194]

>>12031151
I was really talking about the concept of proof books, or "heuristic" ones. Have you ever read one?

[Anonymous No.12031210]

>>12031194
Ish. Had a discrete class in my freshman year which doesn't seem far from how to prove it. Don't knock it till you try it

[Anonymous No.12031373]

>>12030883
Yes, that Nikolaj. It seems he wasn't the one in question, though, but he's pretty handsome regardless.

[Anonymous No.12031596]

>>12028440
>still 0 solutions posted.

[Anonymous No.12031607]

>>12030264
How do I get into topology? I've enjoyed algebra a lot, but I've mostly focused on the side of complex analysis which went into analytic number theory, special functions and so on and neglected topology. I mainly want to learn this to get to a deeper understanding of Riemann surfaces and catch up on differential geometry.
Any recommendations? Thanks in advance.

[Anonymous No.12031618]

>>12031596
The equivalence relation basically boils down to the binary sequences having all digits the same except a finite number. This leaves you with equivalence classes of infinite strings so cantors diagonal argument still applies, meaning the cardinalities are equal.
I would have posted earlier but I thought someone else got it already

[Anonymous No.12031637]

>>12031618
>The equivalence relation basically boils down to the binary sequences having all digits the same except a finite number
It doesn't.
>This leaves you with equivalence classes of infinite strings so cantors diagonal argument still applies, meaning the cardinalities are equal.
Even if it did boil down to what you said, Cantors argument wouldnt work. And even if it did, all it would do is show that it's uncountable. That does not prove that it has the same cardinality as X.

[Anonymous No.12031889]

>>12031596
>>12028440
Okay I'll post. [0,1]^N has the cardinality of R, so if we show that X/~ can not be countable, then it must be equal to R.
Assume x_n enumerates X/~. Let x_n,k be a sequence which is a representative of the equivalence class x_n. If we fix a k and consider the set {x_n,k: k in N}, then this set can obviously not be all of [0,1]. We pick a number y_k in [0,1] which is not in this set. Then the sequence y_k is different in each k to each sequence x_n,k, in particular not equivalent. We have found a new equivalence class with represenative y_k. Therefore our list x_n was not surjective.

[Anonymous No.12031894]

>>12031889
I meant the set {x_n,k: n in N}

[Anonymous No.12031927]

>>12031889
>so if we show that X/~ can not be countable, then it must be equal to R
How so?

[Anonymous No.12031928]

>>12031889
Also how are x_n,k in [0,1]? Arent they just 0 or 1?

[Anonymous No.12031933]

>>12031607
isham book

[Anonymous No.12031936]

>>12031889
this is why everybody thinks the law of excluded middle is a joke.

[Anonymous No.12031950]

>>12031928
lmao I read it as the interval... nevermind my post then

[Anonymous No.12031959]

>>12031927
Well irregarding the fact that I misread the problem, is it really not sufficient to prove |N| < |X| <= |R| to conclude |X| = |R|? Because the continuum hypothesis is independent of ZFC or some shit? This goes beyond my understanding. How the fuck can I just say uuh I guess this might be an explicit counterexample to the continuum hypothesis.

[Anonymous No.12031971]

>>12030560
eckmann-hilton

[Anonymous No.12031975]

>>12031959
There is a simple proof within ZFC that doesnt use CH.

[Anonymous No.12031996]

>>12031975
I'm intrigued. A proper diagonalization argument to show that X/~ is uncountable should be the following: assume x_n is a sequence of infinite binary strings. We want to find a binary string which is nonequivalent to any of these. We call this number x.
We set every other digit of x to be the opposite of x_1 in that position.
Then we set every 4th digit of x (shifting pur starting point so we dont overlap with the previous digits) to be different to x_2 in that position.
We do this for every x_n and thereby find our number x. Because for every n a fixed percentage of of digits between x_n and x is different, they are nonequivalent.
Then by the law of excluded middle I have either solved the problem or disproven CH qed.

[Anonymous No.12032069]

>>12031996
Youre very very close to the actual solution (without using CH). Try thinking about it a bit more.

[Anonymous No.12032072]

>>12030560
poincare

[Anonymous No.12032075]

>>12030560
Concepts I understand - arrays of numbers duality.

[Anonymous No.12032116]

>>12030264
Since these threads are almsot exclusively related to algebra, I ought to add some stats.
Is there an equivalent to Markov chains, but such that the probabilities of transitions are time dependent?

[Anonymous No.12032124]

>>12032116
non-homogenous markov chains?
i'm not sure about finding resources for these, but have fun

[Anonymous No.12032125]

>>12032116
Sounds like you're looking for stochastic differential equations.

[El Arcón No.12032127]

>>12030560
Cartesian vs polar planar coordinates.

[Anonymous No.12032135]

https://arxiv.org/pdf/1410.1214.pdf

>Will a physicist prove the Riemann Hypothesis?

[Anonymous No.12032168]

choose your fighter
https://homepage.univie.ac.at/herwig.hauser/bildergalerie/gallery.html

[Anonymous No.12032191]

total fucking brainlet here
pls tell me (step by step cos im stupid) exactly how u solve for x in pic related

[Anonymous No.12032198]

>>12032191
Fuck off to /sqt/

[Anonymous No.12032211]

Pill me on pointless topology

[Anonymous No.12032212]

>>12032191
Multiply by (x-2)
> 3 = y*(x-2)
Expand the right hand side
> 3 = xy - 2y
Add 2y
> 3 + 2y = xy
Divide by y
> 3/y + 2 = x

[Anonymous No.12032221]

>>12032069
Okay I think I've got it. We know that |X/~| <= |R|, so finding an injection f: |R| -> |X/~| should finish the proof.
To do this we need to insure that one wrong digit when comparing x and y (in X) leads to a consistent percentage of wrong digits in f(x) vs f(y).
We define f(x) in the following:
every other position is filled with x_1
every fourth position (starting with the earliest nonfilled position) is x_2
every eighth position (with offset as before) is x_3
...
This then defines a sequence f(x).
If x != y, then there exists a k in N where x_k != y_k. Then every 2^k-th position in f(x) and f(y) is different, so they form different equivalence classes.

[Anonymous No.12032228]

>>12032198
forgive my ignorance
>>12032212
thank you kindly

[Anonymous No.12032253]

1 + 3 + 9 + 27 + 81 + ... = -1/2

[Anonymous No.12032264]

>>12032211
Let's start with a topological space and consider its topology. Since this is just the set of all the open subsets, it can be ordered by inclusion. It has a top and a bottom element, namely the whole space and the empty set, and it has the join and meet operations (union and intersection), so it will give you a very nice lattice. Then we notice that many of the topological properties can be formulated without actually using points in any way. For example, continuity of a map X -> Y means that the induced function from the power set of Y to the power set of X, taking each subset to its preimage, restricts to a function from the topology of Y to that of X, and this will in fact commute with the union and intersection etc. making it a morphism of lattices. Now, pointless topology uses the same idea, but in more generality. You have frames and locales, which are opposite categories to one another, and the topology lattice (morphism) thing I described is a frame (morphism). It turns topological considerations into order theoretic and logical ones without going all the way to topos autism. Your locales/frames can be exotic in the sense that not all of them arise from topological spaces. One also has a Tikhonov theorem independent of AC. If this surface scratch sounds nice, then do enjoy. That's all I remember of it.

[Anonymous No.12032293]

>>12032253
[math] \sum_{s=0}^\infty x^s = -\dfrac{1}{x-1} + \dfrac{1}{x-1}\lim_{n\to\infty} x^n [/math]

?

[Anonymous No.12032319]

>>12032211
The point is to use only operations on opens, but operations preserved by f^-1.

Those operations are finite meets and arbitrary joins. Those ops are stable under pullbacks which is the most important tool in geometry. The whole apparatus of bundles can be used..

A classical point of X is now 1->X, but you can generalize this to any locale map now, ie Y->X is a point of X, and Y is a generale locale.

With this notion of general point and the operations of finite meet and infinite union, you get all the topological constructs .

The major feature of this is that you work on constructive topology, so you have to get good at proofs, not relying on FOL.

https://ncatlab.org/nlab/show/point-free+topology

[Anonymous No.12032350]

>>12032168
Vis a Vis sounds and looks like a meme character

[Anonymous No.12032394]

>>12032221
Bingo! First correct solution. Took you all 1 day though, which means none of yoh belong in maths.

[Anonymous No.12032407]

>>12031933
isn't this just a meme

[Anonymous No.12032427]

>>12032394
What's with the infatuation from the undergrads with classical maths?

[Anonymous No.12032437]

Post standard phrases used in mathematical books/papers. I'll start
>thus
>hence
>it follows that
>Now, we have that
>It holds
>Therefore
>Consequently

[Anonymous No.12032444]

>>12032437
Kill yourself

[Anonymous No.12032446]

>>12032427
Idiot.

[Anonymous No.12032454]

>>12032444
never read that one before

[Anonymous No.12032458]

>>12032437
>tfw use all these terms constantly but usually completely inappropriately

[Anonymous No.12032489]

>>12032446
Learn to code.

[Anonymous No.12032497]

I have been fiddling around with a certain definition for a while, trying to get a nontrivial result. Since I'm a bit stuck I want to see if someone here finds it interesting.

[Anonymous No.12032500]

>>12032497

[Anonymous No.12032502]

>>12032497
>>12032500

[Anonymous No.12032506]

>>12032489
No need to. I already can. How is that relevant to you being an idiot though?

[Anonymous No.12032516]

>>12032506
Mathematica doesn't count, tranny.

[Anonymous No.12032596]

What do I need to know to make/code animations like in this video
Skip to the end
https://youtu.be/qhbuKbxJsk8

[Anonymous No.12032660]

is row vector different from column vector?

[Anonymous No.12032663]

>>12032660
No. Both are just arrays of numbers.

[Anonymous No.12032667]

>>12032660
They're just different representations of something.

[Anonymous No.12032669]

>>12032596
I see where this is going.

[Anonymous No.12032681]

>>12032660
They're not fundamentally different but you may sometimes see one used to represent a vector while another is used to represent a dual vector. But they aren't inherently different.

[Anonymous No.12032697]

>>12032681
so they are just R^n represented differently?

[Anonymous No.12032739]

>>12032697
Having chosen a basis for a vector space V you have a bijection V to K^n where K is your field of choice

[Anonymous No.12032756]

bros... does posting anime girls make me smarter...

[Anonymous No.12032826]

>>12032437
Since [insert statement],

[Anonymous No.12032828]

>>12032739

[Anonymous No.12032832]

>>12032437
[states some fact about something]. *the reader scratches his head for 30 minutes trying to figure out why that would be true* Indeed, [proof]

[Anonymous No.12032841]

>>12032828
>Phoneposter
>Frogposter

[Anonymous No.12032842]

>>12032135
a physicist has already disproved it, and his name is Jonathon Tooksy

[Anonymous No.12032851]

>>12032832
Stop it's too real.

[Anonymous No.12032859]

>>12032697
The vectors don't necessarily have to be real. Vectors can be thought of as being basically like the way you're thinking of them now.
Technically though, one thing which you're implicitly doing is conflating points in [math]\mathbf{R}^n[/math] with vectors. That's not really what vectors are; they're really functions, or operations (you often represent them with arrows, for example, representing a kind of direction, not just a point), which can be represented with an array of numbers.
This is just the same thing as how you might represent a function with a matrix. The function isn't actually the matrix. It might change, for example, under a coordinate change. The actual entries are just a way of representing it when you have a coordinate basis.

[Anonymous No.12032868]

What's unirocally the hardest HW/exam question you've had?

[Anonymous No.12032880]

>>12032868
All of them have been easy as fuck because I'm a genius.

[Anonymous No.12032883]

>>12032828
Kek, disregard me I suck cocks. I may write something more coherent in a few hours

[Anonymous No.12032890]

>>12032859
I wouldn't listen to this guy, about half of this is a trash way of thinking.

[Anonymous No.12032893]

>>12032880
Same here. The only reason I haven't posted my solutions to the Millennium problems is because I'm already a billionaire and I don't want to ruin it for the rest of you stupid losers.

[Anonymous No.12032899]

>>12032890
I'm not going to give him a formal definition when he's having a hard time with the basic ideas. That's no help.

[Anonymous No.12032908]

>>12032868
I think show that in [math]\mathbf{Z}/2\mathbf{Z}[/math] the diagonal of any symmetric matrix is in its column space was quite tricky when I first got it, which was in my first linear algebra course.

[Anonymous No.12032918]

hello

[Anonymous No.12032946]

>>12032908
Scratching my head rn thinking how to solve this.

[Anonymous No.12032959]

>>12032946
yeah it was a real arsehole of a question for an undergrad course lol

[Anonymous No.12032971]

Well well well

[Anonymous No.12032980]

>>12032899
In what sense is a vector "really" a function? I think your understanding of linear algebra is actually quite weak if you think of a vector as a direction, and that is only going to confuse someone new.

[Anonymous No.12032986]

>>12032918
goodbye.

[Anonymous No.12032995]

>>12032986
Ugh, worst Ouija board ever, didn't even let me ask it the Riemann Hypothesis

[Anonymous No.12033003]

>>12030264
Its tiring. When I visit /sci it should redirect to /math general. Christ! I have to CTRL+F math and then come here.

[Anonymous No.12033011]

>>12033003
I know that feel.

[Anonymous No.12033018]

>>12024914
based

[Anonymous No.12033023]

>>12032859
You are making me more confused.
>The vectors don't necessarily have to be real.
In vector calculus book, author talk about elements bein real numbers. What is your idea?

[Anonymous No.12033038]

>>12033003
>>12033011
I just put 4chan.org/sci/mg in my bookmark bar.

[Anonymous No.12033040]

>>12032832
this. i have to read multiple times the same sentences like a crazy person before I either make my own biased judgement and misinterpret the author or get over it by accepting it to be true.

[Anonymous No.12033042]

>>12033038
thanks it will remove 2-3 steps.

[Anonymous No.12033057]

>>12033023
There's no reason why they have to be real. They could be complex numbers, or something else.

[Anonymous No.12033080]

>>12032980
>you think of a vector as a direction
that isn't what I said, but I'm not invested enough to really have a spat over this

[Anonymous No.12033136]

>>12032908
Ok how do you solve this?

[Anonymous No.12033230]

>>12032908
I actually don't know how to solve this.

[Anonymous No.12033244]

>>12032908
>in my first linear algebra course
what university does this as an introduction? fucking based

[Anonymous No.12033251]

>>12032908
Can’t you just do a case study here?

[Anonymous No.12033279]

>>12033251
The lecturer who set the problem is from Ljubljana. He took pride in giving problems almost nobody would get right. He was gleeful when people said they couldn't do this one lmao

[Anonymous No.12033287]

>>12033279
Sorry >>12033279 meant for >>12033244
The problem isn't impossibly hard, it just relies on making the right observation first.

[Anonymous No.12033292]

Sophomore taking analysis this upcoming semester, been reviewing proofs over the summer and done some really light reading in baby rudins, can anyone give me any advance and pill me on analysis?

[Anonymous No.12033300]

>>12033287
Share your solution.

[Anonymous No.12033308]

>>12033292
Don’t forget the two magic words: “triangle inequality”.

[Anonymous No.12033324]

>>12033279
Absolutely based.

[Anonymous No.12033378]

I still don't like set theory. i will forever not like it. it just doesn't feel natural or right no matter how much i try. not books, not videos, not khan academy, nothing.
my learning process with math in general is not understanding anything at first then it becoming embedded in my mind once i understand the logic behind it. yknow i see a question and i know right away that i need to use this. this hasn't happened for set theory, not since high school when i got first introduced into set theory. 6 years and it still doesn't make any sense or feel right. never will... never will...

[Anonymous No.12033385]

>>12033378
I take it you mean the elementary use of naive set theory which is needed to do any math at all, which basically amounts to you saying that you don't like or know how to do math.

[Anonymous No.12033403]

>>12033385
i can still do math without knowing that shit fuck complements dick fart product ass

[Anonymous No.12033406]

>>12033300
>>12032908
>>12033300
ok
There are 3 solutions I think I remember to this. You can do this by induction, I think you can do this by decomposing the matrix, and I'll post another way. All of these that I remember involve you just noticing because it's [math]\mathbf{Z}/2\mathbf{Z}[/math] that symmetric matrices are also skew-symmetric matrices as the same thing.
Let [math]A=(a_{ij})[/math] be [math]n\times n[/math] symmetric matrix and the diagonal be [math]u=(a_{11},\dots,a_{nn})[/math]
then you take some vector [math]v=(v_1,\dots,v_n)[/math] such that [math]Av=0[/math] and then all that is left is to show [math]<u,v>=0[/math] and it must be in the column space.
You can take [math]v_1=v_2=\cdots=v_k=1[/math] but [math]v_{k+1}=\cdots=v_n=0[/math]
then [math]a_{k+1i}=a_{ii}+\sum_{j\neq i}^{k}a_{ij}[/math] for all [math]i[/math] and
[math]a_{k+1,k+1}=\sum_{i}^{k}a_{k+1i}=\sum_{i}^{k}(a_{ii}+\sum_{j\neq i}^{k}a_{ij})=\sum_{i}^{k}a_{ii}[/math]
but
[math]<u,v>=\sum_{i}^{k+1}a_{ii}[/math]
and since entries are in [math]\mathbf{Z}/2\mathbf{Z}[/math] this is zero by above, so [math]u[/math] is in the column space
I hope I didn't make any typos with indices etc

[Anonymous No.12033410]

>>12033406
ok i fucked up some of the latex but I'm not going to retype it, I think you can read it anyway

[Anonymous No.12033417]

>>12033406
i mean the other way to do it is to use some properties of skew-symmetric matrices, this way you don't need anything too fancy

[Anonymous No.12033428]

>>12033406
Huh? I'm very confused by your proof.
Can you just take v to be 0? If not, how do you guarantee such a v exists?
Why would <u,v>=0 guarantee that u is in the column space?

[Anonymous No.12033432]

>>12033403
Color me skeptical.

[Anonymous No.12033433]

>>12033432
2+2=4

[Anonymous No.12033446]

>>12033428
You can swap the columns around so you can order all the 1s of v first so you can choose this v without loss of generality
Null space is orthogonal to column space because it's symmetric.

[Anonymous No.12033465]

>>12033446
*columns and rows

[Anonymous No.12033485]

>>12033446
Why would such a v exist in the first place?
For example, when the matrix is the identity then no such nonzero v exists.

[Anonymous No.12033492]

>>12033485
The case where v is 0 is trivially in the column space

[Anonymous No.12033494]

>>12033446
What I'm saying is, what do you do in the situation where A is nonsingular?

[Anonymous No.12033498]

>>12033433
I don't do Nazi math, sorry.

[Anonymous No.12033514]

>>12033406
>symmetric matrices are also skew-symmetric matrices as the same thing
All matrices over Z/2Z are skew-symmetric.

[Anonymous No.12033521]

>>12033514
I think something has gone wrong.

[Anonymous No.12033523]

>>12033521
Your proof still makes 0 sense to me. Can you write it out again but now with the steps explicit? Sorry I'm a bit slow.

[Anonymous No.12033526]

>>12033514
Are they, though?

[Anonymous No.12033539]

>>12032497
wtf is B_r

[Anonymous No.12033558]

>>12033523
Sorry I just wrote out pretty badly, it's hard to write a long post and see what I'm saying with all this tex and everything building up
It's not your fault, I know what I wrote leaves some things to fill in the blanks
>>12033514
No this is false, e.g. just make one corner 1 and everything else 0, symmetric means skew symmetric in this field

[Anonymous No.12033577]

>>12033539
B_r(0)

[Anonymous No.12033578]

Give me a hint
>prove that in R, dim null[(T^2+aT+bI)^k] is even for all k if a^2<4b
Just a hint

[Anonymous No.12033662]

>mfw I spent 15 minutes on a chapter on limits trying to understand why the book uses ≤ in a proof, only to see the author later referring to the same proof using < instead

Why do they do this...

[Anonymous No.12033666]

>>12033662
Humans are imperfect.

[Anonymous No.12033675]

>>12033666
b-but I thought maths was all about perfection

Seriously though, I'm trying to understand epsilon proofs in babby's first analysis, some of the expressions look like the author just pulled them out of his ass in some deus-ex-machina fashion.

It's really frustrating not knowing the reasoning behind why a certain inequality is best solved with epsilon or epsilon/(2|A|+1). Is there any way I can see the reasoning or do I have to accept that analysis is about magical woowoo statements.

[Anonymous No.12033676]

>>12033675
These proofs are polished up versions, they're not how a mathematician normally comes up with them initially.
Examples should always take priority in boosting your understanding.

[Anonymous No.12033679]

>>12033675
>analysis is about magical woowoo statements
This

[Anonymous No.12033695]

>>12033675
You need to stop thinking that this random expression is the idea behind the proof. What matters is what you can make small or big dependent or idependent of which other variables.
When you see an epsilon or a delta, think "as small as needs to be". When you see an N think "as large as needs to be". What matters is which variables depend on which others, i.e. the order in which you "let" and "choose".

[Anonymous No.12033710]

>>12033577
imma go to bed then take a look at this. at a glance it reminds me of a few of the local objects in math, like a local homology group in flavor. we can always choose compact representatives. if we are fixing a point then maybe the ambient space is really the X\[0]. idk im very tired

[Anonymous No.12033768]

>>12033695
>>12033676
>>12033679

Thanks anons. Yeah I guess it's just frustrating because I feel like these authors are on some cloud 10 level of advanced maths that I haven't touched. But I guess it's like seeing an asian kid play some piano concerto really well or something when I'm just learning Fur Elise. Ok, end of blog

[Anonymous No.12033905]

>>12030770
Sounds like someone hasn't accepted the godliness of elliptic curves yet.

>>12032596
>For those of you who’d like to play around a bit with the stunning times table diagrams that we discuss in this video, download the .cdf file http://www.qedcat.com/cardioid.cdf and open it with the free cdf player which you can download from Wolfram Research (the people behind Wolfram Alpha and Mathematica). If you have access to Mathematica you can also open my .cdf file in Mathematica and play with the code.

[Anonymous No.12033939]

>>12030770
https://en.wikipedia.org/wiki/Monster_group

[Anonymous No.12033943]

>>12033675
Technically all the epsilon variations are just to make the proof pretty. It doesn't matter if your quantity is less than epsilon or epsilon over two but Mathematicians of course want elegance and clarity in the final statement.
What you want to do is FIRST just let epsilon, delta, etc. be arbitrary and go through the motions of the proof to see what your final sum is. THEN you can go back and fix your delta or whatnot so that the inequality relates to just epsilon (since a lot of our definitions relate simply to epsilon, e.g. consider the definition of sequence convergence).
If you don't know what I mean, essentially in Elementary Analysis what you want to do is find or design inequalities by relating definitions, etc. so when you check a statement (usually you want to say that it's less than an arbitrary positive number) you can write out an inequality by examining the individual terms and their respective inequalities. Hence the fixing aspect, since often multiple terms will be less than an arbitrary positive number by definition but if you let them all be epsilon, you'll come out with some proportion and in more convoluted proofs, you come out with proportions involving other quantities. E.g. you end up with multiple terms when you apply the triangle inequality several times, etc.
Analysis isn't that strange; how novel it seems when you're first exposed that may make it seem so. Hopefully this doesn't confuse you/ I don't mislead too much, this is a fairly broad suject and of course I'm only thinking about a small portion that I think relates to your frustrations.

[Anonymous No.12033950]

>>12030264
Is linear equation same thing as linear combination?
Is there such thing as quadratic equation(I know there is?) so does that mean, if the above is true that quadratic combination is quadratic equation?

[Anonymous No.12033960]

>>12032596
Graphics API, like opengl,vulkan,directx.

[Anonymous No.12033970]

Is this best Abstract Algebra book?

[Anonymous No.12034092]

>>12033970
No.

[Anonymous No.12034101]

where is fraleigh in the algebra textbook tiers?

[Anonymous No.12034136]

>>12032516
If you're intimidated by classical analysis and geometry you don't belong in science or math.

[Anonymous No.12034155]

>>12033943
No that actually really helps. Thanks for taking the time to write it out. It makes sense that the final crazy inequality is then reverse-engineered to look like epsilon so that it's all much cleaner.

Thanks anon. It's nice knowing I'm not the only one struggling with this.

[Anonymous No.12034173]

>>12034155
Do you understand why [math]\frac{\epsilon}{2(|A|+1)}[/math] was used in this proof? I assume it was one of the limit theorem proofs ie. The limit of a sum is the sum of the limits and so on?

[Anonymous No.12034196]

>>12031596
jokes on you, i missed last thread cuz i was moving back to school
the equivalences classes are in a clear bijection with the set of real numbers from 0 to 1 inclusive = R
just take the map onto [math]\displaystyle \lim_{n\to\infty} e(\vec{x}, \vec{0}, n) [/math]
and then since X = 2^N = R = X / ~, we're done

[Anonymous No.12034209]

>>12034173
Yeah you're right, it was proving the product of two limits is the limit of their product

I think I got it? The final thing ends with trying to show that [eqn]\frac{\epsilon}{2}+|A|*\frac{\epsilon}{2|A|+1} \leq \epsilon [/eqn]

And I get how the denominator ensures this possible inequality. I guess it was just a matter of perspective in terms of understanding that these expressions are better understood as reverse-engineered, not planned forward in advance.

[Anonymous No.12034480]

Love group theory, lads.

[Anonymous No.12034664]

Proofs, or rather the presentations of proofs in textbooks, are essentially algebraic in nature. That's why most analysts don't care about proofs beyond the mere knowing of their existence.
Which is unfortunate because their disdain for logic as a discipline blinds them to the profound topological structure of proof space.

[Anonymous No.12034687]

Based

[Anonymous No.12034711]

https://www.math.ucla.edu/~pak/hidden/papers/Arnold-survive.pdf

[Anonymous No.12034829]

>>12034711
Tldr? My eyes glazed over reading that

[Anonymous No.12034860]

>>12034687
>>12034711
(((Bourbakists)))

[Anonymous No.12034939]

What do you think of this?
https://en.wikipedia.org/wiki/Mathematical_anxiety

[Anonymous No.12034941]

>>12034711
based, all bourbakists should be shot

[Anonymous No.12034944]

>>12034939
Byproduct of western anti-intellectualism.

[Anonymous No.12034955]

What do you think alien mathematics would be like?

[Anonymous No.12034970]

>>12030413
Is your img something to drive for or something to mock?

[Anonymous No.12034974]

>>12034196
That limit wil be infinite in most cases.

[Anonymous No.12035004]

>>12033578
>>12033578
>Give me a hint
It looks like a quadratic equation and its discriminant...

[Anonymous No.12035021]

>>12034955
Pretty similar to ours.
The real number system is basically the only sensible one to come up with, there is a pretty obvious path (counting things (naturals) -> negatives (integers) -> multiplication/fractions (rationals) -> roots of equations (algebraic numbers) -> solutions to geometric problems (reals)).
A lot of mathematics comes from real world applications, I imagine they would have less of a focus on algebraic geometry than modern mathematics does as in some ways that's the least applied thing.

[Anonymous No.12035044]

How does one actually get good at math based problem solving?
If you're a brainlet, practicing will be insufficient.

[Anonymous No.12035100]

>>12034955
It ought to depend on the physics of their local "observable" universe: specifically, their geometry will determine the kinds of syntactic expressions that they can form, while their topology will govern the semantic (really information-theoretic) content of their proofs.
Contra to >>12035021, aliens living in a Malament-Hogarth spacetime, or at a scale where quantum effects dominate, would develop a style of mathematics that can only be translated into ours with difficulty, if it can at all.
You can get a flavor of this "exotic" mathematics by thinking about artificial intelligences: computers aren't quite aliens, but they have a syntax and semantics in the sense described above, and they operate on a logic that's subtly different from the classical reasoning that most of us are used to. (For example, the popular association of computers as operating on bits and "booleans" is misleading: Boolean logic only has True and False but no Null, undefined behavior doesn't exist, and nonterminating programs are deficiencies in the implementing environment rather than bugs in the logic. But this is getting off-topic.)

[Anonymous No.12035102]

>>12035100
retarded pseud faggot

[Anonymous No.12035158]

>>12034970
>mock people who improve themselves
y tho

[Anonymous No.12035186]

I kind of fucking love the structure of Basic Mathematics by Serge Lang. By which, I mean that I appreciate that he really builds up all of the different concepts, such that you definitely always have enough information to prove the stuff that it's teaching, before you read the proof it provides.

Are most math textbooks like that? Not just proof-based, but where the topics are ordered and built up such that you can prove examples before they're actually proven by the book?

[Anonymous No.12035192]

>>12035186
No. Most books are unintuitive, poorly organized, of inconsistent clarity and strength of insight, and with exercises that either act as a dump for results the author is too lazy to prove but should (see: Royden, Sternberg and Loomis) or filled with retarded special cases and extremely tricky but not at all enlightening cases. Lang actually does this in his analysis book and Rudin does this in Chapters 9-11 of his book as well. Most textbooks are fucking horrible. Spivak is another book that is sort of organized how Lang’s Basic Mathematics is.

[Anonymous No.12035199]

>>12035192
I see. That's a real shame, all textbooks should be organized like this. Are there good authors that regularly write tbeir textbooks in this fashion? Would I be better off just reading overview papers on whatever area I want to study?

[Anonymous No.12035201]

>>12035186
all bourbaki books are like this, this is why undergads hate them

[Anonymous No.12035208]

>>12031607
Seconding topology rec

[Anonymous No.12035210]

>>12035199
No you should read textbooks lol you’re in no position to read academic papers if you’re going through Lang’s book. The best strategy is to dl as many texts as you can and to go over the table of contents and then skim the first few chapters. Learning to discern if the author is a miser, poor writer, overly wordy is part of the process. Don’t be too discouraged most textbooks for the sciences are much worse, with inferior quality of exercises and significantly less care put into the structure of the text than what mathematicians tend towards as the standard. There is no Spivak or Rudin for chemistry or biology. Also, my opinion is not necessarily what you’ll experience on your own. I was told Rudin was very dry and unintuitive and it took a while for me to realize his was sort of unimportant to learning basic analysis and now I really appreciate the independence of thought he expects of you.

[Anonymous No.12035221]

>>12035210
I don't mean right now, obviously, I just mean when I am ready to learn a particular topic (e.g. i have enough background to consider picking up a textbook on it, I would instead find some other paper/review and learn it through that, or follow whatever trail it may have).

Thanks for your advice though anon, I suppose I'll have no choice but to just get a fuckload of resources and see what sticks.

[Anonymous No.12035231]

>>12033539
metric spaces go B_rrrrrrr

>>12031889
>We know that |X/~| <= |R|, so finding an injection f: |R| -> |X/~| should finish the proof.
Might not satisfy this guy >>12031936 since the Schröder–Bernstein theorem implies LEM
:^)

[Anonymous No.12035239]

>>12032908
>>12033406
how the fuck does an undergrad course require this?
I get it now that I see the proof, but easily 95% of undergrads would never solve this problem

[Anonymous No.12035246]

>>12035231
>that cameltoe
mamma mia

[Anonymous No.12035284]

>>12035100
The idea that aliens would have three state logic or otherwise is interesting since the Indians did exactly that with their idea of mathematics, although the rest of this is just CS memery

[Anonymous No.12035610]

Any good AG textbooks to read alongside Hartshorne? I'm currently stuck in chapter ~2.6 on divisors. I was using Bosch's AGCM book but it basically only covers up to chapter 2.8 without that much detail (or actual computations).

[Anonymous No.12035661]

>>12032437
>By yoneda,

[Anonymous No.12035670]

>>12030493
>The better venn diagram
and actually the best venn diagram

[Anonymous No.12035673]

>>12032437
>it is easy to see

[Anonymous No.12035693]

>>12032868
The one that comes to mind is as follows, in 2 parts:
>Show that if $f:X \rightarrow Y$ induces an isomorphism in homology with coefficients in $\mathbb{Z}/n\mathbb{Z}$ then it induces an isomorphism in homology with coefficients in any abelian group where every element is killed by some power of $n$.
>Show that, if $f:X \rightarrow Y$ induces an isomorphism in homology with coefficients in $\mathbf{F}_p$ for all primes $p$, and $\mathbb{Q}$, then $f$ induces an isomorphism in integral homology.

[Anonymous No.12035695]

>>12035693
F I don't know how to embed tex on this board

[Anonymous No.12035715]

>>12035695
[math] and /math in similar brackets.

[Anonymous No.12035739]

>>12035715
oki
--Show that if [math]f:X \rightarrow Y[/math] induces an isomorphism in homology with coefficients in [math]\mathbb{Z}/n\mathbb{Z}[/math] then it induces an isomorphism in homology with coefficients in any abelian group where every element is killed by some power of [math]n[/math].
--Show that, if [math]f:X \rightarrow Y[/math] induces an isomorphism in homology with coefficients in [math]\mathbb{F}_p[/math]$ for all primes [math]p[/math], and [math]\mathbb{Q}[/math], then [math]f[/math] induces an isomorphism in integral homology.

[Anonymous No.12035824]

tell me mg, what do you see in this

[Anonymous No.12035845]

>>12035824
Dots and lines.

[Anonymous No.12035894]

>>12035824
Crude diagram of woman lying flat on her back with a gaped blown out pussy

[Anonymous No.12036073]

>>12035894
that's what I was thinking too.

Now a harder one

[Anonymous No.12036083]

Ok be real with a newfag tourist here. Is nwildberger legit? I want to follow some math as a hobby, just because doing no math at all is not a good life. Pls no troll, doing 600 hours of schizo reinvented math as a mistake is not funny.

[Anonymous No.12036119]

>>12036083
Just read a book about arithmetic

[Anonymous No.12036123]

>>12035824
two cubes

>>12036073
machines working on a production line

[Anonymous No.12036130]

>>12036083
his course on algebraic topology is ok (but a bit to simple).
his views on finitism etc are not worth spending time on, regardless whether or not they are legit.

[Anonymous No.12036131]

>>12035004
I recognize that the polynomial has no roots and I assume that the proof should go something like, "each application of p(T) cant remove eigenvectors of space, only eigenpairs" but i cant figure out how to prove that

[Anonymous No.12036164]

>>12036073
Snooker player attempts to throw other snooker player off by poking stick up his asshole while he's trying to aim

[Anonymous No.12036166]

>>12030264
Have you ever come across a power tower in analysis?

[Anonymous No.12036216]

>>12036123
>two cubes
I think you can only see one cube at a time

>>12036164
might be the right answer

[Anonymous No.12036218]

>>12036130
Whether or not his views on finitism are correct (they're probably not), there's definitely a sense in which the "reals" are way less real than natural numbers and the undecidability of the continuum hypothesis in ZFC is a testament to this.

[Anonymous No.12036232]

>>12034974
meant to divide by n like the original post

[Anonymous No.12036316]

>>12034939
huge correlation between parents contributing and those who were 'never good good at maths so why try lol'
mathematical incompetence is not shamed, sometimes even gone so far as celebrated between underachieving adults. this filters down to children ad nauseum and is somehow acceptable in the west

[Anonymous No.12036377]

The hell kind internally boil.
The rainbows shine through the cracks.
Waves crest beneath the ave.
The concrete stretches far and fed.

Tomhet woke to a falling smooth sound
With subtle fuzz from early form digital
Grooved into the indents in the rock over the strait
Hand on rifle, ready to fire from base
The boat continued its line

Deep breathing in
Fully out, too
The flesh was not dry like the water
Where the sailors would soon drown

[Anonymous No.12036382]

The hell kind internally boil.
The rainbows shine through the cracks.
Waves crest beneath the ave.
Concrete stretches far and fed.

Tomhet woke to a falling smooth sound
With subtle fuzz from early form digital
Grooved into the indents in the rock over the strait
Hand on rifle, ready to fire from base
The boat continued its line

Deep breathing in
Fully out, too
The flesh was not dry like the water
Where the sailors would soon drown

[Anonymous No.12036530]

Also I wanna thank the anon who posted Songs of Grief and Solitude. Been listening to it for the past few days and it has been really good for me in these trying times

[Anonymous No.12036554]

>>12036530
Cheers, lad.

[Anonymous No.12036594]

What is the relationship between midpoint and average velocity? Why is the midpoint of the velocity function the slope of position on the same interval

[Anonymous No.12036614]

>>12036594
Absolutely no relation between the two. They're completely independent.

[Anonymous No.12036620]

>>12036594
This is some of the worst handwriting I've ever seen.

[Anonymous No.12036734]

>>12036594
This is really not a good post

[Anonymous No.12036735]

>>12036614
>>12036620
>>12036734
Stop it lads he’s already dead!

[Anonymous No.12036736]

>>12035610
bump

[Anonymous No.12036738]

>>12031607
Thirding

[Anonymous No.12036740]

>>12036738
>>12031607
>>12035208
Use Munkres.

[Anonymous No.12036760]

>>12036614
For constant accel they certainly are

[Anonymous No.12036784]

>>12033279
>The lecturer who set the problem is from Ljubljana
damn knew ljubljana was tough but this is another level lmao
t. koper

[Anonymous No.12036788]

>>12035239
ex-yugo schooling is extremely hard and challenging

[Anonymous No.12036803]

>>12036788
Why is eastern Europe so intense with math?

[Anonymous No.12036805]

>>12036760
Oic

[Anonymous No.12036916]

>>12030560
homological geometric langlands mirror symmetry

[Anonymous No.12036931]

>>12032660
you can multiply a row vector by a column vector (of the same length) but can you multiply a row vector by another row vector?

[Anonymous No.12036939]

>>12032868
had to prove weyl's equidistribution theorem as homework in 1st year analysis class. probably was the hardest problem i had relative to my amount of knowledge at the time

[Anonymous No.12036946]

I feel like (and probably am) a retard going through Lang's Basic Mathematics from the beginning. I can basically do everything Precalc but I'm reviewing foundations because none of it really stuck in schooling. To give you the idea of the type of soup brain I have, I legit had to think for a half min why "If a + b = 0, then b — —a and a = —b" is true. I can immediately intuit why but it being explained in algebraic notation instead of "if one number plus another number equal zero then they must be inverse to each other" fucks with me a lot. Please tell me I am not the only one.
I just gotta push through. One day I will get to play with the big kids /blogpost

[Anonymous No.12037019]

>>12036803
socialist heritage

[Anonymous No.12037045]

>>12031607
Look the notes of your collage in a intro course in topology, look at references. Ask the teacher / follow the lectures.

[Anonymous No.12037071]

>>12036784
>damn knew ljubljana was tough
Did a post-doc at the mafija, those were good times...

[Anonymous No.12037089]

>>12036946
I'm another brainlet but I get that sometimes yeah. I can feel that something is true, or why it is what it is, but struggle a lil bit with the rigorous way of saying it.

[Anonymous No.12037196]

Consider a convex set [math]S[/math] in a real inner product space. What the fuck is the set
[math]\{ x: \langle x, s \rangle = 1 \; \forall s \in S \}[/math]?

[Anonymous No.12037203]

I just started integral calc from teaching myself differential calc. Why is this so much harder? I'm not having much trouble with u-substitution thus far but looking a few pages ahead in the textbook is making the shit run down my legs.

[Anonymous No.12037225]

>>12037196
Are you sure that should be equals rather than less than or equals? I think that set is gonna be empty for any S with a non-empty interior because if [math]\langle x, s rangle = 1[/math] then you can find a point [math] \lambda s[/math] so this is not the case.

[Anonymous No.12037232]

>>12037196
[math]\emptyset[/math]

[Anonymous No.12037234]

>>12037225
Yes I'm familiar with the usual polar set in geometry which has an inequality in the definition. I'm asking specifically about the one with equality because I have zero intuition for what it is.

You're right that it only makes sense for sets with empty interior.

[Anonymous No.12037240]

>>12037234
The only convex set with empty (relative) interior is a single point, so it's basically uninteresting.

[Anonymous No.12037286]

>>12037196
hm. let S* be the set in your definition. then clearly if x is in S*, then it is also in aff(S)* where aff defines the affine hull (smallest affine space containing S). it's looking like S* is something weird related to the orthogonal complement of the subspace which defines aff(S)?
but I think it won't make sense in general, only for some specific cases

[Anonymous No.12037375]

Im new into group theory, I think I get what a group is but I'm not sure yet.
From what I understood, a group is just a way for <something> to retain a certain property after a certain action. Is this right?
Assuming for example that there is a tiling space and each tile has a colour assigned to it, if an action entails changing the colour of a certain tile or swapping two tiles, if we after such and action/series of actions the tiling space retains some random property, can this be called a group?
If it can, does that mean something like a magic square is 'symmetrical' in the sense that the property of all the rows and columns adding up to a certain number is preserved even if the numbers in the boxes are changed?

Im like 90% sure this is wrong but I really have nowhere else to ask.

[Anonymous No.12037424]

>>12037375
Do you know the formal definition of what a group is? They come from something a bit similar to what you describe (actions which are invertible).

[Anonymous No.12037462]

>>12037424
I don't know the formal definition, mainly because it always goes over my head. Formal definitions are always make stuff sound more complicated than it is, but I guess that's what teachers are for.

[Anonymous No.12037492]

>>12037462
The origin of groups in describing symmetries is probably more confusing than the basic definition of a group. You're better off seeing how groups work work and some simpler examples before you see complicated applications imo.

A group [math] (G,*) [/math] is a set [math]G[/math] along with an "operation" [math] *[/math] on that set.
The operation takes two elements [math]f,g \in G [/math] and gives you a third one, which we write [math] f * g [/math]. Then there are some rules the action must follow. We need an identity, which is an element [math] e \in G[/math] so that for all [math] f \in G [/math] we have [math]e*f=f=f*e [/math]. We need an inverse for every element [math]f [/math], which is an element [math]g [/math] satisfying [math]f*g = e = g*f [/math]. Finally we require "associativity", which is saying that [math] f*(g*h) = (f*g)*h [/math].

As an example the integers are a group with the addition as the action, but the natural numbers aren't (why not?). Try see if you can work out what the identity and inverse would be.

[Anonymous No.12037574]

>>12037375
Groups are collections of symmetries under a certain operation.

[Anonymous No.12037829]

>>12037492

Seeing it as just criteria and rules that aren't tied to anything specific helped a lot. The idea that it has to do with symmetry is just really prevalent in practically every explanation. So thanks.

Identity: add zero?
Inverse: you would need negative numbers which is why natural numbers wont work
Associativity is true for addition.

[Anonymous No.12037847]

>>12037829
>Identity: add zero?
>Inverse: you would need negative numbers which is why natural numbers wont work
>Associativity is true for addition
Perfect. Are the real numbers a group with multiplication?

[Anonymous No.12037914]

>>12036218
>Whether or not his views on finitism are correct
They are neither correct nor incorrect. They are a choice (but a boring one)

[Anonymous No.12037933]

>>12037847
No, because infinite sets do not exist

[Anonymous No.12037946]

>>12037933
[math]\mathbb{N}[/math]

[Anonymous No.12037952]

>>12037946
[math] \mathbb{N}[/math]o

[Anonymous No.12037978]

>>12037933
>What is a Cauchy sequence

[Anonymous No.12037984]

>>12037952
https://en.wikipedia.org/wiki/Axiom_of_infinity

[Anonymous No.12038029]

>>12037847
They shouldn't be right? Cause you would need 1/x to act as the inverse and for x = 0 that doesn't exist. So e∈G is not fulfilled.

[Anonymous No.12038054]

>>12038029
Does the set of all 2x2 invertible matrices with real entries form a group?

[Anonymous No.12038091]

>>12030264
I'm high rn ann.t t past precalc. Please explain this image for me.

[Anonymous No.12038097]

>>12038054
The determinant of a matrix does not exist for all real values, so no.

[Anonymous No.12038104]

>>12038097
wait sorry you said invertible, so it should exist,
with the inverse matrix acting as the matrix and the identity being E.

[Anonymous No.12038115]

>>12038104
*acting as the inverse

[Anonymous No.12038390]

subspace spawned by some vector is also spawned by scalar multiplication of that vector.
can someone explain this why it is so?

[Anonymous No.12038392]

>>12038390
A linear combination of a single vector is a scalar multiple of that vector.

[Anonymous No.12038396]

>>12037933

[Anonymous No.12038408]

>>12038392
IDK. reading Artin and brain is on high temperature. The feeling of bein brainlet generating emotions like not living up to desired intelligence, low self esteem because realizing it's difficult to understand small thing meanwhile Terrence Tao can understand in seconds is generating body heat and vomit.

[Anonymous No.12038418]

>>12038408
You need to not care how smart others are, or you're ngmi.

[Anonymous No.12038421]

>>12037203
Integration is g-loaded in a way that differentiation typically is not. Brainlets and brain AIDS fops will belittle it but solving diff eq’s, integral equations and whatnot by hand is extremely good for your mind and a good test of intelligence. If you want some difficult integrals try the first set of exercises in chapter 18 of Spivak’s Calculus.

[Anonymous No.12038477]

>>12038421
Lmao I remeber being a retarded undergrad

[Anonymous No.12038489]

>>12038477
Not an argument.

[Anonymous No.12038669]

>>12038477
Not him but I do think undergrad courses now have de-emphasised anything involving calculation to an unhealthy extent.
You do have to couple mastery of the abstract with mastery of messy work like a hard integral from time to time. Otherwise you'll miss out on stuff like Hardy's theorem on the Riemann zeta function and so on.

[Anonymous No.12038833]

>>12032868
in measure theory. There was this probability exercise that needed some hard combinatorics. Noone solved it

[Anonymous No.12038836]

>>12035739
ok. my first idea would be to try to use the naturality of the universal coefficient theorem. would that work?

[Anonymous No.12039203]

>>12037196
>⟨x,s⟩=1
?

[Anonymous No.12039588]

this is very cool

https://youtu.be/8Y0b7e4OIUQ

[Anonymous No.12039598]

redpill me on spherical harmonics

[Anonymous No.12039600]

>>12039588

[Anonymous No.12039661]

>>12039598
Special functions as a whole are based

[Anonymous No.12039751]

>>12039600
no

>>12039598
>>12039661
>it's all just matrix coefficients of various Lie group representations with orthogonality properties in the form of integrals that are induced by the Haar measure over polynomials of said matrices?
>always was

[Anonymous No.12039841]

If multiplying two rational numbers always gives a smaller rational number how does x^2 ever get to 1?

[Anonymous No.12039848]

>>12039841
1·1=1 in Q

[Anonymous No.12039860]

>>12039841
[math]1 \in \mathbb{Z} \Rightarrow \frac{1}{1} \in \mathbb{Q} \\ \frac{1}{1} * \frac{1}{1} = \frac{(1)(1)}{(1)(1)} = \frac{1}{1} = 1[/math]

[Anonymous No.12039864]

>>12039860
>>12039848
but what about satisfying 0<x<1

[Anonymous No.12039880]

>>12039864
For all x<1 in Q (or R, for that matter), x^2<1.

Both are metric complete, so the limit x to 1 is of x^2 is 1. The definition of the limit x to 1 doesn't use x at 1.

[Anonymous No.12039888]

>>12038408
iktfb

[Anonymous No.12039934]

>>12038836
Yeah that's part of it; in my solution, the major barrier which needed cleverness to solve is that the case of non-finitely generated coefficient groups, where it's not so clear how to use UCT to help.

[Anonymous No.12039971]

Is there a theory of integration for distributions. Naively I would think yes because of shit like the integral of the dirac delta being the heaviside step function, but is there something like that?

[Anonymous No.12039986]

>>12038669
Not denying that. But saying shit like "integration is g-loaded" is exactly what a retarded undergrad would say.

[Anonymous No.12039995]

>>12039880
so the neighborhood with midpoint x and radius r, x-r<x<x+r, as r converges to x, the convergence is always within the range so the mapping is continuous?
As in for all x < 1 exists y st y<1?

[Anonymous No.12040076]

Can someone give me a worded definition of what a derivative or differentiation actually is?

[Anonymous No.12040089]

>>12040076
Its slope but with an infinitesimal change. But with the algebra working for dividing out the change regardless of size, so it applies to infinitesimals anyway

[Anonymous No.12040111]

>>12040076
Don't listen to >>12040089 Infinitesimals are a meme. The derivative of a function is the slope of the tangent line at that point. How do we find this slope? Remember given two points in the plane you can easily calculate the slope of the unique line that goes through that point. Then you just take the limit of the secant lines slopes by fixing the point where you want to find the tangent slope and then taking an arbitrary point away from it and looking what happens when it gets closer to the point.

[Anonymous No.12040152]

>>12039971
"integration for distributions" has tautologous character, if you then speak of distribution that act by integration. I suppose "functional analysis" is what you look for.

[Anonymous No.12040155]

What course nearly killed your interest in math?

[Anonymous No.12040156]

>>12040076
>>12040089
could you stop talking about this baby shit here

[Anonymous No.12040166]

>>12031607
From metric spaces

[Anonymous No.12040191]

>>12040156
I'm talking about the literal definition of differentiation. You add h, you divide out h. doesnt matter what h is. Thus it can be a limit/infinitesimal for free

[Anonymous No.12040197]

>>12040076
Something that satisfies the Leibniz rule.

[Anonymous No.12040202]

>>12030614
Link?

[Anonymous No.12040489]

>>12039934
hint?

[Anonymous No.12040679]

>>12040489
Along the way, one should note/prove that filtered colimits in Ab commute with homology, and try to use that to reduce to the case that the coefficient group is finitely generated.

[Anonymous No.12040723]

>>12040679
what about the second one >>12035739

[Anonymous No.12040726]

>>12040152
More in terms of distributional calculus.

[Anonymous No.12040768]

>>12040723
Let [math]\mathbb{Z}_{p^\infty}[/math] be the Prufer [math]p[/math]-group defined as the direct limit of [math]\mathbb{Z}/p^n\mathbb{Z}[/math] for [math]p[/math]. Then, there is a short exact sequence
[math]0 \rightarrow \mathbb{Z} \rightarrow \mathbb{Q} \rightarrow \bigoplus_{p \text{ prime}} \mathbb{Z}_{p^\infty} \rightarrow 0.[/math]

[Anonymous No.12040790]

Let X be a symmetric positive semidefinite matrix, and let P be a projection onto some subspace of symmetric matrices.

Is it true that trace(P(X)) <= trace(X)?

[Anonymous No.12040792]

>>12030264
Sort of a /g/ question, but what software do I need to learn for mathematics? I'm entering a math undergrad program next week and I want to be familiar with helpful programs. I'm learning latex, any (libre) calculator recommendations?

[Anonymous No.12040794]

>>12040768
Ok, I see how you'd arrive the solution from here on but Jesus, I would've never come up with that

[Anonymous No.12040829]

>>12040790
What's a projection in your case?
Is the constant map to the scalar 1 a projection here?

[Anonymous No.12040847]

>>12040829
Symmetric matrices form a vector space, I mean a projection as an idempotent linear transformation in this vector space.

[Anonymous No.12040857]

>>12040792
None (other than [math]\LaTeX[/math]) unless you go into applied math. But if you DO need Mathematica, Maple, etc, it will depend on which one your institution uses

[Anonymous No.12040886]

>>12040794
It was a pretty stressful day coming up with it. To be fair, on the previous problem set we had seen the Prufer group, so we had a bit of help.

[Anonymous No.12040904]

>>12040790
I dont think so. If you put the positive definite matrices in the direct sum represantation I don't see why the one in the image couldn't have a diagonal with higher values if the one in the kernel are small enough.

[Anonymous No.12040909]

>>12040857
small nitpick: some pure math subjects are aided by software, such as snappea for geometric topology or pretty much any CAS program for heuristics in algebra/associated subjects. That being said, you generally learn the software when you need it (other than [math]\LaTeX[/math], which everyone should have learned yesterday)

[Anonymous No.12040988]

Just started Hatcher and I need someone to spoon-feed me and explain CW complexes. My dumb brain can't even wrap my head to solving a proof for cell complexes (i.e. if X is a cell complex the following are equivalent: X is connected, X is path connected). The definition of connected I have from topology just doesn't make sense for me anymore in Algtop. I don't even know where to start :( any advice on how to write algtop proofs or advice to think about this stuff would help.

[Anonymous No.12041133]

bit of a babby question, but what experiment/data set motivated differential equations of the form
Ax'' + Bx' + C(x) = 0
or is it just generalisations of motion/heat stuff?

[Anonymous No.12041363]

>>12040988
that the following are equivalent
>X is connected
>X is path-connected
Is not only true for CW complexes but for every locally path-connected space (Hint: show that for a locally path-connected space X, its path-components are open sets.)
So, you still have to show that CW complexes are locally path-connected. Do you think you could prove this?

[Anonymous No.12041995]

Can I go directly to measure theory based probability if I already know undergrad analysis? If so what books can you recommend?

[Anonymous No.12042022]

>>12041995
Yes and Cohn

[Anonymous No.12042024]

>>12041995
>if I already know undergrad analysis
Measure theory based probability is undergrad analysis...

[Anonymous No.12042154]

>>12030560
Algebraic numbers and matrices.

[Anonymous No.12042586]

>>12040857
Learn to use a proof assistant, it's cool stuff.

https://xenaproject.wordpress.com/

[Anonymous No.12042655]

>>12041133
Pendulum/spring with damping

[Anonymous No.12042659]

new thread pls

[Anonymous No.12042752]

>>12042655
neat, I take it x' is the friction