/sci/ - Science & Math

https://lukebenjaminralston.wordpress.com/
OP pic from this website

>>12441413
that's a weird essay from my point of view:
the claim that "R is the biggest jump in sophistication" is also very subjective, throughout my education i've seen people baffled by fractions or complex numbers rather than R

to me, "IVT and real numbers" is an even more basic concept than "roots of numbers"
when you first encountered [math]\sqrt{2}[/math] how did you think about it? well i'm sure most people do one of the following:
1) they have intuition about "continuity and IVT" and they understand here that there's gonna be a number that gives 2 when squared
2) they think "well whatever this [math]\sqrt{2}[/math] is, it's somewhere between 1.4 and 1.5, it's also between 1.41 and 1.42, and so on and so on, so it's somewhere there on the fucking line", now you could argue that this is intuition about "infinite decimal expansion" or about "taking a limit of an increasing/decreasing sequence" which is very close conceptually "supremum/infimum of a set"

i'm confident you could give an axiomatic definition of "real numbers" to a high schooler based on the description "real numbers contain the rational numbers, there's the order < on reals, and bounded sets have supremums"
this is how you attain rigor with regards to real numbers

Why does N exists? is it because the axiom of set theory tells you the set exists? no, the axiom of infinity was invented, because we wanted set theory to conform to our intuition
why does Q exists? because you constructed it out of N? no, it's the other way around: when you are an undergrad studying set theory, the fact that you can build "stuff that looks like rational numbers" gives us confidence that the language of set theory is expressive enough to include the math we knew so far
does Z exist because you constructed it out of N? no, same argument as above
and just like Q and Z, the construction of R in terms of dedekind cuts or cauchy sequences serves as an argument that set theory makes sense; NOT THE OTHER WAY AROUND

>>12441467
you can try this book:
https://drive.google.com/file/d/12rn1XuXp3uVo0T5uJJzqF-yDWutC6s1J/view
just pick out the simplest chapters probably the ones in the front

>>12441728
>the construction of R in terms of dedekind cuts or cauchy sequences serves as an argument that set theory makes sense; NOT THE OTHER WAY AROUND
Why not? Without constructing the reals you wouldn't even know what you're talking about.
>the claim that "R is the biggest jump in sophistication" is also very subjective, throughout my education i've seen people baffled by fractions or complex numbers rather than R
It's really not. You go from countable to uncountable, from describable and computable to completely uncomputable and indescribable. You go from tables and chairs to unicorns and dragons.
The complex numbers are very easy comparatively because you can just view them as ordered pairs of numbers constructed earlier. No need for any infinitary arithmetic or uncomputable, indescribable processes.

>>12441728
I agree with >>12441785 that R is really more involved than N, also conceptually. Even if it's indeed a big jump to go from finite to infinite, the "x mapsto "x+1" nature of N that covers all of N makes it more of a given.

I don't know why you speak about justification of set theory at the end, but here some remarks to your statements.

>sqrt(2) is, it's somewhere between 1.4 and 1.5, it's also between 1.41 and 1.42, and so on and so on
To the extent that this discussion is about exitence, I think we can split the discussion up more, in at least three parts:
* Discussing individual reals .
* Discussion about the collection of real number, object with arithmetic
* Discussion about R, the set of real numbers that is, then, a mathematical object in itself

>to me, "IVT and real numbers" is an even more basic concept than "roots of numbers"
There's a good intuition that IVT makes sense, but for this to imply something about the real numbers you need to make the jump and say a line is a somehow ordered collection of atomized, identifyable objects.

>no, the axiom of infinity was invented, because we wanted set theory to conform to our intuition
Why did you not just say "wanted set theory to include an object representing the collection of real numbers"?
I don't think Infinity is a good candidate to justify "because intuition"

Isn't it crazy how almost nobody ever proves that (ab)c=a(bc) for all a,b,c means you can unambiguously remove all parentheses, and we just all assume it's true without even verifying it?

>>12441728
good job

>>12442082
I'm not surprised, because at the point where you'd understand a proof of this, you've already had years of encountering evidence for it (in natural number multiplication)

>>12442082
general associativity holds in as little as a semi-group and can be proven easily via induction on a recursively defined multiplication.

>>12442082
Isn't it crazy how people who don't even know the word "associative" can't into algebra?

Shafarevich Basic Algebraic Geometry I study group starting around 15th December (in a week). Come join us
https://discord.gg/VavZCQmbr8

*cums inon klein bottle*

>>12442082
cuboid volume
rotation preserves it
intuitively

>>12442082
That's one of the first couple exercises in Grillet.

>>12441413
tag urself im U

No but really that was kind of neat

How can I construct a non-homogenous poisson process given a non-homogonous poisson point process defined by a measure distinct from the Lebesgue measure?

Testable hypothesis:
Dyscalculia of N items is considered the inability to near-instantly count those N. Most people can instantly count 4 items, some with dyscalculia can do 3 but not 4, some fewer, and above average people can do more than 4. I hypothesize that it boils down to simplices and being able to deform them. 3 elements is a triangle, a 3 simplex, and 4 is a 4 simplex, a tetrahedron. When one sees 3 and computes it instantly, they're perceiving the triangle. If one fails to perceive 4 instantly, they're failing to perceive a tetrahedron. We can test this on individuals with 4-dyscalculia but not 3-dyscalculia by seeing if they perform normally on plane geometry but subnormally on 3d geometry, all though if the test fails it would be inconclusive for other reasons.

>>12441656
Redpill me on formal groups, particular in relation to the formal groups of elliptic curves.

>finish calc III final
>highest grade is an 89
>I got an 89

What is /mg/'s view of 3blue1brown? He offers in-depth explanations of calculus beyond rote memorisation and formula-punching. He explains *why* integration and differentiation exist.

>>12444819
I like him. I literally got through calc i-iii by rote memorization, with only the vaguest idea of what I was doing. If those videos existed while I was still in college, I think I would have liked math more.

>>12444819
should be required watching in high school

>>12444819
As the resident brainlet, I like him. I liked the linear algebra series more if we're talking thar kinda thing though.
I like the problem videos, or the ones where he goes hey look at this weird shit, let's find out why it is the way it is

>>12444850
>>12444887
>>12444899
Engineering nigger here. I concur with these posts. I wish I had gotten these kind of explanations in high school.

Is implicit (?) or parametric function definition more general?

>>12444819
>He explains *why* integration and differentiation exist.
it doesn't, it's formalism

how to turn my ways from /lit/ schizo to /mg/ chad?
I know basic calculus and some logic from reading analytic philosophy.

>>12444819
you needed someone to tell you there's area under a curve? lmao.

>>12444819
he's good, if you use the content correctly.
>3blue1brown
>book
>solve problem
If you're just watching it I don't imagine much getting through

>>12445025
read some intro to proofs book or an intro to abstract algebra book, then come here again

>>12445160
He really hammers the "math is not an spectator sport" point in each of those videos. Even gives you some homework. But yeah, he really made me want to read more and from better books.
>>12445025
Not a chad but I'm at a somewhat similar level and working through some number theory while reading Borges
Maybe try that

>>12445025
Never give up being a schizo, it makes you better at math if you learn to see clearly even while being schizo

>>12441656
someone redpillme on general relativistic internal set theory

>>12441656
whats 2+2?

>>12445494
It's 2+2, because addition is commutative.

stop watching youtube and go read a book

I did it, guys
I got a B- in Calc 2

can someone explain to me brainlet how a "big intersection" of a (countably) infinite sequence of sets A1 ⊃ A2 ⊃ A3 ⊃... can ever be empty? my question in particular asks for each set being compact and the space being metrizable, but i dont see how this is ever false...

>>12445630
nicely dunn mai frienn

>>12445691
thanks fren

>>12442082
https://groupprops.subwiki.org/wiki/Associative_implies_generalized_associative

>>12445494
well,it's not 3+1, because c'mon, it looks different

>>12445025
Read this first:
https://plato.stanford.edu/entries/philosophy-mathematics/
So that you can understand why there are many pseudo-controversies on this board, because math is still object of philosophical disputes. So sometimes you should do math and sometimes you should step back, ask inconvenient questions and think about the big picture, but acknowledge that there are different times, spaces, moods and people for each thing. If you make this distinction i think you will be fine. Not quite sure, but i thing i'm quoting D'Alembert's by saying this: “Go forward and faith will follow”.

>>12445610
I don't have wifi no mo anon, I can't watch shit
What are you reading

>>12441728
Then name a rational not generated by the naturals. Or a natural not generated by another natural

>>12441728
>when you first encountered √2 how did you think about it? well i'm sure most people do one of the following
The length of the hypotenuse of a right isosceles triangle, in ratio to the length of one of its sides.
I'd be surprised if anyone (outside of maybe the New Math generation) thought about it any other way, as it would entail that that person had learned symbolic algebra before shape and length.

>>12442511
Dubs. What are the pre reqs for that book?
>>12444211
>>12444899
>>12445311
Dubs

Is it possible to balance self-studying maths and a software engineering job? I have no choice but to go to the industry in this third world shit hole since I am the breadwinner in the family. I'm mostly interested in Analysis, but what mathematical topics would be beneficial if I ever pursue software?

>>12441656
Can someone tell me what exactly is going on in the last step here?
The way I see it, you divide both sides by cos(θ), and then you have tan(θ) = -2.
And then you should get θ = arctan(-2). What am I doing wrong?

>>12444819
absolute quack, tries to do everything with nice geometric pictures, ignoring the formal necessities

I need some non-homework help.
I'm working on writing relationships of some number autism I've come across and I've gotten to a point where the sequence goes 1, 7, 19, 37, 61, 91... and the relationship between then comes from breaking them down to 1, 6+1, 18+1, 36+1,
... and broken down further to 0(6)+1, 1(6)+1, 3(6)+1, 6(6)+1, 10(6)+1... and so on which works because 6 is the underlying autism factor here. So while I can express this relationship as y(6)+1, y itself is something I can't write as a relationship without it being recursive as y = y (of the previous value in the sequence) + (the current position in the sequence).
If any of you guys can help me find a way to express this relationship, I'd be appreciative.

>>12446284
I hope it is because that seems like the route I'll have to take. As for maths topics, combinatorics for general programming and then it depends on your interests. If you want to do machine learning then it's probability and statistics, if you're interested in graphics then it'll be useful to know some differential geometry. Might also be worth knowing linear algebra though I'd suspect you already know it.

>>12446417
Well, I found a relationship of [(n)3 - (n-1)3 - 1]/6 = y but I feel there's a more intuitive way to write it out.

>>12446284
>>12446443
it would help immensely if you already have a rough idea of what topics you are interested in

>>12446417
I really doubt this isn't homework, but I'm feeling friendly.The [math]n[/math]th y value is just the ([math]n-1[/math])th triangular number, given by [math]\frac{n^2-n}{2}[/math]. I immediately recognized the sequence.

I don't know what kind of background in calc etc. you have. Lazy method to arrive at a solution here: take the difference between the entries [math]6n[/math] as the derivative, and then anti-differentiate to [math]3n^2 + C[/math]. So the sequence formula must have [math]3n^2[/math] as its largest term, and by a little trial and error we can find it's [math]3n^2 -3n + 1[/math].

Taking our original equation,
[math]6y + 1 = 3n^2 - 3n + 1[/math]
[math]6y = 3n^2 - 3n[/math]
[math]y = \frac{n^2 - n}{2}[/math]

hey /mg/

>>12446761
Its not homework, I'm trying to find a reason pic related works like it does. Top one is for (n)2, bottom is for (n)3. I'm hoping to find running links that can explain why (n)4 doesn't work the same.
Phoneposting from work so thats why I can't into Tex or decent handwriting.

>>12446812
[math]n^4[/math] is a quartic polynomial, so you just need to do it one more time.
Look up (linear) difference equations.

>>12446832
>do it one more each time
Explain a bit more what you mean by that because this is what you get when you try doing it with n^4.

>>12446841
>256-81=170

>>12446849
You try being a 'tist dealing with unending waves of people's bullshit and keeping your brain working right.

>>12446870
So this is the power of American education

>>12446880
Its the power of stress, really.

>>12446886
Adding to this, kinda weird that I didn't think something was off considering I first got a taste of this when I was still in high-school. I doubt I got it wrong then, but I genuinely remember there being a point when it breaks so I suppose I just accepted it.

Anyone here studies math in Scandinavia? Are their universities good? How hard is it to get into one as a foreigner?

>>12445687
A_n=[n,infinity)

>>12447395
Copenhagen seems very good, Trondheim and Bergen are good, I guess, Stockholm seems good. I would really recommend Copenhagen and Stockholm because of their reputation, and Trondheim because Markus Szymik is a very pleasant guy. But, this is from an algebraic topologist and that is my only touch with those places. If you are interested in something else, then maybe not.

>>12447395
Good for PhD, not good for bachelor/master (the level is higher in france/germany in bachelor/master)

>>12446443
I've seen lots of applications of combinatorics in CS, though I probably need to finish undergrad Analysis first before branching off.


>>12446612
I'm quite interested in non-meme AI and quantitative finance in general. And also some cutting edge applications of continuous maths in CS.

>>12446342

sin(x) = -2cos(x)
sin(x)/cos(x) = -2
tan(x) = -2
atan(tan(x)) = atan(-2)
!= -tan(.5)

The conclusion is wrong. There is no such property of atan(x)

>>12447561
Recall atan(x)=y+n*(pi/2). He just isn't using the principal value in his proof, which is awkward but correct in some sense.

>>12445687
it's not true if all sets are supposed to be compact

>>12445910
>D'Alembert's by saying this: “Go forward and faith will follow”.
I prefer Terry Davis' quote "Entertain God and your ass will follow".

Can anyone explain to me what's the actual use for Banach/Hilbert spaces? I want concrete examples of cool things done with them. Oh and don't give me "look at this theorem about Banach spaces", I want things where Banach spaces are used as a TOOL and not an end in itself.

>>12447662
look up how to solve heat equation or wave equation using fourier series

>>12447673
As far as I understand this doesn't actually use Banach spaces, people discovered fourier series way before they knew about functional analysis. I've seen the proof of convergence of fourier series in L_2 which uses tools from Banach spaces but that's not what I'm asking about. I want actual cool things outside of pure functional analysis that came FROM the explorations of banach spaces. I don't care if it's used as an elaborate theory to justify some theorem that was already known and empirically verified before.

>>12447662
They're all over mathematical physics and PDE.

>>12447699
Can you give me one cool example that you like?

>>12442082
Not crazy because it's so bleeding obvious. Also one of the first exercises in Spivak's meme calculus text.

>>12447768
>Also one of the first exercises in Spivak's meme calculus text.
Are you sure about that? Just went through the first two chapters in the book and couldn't find the exercise anywhere.

>>12447778
Chapter 1, exercise 24. It's not phrased in terms of groups or semigroups but it's what you're asked to prove.

How difficult is "Linear Algebra Done Right" by Sheldon Axler? I'll be taking the honours version of Linear Algebra this winter and the class uses that book. I have taken an intro course to Linear Algebra and Discrete Maths, both of which I did good on. I was wondering if it is doable for me since this is technically a second-year course (I'm a first year) and I've done all the pre-requisites for it.

Was it cope?

>>12447830
Mega cope. Especially since he's Asian, i.e. someone with ZERO creativity.

>>12447793
It's probably good for your level. Try reading Axler's "Down with determinants" (found online) this weekend and if something feels difficult to understand post a question about it to /sqt/. I promise I'll lurk /sqt/ this weekend so even if nobody else answers your question I'll write something within a day or so. That is, if you even need any help.

is there any sort of general reasoning to finding the group of symmetries for an arbitrary object in [math]\mathbb{R}^{3}[/math]?

>>12447875
For a bounded object, the symmetries all fix the center of mass, so you just need to find the component of [math]O(3)[/math] which fixes your object.
I think you could also use the physics inertia tensor to cut some symmetries off.

>>12447846
Thanks, anon. I appreciate your reply and I will read it this weekend.

>>12447844
if asian people have zero creativity then how did they create anime? fuck you nazi

>>12447959
>Create anime
>Is made after japs were given disney films in interment camps
>Is the same tired shit over and over again

When you will damn nerds realize all your analysis on math axioms and shit doesn’t matter in the real world. I learned this shit 5 years ago and all I do now is algebra 1 math making 4 figures kiss my ass

Whet is the sexiest class of fractals known?

>>12442082
i was asked to prove this back in discrete math and it's just a fucking annoying induction proof on trees.

>>12444819
it's great, as long as it's supplemented by exercises and rigorous learning. should be used to introduce topics in high school calculus and freshman linear algebra and differential equations.

>>12445687
The whole point of compactness is that nested sequences of compact sets have nonempty intersection. This is a way to define compactness, in fact (any countable collection of closed sets with the "finite intersection property," i.e. such that any finite subcollection has nonempty intersection, has nonempty intersection overall.

>>12447662
you're joking, right? all of quantum physics is done in hilbert space. a quantum state is a ray in a hilbert space (or, more precisely, a well-behaved linear functional on the algebra of bounded operators on a hilbert space). without hilbert spaces there is no modern physics.

>>12447561
wouldn't x=atan(-2)

Damn nerds .

Find [math]p(x),q(x)[/math] if [math]y_1,y_2[/math] are two solutions for the equation:

[math]y''+p(x)y'+q(x)y=0[/math]

[math]y_1=x^2+1[/math]

[math]y_2=x^3+x[/math]

I tried calculating [math]y_1',y_1''[/math] and [math]y_2' y_2''[/math], then substituting and equating the two polynomials coefficients for each power of [math]x[/math] but that lead to nowhere. Any ideas?

Could it be that all formal theories that are inconsistent have short proofs of 0=1?
For example, as far as I'm aware, whenever someone found an inconsistency in someone's formal theory, the inconsistency had a very short proof (just think of X={x| x not in x}).
Now my question: do we know of any INCONSISTENT formal theory whose recursive axiom (schema) we can write down on the blackboard but whose proof of 0=1 takes up more space than it's physically possible to get in the universe?

>>12448386
[math]y_2=xy_1[/math]

Write down the two equations you get and use that fact to get rid of one of [math]p,q[/math].

>>12447467
I'm actually interested exactly in algebraic topology, thanks. Where do you study?

>>12447467
I'm actually interested exactly in algebraic topology, thanks. Where do you study at?

>>12448449
post was better without animu
[math]\mathfrak{FUCK\ YOU}[/math]
simple as

>>12448455
Anime girls and math goes hand in hand, fren, there's no better combination.

>>12448449
In the UK, but I would have applied to the places I mentioned should they have had open positions back then. I've been to seminars with folk those places, really liked the Copenhagen Jespers and Markus Szymik as speakers, mathemagicians and nice people.

>>12448037
>doesn’t matter in the real world
This is math by definition. When will you realize that they don't care?

>>12448475
How's the countryside in the UK? Are there any good universities in those areas?

>>12448442
didn't really help, doesn't remove either one of them

>>12448529
Another hint: Multiply the first equation with x and substract that from the second.

complex analysis is gay

Every rational number can be written in infinitely many ways (1/2=2/4=3/6=4/8=...) Why so many people have issues that some real numbers can be written in two different ways (1=0.99999.....)?

>>12448526
I can't say for sure. I'm just a dumb foreigner here. I guess the important thing is to find a good supervisor with an interesting topic. Then pray for your local deities for funding. Nevertheless, I recommend Denmark and Norway.

>>12448577
Schizophrenia, idiocy, autism. Nothing wrong with deciding to work with something else though.

>>12446068
I tried to ignore this but I just can't. Why did you go through all the dubs? Who cares? Dubs happen 1/10 times and there were about 50 posts when you replied

>>12448577
I don't think that people think of decimal expansions in the same way they think about ratios. Obviously, they're wrong. But I understand it. Before I knew what I was talking about I viewed the decimal expansion as defining the number and of a ratio as simply being a representation of the number (the ratio is actually the definition for rationals, with an equivalence relation - for reals, the definition is usually not decimal expansions, so no one really mentions the equivalence relation on decimal expansions).

>>12448664
Interestingly, 3 of them were 11s. That's got to be out of the ordinary.

>>12448684
It definitely is out of the ordinary but one should expect at least something to be out of the ordinary. right now there have been about 110 replies, and we're a little low on dubs with only 9 dubs. But we do have one trip. All in all everything looks pretty reasonable

>>12448699
Dubs

Anyone here have an obscene number of take home exams because of Covid? I’ve been doing 12-14hrs of math per day in December trying to finish them all.

>>12448699
Check'd

>>12441656
How would you topologically map surface of 3D fractal? You would have to use "infinity" sized real space even for a tiny bit.

>>12448760
>12-14hrs of math per day

Is Topological Optimization real maths?

>>12448537
still, I end up with

[math]x^2p(x)+4x+p(x)=0[/math]

which is absolutely useless.

>>12449152
Anon are you high? This literally gives you [math]p(x)[/math]

Pardon my French but an holomorphic function has the same domain of convergence as its derivative, right?

>>12449330
A holomorphic function is defined on an open set, so yes.

>>12449382
Thanks.

[math] e^x = \sum_{k=0}^{\infty} \frac{x^{k}}{k!} [/math]

>>12449718
>∞

>>12441656
>spend 30+ minutes on a question
>"you missed the part where you show me how to do basic arithmetic and as a result you lose marks on an otherwise 100% correct answer"
damn do they actually hire monkeys to mark these papers

>>12449788
[math]e^{\infty} = e^{-\infty}[/math]

>>12449956

TAs obsessed with entry tests will do that, they're just coping with that fact that university is not about solving a JEE everyday

>>12449152
>which is absolutely useless
I'm not that anon but learn some humility and appreciation. The other guy has held your hand through the entire problem and is trying not to give you the answer but you're too buttfuck stupid to do simple algebra

>people who post 3D women are logicians
>people who post anime are algebraic topologists and algebraists
>people who post touhous are geometers and physicists
What's the frogposter field?

>>12450938
Whatever you crave my friend

The current hierarchy of insanity goes like
>Standard mathematics
>Finitism
>Ultrafinitism
If mathematicians were sane people the hierarchy of insanity would look like
>Standard mathematics
>Infinitism (acceptance of w as a completed infinite and a model for PA)
>Ultrainfinitism (large infinities)

>>12451107
(((Large infinities)))

1 2 4 5 7 8 10 11 14 17 20 22 25 28 40 41 44 47 50 52 55 58 70 71 74 77 80 82 85 88 100

1 2 1 2 1 2 1 3 3 3 2 3 3 12 1 3 3 3 2 3 3 12 1 3 3 3 2 3 3 12

1 2 1 2 1 2 1 1 1 1 2 1 1 4 1 1 1 1 2 1 1 4 1 1 1 1 2 1 1 4

>>12442511
Are there any other kinds of groups like this?
Seems like an interesting thing to try but that book is a bit advanced for me at the moment.

What the fuck is wrong with geometers? It seems just so that they can abuse notation and meme about meme elegance all of the field rests into seeing if their objects are actually well defined in some fucked up convoluted way were half of the time they just focus on the meme algebraic properties any retard can verify, and sneakily shy away from the hard analytical arguments. Reading their texts is so fucking horrible.

>>12451142
you have solved the oy vey hypothesis

What's the mathematical term for a 2D geometry or surface represented in 3D? I'm about to write capsuleFlat or capsuleBillboard ,but if there's a math term, I'm willing to take it.

>>12451384
You talking about an embedding?

>>12451384
Surface?
I don't think we would represent 2d geometry in 3d. We would just study 2d directly. Maybe an embedding is close to what you're looking for

>>12451441
>>12451443
considering my question, you guys are 100% right. But considering it's computer graphics, I'm a stay a brainlet and write billboard

In Euclidean space, when measuring the length spanning between two adjacent natural numbers sharing the same axis, must one account for the width displaced by the pair of numbers which form the boundaries of the interval?

>>12451669
per euclid: "a point is which that has no part", and thus presumably it has no width

>>12451876
Would this change if these were two points on the real number line, whose whole parts remain the same, with decimals of repeating zeros? The word "between" would imply that this is a closed boundary, so the measure of distance should not begin on that exact point, correct? The set of numbers in the interval must not include the numbers themselves, or we would not be measuring the distance between them, but rather the distance from one to the other. If you were measuring the distance between Shenzhen and Moscow, you would start at the borders of each, but the distance from Shenzhen to Moscow would start from within. Euclid was only a man, and even that's questionable, in either case his word is not law. I posit that the numbers at each point have an infinitesimal width.

>>12444956
From a parametric description you can compute (at least if you're only dealing with multivariate polynomials) an implicit description by projection. I don't believe such an easy method exists to go back, and in fact there should be implicitly defined varieties that don't have parametric descriptions.

>>12445860
Based. Always remember the difference between definitional equality and reductional equality. Fuck set theorists.

>>12446363
Midwit take.

>>12448843
Yes. Post a text or something that sounds interesting.
>inb4 some lame weak theory that doesn't solve anything

>>12452154
>It's just FEM and has nothing to do with topology

12447662
Can anyone explain to me what's the actual use for schemes and sheaf cohomology (as opposed to just studying varieties)? I want concrete examples of cool things done with them. Oh and don't give me "look at this theorem about Schemes spaces", I want things where Schemes are used as a TOOL and not an end in itself.

>>12452177
1. varieties
2. anon did you get lost in schemes space again?

>>12448170
>all of quantum physics is done in hilbert space
Dumb undergrad

>>12451196
The book is not advanced at all, try it sometime.

>dumb highschooler
>dumb undergrad
>dumb grad
>dumb scientist
>dumb minor medalist
>dumb.....
What the fuck is wrong with you people and your faggot upturned noses. Can't you be reality for once. It's all bullshit. Just do math to support the human race and live well and pray to God.

>>12452302
>>12448170
There's no need for either of you to be snobbish faggots. Stay humble and stay free spirited.

>>12452177
>>12452216
He probably meant manifolds, it translates to 'varieties' in some languages.

>>12452311
>>12452316
>t. Pissed undergrad newfags
This general has always shitted and hated undergrads because of your petulance and stupidity.

>>12452333
I'm not even in college retard. I'm a comfy NEET. I don't give a shit what your "ranking" in society is, just don't be snobbish. College is literally just a government stamped badge.

If I proved the inconsistency of PA, would I get a cool prize?

>>12452341
>NEET
>I don't give a shit what your "ranking" in society is
Color me surprised!
>College is literally just a government stamped badge
>t. NEET who has never been to a college, never done a research on his life and never had contact with academics that are at the center of their fields

>>12452362
>t. Peter Keating

>>12452362

>>12452362
holy shit, get the fuck out of our general literal moron. you are not worth talking to.
>>12452302
correct me if i'm wrong, i'm not a physicist, but i believe that a state is a positive continuous linear functional on an appropriate operator algebra.

Do any anons know any graphic novels/short stories I can find online with this sort of fever dream feeling to it?

Let's say that I have open square (square without borders). Distance between points [math]x[/math] and [math]y[/math] is minimum time needet to get from point [math]x[/math] to point [math]y[/math] if you travel with unit speed. This is just Euclidean metric on square.
If we add a portal between points [math]A = (-0.5, 0)[/math] and [math]B = (0.5,0)[/math] that takes some time, let's say 0.5 seconds to get from [math]A[/math] and [math]B[/math] we get some topological manifold.
It is locally Euclidean because every point has neighborhood homeomorphic to [math]\mathbb{R}^2[/math] - for points [math]A[/math] and [math]B[/math] just take ball with radius less than [math]0.5[/math].
Hausdorffnes and countable basis are just as trivial.

By Whitney embedding theorem we know this can be embedded in [math]\mathbb{R}^4[/math].
Can it be embedded in [math]\mathbb{R}^3[/math]?
What is this homeomorphic to?

Why do worded problems confuse the fuck out of me, but straight up equations don't? I was never bad at English in school.

>>12452508
More symbols and it uses a different processing pathways so random noise from linguistics leaks in. Use your visualization or vocal system to directly reformat the word problem into an equation or diagram, and it's easier.

>>12452506
>we get some topological manifold
No, you don't.

>>12452524
Yes I do

>>12452539
Prove it's locally Euclidean at A.

>>12452542
ball around A with radius 0.25 is just normal Euclidean ball around A since portal takes 0.5 seconds or whatewer. I wrote that already, you just can't read

>>12452506
why don't you try to write down "portal which takes 0.5 to get through" in terms of topology and see what happens

>>12452565
First of all what you defined isn't a metric. Second of all, if a ball B_1 of radius say 0.6 about A is the usual open ball about A along with the point B and you say that B_1 is open, then you can intersect B_1 with a ball B_2 of small radius centered near B which shows that {B} is an open set. Single points are not open in Euclidean space.

>>12452588
Nevermind, the ball B_1 should contain a Euclidean neighborhood of the point B, not just B. The only way I can see to topologize this right now makes it homeomorphic to the square.

>>12452571
>>12452588
Not that anon but wouldnt the issue with his concept be that there'd have to be a path on the 2d plane to represent the portal, you could have extra space but thatd inherently give it a 3rd dimension. But other than that I dont see why his structure is unworking. It's like a square where a non euclidean "thread" which portrudes into the 3rd D, connects two points

>>12452610
Well anyway it's either not locally Euclidean or if you complete the distance operation to get a metric space it's just the square. There was no actual topology given so either of those is a good answer.

>>12452621
No, in topology you are allowed to have shapes like that existing by themselves. They don't have to live in the plane or 3d space or anything.

Broke: irrational numbers are illogical
Joke: rational numbers are illogical
Woke: zero is not a number
Bespoke: one is not a number

>>12448760
>obscene number of take home exams
yes
last semester was worse tho
>12-14hrs of math per day
lmao how

>>12452629
How is it just the square, I don't see that

>>12452634
I don't understand that. Isn't the concept of dimension arising from degrees of freedom an object within the shape can take to move? So wouldnt the shape naturally define a number of dimensions for itself

>>12452655
It does define number of dimensions for itself. Both Klein bottle and sphere are 2-dimensional, however Klein bottle can't be embedded in 3d space, but sphere can

>>12452650
Write down the distance function using the "portal" to make trips shorter whenever possible. With that you'll get an actual metric which you can show gives the same open sets as the usual Euclidean one.

>>12452650
balls would be normal or pairs of balls
a pair of balls is the union of two balls
unions of open sets are still open sets and are still in the topology
you should be able to isolate one of the balls in the pair using intersects
therefore a normal square and this have all the same open sets

>>12452736
Yeah, all balls can be nested, it's actually trivial

>professor says my proof is circular reasoning
>tell him that all math is circular reasoning
>mfw

>>12452807
No, it's like roots from a seed. The results of an axiom can't necessarily prove an axiom, sometimes numerous axioms can give that result

>>12452807
>be me
>tell my professor i have a proof that any positive integer can be written as a sum of primes
>he says it's false
>tell him that he can't contradict the goldbach conjecture
>mfw

>>12452837
1 cannot be written as a sum of primes
where is my prize sir

>>12452853
2+(-3)

>>12452853
Idiot, you can't contradict the conjecture!!! Undergrads nowadays, Tengri have mercy on us all...

>>12452856
>1 | -3, -1 | -3, 3 | -3 and -3 | 4.
Too many divisors

>>12452865
>what are primes in a ring

>>12452837
If we assume 1 is prime, then all positive integers can be written as the sum of two primes.

>>12452837
Primes were made to be multiplied, not added

>>12452936
>>12452956
if you can't see how the tranny made a parody of that one brainlet's post then please leave

What is probability that COVID-deniers will become EXTINCT?

>>12452974
>Cares for covid victims
>Advocates for the death of Covid deniers
Make up your sick mind, leftist.

>>12452995
You can also stop being a COVID denier by choice, retard

>>12452995
>Cares for covid victims
>Advocates for the death of Covid deniers
Humans are sentient beings. Not every specimen of [math]Homo\ sapiens[/math] fulfills my standards.

Why are polynomials so hard? I'm trying to prove the theorems about their roots and my brain is stumped. Any intuition-tips?

>>12452506
>it's an "anon reinvents the quotient metric" epísode

>>12453041
are you a phd?

I did it anons. I proved that a real polynomial of degree N has at most N roots. To be fair I saw a proof 9 months ago but still I feel proud of myself. Polynomials were always harder for me. Now I just need to prove that if it's got rational coefficients it's got rational roots.

>>12453182
> Now I just need to prove that if it's got rational coefficients it's got rational roots.
lol good luck with that

>>12453182
What are the roots of x^2 - 2 ?

>>12453250
>eons of evolution so it can do a lame joke using math

>>12453189
I feel like I got a proof.
Assuming it's got roots, then its constant value is just the root times each coefficient, summed up. And since its constant and coefficients are rationals, and the sum of an irrational and rational is irrational (because of subtraction contradiction), then each subterm in the coefficient must be rational. So the root, times a rational coefficient, is rational. And by division contradiction, an irrational*rational cant be rational, so root must be rational.

>>12453250
Oh....

So I'm supposed to show that the set of roots to rational coefficient polynomials is countable. I thought this meant the roots would be rational... Is it simply something like rationals + square roots?

>>12453264
The error in this proof is that it only works if the polynomial has an x^1 term in it, x^n can add roots

>>12453264
>>12453289
Okay I think I got it. The set of algebraic numbers is a countable union of Q with each nth root of each Q. This can be seen by a modified version of the aforementioned proof where you take the lowest power term in the polynomial's constant, which is root*Qcoefficient^n, which is a Q, meaning root is some nth root Q, always.

And countable unions of countable sets are countable.

>>12453351
>The set of algebraic numbers is a countable union of Q with each nth root of each Q.
This is false. Look up Abel-Ruffini's theorem.

If you already have the fundamental theorem of algebra you can literally just count the number of polynomials in rational coefficients and be done.

>>12453380
>just count the number of polynomials in rational coefficients and be done.
But you will never stop counting.

>>12453363
It is false? Then why don't you write down the number which is a counterexample

>>12453363
>In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients.
>arbitrary
But Munkres told me to use rationals!

>>12453394
I can't write down the "number" because it doesn't actually exist but I can write down the polynomial:
x^5 - x - 1=0
It cannot be formally solved by taking roots of rational numbers and arithmetic.

>>12453406
well then if the """roots""" as you said it yourself """don't actually exist""" then there are no fucking roots and there's nothing to be solved here

>>12453406
>because it doesn't actually exist
You can just use the Bring radical and write it as a power series if you wany something more explicit. It's ridiculous to say it doesn't exist.

>>12453412
Not him but "unsolvable in radicals" doesnt mean "nonexistent" it just means the breadth of radicals is disjoint with the breadth of quintics. Imagine if we lived on a planet where there were, I don't know, geothermal vents that gave off pressure in a way that mapped to quintics. Then our base math would be performed in quintics and it'd seem as natural as square roots feel to us earthlings.

I know I am supposed to solve this by reduction of order: [math]x^4y''-a^2y=0[/math] (whereas a is a real number) and [math]y_1(x)=xe^{a/x}[/math] is a solution to the original equation

but for the life of me I can't get to the point where I can substitute [math]u=v'(x)[/math]. After substituting [math]y_2=v(x)y_1[/math] it just becomes a huge mess.

What am I doing wrong

I have a stupid question on noetherianity, the ascending chain can be "locally" stactionary? i. e. let [math]I_1,\dots[/math] be ideals and such that form an ascending chain of ideals.
For some [math]k, m[/math] we have that [math]I_k = \dots= I_{m+k}[/math].

Basically what I'm asking it needs to be strictly increasing or not?

It seems to me that the equivalence proof between finitely generated and ascending chain condition doesn't require the chain to be strictly increasing.

>>12453553
If it's not strictly increasing you can just remove the terms where they're constant to get a strictly increasing sequence.

>>12453575
thanks anon

>writing a maste thesis on algebraic topology
>still have no idea what an open set is

You guys are still craving to your dreams and hopes from when you were young, but it's time to face reality frens, we won't be the next Gauss, we won't win a Fields medal and that's ok, once you guys accept it you'll be able to see how wonderful the Hakuna Matata philosophy is.

>>12453646
>he thinks I do math for prestige
my dude it's gucci doing math, that's all

>>12453628
Stop this at once.

>>12453628
>writing a master thesis on algebraic topology
>still have no idea how to talk to a female

Is Algebraic Topology easier than Algebraic Geometry? I'm a brainlet and I'm too old already so I wanna specialize in a cool field that's not very autistic like Category Theory and Algebraic Geometry. I've been thinking of specializing in AT, pre-requisites are just Group Theory and Topology so it's not as autistic as AG right?

>>12453684
Shit image, should be totally reversed

>>12453684
>I'm too old already
If you're concerned about what's «autistic» you're definitely underage or have the mentality of a child.

>>12453696
Age is definitely a factor for succeeding in modern academia. I'm 24, almost 25 and I know a lot of doors have already closed to me because of that, it's not a huge deal sure, but I probably can't get into a top 100 university for a PhD program anymore. Of course this is just me because I know my own limitations, I'm not a genius, I'm a normal person, so if you are a genius and it gets reflected on your work then those doors are still open for you.

>>12452865
>-3|4
?!?

>>12453646
Biotech is easier than math. Biotech can easily expand working memory which is 1/2 of intelligence (the other being creativity). I have a few concepts I'm playing with already, if you really wanna be good at math go into biotech.

>>12453628
An open set is a set that doesn't contain any of its boundary.

>>12453773
An open set is not closed.

>>12453805
You're thinking of a non-closed set.

https://www.strawpoll.me/42265108

The Differential and the Integral Calculus: a New Foundation

Let [math]\displaystyle h = {1\over N}[/math] where [math]N[/math] is the greatest integer. The quantity [math]h[/math] is called the [math]\it resolution\ of\ the\ universe[/math]. We now define the [math]\it differential[/math] of a variable [math]x[/math] as [math]dx \stackrel{\rm def}{=} x + h[/math]. I think this gives a novel and simplified take on the calculus, that has escaped many until now. I have derived ([math]\it\, pun\ intended!\, [/math]) many results starting from here. Of course, it is not complicated enough for maths professors to prefer – but I much prefer a foundation that an elementary schooler can understand.

>>12453949
But there is no greatest integer: you can always add 1.

>>12454014
Yuh? How?

>>12454020
Well, that depends on your semantics. If you view integers as strings of strokes on a whiteboard, then to add one just draw a stroke.

>>12453949
>dx = x + h
Did you mean to say dx=h, i.e. a small value?

Is this correct because it seems weird but correct:
>for each N create a cartprod of N Z+s
>create an countable union of these products
>its still countable because at each N you have a countable set so its just a countable union

>>12454060
>N Z+s
what's N?

Yes seems countable.
This case maybe even without Choice.

>>12454108
N as in each element of Z+

The fuck?

>>12454060
why not, you could easily count through that
it's simpler than the unintuitive fact that the product of a countably infinite amount of countably infinite sets is also a countably infinite set

>>12454133
That's false.

Are there any numbers for which it's undecidable whether or not they're transcendental vs algebraic? How about irrational vs rational?

>>12454133
{0,1}^w

>>12454127
>For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
Real projective line?

>>12454137
Up to skolemization*

>>12454153
Look up what consistency means before you comment.

>>12454133
>>12454137
>>12454142
*union, fuck

>>12454178
I'm just trying to be creative anon. None of this stuff really matters except when we make rocket ships and space suits.

>>12454153
>Real projective line
yeah there's no n on the real projective line so that S is 0 either way

>>12454133
>unintuitive fact
Probably relies on wild axioms, so that's not a good description.
Call if ZF theorem, if you will

>when we make rocket ships and space suits
doesn't matter either

>>12454133
Countable union of countable sets has a very intuitive proof though

look math was supposed to be about figuring out new facts about numbers
instead some wankers turned it into questioning more and more basic facts, and here we are questioning whether PA is consistent
if not for this shit clogging up our brains, we would be teaching proof of FLT to undergrads

>>12454229
for finite n sure

>>12454229
Wrong. What you showed is a proof that NxN is countable. The proposition that a countable union of countable sets is countable is not intuitive at all (in fact, it is false).

>>12454233
Why do you care what we worry about, tranny? Go study your proofs of FLT and leave us alone.

>>12454233
I don't know if I can fully agree. Something about the unknown has always drawn humanity forward, and infinities and paradoxes are part of that. On the other hand, it is really a waste to spend excess time on it, it'll reveal itself springing out of more tangible inquiry, just like quantum mechanics did. If you mean Faster than Light Travel by FLT, I think it's possible. Alcubierre drives might be able to be made with the casimir effect and a few years worth of USA's energy consumption!

>>12454233
Ahem, ladies and gentlemen, I have an announcement.
Fuck numbers. I don't care about numbers and I don't care about FLT.

>>12454241
But a countable union of countable sets is countable...

>>12454233
Based

>>12454268
He means Fermat's Last Theorem anon

>>12454463
No, he means Femboy Lookingfor Top idiot.

let P={n in N\{1} | n_r =/= n_p+n_q fpr r>p,q}

>>12454396
Prove it.

>>12454519
Sets A_i, element j of A_i is a_ij. Define a map by f(a_ij)=(2^i)*(3^j). Assuming the A_i are not disjoint only can give you a smaller set. The map f is injective by FTA.

>>12454127
exponentiation is suspect

>>12452492
I wish I could give you an answer, but if films are also ok try Naked Lunch. Not math related at all but it felt like a fever dream to me. Has a nice soundtrack as well.

>>12452492
Ripples in the dirac sea

>>12454557
How?
You just define it like any other operation
b^1=b
b^s(n)=(b^n)b

>>12454872
Thank you

>>12454803
I believe it will be a few thousand years before I get around to watching that, but it's in my memory now, thank you

>>12454540
Given an [math]a_{ij}[/math], how do I even know which [math]A_i[/math] it's from

>>12455012
I don't think you're going to live that long bro.

>>12455058
We will see about that now won't we

>>12454519
>>12454540
>Sets A_i, element j of A_i is a_ij. Define a map by f(a_ij)=(2^i)*(3^j).
If you read "countable" in the "enumerable" direction A->N, with powers of 2 and 3 (an answer exactly like this is also on the SE thread of the topic) instead of N->A, it might even get a tad more difficult than in the other direction. I think, not sure, that with A in the domain, it might raise questions like whether the procedure being given a [math]a_{ij}[/math] in the union of all [math]A_i[/math]'s automatically means we know which [math]A_i[/math] that [math]a_{ij}[/math] is from.
In any case, almost everybody will take their functions apriori be packed with so much information that the choice involved in the N->A proof goes through.

That said, here's a nice rant against is

http://math.fau.edu/Richman/docs/venice.pdf

>>12455216
That's nice but it's not really my bag.

>>12441673
String theory is cringe ngl

Studying then: candle light, nicotine and tea
Now: cancer blue light, weed and sugary coffee

I'm gonna out myself as a pure mathematician to my parents today, wish me luck!

>>12454241
a countable union of countable sets is indexed surjectively by N x N when you represent each set as a sequence and then take the countable union to be the sequence of sequences. are you stupid?

>>12456542
>not using f.lux or another blue light filter
>not still drinking tea
>le drugs
ngmi

>>12456712
F. Lux can have side effects on parts of your brain. I wouldn't use if I were you.

>>12456716
what the fuck are you on about

>>12444819
He cute

Has acid helped anyone with math? I've done it twice ,(huge fuckin doses brah), and both times I noticed a marked improvement in my ability to do math

>>12456728
I read it in a study sometime ago, can't find it again right now.

>>12447830
>tfw almost exact age galois was when he died
>tfw published nothing
Brehs, it's ogre.

>>12452995
>>12453027
>>12453031
I have COVID right now and I've told nobody and done nothing to protect other people.

>>12456763
And the fact that someone could have died because of your negligence doesn't bother you at all?

>>12456766
People die all the time

>>12456768
Alt-righters's true nature right here everyone!

>>12456768
Hypothetically, what would motivate you to get a bit more bothered about spreading COVID? Obviously, society has laws against murdering people to stop people like you from just killing others when it would be convenient for your goals. But do we really have to go that far with the chink flu?

https://youtu.be/pTnEG_WGd2Q

>>12456786
Go back to bunkerchan

>>12456787
>Hypothetically, what would motivate you to get a bit more bothered about spreading COVID
Nothing, diseases are natural phenomena and serve a purpose. In forestry conservation, you cut and burn old growth and replace it with the new growth, why are people any different?

>>12456809
>People are trees
Jesus, you alt-right people are so fucking dumb.

>>12456814
>alt-right
Spook.
People are life

nazis are cringe

Sieg Heil!

>>12456828
I'm extremely disappointed in you, touhouposter, I thought you were smart...

>>12456745
you're garbage at math to begin with and you will never accomplish anything.

>nooooo you can't just allow the cycle of life and death to proceed as it has for billions of years
>you have to save all of these old and immunodeficient people you fucking nazi
I hope you idiots realize that by calling and attributing everything to nazism, you make nazism an increasingly big tent platform? You are creating your own worst nightmare

>>12456809
you are not human, you are mentally ill

>>12456850
>i want people to die!! die die die die!!!!!
>now this dumb argument which isn't even remotely sound
this is not your thread, find another thread

>>12456859
I made an offhand comment about me having COVID and not giving a fuck and this caused you to spiral into an autistic fit

>>12456840
I think this is the fifth time I read this exact post.

>>12456864
That should show you that you need to be better then...

>>12456859
not him but he kinda has a point

after putting an end to massive starvation through green revolution and infantile death with vaccines we've become so afraid of death that we forgot something as natural as people dying

I'm not happy about it but what can we do? to be fair if some people are weak enough to die from covid, which has a 99% survival rate and is clearly not as bad as the medias want us to believe, they were already on the verge of dying

Not saying that we should kill them or anything we are dealing with this covid stuff in a disproportionate way

>>12456895
I'm not even defending you you're obviously retarded

but I agree with your post here >>12456850

>>12456890
I wonder how you got into mathematics being so dumb?

>>12456902
Nice argument

>>12456902
Do you know how much people die each year from the common flu? Pretty sure you don't and you probably don't care.

>>12456916
Your retarded logic is
>If death is natural then I shouldn't give a fuck about infecting other people with Covid
If you can't see how stupid that is, then no argument will convince you.

>>12456763
>I have COVID right now and I've told nobody and done nothing to protect other people.
Any chance this shithead gets sentenced for bioterrorism?

>>12456921
That's not what I said. Willingly infecting other people is retarded hence this post >>12456899

All I'm saying is people die, all the time. I work in a hospital I know those things. Most people have been so disconnected with reality that we consider the death of an elder with comorbidities a tragedy. It sure is sad, especially for the family but that's the cycle of life. Not a tragedy.

>>12456935
>Zeeee-ro

>>12456936
>Willingly infecting other people is retarded
I wasn't saying that I'm coofing on every surface that I can, I just mean that I'm treating it like any other mild cold

>>12456860
your offhand comment provides a window into your despicable lack of moral fiber
>>12456890
just because something is natural doesn't make it good. suffering and death are objectively bad, and it is only logical to have a healthy apprehension of them.

>>12456965
>your offhand comment provides a window into your despicable lack of moral fiber
In what way is "stopping the spread" moral? You're making an asumption

>>12456940
you're a murderer, and you don't even care about it
>>12456936
sounds like you're the one who's disconnected from reality. the average person observes relatively few deaths over a lifetime. as someone who works in a hospital, you are surrounded by it. it can be both part of a life cycle and a tragedy, the two are not mutually exclusive. inevitable things can be bad.

>>12456973
>people hypothetically could have died from my actions ergo I am a murderer
That's illogical and ridiculous.

>>12456972
death and suffering are objectively bad, especially when experienced by people who have not exerted a net positive amount of suffering. anyone who exerts a net positive amount of suffering is morally incorrect.

>>12456979
>death and suffering are objectively bad
Prove it

>>12456977
no, it is quite sane and your disregard of such a notion simply unveils what we had all assumed: you are a self-obsessed schizoid.

>>12456985
>no, it is quite sane
You're presupposing that anyone even died of covid because of me, my state has only had 1.3K deaths total

>>12456981
i consider this to be the single most fundamental axiom of morality. i find it laughable that there is anyone in a sound mental state who wouldn't.
it's like you're asking me to prove that if two sets contain the same elements, then they're the same set.

>>12456965
>just because something is natural doesn't make it good. suffering and death are objectively bad, and it is only logical to have a healthy apprehension of them.
Did I say otherwise?

I just can't stand the hypocrisy. Most people don't care about the common flu, they never did.

Why didn't people wear a mask last winter? And the previous? And every winter for that matter? But of course the medias didn't tell you about that 24/7, you couldn't care about it then.

Our reaction to covid is disproportionate that's all I'm saying. Feel free to call me a nazi.

>>12456987
Justify your use of this axiom

>>12456986
i am not presupposing anything, i am suggesting that the expected value of the number of people you have killed of covid is significantly higher than that of the average intelligent person. it may be below 1, i'm sure it is. it's still orders of magnitude more than that of others.

I'm literally seeing 50+ straight posts of non-math related content and no one's getting banned. Amazing! Congrats to the mods for another awesome job!

>>12456992
Yes, the small statistical variance away from zero for me is in fact not technically zero, but in practical terms, it is.

>>12456988
because we currently have annually distributed and well-tested vaccines for the common flu. if you get your flu shot, you're usually good. this will stop being such an issue in a few months, of course, assuming no further hiccups.

>>12456994
we're talking about math, look i mentioned expectations and axioms. those are math.
>>12456989
in what logic? again, this should be an obvious starting point.

>>12457002
That's your burden, not mine. I said that I don't care, you said that I should. Convince me.

>>12456973
>sounds like you're the one who's disconnected from reality.
Death is a reality whether you like it or not. It doesn't make it unimportant but there is stricly nothing we can do about it.

>it can be both part of a life cycle and a tragedy
We're just arguing over semantics. Half of Europe dying from the plague is what I would call a real tragedy. A 80 years old with comorbidities dying after contracting a flu, in my opinion, is not.

Getting really angry looking at combinations for a deck of cards. I reduced the deck by an arbitrary number of ranks just to test my understanding and my numbers are way off.

>>12456989
Game theory does this, somewhat. If you start from a society with only 2 people in it, and imagine you are one of them, you model it as an iterated prisoner's dilemma and refer to the known fully solved case. I'm just saying, in such a case it is in your own interest to play a strategy which minimizes the other player's suffering. Then you just iteratively add more players, and see that with suitable assumptions on the payoffs the same conclusions generalize to arbitrary number of population. I'm not even that anon, but I used to do some game theory. This has sometimes been connected with evolution, as a justification for why species have evolved to have compassion

>>12457035

>>12457035

>>12457035

>>12457031
Doesn't that work only if you iterate the number of rounds before iterating the number of players? If you do it the other way around (and I don't see any a priori reason why you shouldn't), you remain at the globally suboptimal Nash equilibrium as featured in the tragedy of the commons.

>>12457068
That's only if you assume the payoffs has such structure that one player's strategy can reduce payoffs for all others simultaneously

>>12457079
>the payoffs has such structure that one player's strategy can reduce payoffs for all others simultaneously
But that's what the tragedy of the commons is: it's individually rational to abstain from cooperation, even if the result of collectively doing so is globally suboptimal.

>>12456711
>when you represent each set as a sequence
How do you do that?

>>12456716
Doing math can have side effects on parts of your brain anon. So can watching television, lack of social interaction, laying in bed all day, letting your chores pile up and ignoring them, leaving bills unpaid, losing close connections with family members, and even just reading a book.