/sci/ - Science & Math

>>11532134
It's a shame journals don't publish who the reviewers were. It'd be funny to see the names.

Occasional reminder to work with economists.

>>11532165
Economics is a BS science, ask Taleb.

>>11532134
>pic
Wait, is that real? IUT confirmed now?

>>11532230
>Kyoto confirmed their theory is confirmed
Geee

>>11532165
>economists
lol imagine believing in this shit

>>11532165
This has to be a joke right? Economists have nothing to offer for anyone.

>>11532239
I see. Thanks. Was worried there for a bit.

>>11532165
Modern day alchemy. Pure bullshit. Paul Krugman especially.

>>11532165
The question economists should answer is how much better off the world would be if we had shot every single one of them!

>>11532360
Is Game Theory modern day alchemy? Many fields of theoretical economics have essentially become sub-fields of topology, analysis, and other branches of mathematics.

Whether or not economic theory is good at predicting human behavior is a different question, and it is one that not many theorists (including myself) are not concerned with.

I've long used doku-wiki for my notes but wanted something more lightweight and so put this open source local server together, pic related. At the moment it's a one Flask post routine, some python file handling scripts some rudimentary html plugging, including MathJax. You fix a root dir in the config and the filetypes of interest and then it will let you search all files and render the files.

My web dev skills are very basic, so there's lots of room for improvement. Inputs welcome!

https://github.com/Nikolaj-K/wiki-server

>>11533045

>>11533045
Not to be mean, but.
Why not use something like vim wiki? You are already writing markdown and you could entirely skip having to run a server in the background (something not very lightweight).

>>11533149
Didn't know it, but I also want to extend the thing with some graph tools and I also don't know the language vim is written in.
I had previously used dokuwiki and graphviz here

https://graph.axiomsofchoice.org/?to=grand_canonical_partition_function

but plugging those different libraries together gets unwieldy and I didn't like to adopt to all the file standards. 4chan'esk plain text suffices.
But I donno, I just did this and I'll find out if it gives a good working flow.

>lightweight
I didn't benchmark it, but can a flask server with one post function make issues?

>>11533255
>but can a flask server with one post function make issues?
Not really, but you are still essentially running a local server to serve markdown files, which is some serious overkill.

But the idea of being able to include automatically generated plots into your files seems pretty cool.

>Decide to get back into mathematics and apply for a PhD after three years break.
>Program starts in october (if I get accepted) so there are still 5 months for preparation.
>Do it right this time. Study textbooks seriously and try to solve as many problems as I can.
>Everytime I pick up a textbook, I realize there are three more I want to read.

How do you not get insane with the sheer amount there is to learn? I'm taking again algebraic geometry from the start, but there's just so much.

>>11532134
is mochizuki really left handed?

>>11533328
If you have tests, try to understand the matrial in the tests.
If you have a project, try to understand the matrial in for the project.
Organize the stuff you read.
Explain it.
Try to solve a problem. That's my inputs.

why do I find concepts from analysis much “easy” to understand intuitively just by looking at the general constructions, but for algebra I need to look at explicit examples for everything and it takes 5x as much time to understand wtf is going on?
Is algebra the brainlet filter?

>>11533487
algebra only makes sense once you know every single thing about every other piece of math prior. until then, you just have to go with the flow.

>>11533496

this is 115% accurate

>>11533496
This is the best advice I could ever give someone, especially when they just have to do math in school or something.
Literally just go with the flow and just do whatever the teacher tells you to do even if it doesn't make sense. Just do it because they said so, seriously. It's that easy.

>>11533369
That' the thing about number theory though.
It feels like you need to go through so much material before you can even consider a project.
After my master's degree I had a basic understanding of algebraic geometry and algebraic number theory, that I now need to rebuild.
But even then, I feel like there's so much material I need to go through to even start being serious about it.
I need to learn class field theory, elliptic curves, etale cohomology and topoi theory...

As I want to do things right, I spend time on everything.
When I was doing my master's thesis I had to rush through learning algebraic geometry, and I had a very fragile understanding of anything.
It's very easy with scheme theory to get lost in the flow of arrows and maps. And suddenly you have to write a proof and you realize you barely even understand what the image of a morphism is since your set-theoretical intuition is worthless here and you forgot how sheafification work.

Sorry, I'm mostly just ranting as if /mg/ was my personnal blog but I'm curious if there are any number theorists here who have been through this or something like this.

>>11531805
Notice that vectors [math]v=\{v_i\}_{i\leq k}[/math] with [math]k>2[/math] satisfying [math]\sum_i v_i = 0[/math] cannot be colinear, hence they span a (possibly concave) polygon. Denote this polygon by [math]D_v[/math], the quantity defined by [math]f_j(v) = ||\sum_{i\leq j}v_i||[/math] then computes the length of a vertex-to-vertex chord within [math]D_v[/math], hence [math]f(v)=\max_{j\leq k}f_j(v)[/math] computes the length of the longest vertex-to-vertex chord in [math]D_v[/math].
Now permutation of the vertices constitute a homeomorphism of the polygon, and we know that polygons are contractible so we can suppress [math]\operatorname{vol}D_v[/math] to however small value we like with a homeomorphism. In particular, for any [math]C'>0[/math] we can find a simplicial homeomorphism [math]h[/math] such that [math]\operatorname{vol}(hD_v) \leq C'[/math]; this automatically shrinks the length [math]f(v)[/math] of your maximal vertex-to-vertex chord. The problem then becomes showing that, for any such [math]h[/math], we can find [math]\sigma \in S_k[/math] such that [math]h D_v = D_{\sigma(v)}[/math].

>>11533565
I was unaware actual scientists browse this shithole

>>11533585
I'm not an actual scientist, just an aspiring one.
But I guess I started coming here nine years ago when I started uni and I just kept the habit through undergrad and grad school.
I do.'t really know where else to go to have casual discussion about maths.

>>11532143
Angry mathematicians sometimes send bombs.

>>11533328
No matter how much maths you do, you will still remain a boy.

he's even on the tele

So I tried to learn Linear Algebra with Axler but the first page has set theory terminology that I haven't studied yet. Should I read a set theory book then return to Axler or pick a different LinAlg book and return to Axler in two months for a quick refresher?

>>11534049
You can pick up what you need about set theory from wikipedia.

BROS how does this work!?

>>11534058
The person that made this doesn't know what a limit is

>>11534063
Can you explain?

>>11534068
Yes I can

>>11534068
Depends, if you are someone who doesn't accept the formal definition of a limit (epsilon-delta), then no, I don't want to stink up /mg/ with this

If you don't know what an epsilon-delta proof is, then sure

>>11534071
>>11534073
Whats wrong with the way limit is used in the pic?

>>11534078
What limit. They don't use limits

>>11534080
I guess you don't use your brain.

Mind answering me this, but who do you think is using your brain when you aren't using it?

>>11532199
Based.

can one of you 300k/year math majors tell me why this is the case? i cannot find any info on how that line makes any sense

>>11534112
This is 11th grade math, if the coefficient of the nth order differential is zero then it is not an nth order differential, if the converse were true then any differential equation could be called any order by just saying that the highest order differential has its coefficient zero

>>11534117
but he says
>otherwise the order of the equation is less than n
why would it be less than n specifically, if an=0 could it mean it could be any order?

>>11534123
it needs nth derivative of some variable.

>>11534144
so it cant be any order or can it be any order

>>11534152
Well i guess that you mean that there could be a derivative present of order biggrt than n multiplied by zero. But then we do not have a clear definition of the order of an equation since we could add as many of such derivatives multiplied by 0 as we want and it will not change result. So we stick in the defunition that the coefficient of nth derivative is not zero, so that the highest derivative of a variable present is effectively n

>>11534208
maybe i'm misunderstanding you? i get that, since that's just what was said here >>11534117 but that doesn't answer why an = 0 necessarily means the order is LESS than n. it could be greater than n, if that's what he really meant. but then why did he specify less than n?

If a 5 star rating system is bumped up to 6, whats the formula to convert it to 5 stars again? eg restaurant is rated 4.9/6 and I wanna see its score if it was rated out of 5 stars.

>>11534256
If x is a rating out of 6 stars, the rating out of 5 stars is
x*5/6

>>11534258
Oh my hero. I have been googling for a week to find an answer but I couldn't explain it right

>>11534244
if an=0, then your term with most derivatives is n-1, so it becomes a dif equation of order (n-1)th. or if a(n-1)=0, then it would be n-2.

>>11534244
>>11534282
it is just a matter of definition. a polynomial of order 7 has a7 x^7 + a6 x^6 +... = 0, right? if a7 = 0, obviously, it becomes a polynomial of order 6 if a6 != 0. or of order 5 if both a6 = 0 and a7 = 0.
a polynomial of order 7 NEEDS TO HAVE a7 != 0, otherwise the order is < 7.

>>11532435
Game theory is its own thing, its not economics.

>>11533585

remember to swallow when you're done

I'm writing homework for somebody aged 9.
Does the following look good:

This technique teaches you how to multiply any number by eleven, easily and quickly.
We will take a few examples and from these you will see the pattern used and also how
easy they are to do.
So, to begin let’s try [math]12[/math] time [math]11[/math].
First things first you will ignore the [math]11[/math] for the moment and concentrate on the [math]12[/math].
Split the twelve apart, like so:
[math]1\;2[/math]
Add these two digits together [math]1\;+\;2\;=\;3[/math]
[math]1+2\;=\;3[/math]
Place the answer, [math]3[/math] in between the [math]12[/math] to give [math]132[/math]
[math]11\;X\;12\;=\;132[/math]
Let’s try another:
[math]48\;X\;11[/math]
again, leave the [math]11[/math] alone for a moment and work with the [math]48[/math]
[math]4\;+\;8\;=\;12[/math]
So now we have to put the [math]12[/math] in between the [math]4[/math] and [math]8[/math] but don’t do this:
[math]4128[/math] as that is wrong...
First, do this: Place the [math]2[/math] from the twelve in between the [math]4[/math] and [math]8[/math] giving [math]428[/math].
Now we need to input the [math]1[/math] from the twelve into our answer also, and to do this just add
the one from [math]12[/math] to the [math]4[/math] of [math]428[/math] giving [math]528[/math]!
Ok, one more
[math]74\;X\;11[/math]
[eqn]7+4\;=\;11[/eqn]
[math]7[/math] (put the [math]1[/math] from the right of [math]11[/math] in) and [math]4[/math]
then add the [math]1[/math] from the left of [math]11[/math] to the [math]7[/math]
[math]74\;X\;11\;=\;814[/math]
This is a really simple method and will save you so much time with your [math]11[/math]times tables.

>>11534058
It doesn't. Since basically everything in it is wrong.
Read a book on analysis, that will clear things up.

>>11534445
I also have made this because it came up and I think it's helped:

Adding Time
Here is a nice simple way to add hours and minutes together:
Let's add 1 hr and 35 minutes and 3 hr 55 minutes together.
What you do is this:
make the 1 hr 35 minutes into one number, which will give us 135 and do the same for
the other number, 3 hours 55 minutes, giving us 355
Now you want to add these two numbers together:

135
355
____
490

So we now have a sub total of 490.
What you need to do to this and all sub totals is add the time constant of 40.
No matter what the hours and minutes are, just add the 40 time constant to the sub
total.
490 + 40 = 530
so we can now see our answer is 5 hrs and 30 minutes!

Just dumping it over here in case anyone needs math olympiad books

https://drive.google.com/file/d/1yWzACbYHWKkUnPWT9Hx0B5mcLT7YMChY/view?usp=sharing
Google Drive link (zip folder of around 200 pdf files, I think it also includes a lot of AoPS books and articles)

Some of my favourites:
- Arthur Engel Problem Solving Strategies
- A Primer for Mathematics Competition
- 360 Problems for Mathematics Competition by Titu
- Pell's Equation by Barbeau
- Geometry Revisited by Coxeter
- Math Problem Books by Kim Y. Li
- Number Theory by Naoki Sato
- Number Theory for Mathematical Contest by David A. Santos
- Mathematics Olympiad Challenges by Titu
- Problems in Elementary Number Theory
- Cauchy-Schwarz Master Class
- The Pleasure of Math by Goodman
- The USSR Olympiad Problem Book
- Paul Zeitz The Art and Craft of Problem Solving
- Everything in the 101-104 folder by Titu and Feng
- Contest Around The World by Titu
- Diophantine Equations by Titu
- Challenges in Geometry by Bradley CJ

It also includes some interesting articles:
- writing_solns.pdf (guide for writing concise solutions)
- MATH_PROBLEM_SOLVING_AND_MATH_INVESTIGATION.pdf (quick slides about problem solving)
- What Is Good Mathematics.pdf (just an interesting read about math)

>>11534538
Rehost it on Mega

>>11534445
>>11534472
These are fucking awful, don't come back here.

>>11534448
can you prove it, or or are you just handwaving and pretending to know more than you really do?

>>11534244
That statement is in reference to the provided definition, tard. The provided definition doesn’t include any terms greater than n.

>>11533867

The blackpilled murderer you're referring to had given up on the pursuit of mathematical knowledge by then.

>>11534058
>>11534583
> but 0.999... does indeed exist in S, for ALL of N is infinite
This is wrong. Anon defined S to only contain finite decimal expansions.
That is, only elements of the form 0.999...9 (finitely many 9s) exist in S.

>>11534689
But S was said to be an infinite set?

like what about that sum formula, that made sense right?
(Sum S*[m]) = S[p] ?
Does S* also only contain finitely many 9's?
It seems like the formula suggests if adding all elements of S* makes 0.999... , then that would have to be in S.
But you're saying S only contains finetely many? So S* also contains finitely many?
Or N contains finitely many numbers?
i don't get it.

>>11534756
N is the set of all natural (finite) numbers. 1,2,3 are natural numbers. So is 10000.
2.3, pi, infinity are not natural numbers.
>But S was said to be an infinite set?
Yes. S is not a finite set, so it's an infinite set.
>like what about that sum formula, that made sense right?
>(Sum S*[m]) = S[p] ?
Yes, this is true.
>Does S* also only contain finitely many 9's?
S* is a set each of whose element is represented by a finite decimal expansion.
As a set, S* has infinitely many elements.
>But you're saying S only contains finetely many?
No, S and S* are both infinite sets.
>Or N contains finitely many numbers?
No, N is also infinite.

The fact that a set is infinite does not mean infinity, whatever you mean by it, is an element of the set.
What are you not getting?

>>11534583
>can you prove it
Yes.
For example the first sentence is wrong.
The "Axiom of infinity" does not define anything at all, making already your first sentence wrong.
Reading to the end your conclusions 1. to 5. are all false.

So both your premises and your conclusions are wrong.

>>11534058

All that really matters is the last line. This is the word of God. Deus Vult!

>>11534807
s* has infinitely many elements. If each element adds together, then its a decimal with infinitely many decimals.
the formula states that any summation of elements of s* creates a number which is also in S.

I don't understand why you think this suddenly stops working at infinity?
s*[1->4] = s[4]
s*[1->999] = s[999]
s*[1->inf] = s[inf]
why would the last case not be true?

because they don't have souls.

>>11534058
>it's

>>11534823
let a little bit of formalist philosophy into your life

>>11534756
>Or N contains finitely many numbers?
you are saying that N contains only finitely many numbers, because in your own words, the size of N is ∞, but in your own words, ∞ is an "undeterminable" and very large but finite number

Who here /paraconsistent/? TFW you realize it's not just the Law of the Excluded Middle, but also the Law of Non-Contradiction that is invalid and only the law if identity is universally valid, and your understanding of the truth of the LORD is magnified great-fold.

>>11535076
I have a sweet spot for paraconsistent logicd, but I mean they generally only reject the principle of explosion / ex falso quodlibet and not the law of non-contradiction.
In fact, since the law of non-contradiction is provable constructively in a line, the semantics of a paraconsistent without non-contradictions will generally be quite exotic.

In any case, since most of the time I have to deal with numbers in one way of the other and I haven't seen arithemtics in that context, paraconsistent rarely enter my thinking in praxis - for better or worse.

I'd argue the most hands on thing that you strip away when going down the paraconsistent route is the disjunctive syllogism
[math] ((A \lor B)\land \neg A) \to B [/math]

>>11534858
>I don't understand why you think this suddenly stops working at infinity?
I don't understand why you think this also works at infinity

the burden of proof is on you. you're using a "principle" that if something is true for a finite subset, finite subsequence, finite number of steps or whatever, then it must be true also at infinity (whatever that means). if you think this is true, then prove it.

protip: you can't, because it's totally wrong. counterexamples:

0.999... ≠ 0.9
0.999... ≠ 0.99
0.999... ≠ 0.999
...
0.999... ≠ 0.999...

{1} finite set
{1,2} finite set
{1,2,3} finite set
...
N finite set

checkmate, faggot

Threadly reminder to work with physicists.

If you have two random variables X_1 and X_2, both being normally distributed, is there any linear combination of X_1 and X_2 that is *not* itself normally distributed? I'm thinking if X_1 = X_2 then X_1 - X_2 = X_1 - X_1 = 0, which is not normally distributed (unless you count the dirac delta as being normally distributed).

Are there any other examples? I know the answer is no if X_1 and X_2 are independent, which follows from the properties of multivariate normal distributions, but lets assume they're not independent

>>11535262
No

>>11535262
https://en.wikipedia.org/wiki/Normally_distributed_and_uncorrelated_does_not_imply_independent#A_symmetric_example
>>11535273
Shut up.

>>11535074
Ahem, excuse me ladies and gentlemen, I have an announcement.

God bless the principle of explosion, and God bless America!
Paraconsistentfags can fuck off out of my thread.

>>11535076
Ahem, excuse me ladies and gentlemen, I have an announcement.
GOD BLESS THE PRINCIPLE OF EXPLOSION, AND GOD BLESS AMERICA!
Paraconsistent fags may now fuck off out of my thread.

>>11534923
?

>>11535262
You should be able to create weird dependencies by taking a normal X_1, applying the CDF to get a uniform [0,1] variable, breaking the range 0 to 1 into segments and shuffling them, and applying the inverse CDF to get X_2. The distribution of the result should be normal again, but the distribution of X_1 + X_2 could be non-normal.

>>11535300
All that is needed is the law of identity, the LAW of the ETERNAL GOD

We've heard of trace and determinant, but what about the other coefficients in the characteristic polynomial? Why are they never used?

>>11532134
I'm the same anon who found out how to define [math]\sum[/math] and [math]\prod[/math] operators in case when there are no summands that is that [math]\sum_1^0 a_i[/math] should equal 0 and [math]\prod_1^0 a_i[/math] should equal 1 (generally the neutral element of a group where these operations are defined)

Now, did you know that equivalence relation can be defined only in terms of the relation itself?
Inb4 everyone knows that too because I have only seen definitions like "R is an equivalnce relation on A iff ..." using the second set A on the internet

>>11534538
Are any of those not on libgen yet? downloading for the lols anyhow

can mathematics prove the existence of God?
If not, then what use is it?

>>11535408
>Now, did you know that equivalence relation can be defined only in terms of the relation itself?
what do you mean ?

>>11535426
>can mathematics prove the existence of God?
No.

>If not, then what use is it?
Cars, Planes, Bridges, Building, Computers and so on.

>>11535408
>I'm the same anon who found out how to define [math]\sum[/math] and [math]\prod[/math] operators in case when there are no summands that is that [math]\sum_1^0 a_i[/math] should equal 0 and [math]\prod_1^0 a_i[/math] should equal 1
this is a commonly accepted convention, and a relation is just a particular set of ordered pairs, snowflake.

>>11535408
Can we get this guy a fields medal already?

>>11535408
>I'm the same anon who found out how to define ∑∑ and ∏∏ operators in case when there are no summands
WOW. Did my professor learn this fact which was well known for hundreds of year from you?

>>11535408
That's standard.
For two disjoint sets [math]A, B[/math] we want [math]\sum _{i \in A \cup B} a_i = \sum _{i \in A} a_i + \sum _{i \in B}a_i[/math], and similarly for products, for all the obvious reasons. In fact, you can use those formulas as inductive definitions of sums and products.
Then, the values for empty sets come naturally.

>>11535089
Hmm... you may be mentally challenged.
Your counter-examples are also meaningless.

>>11535427
I mean that you can define
forall R R is an equivalence relation iff P[R], where P[R] is some predicate, depending only on R.
Basically the connection between two definitions is this:

forall R,A if R is an equivalence relation on A then A = field(R)
from which follows that we should define equivalence relation in terms of R as follows:

forall R R is an equivalence relation iff R is an equivalence relation on field(R)
On the internet and in the books where is a definition:
\forall R,A R is an equivalence relation on A iff R is a subset of A [math]\times[/math] A and R is a reflexive,symmetric,transitive relation on A which is basically a predicate P[R,A].
>>11535444
this a commonly accepted convention maybe in programming not in maths, also read the second part more carefully, I was talking about an equivalence relation.

>>11535488
>this a commonly accepted convention maybe in programming not in maths
False.
It is commonly accepted in maths.

>>11535488
The predicate must depend on A because if A is expanded R could stop being an equivalence relation.

>>11535488
>>11535506
For example, the relation
R={}
is an equivalence relation on the set {}
but the same R stop being an equivalence relation on the set
{{}}

>>11532134
>accepted for publication
I 100% expect that viXra is going to accept my revised paper in the next 48 hours

http://s000.tinyupload.com/index.php?file_id=19820893044248954463

>Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underling foundations, we present a basis for a topology.

>>11535468
hey, long time no see

>>11535488
It is very much accepted in maths, e.g. when defining binomial coefficients and other number-theoretic constructions. I know you were talking about an equivalence relation; I was pointing out that your definition in terms of the relation itself is trivial if we simply consider a relation [math]R[/math] to be a set of ordered pairs, writing something like [math]a \sim b[math] iff [math](a,b)\in R[/math]. It's easy to write the three properties the set [math]R[/math] should verify to be an equivalence relation, with no allusion to a "second set". However, the use of a second set can be useful to construct a relation -over- a set, which is in practice what mathematicians do. All of this should be painfully obvious to a working mathematician — heck even a student.

>>11535512
>I 100% expect that viXra is going to accept my revised paper in the next 48 hours
I could submit pic related and they'd accept it in less time. That website is a fucking joke and breeding grounds for schizoids such as you.

>>11535518
>schizoid
That word doesn't mean what you think it means. Seriously, look it up.
Tooker is a person who suffers from schizophrenia, not a schizoid. Get it right.

>>11535512
>hey, long time no see
How the fuck did you recgonize me?

>>11535518
nice

>>11535520
How do you know that he did recognize you? Are you friends or something?

>>11535515
binomial coefficients have nothing to do with when an upper sum index goes below a lower index
a ~ b iff (a,b) in R is just a notation what the fuck are you talking about.
I have proved that if a relation can be an equivalence relation on some set then that set should necessarily be equal to the field of that relation - this has surely been proved before me but this is not trivial if you don't think about it.
>>11535510
what's {}? the empty set?

>>11535522
Hi Tooker. Your paper is over 100 pages. That's pretty long! How did you type all of this out? Do you have a computer? I was under the impression that you only had access to a phone.

>>11535525
>what's {}? the empty set?
Yes. It's standard set-theoretic notation.

>>11535506
>>11535510
it must not because R can only be an equivalence relation on ONE set, namely its field. That's what I have discovered. And that's why we don't need the second set A and can replace it with field(R).

>>11535531
someone throws a random set R at you. how do you check if that set is an equivalence relation ?

>>11535531
>on ONE set, namely its field
You can have equivalence relations on arbitrary sets, fields are not necessary.

>>11535531
Ah ok so you're retarded.

>>11535533
by field I mean
field(R) := dom(R) [math]\cup[/math] range(R) where dom(R) := {x | exists y (x,y) in R} and range(R) := {y | exists x (x,y) in R}

>>11535089
I'm using a pirinciple that if something is true for any case, it is true for all cases.

By this principle, if you feel the result damages your conjac jelly brain, what you have an issue with is whether or not the ability to account for ALL elements of an infinite set is viable, intelligible, or allowable. This notion is the the first point takeaway from the proof
>1. infinite arithmetic may be undefined

>>11535523
I dunno if he recognized him, I'm mostly just leaving an opening for him to reply with a joke.
I'm also curious over who the hell did he think I was.

>>11535536
you must be over 18 to post here

>>11535539
>I'm using a pirinciple that if something is true for any case, it is true for all cases.
lol

>>11535541
>referring to myself as him
Fuck, I'm going insane.

>>11535532
I compute its field and then check if it is an equivalence relation on its field. If it is then it is an equivalence relation, if it's not then it's not an equivalence realtion. Moreover if it's not then it's not an equivalence relation on any other set A.

>>11535549
what is "its field ?"

>>11535551
>>11535537

>>11535551
for example if we take R := {(1,1), (2,2), (3,3), (1,2), (2,1),(1,4)} then dom(R) = {1,2,3}, range(R) = {1,2,3,4} and field(R) = {1,2,3,4}

>>11535544
It's either infinite arithmetic is undefined or there exists the ability to accommodate all elements of an infinite set, which is bijective with accommodating all elements of an infinite arithmetic function.

It really can't be both.
[eqn]\sum_{n}^{\infty}[/eqn] and [eqn]\lim_{n\to\infty}[/eqn] are either definitely finite functions, or [eqn]\to\infty[/eqn] allows the ability to account for all all elements of infinity.

in the case that they were definitely finite, [eqn]\sum_{n=1}^{\infty} \frac{1}{10^n}[/eqn] cannot be said to honestly produce 0.111..., unless the dotdotdot notation is meant to mean "arbitrarily finite".

>>11535574
holy fucking shit you're stupid. Please refrain from posting in this thread.

>>11535559
That isn't a definition.

>>11535549
Is {(1,1)} an equivalence relation?

>>11535700
Quit projecting niggertard. Your own feeling of retardation after reading that post is literally just (You).

Can you even determine whether or not infinite calculus accounts for infinite terms?

Inb4 some other stupid bullshit you'll say instead of an honest answer.

>>11535766
The field of a relation R is UU(R). Basically all the elements of the underlying set used in the relation.

>>11535804
>Can you even determine whether or not infinite calculus accounts for infinite terms?
can you even explain what is this schizo shit supposed to mean mathematically ?

>>11535815
Please answer >>11535772

>>11535822
Is it reflexive, transitive and symmetric?

>>11535830
That is what it means to be an equivalence relation.

>>11535819
It's simple bro
[math]\sum_{1}^{\infty} 1[/math]
Does this sum equal an arbitrary finite number, becuase infinity cannot account for all numbers in [math]\mathbb{N}]/math]?
Or does the sum equal [math]\infty[/math], otherwise known as divergent, or else otherwise known as pajeetretard math [math]- \frac{1}{12}[/math]?

Does [math]\to\infty[/math] account for all elements, or only an arbitrary finite amount of them?

>>11535837
What is the underlying set?

>>11535845
Why would you need to know?? Just do this: >>11535549

Rate my bait image.

>>11535845
Thats exactly the point. Being an equivalence relation as a property depends on the underlying set. Therefore just knowing the relation is not enough to tell if its an equivalence relation

>>11535855
It isn't an issue with the education system. Almost nobody needs to know a precise definition of the reals for anything.

Although I do believe that every person who enters a university should be forced to.

>>11535851
Because { (1,1)} is an eq rel on {1}, but not on {1,2}. Reflexivity means every element must be in relation to itself. In other words field=underlying set.

>>11535855
well done

>>11535863
>Because { (1,1)} is an eq rel on {1}, but not on {1,2}
Exactly!

So >>11535549 is an idiotic thing to say and obviously wrong!
That's exactly my point.

>>11535867
Based midwit btfoing retards on a higher mathematics thread.

>>11535870
Someone's got to do the grunt work!

>>11535855
>diddlerkid cuts

>>11535839
first question: it diverges
second question: it accounts for all elements, but the implementation is via arbitrary finite amounts, because that's the only way we can reason about infinity

>>11535929
So you're saying arbitrary finite amounts can account for all elements of an infinite set?

This means infinity is an arbitrary finite number, so it must also exist inside [math]\mathbb{N}[/math].

>>11535929
>via arbitrary finite amounts, because that's the only way we can reason about infinity
This is not quite the reason. The actual reason is that addition is a binary operation, hence is only defined on finitely many terms. Epsilon-N definition of inifinite sums is an attempt to extend the notion of addition to infinite sets of numbers.

Why is it so difficult to check whether [math]\pi+e[/math] is a transcendental number?

>>11535946
Because it is extremely hard to reason about an arbitrary real number which you can not easily define through basic analytic methods.

>>11535938
>So you're saying arbitrary finite amounts can account for all elements of an infinite set?
answer to this depends solely on what you mean by ""account"". why don't you read the actual definition of an infinite sum and decide for yourself?

>This means infinity is an arbitrary finite number, so it must also exist inside
non-sequitur

>>11535959
It's super easy to define it through basic analytic methods: it's the single root of the first degree polynomial [math]x - (\pi + e)[/math].

Hey there, made some shrimp and mushroom fettuccine alfredo and paired it with cream soda since I don't drink alcohol, how are you anons fairing? What the fuck are D-modules? They're actually pretty cool and nice example of mathematical structures arising out of studying physical ideas.
https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Coutinho593-604.pdf

>>11535987
>It's super easy to define it through basic analytic methods
>It's a root of a polynomial in R[x]

>>11535987
WOW! This definition tells us really ALOT!
Also, even addition is an "analytic method"...

But that obviously isn't the point

>>11535987
Interesting suggestion.
I'd like to present something, as well:
We call the set of transcedental numbers [math]T[/math]. Then, [math]\pi + e[/math] isn't transcedental if and only if [math] H_1 [ ( \mathbb{R} - \{ \pi+ e \} ) \cup T ] \cong \mathbb{Z}[/math].
This is a clearly stated topological version of the problem, and I hope a solution might come with further advances in algebraic topology.

>>11536011
My bad.
*[math]H_0 [ ( \mathbb{R} - \{ \pi+ e \} ) \cup T ] \cong \mathbb{Z}^2 [/math]

Why is torsion in algebra called that way?
I assume it's because it came from some property of a geometric object or something like that.
The purely algebraic definition of it offers no clue to the reason it's named that way.

>>11536020
https://math.stackexchange.com/questions/300586/where-does-the-word-torsion-in-algebra-come-from

I should say lmgtfy but whatever.

I also like this logical funfact
https://en.wikipedia.org/wiki/Torsion_group#Mathematical_logic
or more broadly
https://en.wikipedia.org/wiki/Nonfirstorderizability

>>11536020
torsion elements - elements with finite order
an element g with finite order - then <g> is a (finite) cyclic group
cyclic - has something to do with rotation - just like "torsion" in physics

at least that's what I think about it, maybe it was a translation from german or other language

>>11536020
Think of them as roots of unity.

>>11532360
>Paul Krugman especially
Love it when people immedaitely out that they use political bias to dismiss things instead of evidence and analysis

>>11536038
>maybe it was a translation from german or other language
Guess what the Germany word for "torsion" could be.

>>11536020
what about FLAT MODULE ??

>>11536011
>>11536018
use something more convoluted and less known, add a 2-page introduction and 3 pages of bibliography, and voila you're ready to publish a paper

>>11536049
>FLAT MODULE
CUTE!

>>11536049
>what about FLAT MODULE ??
I remember looking this up in my algebra class.
There's canonically no correct answer to why flat modules are flat, because the person who invented the word was Serre and when people asked him why he chose it his answer was
>I don't remember lol

I wanna self study real analysis. I struggled up to chapter 3 of rudin but couldn't handle it anymore. I found solutions to Abbott and Bartle, which one is recommended? I have an undergrad and masters in EE don't make fun of me.

>>11535804
You'er the kind of person who writes emails to math professors claiming you've found a way to trisect an angle with just a compass and straight-edge.

>>11536079
forgot to mention my end goal is probability theory, but for that I need measure theory

>>11536083
I'll just say that if you want to truly understand the rigorous foundations of probability theory, there's a long way ahead of you. but kudos to you anon

>>11536054
So something like [math] \Sigma = ( \mathbb{C} - \{ \pi + e \} ) \cup T [/math] is a Riemann surface, and then I choose some 4-manifold with a complex structure and show that the Gromov-Witten invariants do something if [math]\pi + e[/math] is transcedental?
Wanna be my coauthor?

>>11536090
Topology and measure theory is pretty much all you need to get started desu

How does /mg/ switch from no posts for 10 hours to a stream of banter and shitposting within an hour?

>>11536090
Ya I am aware I have at least 3 (real analysis, measure theory, then finally probability theory) subjects to learn but I really enjoy this stuff

>>11536079
Abbott is the de facto book for "I'm struggling with another book and I need gentler explanations".
The main selling point of the book is that it makes everything as easy and intuitive as possible, the tradeoff being that it doesn't go all that deep, but if you're struggling to get the basics you don't need to worry about deep right now.

>>11536094
don't forget that the starting point is EE

>>11536099
thanks anon. I was leaning towards Abbott but didn't want to bias others who might answer. I'd like to hear more opinions but I 100% understand my place (ie not good at real maths).

>>11535983
"accounting for" is fairly simple english.
If it's possible to account for all elements of an infinite set, it's an assumption that every element in the set has been observed. In relation to infinite arithmetic, it would be the assumption that every possible step or partial sum was solved.
It's impossible to make the observation that anything could certainly continue infinitely if ∞ is meant to be literally endless. Just because an end is not observed does not automatically exclude the possibility it merely continues much further to a finite end than you imagined or would be willing to observe.
This is a temporal quality of physical existence in relation to doing a task and then stopping the continuation of that task because you get tired or bored or make an assumption of fruitlessness.
If infinity is endless, it's impossible to observe to ascertain with certainty, which means any arbitrary task that is cut short of completion for temporal reasons might as well be equivalent to infinity as well, even if it may have had a definite end.
Calculating the digits of TREE(3) is an example. It is assumed to definitely be a finite natural number, but the task of calculation would be boring, tiring, and ultimately fruitless while also never actually being completable.

So does the set of [math]\mathbb{N}[/math] contain ALL/EVERY Natural number?
Basically, does or doesn't N observe every natural number?
does: [math]\infty_a[/math], the set is complete and contains ∞ as an element.
doesn't: [math]\infty_b[/math], the set is incomplete and doesn't contain ∞ as an element.
>[math]\sum_{n=1}^{\infty_a} \frac{9}{10^n}[/math] = 0.999..., a number with ∞ decimal places and a notion of completeness upon the ∞'th arbitrary finite element.
>[math]\sum_{n=1}^{\infty_b} \frac{9}{10^n}[/math] = 0.999..., a number with an arbitrary finite amount of 9's and a notion of incompleteness.

>>11536092
This is out of my league, I barely know what is a Riemann surface. Just mention me in the acknowledgements.

can someone help me:
How do I solve:
sin(a-b) sin(b-y) sin(y-a)
——— + ——— + ———
cosacosb cosbcosy cosycosa

>>11536081
I wrote a comment on a mathologer video and he responded and reee'd at me, that's as far as I'll go.

>>11536114
you start by deleting that atrocity against mankind and reposting it in LaTeX

>>11536114
>How do I solve:
This is an algebraic expression, what exactly do you want to "solve".

>>11536123
i mean simplify

>>11536114
there is a formula for sin(a-b)
use it
there's also a stupid questions thread for all your homework-related needs
use that too

[math] f(\chi)=\sum_{i\ge 0}\frac{g_i}{g_0}(\chi(1)-\chi(G_i)) [/math]

>>11536125
The super pro tip is to look at this website: https://en.wikipedia.org/wiki/List_of_trigonometric_identities

>>11536136
yeah still can't do it

>>11536147
it's been 5 minutes
you didn't try very hard

>>11536152
When I posted this I already had thought like 30 min bruh, and is this really that hard that no one itt can do this?

Is there a complex analytical non-constant function with periods 1 and [math]i[/math]?

>>11536167
>is there a non-constant holomorphic function on the torus, a compact Riemann surface?
No.

>>11536166
>no one itt can do this?
Type it into a CAS for Gods sake...

>>11536175
What about 1/P(z; 1, i) where P is Weierstrass's elliptic function?

>>11536020
You have to do some twisting if you want a non-nullhomotopic map [math]S^4 \to S^2[/math].

>>11536049
No twisting done.

>>11536167
>>11536175
But if you allow for meromorphic, you can choose your lattice as you wish, e.g. via

https://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions#Definitions

>>11536167
if it's periodic, it's bounded
if it's bounded, it's constant

>>11536166
no, it's so easy that nobody wants to be bothered writing out your entire homework solution for you while you sit and watch

>>11536183
so you can't do it?

>>11536207
>so you can't do it?
No. I would type it into a CAS, no point in wasting time doing basic algebraic computations when a Computer can do it better...

>>11536207
Yeah, I can't do it.
Try asking somewhere else.

>>11536213
and where would i find this fancy-smanchy CAS?

>>11536185
probably still not C infinity at the inverse poles I suppose

>>11536185
probably either still not C infinity at the inverse poles, or the zeros make problems with the inversion again, I suppose

>>11536217
>and where would i find this fancy-smanchy CAS?
Google.
Maxima, Wolfram alpha, etc.

>>11536167
>>11536175
>>11536185
Given a line bundle [math]E\rightarrow\Sigma_g[/math] you can count the number of non-constant holomorphic sections [math]\Gamma(\Sigma_g,E)[/math] via the holomorphic Euler characteristic [math]\chi(E)[/math]. If we write, WLOG, [math]E\cong L^k \otimes \mathcal{K}^s[/math] where [math]L[/math] is the Chern generator and [math]\mathcal{K}[/math] is the canonical line bundle with [math]k\in\mathbb{Z}[/math] and [math]s\in\frac{1}{2}\mathbb{Z}[/math] (existence of Spin structure), we see that by Riemann-Roch [math]\chi(E) = \operatorname{dim}H^1(\Sigma,E) - \operatorname{dim}H^0(\Sigma,E) = \operatorname{deg}(E) + 1-g = k + (2s-1)(g-1)[/math]. If applicable, you can then obtain [math]\chi(E)[/math] from [math]H^0(\Sigma_g,E)[/math] from Kodaira vanishing. Hence generally speaking, on the torus we have [math]\chi(E) \sim k[/math] where [math]k[/math] is the Chern number of [math]E[/math].

>>11536066
I'm gonna have to know the sauce, dawg

>>11536342
Hibike Euphonium.

>>11536286
the question whether 1/P(z; 1, i) is holomorphic has something to do with spin structure??

>>11536286
complicating the answer to such a simple question is the most brainlet thing i've ever seen.

is yukariposter here?

>>11536759
>>11536286

Is the inverse inclusion map continuous ?

>>11535855
you can improve the first version by mentioning the "supremum" of the set of {0.d_1, 0.d_1d_2, ...}

>>11536120
>that's as far as I'll go.
Because you're a midwit who will never make it in math.

>>11532134
Are there any neat tricks for computing high dimensional symbolic integrals?

>>11537457
Matlab

>>11535873
lol

Divide the reals into the rationals and the irrationals:
>Between every two rational numbers there are infinitely many irrational numbers, therefore the irrationals are dense in the rationals
>Between every two irrationals there are infinitely many rational numbers, therefore the rationals are dense in the irrationals
Wait, aren't there more irrationals than rationals? A whole cardinality more? What the fuck?
How can two sets of different cardinalities be dense in each other? Surely if one set is bigger then the density relation is only one way.

>>11537457
Fuck that, how about solids of intersection for a few dozen cubes?

How does one try to understand math? I’m on my 3rd fucking bout of calculus in college and I’m losing my fucking mind over it

I've finished precalc and linalg in self study but looking at a checklist shows that the texts I worked with covered everything except trigonometric identities. What's a quick way to learn them?

>>11537567
Just trying to give intuition:
Well if A is dense in B, that just means A is good at approximating B. That is, B can be represented by converging sequences in A. And the "number" of sequences of A is intuitively really large (its about the power set), large enough to match the cardinality of B.
So even though the cardinality of the rationals is small, the cardinality of the power set of the rationals isn't.

>>11537567
>the irrationals are dense in the rationals
>the rationals are dense in the irrationals
Bizarre phrasing. Irrationals and rationals are disjoint so how one can be dense in another?

>>11537737
They cannot. The proper statements would be
>The closure of [math]\mathbb{Q}[/math] in [math]\mathbb{R}[/math] with respect to the norm topology is [math]\mathbb{R}[/math].
and
>The closure of [math]\mathbb{R}\setminus\mathbb{Q}[/math] in [math]\mathbb{R}[/math] with respect to the norm topology is [math]\mathbb{R}[/math].

>>11537101
>inverse inclusion
?

>>11537567
>How can two sets of different cardinalities be dense in each other?
Since you pic just 2 reals a finite distance apart from another and Q is dense in an interval, you make no real use of the reals.

>>11537578
>self study
>quick
The only reason to memorize things quickly in math is to pass an exam, but since you're self studying, it doesn't make sense that you would ask for a brownie point shortcut.

>>11537101
>inverse inclusion map
....the quotient map?

>>11538434
link?

>>11538434
based Scholze btfo'ing Mochizuki

>>11538434
I trust Scholze 100%

>>11538434
>if we just eenie meenie a bunch of non-canonical isomorphisms and run the proof like that it doesn't work
Does Scholze's criticism make more sense in the original paper? Because I genuinely don't get it.

how much studying does it actually take to get near to "expert"-level in a certain field of mathematics. by "expert" i mean understanding the language and producing potentiall novel results.

im slowly getting the feeling with almost every area i study that it really doesnt take that much time (maybe 1-2 years), it just takes a lot of effort and most people have friends/family/etc. is that assessment wrong?

>>11538434
Mochizuki's "proof" of ABC is a failure.

>>11538502
>link?
https://www.math.columbia.edu/~woit/wordpress/?p=11709

>>11538569
Within 5 years a University student gets from Highschool level to being able to do some research.

Certainly with more focused studying of one area getting to a point where you can understand current research should be doable within a few years.

>>11538571
prove it

>>11538584
t. spent years reading about IUT

>>11538595
by that logic all religions are proven

>>11538605
unironically every single monotheistic religion is true (because there exists one eternal infinite god)

>>11538613
i didnt say monotheistic did i now go take your religion elsewhere, abc is proven deal with it QED

>>11538434
https://www.youtube.com/watch?v=c5fts7bj-so
Fuck the Japanese!
Scholze out here dropping a THIRD bomb straight over Kyoto just like Papa Neumann would have wanted.

>>11538613
>unironically every single monotheistic religion is true
False. Mohammed was created by the devil and Jews rejected the Son of God.
Islam was founded on lies and Judaism is a perpetual lie going on for about 2000 years.

What's a good introductory book on Algebraic Number Theory for an undergraduate who has completed an introductory abstract algebra course (and a number theory course)?

>>11538434
>even his cult who claims they understand it has no fucking idea how IUTeich works at all
This gift just never stops giving

>>11538662
>>11538640
>>11538537
>>11538508

>>11538644
neither of these things are true because the devil is not more powerful than god and so if any human calls out to the one true god, he immediately hears.
What you are claiming is a blasphemy against the power of the LORD

>>11538662
It seems they do some serious undergrad strategies to pull this of.
The "everybody knows" shortly before a totally unjustified claim is my personal favorite.

>>11538666
Based prodigy drops a bomb on a crusty halfu who wasted his career.

>>11538667
>so if any human calls out to the one true god
Jews and Muslims do not.

Does anybody have that article where a professor was complaining about remedial math students and the futility of teaching them?

>>11538655
Marcus.

>>11538655
>What's a good introductory book on Algebraic Number Theory for an undergraduate who has completed an introductory abstract algebra course (and a number theory course)?
Ribenboim

>>11538434
>posted four minutes after the blog comment went up
hi Peter.

>>11533618
Physicsforum
Mathstack exchange
/rmath

Thank me later.

If I have an arbitrary real valued function f, divided by a polynomial p of degree n, and I know this is identically equal to a constant, can I conclude that f must be a multiple of p?

>>11538744
>If I have an arbitrary real valued function f, divided by a polynomial p of degree n, and I know this is identically equal to a constant, can I conclude that f must be a multiple of p?
What have you tried?

>>11534538
Did you read all of those books? Would they be useful for someone already on college?

>>11538751
Crying.

>>11538772
Have you tried assuming the equality is true for all non-roots of the polynomial and then multiplying both sides by the polynomial?

>If I have an arbitrary real valued function f, divided by a polynomial p of degree n, and I know this is identically equal to a constant
Equality in what sense?
If it's everywhere you know that the polynomial has degree zero, but surely you mean equality for all non-roots.

>>11538744
>divided
You mean literally divided or "akshually, whenever the denominator zeroes the numerator also zeroes so we define the division by muh continuity"?

Is there any natural and non-trivial action of the automorphism group of [math]\left(\mathbb{Z}/p\mathbb{Z} \right)^2[/math] on [math]\mathbb{Z}/p\mathbb{Z}[/math]?

>>11538543
You're trying to discuss against a fields medalist? Sit down, be humble, you're not at that level, you're just some shit poster on 4chan spamming tohou girls

>>11538434
why would he post something as "important" as this in the comments of a boomer literal who blogger?

>>11538784
Actually divided, denominator is never zero.

>>11538820
>boomer literal who blogger

https://www.math.columbia.edu/~woit/wordpress/?p=11709#comment-235940
Mochizuki bros...

>>11538848
the cope holy shit

How do you pick a field to focus on in your studies? I like pretty much every field of math.

>>11538873
choose one that will give you the most h-index

>>11538864
What's the problem with IUT exactly? Is it like when everybody disregarded set theory in Cantor's time, then it became huge after some years?

>>11538875
It has smell of being wrong.
S&S have pointed out what they believe to be flaw in specific corollary.
Mochizuki says they misunderstand.
Nobody from Mochizuki's circle has written clearer proof or shown other non-trivial result form IUT.
Now IUT paper has been railroaded through peer review (at Mochizuki's institution) and in popular Japanese press so they get grant money etc for IUT

If I had to bet life I would bet it's wrong but Mochizuki et al can ride it out for rest of their careers since it would be to embarrassing to admit.

>>11538875
>What's the problem with IUT exactly?
Various number theorists, some with a Fields medal, say it is false.

>>11538925
That doesn't mean anything, back in the day everyone also said set theory was false.

>>11538828
Then it's just [math]f(x)/p(x) = \lambda[/math], thus [math]f(x) = \lambda p(x)[/math].

>>11538934
>That doesn't mean anything
It does mean a lot actually.
>back in the day everyone also said set theory was false.
[citation needed]

>>11538914
>embarrassing to admit.
That's not how the japanese work, honor is a huge part of their culture and being, if they're wrong, they will admit it and will shame themselves (in the past they would commit Seppuku because of the same) and after that they'd move on. Japan isn't like the west where petty behaviours from people are a given.

What do people mean in differential equations when they say "applying the boundary conditions" ? Is this just a more general way of saying "with the initial conditions?"

I'm kind of grinding through some problems but I'm having trouble knowing exactly what I'm doing here.

>>11538934
>That doesn't mean anything
It absolutely does.

>back in the day everyone also said set theory was false.
Who said that?
The disagreement was about whether set theory should serve as the foundation of mathematics.
It was a debate about foundations, not about results.

>>11538950
That is probably what is meant. Although boundary conditions and initial conditions can mean different things.

>>11538949
Weeb alert.
Also if you subscribe to some form of the guilt-shame culture axis then Japan is a shame culture where the last thing Mochizuki would want to do is admit it's flawed, since he and RIMS would be embarrassed and it would look bad for Japan since their equivalent of NYTimes has praised his proof.

>>11538949
imagine actually believing this lmao

>>11538966
>It was a debate about foundations
that debate is still ongoing

>>11538934
No they didn't, go look at the primary sources like letters etc.
Also much of the criticism towards Cantor was on a more philosophical level of math's foundations etc.
Hilbert wasn't pointing out some specific section of his proofs and asking him to clarifiy.

At this point ABC is at an impasse as Mochizuki's proof will never be further clarified by any of the people that purport to understand it and the critics have already given what they feel is a specific flaw.

>>11538949
t.never been in japan

>>11538980
>that debate is still ongoing
Pretty much irrelevant to my point.

Nobody argued that theorem 34.12 in Cantors paper on set theory was wrong, that simply wasn't the issue.

>>11538972
Dude, they're conditioned since childhood, in school and in their homes, that the most important thing in life is honor, hard work and society. Of course there are outliers, but you honestly think a guy like Mochizuki, with a PhD and a big name in japanese mathematics would be an outlier? His proof might contain mistakes, but for him, they way he sees it now it's perfect, if he found a mistake I'm sure he would be the first to bow and apologize in shame because he's japanese after all, he's not some cunt western professor who'll never admit his own mistakes. I'd rather believe in him than in a german.

>>11538993
Stop watching anime bro it's rotting your brain.

>>11538993
Absolutely retarded and wrong in the first place, but for what it's worth Mochizuki spent most of his early life in the states.

>>11538978
>>11538985
Read up on japanese education and what they're taught throughout elementary school, middle school and high school.

>>11538993
>that the most important thing in life is honor
The MOST dishonor Mochizuki could bring upon himself would be having to retract his paper.

>some cunt western professor who'll never admit his own mistakes
Every professor I have ever had always responded very reasonable to any criticism you brought to him. He either calmly explained why you were wrong or admitted that he was in the wrong and would make a correction.

>>11538993
Did you read Yukio Mishima and think every Japanese is like that?

>>11539000
Didn't know about that, it sure makes things different having an american background, but still, I doubt his japanese followers would be outliers as well. Who knows.
>>11539006
See, you don't know japanese culture, it would be shameful if his paper was wrong, but it would bring even more shame and dishonor if he was deliberately hiding that fact, the japanese mind is conditioned to always admit their mistakes, bow in shame and apologize, then they can start anew, they're taught that throughout their childhood and teen years, it's an unspoken rule in japanese society.

>>11538848
>Kyoto U starting research center for IUT
Imagine being some poor researcher that gets hoodwinked into joining this.

>>11539016
>the japanese mind is conditioned to always admit their mistakes
Do you have a functioning brain?

>>11539016
>the japanese mind is conditioned to always admit their mistakes
where the actual FUCK do you weeaboos get this stuff
it's like you've literally never spoken to a single Japanese human being

>>11539021
Have you ever read up on the japanese educational system? Know how it works? Know what they learn? From childhood they have to go to school alone, sing the anthem, bow to the teachers, study really hard, clean their own classrooms and have jobs. Their society conditions them into the mindset that the most important things are honor, hard work and maintaining society working.

>>11539020
>Ph.D. in Mathgen papers
>any job I want at the IUT research Center
>$300k starting

>>11539030
Lmao

>>11539028
>Have you ever read up on the japanese educational system?
Indeed I am a weeb. You caught me.

But to repeat my question. Do you have a brain or have ever interacted with another human being?

>>11539024
Have you? Don't take 5ch posters as a rule, you idiot, 5ch is the place where they can relieve stress so they just shitpost, but IRL their mentality prevents them from being petty like westerners, of course not considering some few outliers, most of which with poor background or mental issues.

Mochizuki-san pls hire me.

>>11539039
The fact that the first thing that jumps to your mind for any knowledge of Japanese people is "he must be reading google-translated 5ch posts" only confirms that you are an autistic Japan-worshipping weeaboo

>>11539039
>Have you? Don't take 5ch posters as a rule,
lol yes I've met Japanese people IN REAL LIFE

>>11539052
Sure, the one who knows about japanese culture and mentality is you and not me who have read a bunch on that topic, yeah, right...

>>11539060
>nobody but me could possibly know anything about Japan
>why? well you see, everybody knows the only way to know about a culture is to read about it, and I'm the only person who can read

>>11539067
Care to post then the books, papers or articles you've read on the subject?

>>11539045
Would you seriously become an expert in hyperbolic curves and anabelian geometry and read all of Mochizuki's papers if he said he'd hire you to research IUT and shipost about Scholze on the internet?

>>11539070
Care to post the number of Japanese people you've actually met?

>>11538797
Yes, the automorphism group of [math](\mathbb Z/p\mathbb Z)^2[/math] is the group of invertible 2x2 matrices with coefficients in [math]\mathbb Z/p\mathbb Z[/math].
It can act on [math]\mathbb Z/p\mathbb Z[/math] via the determinant for example:
[eqn]\begin{pmatrix}a & b \\ c & d \end{pmatrix}\cdot x = (ad-bc)x[/eqn]

>>11539078
Oh shit, of course. How did I not think of those? Thanks.

>>11539058
And it absolutely isn't necessary to have met a Japanese person to realize that they aren't pure angelic beings, but normal humans just like everyone else.

Japan certainly has a more gentle culture then most places and the (admittedly very few) Japanese that I have met where always very kind and respectful, but that absolutely is no reason to attribute to them super human morality.

>>11539120
>no reason to attribute to them super human morality
This. That can only be attributed to the Emperor, a few of his Primarchs, the Grey Knights and his Custodians.

>>11539153
Indeed. Who but HE could create the perfect vision of humanity and who but HIS most loyal servants could be entrusted with creating that vision in the face of humanities innumerable enemies.
Why are you pointing out something so obvious?

>>11538676