/mg/ math general: Voevodsky Edition

WTF? WTF IS THAT?

Why no anime girl image on the OP? Why put a fucking random guy instead of a cute anime girl, you piece of shit?

Hey, I'm a college student who does olympiad problems for fun. Today I came up with a new and really cool solution for a USAMO problem from 1984. Is there any kind of forum where I could just post the proof and have it be under my name? I just want people to know it was my idea.

Right here buddy, just use a trip, faggot.

>faggot
Why the homophobia?

I'm not going to post it here. First because it will die, second because then I can't show it to my peers because remember that from the perspective of outside people, Veeky Forums is le nazi hideout.

It can be shown that Voevodsky is homotopy equivalent to anime.

no one really cares about a new proof for a math Olympics problem...

Because most gays are annoying faggots, so deal with it.

On which basis can you make and uphold that baseless and senseless claim? How many reasearches have you read or done on this particular subject that makes you so certain about its results?

Oh wait, you did nothing because you're a /pol/tard that likes to call everyone a nigger or a faggot in an attempt to ridicule those minorities because you yourself leads a pathetic life where you don't have the right to express those same opinions because you know you'll be even more humiliated than you already are.

Many people do. They are really fun.

Yeah, but not on the level of treating it like some kind of huge achievement. What do you think you'll get exactly for "claiming" that new proof as yours? Nothing at all, man, just post that proof wherever you like.

9209812
9209833

I don't think it is a huge achievement. I just think it's cool. My idea is cool and I just want that in the future when olympiad students start desperately googling "USAMO PROOF" they see my name.

But you just gave me a great idea. I'm going to create a blog where I will submit these kinds of proofs. Thank you.

nice taste in anime desu senpai

Because tripfags are faggots

I think you've misunderstood me. Post it here, bucko.

>believing empirical garbage
Fuck off to and take your dog-eating friend with you.

That's a very egoistical way of looking at Mathematics and Science in general, you're just looking at the recognition for something that is not even worth that much. I'll just leave you with this beautiful phrase from Gravity Falls and hope you can reflect on it and change your thoughts somehow:

"Science is a horizon to search for, not a prize to hold in your hands"

>"Science is a horizon to search for, not a prize to hold in your hands"
Wanna ask me how I know that phrase comes from a kid's show?

But my question for you is that if I know that there is barely any recognition in doing this, and you know it also, then what problem do you have with me wanting my name to be under it?

If I don't do my blog then I have two options. Option 1 is posting it here anonymously or with a trip but then the proof just dies and will never be available for students. The other option is going to a permanent math forum and posting it there but there is no dedicated math forum to just post proofs and if I were to do it at StackExchange or something then it would still be under my name, so nothing changes.

I will leave you with this quote that isn't a quote: "Paul Erdos' first published paper was an alternative proof he discovered for Bertrand's Postulate".

Obviously what I found is not as cool as Bertrand's Postulate, but that is also why I am not seeking publication either.

How do i prove this? I am struggling with this.

>How do i prove this?
Try induction and Pascal's rule.

Just noticed what I have been missing, I am very dumb and it was so easy to spot if I actually had eyes.

>Wanna ask me how I know that phrase comes from a kid's show?
Go on, I wanna have a good laugh at your egoistical reasoning.

Nonetheless, I have nothing else to say to you, just do whatever you want, I don't care, I just don't like your kind of mentality of wanting to "claim" something as yours and doing science/math for recognition instead of pleasure and truth.

Say you have n distinct objects o_1, ... ,o_n and you want to pick 3 of them.

o_1 o_2 ... o_n

you can pick o1 and then you can pick from the rest on the right side in n-1 choose 2 ways

or you can pick o2 and then pick 2 on the right side (picking on the left side would be double counting) in n-2 choose 2 ways

...

or you can pick o_{n-2} and be forced to pick the two only objects on its right (o_{n-1} and o_n)

these are obviously exactly all the ways you can pick 3 objects out of n.

This proves it.

>wanting to "claim" something as yours
It's impossible, what he wants to "claim" isn't even a physical thing.

Somebody asked you anything, pal? Why butt in on other people's conversations like that?

Is something confusing you?

What about stackexchange

No, you're the one confused here since no one was even talking to you... But you still felt the need to say something that no one cares...

>Wanna ask me how I know that phrase comes from a kid's show?
>I'll just leave you with this beautiful phrase from Gravity Falls

Uhhh, because he literally told you?

>tfw fell for the bc calc transfer credit meme
i'm still discovering new gaps in knowledge

You're awfully annoying, do you happen to be a gay?

Speak up. I can't hear you when you trail off like that.

me since I do not have blackboard.

"the virgin anal": rigor circlejerking and proofs of statements that are intuitively obvious to infants (IVT)
the chad calc: what the modern world runs on, intuition and infinitesimals

Any good stats and probabilities problem sets?

In the category of linearly ordered sets, which object is initial?
[math](\mathbb{N},

The answer is quite disappointing and depressing: [math](\emptyset,

>which object is initial?
You're saying as if it has to have an initial object.

Why isn't analysis ever taught before Calculus?

In programming, there's a pedagogical dispute between whether to start bottom up (assembly, c, etc) or top down (java, Python, etc) and this situation of analysis after calc seems analogous, yet I see no one vouching for analysis before or even in parallel to calc

you can argue there's no point in teaching calculus to mathematicians. it's hard to reach a conclusion either way. but calculus is easier to teach, because you're teaching it to all the engineers anyway.

Both are garbage and should be mostly ignored.

>dont teach calc to math students
I think I'm beginning to agree. Though I don't regret learning calc, I wish my school would've allowed me to learn analysis before or during calculus, and did not require taking a whole year of calc.

I feel like I'm learning so much more on my own, and having so much more fun doing it. It's going to be hard to return to school.

>Analysis/Calculus
What the difference? What's each thing exactly about? We don't seperate them in Greece.
You get taught the following in high-school: limits (without a strict definition), continuity, derivatives, integrals, fundamental theorem, rolle's, mean value, bolzano, intermediate value, basic differential equations, etc.
And in the final exams (which decide where you can go for higher edu) the problems presented are pretty damn hardcore.
And then in uni you see ε-δ, sequences, etc.

How would a high-school student benefit from having to prove stuff with ε-δ? I personally see it as an obstacle. You don't need it for basic stuff.

yes, you separate them in greece. if you don't know the difference, you don't know what analysis is.

terms like compacity, uniform continuity, connectedness are at the heart of the theory you need to formally develop calculus, and they aren't even mentioned in calculus

>if you don't know the difference, you don't know what analysis is.
I know the "difference". Both are analysis.

>terms like compacity, uniform continuity, connectedness are at the heart of the theory you need to formally develop calculus, and they aren't even mentioned in calculus
Why the hell would you ever teach that to a high-school student? It's like saying, "hey let's teach those 7 year olds ZFC set theory so that they can understand what a number is.

they're not both analysis. I never commented on high school, I ignored that part because this is an 18+ board

trying to prove an necessary and sufficient condition for density of smooth compactly supported for generalized Orlicz spaces.

>but this means [math]0 = \emptyset[/math]
This actually follows from assuming the existence of an initial object in [math]\mathbf{Set}[/math]. In fact you can even conclude [math]A = \emptyset[/math] for any set [math]A[/math].

>I never commented on high school, I ignored that part because this is an 18+ board
huh? you were talking about teaching and high school is where you introduce analysis.

>they're not both analysis
They are. Just like high-school algebra and abstract algebra are both algebra. One is just a level higher than the other.
If you want to say they are not, whatever.. those are just names. You might as well call it all topology.

>let's teach those 7 year olds ZFC set theory
Honestly I wouldn't teach that garbage to anyone, let alone kids.

>Just like high-school algebra and abstract algebra are both algebra.
Actually this is provably false. It's similar to how "applied math" isn't mathematics.

>you were talking about teaching and high school is where you introduce analysis.
>You might as well call it all topology
you need to be 18+ to post here. I was quite content to reply before you went full nonsense

>provably false

>being able to prove that something can't be called algebra
>algebra isn't well defined
interesting

>you need to be 18+ to post here. I was quite content to reply before you went full nonsense
Oh I see, makes sense.

this is not engineering general

You'd know, wouldn't you?

Thx, makes sense. Indeed disappointing.

Yes I know that existence is not guaranteed, but thx for the correction!

Two follow up questions:
1. What if we take the subcategory of sets at least countable infinite?
2. This should be generelazible, isn't it? For a well founded relation [math] E [/math] which is connex,
is [math](\emptyset,E_{\emptyset})[/math] always initial?

What letters do I pick to denote reflections in a dihedral group?

relatively basic for some here but just learning about the axiom of completeness, pretty cool stuff

It's false though, what exactly is cool about that?

Is homotopy type theory useful for people who aren't just masturbating over topology?

It got me into masturbating over subjects related to algebraic topology, so I guess it is.

r for rotation, s for reflections

Please, help me with my homework. I'm doomed.

For each of the following sets S in [math]\mathbb{R}^2[/math]: (i) Draw a sketch of S. (ii) Tell whether S is open, closed, or neither. (iii) Describe the interior of S, the closure of S, and the boundary of S using set-theoretic language.

1. [math]S=\{(x,y)| x>0,y=\sin(1/x)\}[/math]

2. [math]S=\{(x,y)|\text{x and y are rational numbers in } [0,1]\}[/math]

1. Neither. Interior: nothing. Closure: S plus (0,y) where y is in [0,1]. Boundary: S plus (0,1) and (0,0).

2. Neither. Interior: nothing. Closure: Everything. Boundary: Everything

μ or m for "mirrorring"

anyone want to help a brainlet out?
/sqt/ is dead right now

if x isnt zero then 0< x < x/2

can anything be an axiom?

What do you mean by this?

can an algorithm be an axiom?

Why are proofs regarding properties of the real axioms so difficult for undergrads?

I'm not sure I understand you. Can you elaborate?

>can an algorithm be an axiom?
Yes

How do I reduce an equation to a linear form and determine the values of two of its constants using logarithms? I know how to do it for one constant but two is fucking with my head.

Any proposition can be taken axiomatically to be true.
Axioms are merely the basic building blocks of a mathematical model.
An algorithm is a set of functions. You should try to make a proposition about this algorithm to take it as an axiom.
For example:
* Algorithm A will always output FALSE
* Algorithm B always terminates
* Algorithm C is green
* Algorithm Z is a dog preying on the weak

After establishing your axioms you can begin to see what their logical entailments are.

Logic is not usually used by most people.

Post it in yo mama's butt, everyone will see it

Because they are not used to it. You have to essentially learn a new language. Some people just tunnel-vision and can't think about stuff in a new way.

thats a really nice intuitonal way of proving the statement user, thanks for that

Redpill me on fibre and vector bundles.

>What are they intuitively?
>what are they used for?
>what is the intuition for them?
>what are some important theorems regarding them?

Anyone?

ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/assignments/
ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/assignments/
terrytao.wordpress.com/2008/09/27/what-is-a-gauge/

hello fellow patricians, I'm seeking a script, program or application that will throw a problem at me from a pool of problems from a pool of selected topics

>open libgen
>search for book on that topic
>go to exercise section

What are some rigorous texts in discrete math and related topics?

I know of only Lovasz, Epp and Rosen, and none of these strike me as particularly mathematically 'rigorous'.

This ofc works for [math] \binom{n}{k} [/math] for any [math] 1 \leq k \leq n [/math] .
You can prove [math] 1+2+...+n= \frac{n(n+1)}{2} [/math] this way for example.

>What are some rigorous texts in discrete math and related topics?
Stanley - Enumerative combinatorics

What is included in discrete math that isn't in combinatorics? They always appear synonymous to me

Maybe number theory? I think discrete mathematics is a pretty terrible/misleading term.