/sci/ - Science & Math

>>12025349
first for the decline of western math

Lads why didn't you tell me probability was so cool?

>>12025384
I feel like analysis isn't represented very strongly here. I've never even see anyone mention the probabilistic method in combinatorics hetr, but then again I'm not here all the time.

>>12025455
>hetr
here

wtf lol

>>12025455
>I feel like analysis isn't represented very strongly here
It isn't, almost every analysis problem I've posted every now and then has gone unanswered except for one on a sum of hyperbolic functions

>>12025349
If I have an abelian group [math]A[/math] that has an element of order 2, is then [math]Hom(A, \mathbb{Z}/{2\mathbb{Z}}) \neq 0 [/math]?

>>12025359
>Elliptic curves

>Elliptic Curves

>>12025488
Have you tried using the fundamental theorem or do you want something more elementary?

>>12025500
BASED

>>12025465
Have any examples of analysis questions that went unanswered? I'm curious about the level at which /mg/ gave up on the subject.

>>12025512
>fundamental theorem
what if A isn't finitely generated?

>>12025575
Find the derivative of x^2 at 2 per definition

>One afternoon I went out alone with her on Lake Orta and became filled with desire and we came back and lay on two beds side by side she reading, I pretending to, but with an awful conflict in my mind. After about an hour I said ‘Margaret will you fuck with me?’[3]

>>12025619
It is a complex number, if that helps

>>12025626
>At Los Alamos the secretaries had desks that were open at the front. Some of them stuck cardboard there because, they said, Johnny had a habit of leaning forward, muttering, and peering up their skirts.

i really, really, really don't like set theory

>>12025603
Oh right, I'm being silly. Try the more general subdirect representation theorem of Birkhoff. The description you get will be similar. The basic building blocks are the cyclic groups of prime-power order and the Prüfer groups.

>>12025708
but I i really, really, really like category theory

Anyone here familiar with hypergeometric functions? I'm just interested in one case, the second example on the wiki page https://en.wikipedia.org/wiki/Hypergeometric_function#Special_cases :
[eqn]{}_2 F_1 (a, -; -; z) = (1 - z)^{-a}.[/eqn] Is there a simple way to show this from the series definition of [math]{}_2 F_1[/math]? Obviously the two missing arguments cancel out, hence why there's no need to put anything there, but I'm not seeing the rest. I would like to avoid doing something like a Taylor expansion of [math](1 - z)^{-a}[/math], because that pretty much already assumes you know the answer.

>>12025455
This general and this board are too low iq for analysis.

So in topology I understand why continuous functions are defined the way they are, but is there a name for a function with the property that the image of any open set is open (as opposed to the preimage of a set being open)

>>12025803
Bruh, that's just the inverse function being continuous

>>12025803
An open map.

>>12025808
Not all functions even have inverses.

>>12025808
bruh, you're a brainlet.

>>12025816
Thanks, in hindsight I’m retarded

>>12025826
>>12025820
Thanks, in hindsight I'm retarded

>>12025829
It's cool, names aren't always obvious, but in this case the terminology is pretty straightforward.

How do you guys study your math textbooks?
a) Religiously copy it out text by text?
b) Write only key formulae and concepts?

I've been doing a) but now I come back to my notes and they look fucking disgusting and I'm much rather just read the text, but then by not writing I feel like I'm not ;transmitting' that info through my brain.

Plz help

>>12025795
I've dealt with them sometimes. I'm sorry but I don't think there's an easy way to do what you describe. It would really be best to just compute a formula for the terms in the Taylor expansion of [math](1-z)^{-a}[/math] and then compare to a similar formula for the function.

>>12025865
>copying the entire textbook
why the fuck would you do this? you might as well just read lecture notes only if you can’t appreciate the author’s input unto itself. what a waste of time.

>>12025865
Focus on
1) Doing exercises.
2) Asking your own questions, then trying to answer them, then looking up an answer online.
3) Experimentally computing without a goal in mind.
4) Talking to a friend (or /mg/ about what you read).

Rewriting and rote memorization get you nowhere. You need to practice using the skills you learn and engaging with what you read.

>>12025879
I'm not familiar with these functions, but it sounds like an expert would be able to answer how that identity was originally discovered, which may be a good way to explain how someone might come up with it in the first place.

Bros I am almost at section on the integers in Tao's Analysis I. I am so close to beginning the real analysis part of the book. I am so hype.

>>12025894
>>12025879
Alright well fuck me. I'll just take the result as given. Do you guys know of a "canonical" text on hypergeometric functions to put in my citations?

>>12025717
>Prüfer group
Oh, yea if A is a 2-prüfer group, then f(a/2^n) = 2*f(a/2^n+1). So Hom(A,Z/2Z) =0

>>12025882
Sorry anon, I'm new to this stuff..

>>12025886
Thanks. How do you absorb the info on the page though? Like, when you read through a proof of a theorem, let's say, do you draw diagrams? It's understanding the meat of the text efficiently that has me stuped

>>12025900
We can only hope that your hype continues uniformly throughout the interval in which you study real analysis, and that any deviation from your studies is bounded.

>>12025915
Oh yay I was lazy and spammed the super general situation and it worked lol.

>>12025916
>Like, when you read through a proof of a theorem, let's say, do you draw diagrams?

It depends on how deeply you want to understand the theorem. You should always have some goals or questions in mind when reading, or at least try to anticipate what's coming next by trying to prove the result yourself first. If you try to just absorb theorem after theorem with no goal or direction you're likely to fail to remember much of it because it served no purpose and didn't fit into a narrative.

>>12025953
Ok yeap I get what you mean, and I realise that there are good and bad authors in terms of spinning a narrative for the reader. But after, say Chapter 2 or 3 of a Real Analysis textbook, there's tons of theorems. How do you remember all of those? Is it really just constant application -> subconscious memorisation?

>>12025920

>>12025910
I'm sorry, can't help you with that. I'm no expert, I just had to deal with them in a completely different context.

>>12025964
>How do you remember all of those?

Professional analysts probably don't remember literally all of those. They might memorize most of the ones with names, but your favorite analyst is more likely to reprove something on the spot than remember the exact statement of theorem 12.4.67A in So-and-so's Analysis textbook. They can do this because they understand the actual concepts.

>>12026010
Thanks anon. And it sounds like part of the confidence of not having to memorise is due to a solid understanding of concepts then? Thank you very much, it's really been helpful

Is Cohn or Tao better for measure theory

>>12025455
Analysis is viewed, sadly, as a mere tool to construct rigorously objects that you can then have fun with, the same with general topology. People will cite something else for the details and directly begging wanking their diagrams and geometric intuition that was never actually built, just claimed it can be proven or that with few modifications the general argument should follow. Brainwashed retards who also want to show off they are "pure mathematicians" stay away from fields like PDEs, numerical analysis because it is too applied (showing they don't know what the fuck they are talking about). FFs measure theory is such a powerful tool and it is seen as "dry" by plenty of people. You start sounding like physicists with your meme methods that avoid the important insights of analysis and topology.

>>12026088
The topology people have really been dropping any kind of calculation with the real numbers pretty hard. If I know this finite space has the homotopy type of a sphere, why should I ever bother studying the corresponding manifold? :p

>>12026126
That's why I mentioned general topology and not Alg*braic topology. Lmao they think it is better to use category theory without realizing most of their examples or constructions only makes sense thanks to analysis actually proving shit.

>>12026199
>Lmao they think it is better to use category theory without realizing most of their examples or constructions only makes sense thanks to analysis actually proving shit.
how many topologists do you actually know, anon? you seem to be very aware of what's in their heads.

https://www.youtube.com/watch?v=mH0oCDa74tE

3b1b does it again

>>12026212
I'm venting and exaggerating anon. I just think analysis is pretty cool and maybe people take it for granted :(

>>12025455
most of the general is zoomers and category trannies

>>12025795
One way to do this is just use the generalised binomial theorem and note the definition through Pochhammer symbols/gamma functions.
I'm going to sleep but if you are still stuck when I wake up I'll post an answer for you.

>>12026248
Most of the general is effeminate algebraists

>>12025488
False. Consider S^1. Every element is a square thus there cant be a normal subgroup of index 2. >>12025465

>>12026246
On the flip side we have people here dismissing category theory because it's "for trannies", so there's plenty of insecurity to go around. As a side note, I've never actually met a transsexual mathematician. Do they even exist outside of memes on 4chan?

>>12025795
Didn't read the rest sorry, realised you asked how to see it from series definition.
Yes, it is easier to write a negative integer as the argument of F. Then you can just read this off from the definition. Again, it's just a well known series which you'll recognise.
If you want a more complicated proof, you can use the integral definition or the formal definition with gamma function crap involved but it's not necessary.
I'm not being an asshole here but you should be able to just eyeball the series definition. Write a few terms out and you'll see it.

>>12025349
How old is he?

>>12026280
i.e. just write the series out for F(-n,b;b;z) and you'll see immediately that the series is exactly what you want. Just compare it with the binomial series.

>>12025384
Dude. What is this? You can apply any concept to vectors where the identity of important concept includes division, multiplication, scalar product, cross product.
It's not the beauty of probability, but how two different fields of maths can be used together for a unified representation.

Grant release a new video.
Thoughts on his understanding of groups?
https://www.youtube.com/watch?v=mH0oCDa74tE

what would the mandelbrot plot look like in 3 dimensions?
not just with depth, but if each point represented another point in a plot orthogonal to the original

>>12026287
https://www.stanfordesp.org/teach/teachers/grants7/bio.html
Probably around 26-27.

>>12026262
Is that a bad thing?

>>12026273
Personally no. There are plenty of faggots though, but most of them not obnoxious.

>>12026302
Do people on this general actually like him? He claims to be this savior offering a new perspective on math, but in reality he’s just pretentious and rejects any proof that isn’t visual and he seems to hate any math that isn’t intuitive

>>12026323
It is if you can't fuck them.

>>12026333
He is just 27 and would come around 90 percentile among math general posters in terms of knowledge and understanding of maths topics.

Why are you guys talking about truannies and faggots?
I believe you are all paid CIA assests to distract us from discussing maths.

>>12026262
same thing as category trannies desu

>>12026351
The CIA has no reason to hide anything related to mathematics and especially not within the field of category theory.

>>12026323
It is if they aren’t moving in with me to be my house husband.

>>12026370
>distract
>hide
nice try glow*****

>>12026346
>>12026372
So instead of doing algebra and related things, you think w- they should only be treated as tools for pleasure and housekeeping?

>>12026272
Note that this solution is quite similar to
>>12025915
since the circle group contains the Prüfer groups as subgroups. One could also argue that the Prüfer 2-group has only proper subgroups of finite order so all its quotients are infinite.

>>12026400
*nontrivial quotients

>>12026384
I'd be down for doing math with a hot trans girl, but I don't think there are any to be found studying the subject.

brainlet here, I was wondering, can two infinite sets be different sizes? Like say R is the set of real numbers and N is the set of natural numbers, and they both go on infinitely after 0. I can begin writing the next values after 0 in N (ie. {1,2,3}) but I can never write the next value in R because there are an infinite number of 0s after the decimal point right? Are those sets the same size?

Again I'm a math brainlet and I'm pretty sure this is basic set theory but it just crossed my mind

>>12026453
Yes, look up Cantor's diagonal argument.

>>12026453
that is basic set theory. N is countable infinity and R is uncountable, so yes they are different sizes. Which basically just proves that infinity, much like the concept of 'nothing' is a pretty meaningless invention of human perception and doesn't really exist or have a purpose

>>12026293
>>12026280
Okay, thanks.

>>12026347
What did he work on for his PhD?
>>12026323
No, all that I ask for is balance. Yin waters of algebraist homos matched with the yang fires of the analyst patriarch.

>>12026453
also 0 is not a natural number

>>12025626
nice

>>12025708
>>12025746
I came to like (dislike?) both about the same.

>>12025795
https://youtu.be/dzuUpEFKV3E

For your particular case, maybe
https://en.wikipedia.org/wiki/Stirling_numbers_and_exponential_generating_functions_in_symbolic_combinatorics#Stirling_numbers_of_the_first_kind
helps
(the log exp trick)

>>12026347
>no PhD
>wanted to work on his Python skills
It all makes sense now.

>>12026467
>patriarch
That's a funny word for asocial geeks who are frequently over- or underweight, but okay.

What operating system scientists and maematicians use?

>>12026549
Almost everyone I know uses Ubuntu

>>12026453
That's not the reason there are more real numbers than natural numbers. The rationals have the same property you described, but #Q=#N.

>>12026549
The numerical/computational algebra chads use Linux, everyone else uses Windows/OSX.

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

>>12026600
Cool, this is the first such embedding which was explicitly given.

>>12026508
>overweight
I have a well muscled, tight, athletic form and masculine facial structure.

Megamathlet question incoming: what's even the point of subtraction when it's just addition of some number with it's additive inverse? It just seems like a handicap to use subtraction because of it's anticommutativity; an handicap that can easily be sidestepped by just redefining it as addition of an additive inverse. So why use it at all outside of rudimentary non-negative number math? It just seems like such a counterproductive operation. Or am I just being autistic and overthinking it?

>>12026983
>redefining it as addition of an additive inverse
That is the definition of subtraction you mong.
Just think of a-b as shorthand for a+(-b)

>>12026990
Cont.
Also more rigorously, in any field like the real numbers, the only given operations are addition and multiplication. So subtraction is forced to be defined as addition of additive inverses

>>12026990
I meant "rewriting it" instead of "redefining it".
>>12027012
Okay, yeah. So subtraction is just a + (-b) and division is a * 1/b. Basically just operations that exist as shorthand.
I'm sorry I am actually retarded. I occasionally have bouts of questioning basic shit I know I know but I can't stop obsessively thinking about it, like I need some explanation written in formal logic as to why that basic shit is the way it is so that I know for sure.

>>12027027
http://www2.hawaii.edu/~robertop/Courses/TMP/7_Peano_Axioms.pdf
Give this a read anon I think you might find it interesting

>>12027027
There us actually something interesting there. See the example of subtraction in this paper.
https://jdhsmith.math.iastate.edu/math/4LQR.pdf

>>12026983
>>12027027
You're confused. Subtraction is defined as addition with the inverse of the second argument. This is such a common operation (how many times have you had to pay for something?) that it's worthy of a shorthand notation, and stressing its formal definition to literal children learning it for the first time is less helpful than a more intuitive description.

When is it too late to pursue real knowledge in mathematics? I'm 25, and I have probably a year of study before I can begin even first year stuff. But I love taking the lessons, and doing the exercises, and playing with the software. Has anyone else been here?

>>12027188
Lots of people. Any adult can, by devoting a few hours of real study a day, do all the math taught to children throughout the American school system and be ready to learn calculus at a university within one year. I know multiple people who have done this.

Why do I have to take general ed classes bros. I just want to learn math but I have to waste practically a year of education to classes on not being racist, not being sexist, and not being homophobic

>>12027254
This is why commoners should never have been allowed to attend university. No culture whatsoever.

I am enrolled in a discrete math course this fall. It will be the first proof-based course I will take. Every proof and solution in the book is completely mystifying so far. The solutions all begin with a hypothesis that seems to come from out of nowhere. Once the solution is underway, I can generally follow along but then there is another step that seems to come from out of the blue.

>>12027375
Provide an example of such a baffling hypothesis.

>>12027375
Keep in mind when reading a proof you're seeing history in reverse.

>>12027438
Not him but id be willing to bet it’s induction. Newfags can’t handle the induction hypothesis

>>12027471
It's not induction. That is taught later in the course though. I am supposing that a strong foundation in prepositional logic and understanding proof "methods" will lead to understanding how the proof is attacked better? Does it all boil down to prepositional logic in the end?

>>12027485
Propositional logic+definitions+previously proven theorems
But can you find an example so I can concretely say where the hypothesis comes from

>>12027505
Prove that the arithmetic mean is always greater than the geometric mean. Books (Rosen's Discrete Math btw), says to work backward. He constructs a sequence of equivalent inequalities and ends up with (x-y)^2 > 0. He then continues that he can build a proof based on reversing the steps. How the fuck did he know the backward reasoning was the starting point?

>>12027529
Oh yeah it’s really uncommon for a book to give the reasoning behind the steps of a proof or how they came up with the proof, I think there was a thread complaining about that a couple days ago. Even if you don’t know the reasoning behind the steps, if the actual logic behind the proof makes sense that’s all that matters as far as math is concerned

>>12026549
I code all my simulations with BASIC

>>12027254
Do Americans really?

sorry for the massive amounts of question in a single post, but...

is the rotations of a sphere a group with uncountably many elements?

are there groups with cardinality greater than R? is there a retard proof one which i can understand?

is it possible for there to be a classification of finite simple groups that looks different from the categories we have now?

also: whats the first book on math you will give your hypothetical/imaginary/real child when he/she/they/it ask you for a book on math?

>>12026303
https://youtu.be/ovJcsL7vyrk?t=400

>>12027610
BAS - ed

>>12027584
this is imo a major problem in math texts: if you actually think hard and reach a solution yourself, you will see that the rationale of the approach, but if you don't, or you arrive at a different proof, you will not understand the method of construction. this can only be learned with experience.

>>12027631
>is the rotations of a sphere a group with uncountably many elements?
yes
>are there groups with cardinality greater than R? is there a retard proof one which i can understand?
Probably
>is it possible for there to be a classification of finite simple groups that looks different from the categories we have now?
Like can we group (no pun intended heh) them a different way? Sure, I guess?
>also: whats the first book on math you will give your hypothetical/imaginary/real child when he/she/they/it ask you for a book on math
Fuchs Fomenko

>>12027631
>is the rotations of a sphere a group with uncountably many elements?
Yes, consider irrational rotations.

>are there groups with cardinality greater than R? is there a retard proof one which i can understand?
Sure, take the free group generated by a set with cardinality greater than R.

>>12027645
>Sure, take the free group generated by a set with cardinality greater than R.
You might as well make it abelian too so the construction is easier.

>>12027648
I feel like the construction of a free group is easier than the construction of a free abelian group. One comes from a quotient on the other?

>>12027653
The general construction is easier for groups as opposed to abelian groups because you're taking a quotient of the free magma by a smaller congruence in the case of not necessarily abelian groups, but the usual informal/ad-hoc construction of the free abelian group is easier than for the free group.

>>12027656
True I forgot that you could just take the direct sum of a bazillion Zs

How is it possible for me to become good at math? The reality that everything can be explained with numbers fascinates me, but it seems I'm not fit to become a mathematician, I started studying from null, so I can work and improve my foundations, but each time I try to study the idea of getting an answer wrong makes me anxious, as in I will never understand anything deeper, I won't get hold of the necessary methods to achieve what I want, that I'll be stuck on elementary shit.

>Conway
>Graham
>Fischer
What is it with 2020 and Mathematicians dying?

>>12027856
>The reality that everything can be explained with numbers fascinates me
Please don't fall into the trap of giving math, a man-made "language", mystical properties like being a perfect description of the universe. It's no different than ancient Jews claiming Hebrew was given to humanity by God and saying Abracadabra bends reality to your will.

How he fuck do I solve this?

>>12027893
This

>>12027896
The answer is no. I could prove it more rigorously but think of it like this. The highest and lowest power will always remain because they have nothing to cancel with.

>>12027893
second thing is arabs desu, we don’t say abracadabra.

>>12027925
>we
Jew spotted

>>12027925
I know Jews don't actually use it, it was just an example off the top of my head. It popped up randomly in some Roman manuscript.
Jews do have a thing of mystifying language; the names of God, knowing the name of something is to gain power over that something, that one work of literature I can't remember where a bunch an angel plays Scrabble with a bunch of rabbis with failure resulting in complete dissolution into the aether, or something like that.

this is an extremely retarded and amusing math general edition so far

Also from now on i will capitalize my sentences but not punctuate otherwise

>>12027950
Specifically because not capitalizing is for trannies/women/depressed people/bottoms (i am none of those)

>>12027953
I am several of those, but I try to write properly nevertheless.

>>12027934
Yes, that was the implication brainlet.
>>12027936
All primitive cultures believed in words of power. Sanskrit was held in the same regard. Mantras follow this logic. Even today idiots think words like racist and nigger have literal power over someone’s soul.
>>12027950
If I see your posts I’m going to harass and belittle you. You are a slave.

Prove that 9 + 10 = 21

>>12027955
Let's play minesweeper. I am going to make a guess as to the combination you alluded to and you tell me how many I got right:

are you a tranny and woman?

>>12027955
Writing properly is for gay bottom males, and people with high neuroticism and low creativity!

>>12027958
Actually, 9 + 10 is 21 in some cultures :

>>12027966
shut the hell up harvard

>>12027960
>claims to make a guess
>asks directly

>>12027962
Please just tell me what is the consensus on proper writing!

>>12027958
define 21 to be the symbol that represents
iiiiiiiiiiiiiiiiiii

define 9 to represent
iiiiiiiii
define 10 to be
iiiiiiiiii
define + to be putting strings of i together

>9+10
>iiiiiiiiii iiiiiiiii
fuse
>iiiiiiiiiiiiiiiiiii
compare:
>iiiiiiiiiiiiiiiiiii

By the Holy Vision Matching (of my linguistic culture),
9+10=21

>>12027971
>>12027971
>>12027971
Writing improperly and frees your mind

>>12027971
Just bee yourself

>>12027979

Post studying music
https://www.youtube.com/watch?v=x-WXrh18OFU

>>12028009
>studying music
>not instrumental

>>12028045
>implying vocals cant be instrumental

>>12028009
>he doesn't study to randomly generated harsh white noise
Not gonna make it.
https://www.youtube.com/watch?v=qGLau5MT2s4
https://www.youtube.com/watch?v=Y_XEev1pris
youtube.com/watch?v=BTHVQbUT_8E&list=PLMMTrEN3GJc5fXFn_8fq-WBKGUSB0kFau
https://www.youtube.com/watch?v=WYRoMTd74Y8

/gmmg/

To all you manifold lovers:
>On the rational homotopy type of embedding spaces of manifolds in [math]\mathbb{R}^n[/math]
https://arxiv.org/pdf/2008.08146.pdf
O kurwa:
>Topological dynamics beyond Polish groups
https://arxiv.org/pdf/2008.08471.pdf
Some geometer may like this:
>IBN-varieties of algebras
https://arxiv.org/pdf/2008.01538.pdf

>>12028009
https://www.youtube.com/watch?v=6rQ0ULxhtLc the obvious choice.

>>12028105
Hmm i was stuck on a problem and got zoned out thinking about 9/11 and the United Nations and then i lclicked on and began this album, and it made me want to study. So this is definitely good studying music

This reminds me of another thing, at the end of time when the Major Powers consume all the weakly held energy in the universe, they will all be of right soul, and will collectively agree to make their final battles epic and will-based. They will innervate their Galaxy-Fingers, and they will not foresee the end of the battle. Motion in time will play the chances.

So the future will be worth it anons. Make sure to meditate so you reincarnate well before the final stage of existence, the era of serpent energy, or join me in using your mathematical mindset to develop technological immortality!

>>12028163
Nice! Drudkh's old stuff is 10/10 anyway and these acoustic folk versions are wonderful for studying purposes.

>>12025619
>Find the derivative of x^2 at 2 per definition
no

>>12027631
>is the rotations of a sphere a group with uncountably many elements?
usually theta and phi are used for rotations around the axis and latitude, we can look at just one and see that it is similar to a continuous interval of R -> uncountable

>are there groups with cardinality greater than R? is there a retard proof one which i can understand?
functions on R to R with + (f+g -> (f+g))
this has the same cardinality as the power set of R which has strictly greater cardinality by cantor's diagonal iirc
>is it possible for there to be a classification of finite simple groups that looks different from the categories we have now?
probably if you can find a useful way to do so
>also: whats the first book on math you will give your hypothetical/imaginary/real child when he/she/they/it ask you for a book on math?
one of those logic puzzle(fox,chicken,corn raft type problems) books if they count
id probably let them choose and (if asked)guide them to the appropriate content if they get interested in mathematics
not directly maths but those cross section books were great to help develop spatial reasoning for yung'ns

>>12028009
holy fuck this is a good song
never heard of this band before

>>12027856
>The reality that everything can be explained with numbers fascinates me,
that's very false

Does anyone else feel weird when certain numbers are supposed to be odd/even/prime? Like, 8 feels prime-ish cause its a p^p. Or 9 kinda feels even because its not only divisible by 3, but its divisible INTO 3. So its got a symmetry, while also having a near-2 divisibility. 5 is a factor of sturdy decimals, so it also feels even and not prime. 7 kind of feels like it should have a factor too, but thats maybe just because its lucky. 13 feels too obvious as an unlucky number to be prime, yet it is. 27 sounds like a prime, but its not. 19 is very perfect as a prime.

>>12028348
>>12028327
Two deeply related posts. /mg/ being full of overeducated idiots won’t see anything at all.

>>12028348
Bro, pass the bong already.

>>12028356
I just wanna sperg about numerals with my fellow autists in between the tiresome algebra and daily terrors, alright anon?

>>12028362
*passes bong to you*

>>12028348
57 and 91 should be prime

>>12028348
>near-2 divisibility

>>12027915
Thanks

>>12028383
Also known as quasi-even.

Maths warmup exercise!
Let [math]X = \{0,1\}^\mathbb{N}[/math]. For [math]x,y \in X[/math], define [math]x\sim y \iff \lim_{n \to \infty} e(x,y,n)/n = 0[/math], where [math]e(x,y,n)= |\{ k \leq n : x_k \neq y_k \}|[/math]. It's easy to verify that [math]\sim[/math] is an equivalence relation.
Question: prove or disprove that [math] |X / \sim| = |X|[/math]

>>12028440
If you can't solve this in under 10 minutes you have no place in maths.

Is it a good idea to supplement Hoffman & Kunze with Axler since H&K is meant to be difficult? Also what should I read now that I've finished Pinter? I've seen at least 100 different recommendations for algebra textbooks in the archives, mostly the same Foote fetishist repeating themselves.

>>12028440
What level of math is this? I've never seen such an equation.

>>12028440
https://www.google.com/search?client=firefox-b-1-d&q=omega+set+integer+construction
i'm not into set theory and algebra but i found this.
i used sup R = inf epsilon.
on the set {nil, Omega}.
I don't know what I need to further prove other than that nil has no equivalence relation, idk much about equivalence relation. Should I learn more? It's kind of interesting.

>>12028466
>What level of math is this?
Basic set theory.
>>12028468
What the fuck are you talking about lmao

>>12028477
doh! um.
X without the equivalence relation is still the set X.
Nil breaks equivalence relations, right?
Omega constructs anything with differential equations for all sigma algebras, from an analysis point of view, unless it's the topology which can easily be constructed with omega compliment.

>>12028488
an i forgot to take out OP of my name

>>12028488
/ is not set exclusion, it's the quotient. It means the set of equivalence classes of X.
The question asks you to compare the cardinality of X to that of X/~

petition to rename odd numbers as co-even

>>12028440
absolute value of a set is meaningless
go back to HS

>>12028513
https://en.wikipedia.org/wiki/Cardinality

>>12027584
What is the best book that teaches proof? What is the best technique for learning proof? It seems like doing "practice" proofs is one way but how would I know my reasoning isn't faulty?

>>12028348
agree on 27 and 19. I hate that 1001 is not a prime desu

>>12028499
Couldn't you just take N^-1/{N}, which is in R^2 for vars x and y? So the intersection x and y = !R^2. or ||!lambda||k. mu decomposes on lamdbda i.e. mu << lambda.
Well. Anyways, it looks like you got your homework equations right. Just use ln x and ln y for different measurements. omega will always be omega when you raise it to N that way.

and I think your calculus is right. Omega is open to all sets and cardinalities because it defines all sigma algebras by vanishing the lebesgue integral to infinity and all constructs are inclusive to Omega (measure = mu = 0 lim n -> infinity).
Those are equal, imo.

>>12028561
Get help. Youre clearly mentally unwell.

>>12028561
sorry for the warbgarble at the beginning of my Paragraph there.

>>12028568
What makes you believe that?

>>12028573
None of what you wrote makes sense. It's schizo-babble.

>>12028575
orly?

X iso to binary inf decimals in [0,1)
~ has x~y where they differ in finitely many decimal places, we can think of these as terminating decimals
the rest of the question should fall out straightforwardly, mr basic set theorist

>>12028585
They could differ in infinitely many places. And all you did was restate the problem.

>>12028465
>H&K is meant to be difficult
Why did you get that impression? It's not. It gives a good overview of the subject that is slightly more general than other books; e.g. it usually doesn't assume a finite-dimensional space and does so explicitly when necessary, often providing an infinite-dimensional counterexample. The explanations are thorough and on point, and the only autistic part I remember from when I read it is the whole chapter on the Jordan form.
>Also what should I read now that I've finished Pinter?
Seems like a complete abstract algebra book, you should know the basics by now. I'd attempt the exercises in D&F or maybe check out Aluffi if it's too terse for your tastes. (D&F is more of a reference book than anything.) If you want to research something involving algebra then read something related to that field, e.g. Atiyah-Macdonald for commutative algebra.
Did you just read a whole book on abstract algebra before learning linear algebra?
If you have a background in abstract algebra and somehow are learning linear you might be interested in Roman's Advanced Linear Algebra. Maybe not as a serious read if you're struggling with H&K, just find a .pdf and skim over it to get the "big picture".

>>12028348
>Like, 8 feels prime-ish cause its a p^p
really makes you fink

>>12028440
The sequences x and y are equivalent if the fraction of position where they are different tends towards zero?

>>12028585
>finitely
I donno, but I think I can try to think of two sequences that are different in infinitely many places, but more sparsely so than linear and not finite.
So if I pick a prime [math]p[/math], then two sequences that are forced to be different at the indices k given by the floor of [math]\log(i\cdot p)[/math] for all i could already be equivalent by this definition. I guess this is asking whether there's only few ways in which I can make essentially different sequences still be equivalent in such a way?
That's not a ways to solve the question, but the set of sequences is such a shit mathematical object that I don't even dare to make a guess. Let's say I guess that |X/∼|=|X| can be disproven in a strong enough theory.

>>12028597
>The sequences x and y are equivalent if the fraction of position where they are different tends towards zero?
That's what I said, yes.

>>12028597
>Let's say I guess that |X/∼|=|X| can be disproven in a strong enough theory.
The question has a short, clean and highly elementary solution. Hence <10min limit.

>>12028612
bros... i couldn't figure out the answer...

>>12028440
What does the superscript N on {0,1} mean again?

>>12028594
>Where did you get that impression?
People on /mg/ tend to say it's extremely rigorous, terse, too difficult for first exposure etc. Is it considered difficult because many /mg/ posters have yet to do an 'intro to proofs' course and so they lack the prerequisites?

>D&F, Aluffi
>Roman
Thanks I'll have a look when I'm ready to. I might take a look at Lang since that seems to have some linear algebra too.

>>12028621
It means X is the set of functions from the natural numbers to {0,1}. Equivalently, its the set of binary sequences.

>>12028440
[math] \{0,1\}^{\mathbb{N}} [/math] is uncountable and equal to [math] \mathbb{R} [/math] via Cantor's diagonalization argument, and any equivalence class in [math] X [/math] is countable, since it is a countable union of countable sets, which is countable. By the contrapositive of countable unions of countable sets being countable, [math] |X/~| [/math] is uncountable and equal to [math] |\mathbb{R}| [/math].

>>12028626
First sentence should say isomorphic to [math] \mathbb{R} [/math], not equal.

>>12028626
How do you know that equivalence classes in X are countable?

>>12028624
Ok, and so x_k and y_k I'm assuming are the kth term of the sequence formed by those respective functions x and y?

>>12028632
BTW theyre not. Each equivalence class has cardinality of the continuum.

>>12028634
Yes.

>>12028632
As I said, a countable union of countable sets is countable. Any equivalence class [math] [x] [/math] consists of all the elements which differ from [math] x [/math] in one place, along with all the elements that differ in two places, etc. This is clearly isomorphic to [math] \bigcup_{n\in\mathbb{N}} \mathbb{N}^n [/math].

>>12028637
Sorry, one more question
{k≤n:xk≠yk}

I don't understand what's going on in this set. Are you forming a set of terms in the x and y sequences picking only the terms where they are dissimilar at the same index?

Or have I got this all wrong

>>12028465
Take the Footepill anon.

>>12028640
I already pointed out your error and still you persist in your ignorance. Embarrassing.

>>12028642
>>12028637
Oh fuck me Ok I understand it now.

>>12028645
You never pointed out any error. You asked for my reasoning, and then made a claim with no proof. How about you actually point out my error, instead of being an asshole.

>>12028652
How about you leave my board, brainlet.

>>12028652
God I love math so much.

post the one where you ride a dildo

>>12028612
highly elementary
In what sense

E.g. looking at arguments like
>>12028626
>|X/ | is uncountable and equal to |R|
Say we've proven the quotient countable, why would does it follow that it's |R|

>>12028612
highly elementary
In what sense

E.g. looking at arguments like
>>12028626
>|X/ | is uncountable and equal to |R|
Say we've proven the quotient uncountable, why would does it follow that it's |R|

>>12028667
>Say we've proven the quotient uncountable
But we haven't.

>>12028366
>3*19=57
wtf
>pic related
wtf

>>12028383
>>12028397
Threeven

>>12028512
There is a remainder of one, an odd One (under partition of twos)

>>12028678
not that anon but my rough argument:

The equivalence classes are essentially sets of binary strings that have a finite number of different terms and a (countably) infinite number of similar terms.

Since there is an (uncountably) infinite number of binary strings (as per Cantor's diagonalisation argument), |X \ ~| = |R| = |X|

>>12028693
Just to flesh it out

Since there is an infinite number of binary strings, there are an infinite number of equivalence classes (since you can just make a new equivalence class through Cantor's diagonal method).

Hence |X \ ~| = |R|

>>12028696
>>12028693
What is this?

>>12028440
Make this even harder. Let =, be equality on binary sequences. Prove or disporve. There a Borel function that witnesses, |X/~|=|X/=|. That is, is there a Borel function f so that for all x,y in X that x=y iff f(x)~f(y).

>>12028704
My solution.

Each equivalence class is the set of binary strings that tend to 'approach each other' as n approaches infinity. 'approach each other' meaning x_k and y_k are the same.

Then you've partitioned X into all possible binary strings with 'similar' terms at infinity. But that would be an uncountable set with the same cardinality as the set of all binary strings anyways.

Right?

>>12028713
>My solution
Oh. I thought it was a joke.
>But that would be an uncountable set with the same cardinality as the set of all binary strings anyways.
Why?

>be me
>11th grade
>talking about dividing out a factor
>be confused
>"where does the factor go, though"
>teacher says it goes nowhere
>?
>"its just a new mathematical statement"
and that is how i learned that you can modify things to change their appearance to use them differently

>>12028440
Thought I had solved it but I was horribly wrong fugggg

>>12028723
multiplying by 1 and adding 0 are two of the greatest tricks you can have up your sleeve

>>12028708
Can you explain what you mean by a Borel function in this context?

>>12028693
>>12028696
>that have a finite number of different terms
Why would those elements which are different only be finite?

Also, even if the quotient is uncountable and [math] |R| [/math], how can we show that it's [math] =|R| [/math] in ZFC?

>>12028513
it denotes cardinality dumbass

>>12028696
>that have a finite number of different terms
Why would those elements which are different only be finite?

Also, even if the quotient is uncountable and [math] \le |{\mathbb R} | [/math], how can we show that it's [math]=|{\mathbb R}|[/math] in ZFC?

>>12028736
A Borel relation on XxX, that is a function.

The solution is so simple it amazes me nobody has posted it yet.

>decision in progress
Literally shaking senpai

>>12028366
57 is a Grothendieck prime

>>12028841
what decision?

>>12028857
Editorial manager status. Let's see if Journal of Algebra wants this shit.

>>12027027
Dude I get you, I do the same.

>>12026549
I use windows 10 on my work laptop. I don't have time to spend being a computer janitor.

>>12027962
Reminds me of how japanese men speak like retards because it's manly, somehow

>>12028552
are you legit this new to math?
math is logic spaghetti or logic engineering

Anyone familiar with fractals ? I have a question on the one you get with the equation z^i + c (pic related)
Why does that looks like a fibonacci spiral ?
Please /sci/, my math teacher is 56 and never heard about fractals

>>12028926
>I don't have time to spend being a computer janitor.
This is what happens when you use windows 10, kek it takes like 2 hours to make it non unbearable

>>12028009
https://www.youtube.com/watch?v=hLasVixt3LY

>>12028945
>math is spaghetti
what did he mean by this?

>>12028513
based

>No one has still posted an answer
>Everyone is calling it trivial
Really activates my almonds.

>>12029015
You post it then

>>12029088
N-no you...

(°_°) how do I lern proofs

>>12029141
Read linear algebra done right by axler, worked for me
basic concept is:
>there are things with definitions and symbols that we make up
>there are assumed rules (called axioms)
>there are the rules of logic (part of axioms and basic primitive connections)
>then you see what the axioms say how you can rewrite the definitions, and what new properties you can show they have via logic
>use the new learnings as next level axioms to go further

For about 20 years itll all seem like nonsense. but then itll fit together.

>>12029151
so it's all just logic then

>>12029186
Maybe. Logic fits into a higher aesthetic but that higher aesthetic is hard to see. You could say logic contains aesthetic in its roots though. And those roots show up everywhere in the world, in your life. So it's not abstract and meaningless

>>12029186
no it's all arrays of numbers

>>12028947
>>12028947
z^i is a normal spiral, because ith powers are rotations. its either the c or the z that causes the growing outwards, cause fibonacci is based on addition

>>12029198
Thats not true, there are operators on the sets too, among possible other structures that im not sure if can fit into operators

>>12029206
Operators are just arrays of numbers.

>>12029198
Everything is just the empty sets and sets that contained the empty set

>>12029225
Tthey have to have extra meaning though, to describe how the numbers make other numbers associate. and if you make the descriptions IN numbers, those numbers still have to be described in language. i guess language could be purely numerical though. so sure, all symbols can be numbers, thats fine. Reality and action and perception associated with the numbers is inherently not numbers though

>>12029225
wtf is a number

>>12029273
Empty set is just an array of numbers.

>>12029293
A squiggle that represents (aka is swappable in your mind with) another set of squiggles, namely some bunch of Is
For example
5 represents IIIII
You can also bag the Is into larger groups

>>12029298
If you desire it to be so, then so

The reason why I said array of numbers is not because I actually believe that to be a good answer but to mock by analogy the person who said math is just logic. Concepts are more than arrays of numbers even though they can all be encoded in various ways by arrays of numbers, with varying efficiency. In the same way math is more than logic. No (good) mathematician thinks about math in terms of manipulating formulas and axioms by a fixed set of rules to obtain an expected formula when theyre actually working. They think about actual platonic objects that they manipulate and reason about in their heads, with faith that all their arguments could, with enough time and effort, be formalized if a fool wished to waste his time so. If youre experienced in maths at all Im sure you could remember countless times where the idea of a proof was immediate and abundantly clear in the head when you think about what the concepts mean (i.e. the semantics) even though writing the proof out so that it conforms to usual methods of deduction is a pain in the ass.
When a mathematician talks about a circle he means a circle, not an axiom or a formula. He has an image of a circle in his head and it's absolutely clear to him what he's talking about.

>>12028622
>Is it considered difficult because many /mg/ posters have yet to do an 'intro to proofs' course and so they lack the prerequisites?
I wonder if people here even did those. I think a lot just jump into books/classes

any advice to start learning harmonic analysis by myself?
I have some background on functional anal and PDEs but my measure theory is a bit weak

Question, if P is an integer bigger than one, are P and P+1 relative primes?

>>12029437
(P+1)/P=
>P/P + 1/P
>1+1/P
>if P>1, 1+non int
>non int result
Yes

>>12029437
Doesn't have to be bigger than 1.
If d|P and d|(P+1), then d|(P+1)-P so d|1, so d=+-1.

>>12029362

"The typical 'working mathematician' is a Platonist on weekdays and a formalist on Sundays. That is, when he is doing mathematics, he is convinced that he is dealing with an objective reality whose properties he is attempting to determine. But then, when challenged to give a philosophical account of this reality, he finds it easiest to pretend that he does not believe in it after all."

>>12029568
"The typical 'working mathematician' is a Platonist on weekdays and a computer scientist on Sundays. That is, when he is doing mathematics, he is convinced that he is dealing with an objective reality whose properties he is attempting to determine. But then, when challenged to give a philosophical account of this reality, he finds it easiest to pretend that all he does is manipulate arrays of numbers."

>>12025349
Why is it so hard to find the proof behind polynomials having multiple solutions? Am I searching wrong?
As a complete idiot (which I probably still am asking this), I'd imagine [math]x^2 - 1 = 0[/math] to have only one solution {1}, sure, but noooo, the solution is {1,-1} because fuck me.

>>12029591
If p(x) is a polynomial and p(a)=0, then (x-a) divides p(x) so by performing long division you can find the rest of the solutions.

>>12028348
>8 feels prime because it's a product of primes
Big if true

>>12029619
What compels someone to make a post like this.
>thonk emote
>meme phrase "big if true"
Do you think you're being funny, creative? You didn't contribute to the joke in any way. The meme in your post is at least 3 years old. This is a thread for logical autists. Normies make posts like yours to signal their compatibility with the group, but this is an anonymous website. You're not using a trip. I'm genuinely baffled as to what the point of your post is. Are you just low-IQ with 0 situational awareness? Why are you even on a math thread?
Please leave and never come back.

>>12029632
Have sex.

>>12029632
PhD stuff going bad or why are you so grumpy, little tranny?

>>12029640
I don't even like men to be that muscular. She's all yours bud.

>>12029640
Why? I am not attractive nor am I socialized enough for women to perceive me as conforming to social environment (which is extremely important for women). The only way I could have sex is if I payed for a hooker which is essentially the same as masturbation, the woman will likely not be attractive nor she will be attracted to me, which will make it an uncomfortable experience that will likely crush my self-esteem. Another option is to try to attract a woman myself. To do that I either need a lot of money which I am currently nowhere close to achieving or/and I need to become more physically attractive which would involve spending a lot of time working out as well as developing normie sensibilities so that the woman would perceive me as normal. That would mean watching normie TV shows (all degenerate garbage), listening to normie music, being interested in normie news. All absolute horrorshow. Even after having done all of that, at best I'll be able to attract a 5/10, given I myself am a 5/10 (maybe 4). All women I find attractive sneer at me when I look them in the eye.
All this time I would spend becoming more like a normie I could just as well spend doing maths, a thing that I actually enjoy and which is more optimized to my abilities.
Now you tell me, why should I have sex?

>>12029698
I'm pretty sure this is some kind of neckbeard. I'm not entirely sure how trannies feel about women, but I don't think it's this.

>>12029698
That's pretty pathetic, dude. Is waiting in this thread for someone to post their hw problem so you can reply with a smiling cartoon girl the highlight of your day?

>>12029744
>That's pretty pathetic, dude
Perhaps, although for now I am proud of my virginity. The word pathetic seems to me to be nothing more than a social signal. I doubt there is some deeper philosophical justification involved for your judgement.
>Is waiting in this thread for someone to post their hw problem so you can reply with a smiling cartoon girl the highlight of your day?
Yes.

This is the best /mg/ we’ve had in a while.
Anyways what do you guys think is the most underrated algebraic structure. For me, it’s quasigroups

>>12029757
I dont see any shame in it, you're just being honest and pretty logical honestly. A lot of what you say is true, women are impossible for some of us it seems.

>>12029577
You’re a fucking idiot. What an absolutely knuckledragging thoughtless post lol.

does every space that is homotopy equivalent to a CW complex admit a CW complex structure?

>>12028622
an intro to proofs course will not make you good at math and will not teach you how to le solve proofs. that is not a thing and will never be shown to you. It exists specifically to filter brainlets and to make helpless undergrads part ways with their money. that is it. you need literally no formal training in logic, set theory, or discrete math to do analysis and yet they force countless students to take the course anyway.

>>12029777
Consider a comb. A horizontal line segment with a vertical line segment at every irrational point. It retracts to a line segment so it's homotopy-CW but not itself CW.

>>12029763
It seems like quasigroups are coming back into fashion so they're perhaps not so underrated any more. I don't know about being underrated in research, but lattices and Galois connections are not treated the way they should be in introductory courses today.

>>12027896
The answer is yes. >>12027915
has it wrong because he's only considering polynomials in integral domains. But you have for example in Z/4Z that
(2x + 1)*(2x-1) = -1

>>12029787
>you need literally no formal training in logic, set theory, or discrete math to do analysis
Maybe in 1850. Please don't give us more useless aspiring analysts who think all math after Leibniz is postmodern trash. They're as bad as freshmen who try to memorize the definition of a sheaf without knowing a single example of a ring.

>>12029832
I don’t think all 20th century math is trash, I think navel gazing foundational garbage and the divorce of mathematics from the physical sciences are an abomination. There’s nothing wrong with algebraic geometry I just don’t give a shit about it. My post is directed specifically at morons that think that you can be coached into solving exam questions correctly in a difficult math course much less coached to solve research problems. The idea is ridiculous. You don’t take an intro to science course to learn mechanics, you fucking learn mechanics first semester freshman year because all that’s required is a pulse and an iq above 1 SD

>>12029809
thanks

>>12029848
Oh no. :(

>>12029848
>There’s nothing wrong with algebraic geometry
it's worthless, so is category tranny theory

what are /mg/ approved youtube channels?

>>12026273
>As a side note, I've never actually met a transsexual mathematician. Do they even exist outside of memes on 4chan?
I am. My main interests at the moment are mechanized mathematics, formal logic, homotopical topology. My repository of mechanized proofs: http://hg.gnu.org.ua/hgweb/hol-proofs

I have only met one trans mathematician online. She was into geometry. I wish there were more trans mathematicians.

>>12027188
I think that starting age matters little.

>>12027642
Based.

>>12027856
If your problem is anxiety, get benzodiazepines or SSRIs. If your problem is focus, get ADHD medication.

>>12029982
Flammable maths
Eigenchris
Epic math time

There’s probably more that I forgot, I don’t really watch YouTube that much anymore

>>12029787
I'm a brainlet freshman and this was always my suspicion as well
I think shit like proof books and How To Solve It are optimistic but rather misguided

>>12029982
Post face. You've already doxxed yourself, so might as well show what you look like.

quick question about a theorem i came across relating to vector fields in 2 dimensions:
>if F = <P, Q> is a vector field on an open, simply-connected region D, then if P, Q have continuous first order partial derivatives in D and [math]{P}_y = Q_x[/math] , F is a conservative vector field.
can we conclude that F is NOT conservative if these conditions are not satisfied?

>>12030032
How has he doxxed himself?

>>12030032
I don't know what you are talking about. I don't even come here often nor post

>>12030063
Yes. Partial derivatives commute.

Anyone else studying for the GRE subject test in the next two months? How's it going anons?

>>12030140
Yes I am using the Princeton Review book. I feel woefully underprepared. What are you using to prepare?

>>12030068
Well someone was enthusiastically posting new videos from some YouTube channel recently.

>>12030196
Nikolaj is well known.

>>12030162
I ran through the Princeton book and the ETS practice test in detail over the last several months, but the bulk of the studying I've done has just been going in depth on old calculus stuff, particularly vector calculus and complex analysis (Stewart and Conway mostly, though Conway is overkill). I did all the exercises in chapter 2 of Gamelin and Green have been doing a lot of surface level questions in graph theory, probability, and combinatorics. The hard part is making sure that there's not a single little thing I'm missing. The test is just so damn broad and focused on calculations and quick "theorem check" problems. I've also perused all the theorems in Linear Algebra Done Right. That thing is a great reference.

>>12030002
Neat, I've never even considered that a trans man might do math. I always think of the women when people say "tranny", you know? For how liberal universities are supposed to be I don't meet many gay people, much less transgender ones.

>>12030205
Okay, well I don't know them.

>>12030209
You are doing a lot more than me. I thought I could prepare for the exam in a month so I started in August with my test date on September 12th. Do you know what are of mathematics you want to study?

>>12028843
kek

>>12029982
I unironically like 3b1b.
But I don't know of many.

Recently I found CHALK (https://www.youtube.com/c/CHALKboard/videos)) which is cutesy but the guy may be grating to some

Suppossedly Daniel Chan (https://www.youtube.com/c/DanielChanMaths/videos)) is also pretty good but I haven't watched much of him.

That's all I know really.
>>12030007
>Flammable maths
Personally I find him sort of annoying most of the time.

>I want to kill myself
>Give me a hint on this problem i'm stuck on
>Prove that in R, dim null(T^2+aT+bI)^k is even for all positive int k, if a^2 < 4b
????????????????
>will Ethereum go to 1200?

>>12030221
I like algebra and algebraic topology the most right now, but who knows what will happen in graduate school. I'm already graduated, but when I was still an undergrad I bought the Princeton review about a month before the exam, but it didn't feel like enough time. I was weak on calc and complex and my score was just ok. Best of luck to you though.

>>12030210
I am MTF, a.k.a. trans woman.

>>12030264
New thread

>>12030369
Then who the hell is this Mario guy on the page you linked?

>>12030485
It is me. Taking hormones does not changes your name, duh.

>>12030538
Ohh I get it, you just started.

>>12029640
In US, even bellydick is circumcised. Gross.

>>12030543
I am years on HRT. I have not changed my legal name because so far it would not have had any benefit. What matters for me is the biological effects of hormones.

>>12030020
>freshman
>doesn't understand why discrete math is useful in higher level math
Why am I not surprised. Try reading >>12029832

>>12031151
>links to a seething post with no content
>hurr that should show you why you NEED to learn some abominable chimera of set theory preliminaries propositional logic and le ebin combinatorics
Kill yourself insecure brainlet

>>12031608
lol seethe harder that you got filtered