/sci/ - Science & Math

Mhm, For a possible topic, take this 101 on general quaternion algebras over some field

https://youtu.be/tkS_6xY132g

How can I find a cute mathematician/physicist girlfriend?

Hey, got a few questions for all regulars in /mg/:

Are you religious?
If yes, which religion do you follow?
If no, then are you an atheist?
If no, then are you agnostic or something equivalent to it?
How do you see an ascetic life?

I don't want to start any discussions, just want to know a little more about what people here think. Thanks.

>>11119016

not very regular, but I go here every some time

>Are you religious?
No.
>Are you agnostic? Are you an atheist?
I assume you're using the philosophical definitions here, in which case I'm agnostic, not an atheist, but might be an atheist for particular god concepts.

Won't answer last question since I don't really have a good answer. I had to Google the meaning of the word (English isn't my first language) so my understanding of what is meant by it may not be perfect.

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>>11119016
>Are you religious?
no, but semi-spiritual
>If no, then are you an atheist?
no
>If no, then are you agnostic or something equivalent to it?
agnostic, sure.
>How do you see an ascetic life?
that which is of ones passion, in good company and health.

Am I traitor to the noble field of mathematics if I used my really good math scores solely to get into medical school?

>>11119087
On medicine, you'll be saving lives.
On math, you'll be saving the universe.
You decide what's better.

>>11119087
Barely

How do I prove pic related for any p, q distinct primes ?

>>11119004
Nice video. Just one problem, it seems you added by mistake a recording of your ugly bloated face. I suggest you remove it in the next videos, also, please work on your english, the accent makes you sound a tad bit homosexual, which distracts from the mathematics. Keep up the good work and the shilling

When a proof depends on several unrelated lemmas, is it more effective to present each of them separately before connecting them all together at the end (red), or to build them up one at a time as needed (blue)?

With red you can prove the lemmas in full generality, but with blue you get to see how they are applied to the main theorem, which may be more instructive.

>>11119157
I would say the blue approach makes it more motivated and human, and the red approach makes it more clever and mysterious, but possibly a little cold.

>>11119157
Build up the ones that are key to communicating understanding of the main theorem in the text and just stuff the others in appendices.

>>11119016
>Are you religious?
yes
>If yes, which religion do you follow?
catholic

test

>>11119016
>regulars
yikes

>>11119225
Holy based

>>11118998
why the FUCK are you making a new thread when the last one hasn't reached the bump limit?

>>11119225
If you found a mathematical proof that god doesn't exist, would you publish it or would you hide it?

>>11119016
>Are you religious?
No
>If no, then are you an atheist?
No
>If no, then are you agnostic or something equivalent to it?
Pretty much indifferent to the existence of god, so yes.
>How do you see an ascetic life?
I actually thought about giving up my life into scientific research and saving humanity from itself, then I realized it was just my ego taking over me and decided on a existentialistic approach to life.

>>11119263
>If you found a mathematical proof that god doesn't exist
a contradiction. God is beyond the realm of science and mathematics

>>11119016
>Are you religious?
Yes.In my country 99% of the people are.
They take part in two groups,traditionalists that understand it as a philosophy of living and perform some rituals as such,and the hard core group that does everything the church says.
Only small part of the population that origin from mixed marriages are atheists or agnostic.
>If yes, which religion do you follow?
orthodox

>>11119285
>Yes.In my country 99% of the people are.
where are you from?

>>11119277
Show that there is a realm beyond math and science!

>>11119117
Damn, I'm kinda stumped with this one. Proving it with one prime equal to 2 is fairly trivial, but the general proof evades me.

When did you realize you made it anon-kun?

>>11119261
>penultimate /mg/
>ultimate /mg/
you must choose

>>11119524
DEEP DEEP DEEP
DEEP DEEP DEEP
18 NAKED COWBOYS EVEN GETTING FUCKED IN THEIR SLEEP

>>11119263
>mathematical proof that god doesn't exist
That's nonsense, any good concept whose existence or nonexistence can be proven or disprove mathematically is either incoherent, and thus by disproving it you're not actually saying anything about the world, or a tautology, and thus by proving it you're not actually saying anything about the world.


>>11119277
>god is beyond the realms of math and science
What does that even mean? To me, these look like some random words a monkey typed. Please do explain what you mean by the "realms" of math and science and what it means to be beyond them, what you mean by god, and how you know god is beyond the realms of math and science, and finally, why that's relevant.

In university I did a major in computer science focusing on theoretical computer science and I did a minor in math, is it fair to consider myself a mathematician.

>>11119016
I don't know.
Christianity.
No.
Probably not.
Asceticism is for the weak. The strong can experience love, without lust, eat without being glutenous, be good without being full of pride and are in general able of self control.
Asceticism ist for those who can only live in excess and not in moderation.

>>11119263
God isn't a mathematical object.

>>11119680
>is it fair to consider myself a mathematician.
No.

>>11119157
Statement of the theorem, then the lemmas with their proofs, then the proof of the theorem.

>>11119719
this

why is probability so fucking unintuitive? I have to second guess whether flipping a coin is 50/50 anymore god damn

I want to master calculus. how can i do so? i need a job
what career can i get if i just train myself in calculus
im a neet and my highschool didnt even offer calculus or pre calculus
calculus seems so magical

>>11118998
What would be the three dimensional form of trigonometry?

>>11119777
Trigonometry, but with two angles. Do they not teach spheric coordonates in school these days?

>>11119016
>Are you religious?
yes
>If yes, which religion do you follow?
not entirely sure
>How do you see an ascetic life?
very positively

>>11119157
>>11119719
basically this, and you can prove the lemmas in full generality, and explain after how a special case applies to what you actually want to prove

>>11119304
>>11119550
come on, you all know that arguing for or against god is pointless, it devolves to playing with words, without any meaning

>>11119117
might try to write this out later, but on first look, euler-fermat should do the trick

>>11119856
Already tried it, also tried to develop it as a geometric sum, but neither worked.

>>11119016
his: the post

>>11119754
What is an example of it not being intuitive?

Are you talking about the realm of measure theory?

>>11119016
> Are you religious?

Yes

> If yes, which religion do you follow?

I believe in String Theory

>>11119272
>I actually thought about giving up my life into scientific research and saving humanity from itself, then I realized it was just my ego taking over me and decided on a existentialistic approach to life.

Would your waifu approve of your career / performance if she was real?

>>11119851
>arguing for/against theism usually devolves into playing with words without any meaning

I actually agree, and I would go as far as saying that this is a pretty profound observation, but I wouldn't say that means that arguing about it is completely pointless all of the time.

>>11119157
please don't go for the "proving theorem and doing lemmas along the way" stuff, unless you know you can explain everything easily
very often it ends up to be messy, and the proof is scattered throughout the whole paper
I understand the desire to "share your intuition" but I feel like just tried it many times and it is not worth it
remember that most people will just skim through your writing, and barely anyone will read your paper carefully from start to finish. The red style is better suited for such reader.

>>11119205
>stuffing lemmas in appendices
that is an interesting one, I've seen this a lot in CS papers, but almost never in math papers.

>>11120067
Yes

>>11119964
kek

>>11119016
>Are you religious?
yes
>If yes, which religion do you follow?
general theism/monotheism
>How do you see an ascetic life?
i wouldnt mind

>>11120100
I've only ever seen it a handful of times in mathematics, but I really like the idea of stuffing all the proofs in the back of the paper. It's much easier to read things this way because you get what's essentially a very extended abstract up front, so first and foremost you get a solid framework of intuitions about the paper without needing to grind through details of dubious relevance, and then if you're interested, the proofs are there for you to go fill them in.
Everything I've ever read written like this (admittedly very few things) was much easier to work through than stuff written in the standard way.

>>11119754
Pretty much anything involving the material implication is counterintuitive to most people. I'd say this is partly because it has no real counterpart in natural language; e.g. we conflate several notions in the word "if" that don't always agree with its use in logic. Not to mention things like vacuously true statements.

Why is it the last one?

>>11119014
if you want your girlfriend to be both beautiful and intelligent AND competent in a very specific area such as math/physics (and I bet that you also want her to watch anime and shit), your standards are EXTREMELY high. girls like this do exist, but the question is what do YOU have to offer ?

>>11119016
>Are you religious?
Not really.
>If no, then are you an atheist?
No
>If no, then are you agnostic or something equivalent to it?
Yes
>How do you see an ascetic life?
I probably would not be able to go through with it.

>>11119014
Why would you want one? Women exist mainly as a distraction (in a good way) from our main pursuits in life.

can someone teach me math im rly smart just too mentally ill to teach myself

>>11120135
We are reaching the end. The only thing left to finish discussing is god and then we will have covered everything.

>>11120135
I don't know haha. But you're cool. Don't come to uni tommorow.

>>11120327
The thing about learning maths is that ultimately it's a personal struggle. Someone can sit down and walk you through things, explain concepts, etc, but ultimately you won't progress unless you are prepared to fight through things yourself. That feeling of frustration, of uselessness, of stupidity is an integral part of maths and there is no way around that. Grothendieck wasn't the greatest mathematician of the last century because he was a genius, but because he worked ten hours a day for twenty years.

>>11120384
this is true, but guidance is very helpful, especially for someone not born rigorous

>>11120394
>born rigorous
What did he mean by this?

>>11120398
he meant me
I was born rigorous

>>11120394
What do you want to learn anon?

>>11118998
I'm about to go into calculus. what are the best books for reviewing highschool math quickly and effectively?

>>11120569
No need for that, you'll be able to keep up unless you have a big problem with the basics, which would require more than a 'quick' view on high school math.

>>11119774
pls respond

>>11119016
Yes, Muslim.
I think living an ascetic life is a waste of time. Get a wife, live life normally, eat when you are hungry and sleep when you're tired. Lay in bed when you're sick and take care of yourself and enjoy comforts life brings.

>>11120106
>he thinks it’s a joke
Waifuism ain’t a joke either

>>11120184
the same but as a male

>>11119117
dunno, but I'd probs do it by contradiction

>>11119117
Eisenstein's irreducibility criterion

>>11119117
The polynomials
[eqn]Q(x) = \frac{x^q-1}{x-1},P(x) = \frac{(x+q-p)^p-1}{(x+q-p)-1}[/eqn]
cannot have a common root in C, so their GCD is 1 (in Z[x]).
Write [math]a(x)Q(x)+b(x)P(x) = 1[/math], and evaluate at p to show that your two numbers are coprime.

>>11119016
Yes.
Catholic.
I like people, so I wouldn't really go for it.
>>11119110
Absolute kek.
>>11119754
Because you usually need to take a moment and think about why the definition works and what's the point of it, differently from babby calc and linear algebra, where anyone who isn't retarded can instantly grasp the geometry behind things.

>>11121050
i couldnt learn calc...

>>11121050
>I like people, so I wouldn't really go for it.
You could always live amongst other monks.
Also, catholicism is against anime and waifus.

>>11121110
Catholicism is probably the most pro-waifu movement currently on this planet.

>proof starts with "assuming the axiom of choice"

>>11121110
>catholicism is against anime and waifus
What God has put together let no man put asunder.

>>11121138
There's literally no reason to be against the use of the axiom of choice in fucking 2019, researchers will laugh at you if yoh refuse to acknowledge the AoC.

loazer boam burns the infidel

>>11121167
>against the use of the axiom of choice
I'm not though. Writing "assuming the axiom of choice" is the same as writing "assuming [math]\mathbb{N}[/math] exists".

>>11121167
>in fucking 2019
Under what ontological framework is belief in axioms dependent upon the year?

>>11121205
Why don't you suck my dick?

>>11121233
why the homosexuality?

>>11121167
researches in what area? applied mathematics doesn't use the axiom of choice, fuck off

>>11121518
>applied mathematics doesn't use the axiom of choice, fuck off
Stop talking about things you know nothing about.

>>11121138
>proof ends with "a contradiction, therefore the theorem is proved."
AAAAAA

>>11119117
>>11119316
>>11119856
>>11119856
>>11119884
>>11120954
This is Feilt-thompson conjecture, an open problem in mathematics.
>>11120977
I don't know where your proof is wrong, but these two numbers are not necessarily coprimes.
The counterexample is p== 17 and q==3313. The common factor is 112643

>>11119277
Cope

>>11119754
At least you're aware of it. Think of every schmuck that still falls for the gambler's fallacy.

>>11118998
>last one
nice, we finally did all the math?
lets wrap it up lads. job well done.

Anyone coming to Malaga tomorrow? Carles Broto's birthday event.

>>11119016
Atheist. I don't believe in myself.

>>11121640
And on ascetism, it's my way of life.

>>11119297
Crapistan.

>>11121518
>applied mathematics doesn't use the axiom of choice
Yes. Applied mathematicians do not use Analysis, who gives a fuck about DEs, Integration or differentiation anyway? They certainly have no applications in the real world.

When was the latest in your education that you were forced to start producing proofs? I want to compare other's experience because I'm honestly believe we can start teaching proofs much earlier when when I had at least.

I'll offer up my experience first:

High School: No Proofs, basic give problem -> solve problem.

College: Only started doing proofs in Junior year, starting in a specific course meant to introduce proofs using set theory and equivalence relations.

This means that the Calculus courses I took during my Freshman and Sophomore year were effectively taught as I learned math in high school (give problem -> produce solution set). Furthermore, the linear algebra course I took had no proofs in it, it was geared towards engineers so all they did was give problem-> Produce answer, and I can think of only one occasion during my time in that course that I might have proved something trivial about the identity matrix.

>>11121811
>>11121523
? Point me where it uses axiom of choice and no sequential definition of limit does not count, it can be avoided. Functional analysis also does not count, not real maths.

>>11122140
as early as kindergarten, there I proved that God does not exist

>>11122179
>Functional analysis also does not count, not real maths.
Functional analysis is THE most important thing in the modern theory of PDEs, calculus of variation, etc.

Can you even define R without AC?

>>11122140
>When was the latest in your education that you were forced to start producing proofs?
First exercise in University.

>>11122140
If (you include proving the equality of sinusoidal functions (using trig identities) without crossing over the equality){
grade 12
} else{
first semester of uni
}

>>11120398
my first nature was too think nebulously and aurally rather than be able to pinpoint discrete specific concepts

>>11120424
everything, but i guess my main interests are stuff that leads to general relativity, tensor calculus and shit. I also am interested in various wave equations and methods, and wanna get better at pure logic/algebraic reasoning

>>11119042
this is pretty much precisely where i stand as well

Going to do a PhD in Mathematics. I'm pretty interested in Discrete Mathematics and Analysis. What would be a nice field to do a PhD in if I wanted to do industry work afterwards that is not applied? Analytic number theory looks pretty cool but I have never taken a number theory course.

>>11122451
Category theory.

>>11121518
literally all of numerical functional analysis is predicated on cho-
>>11122179
oh
so you're just a complete fucking moron then
listen dude, hahn banach theorem and krein millman theorem are ESSENTIAL to proving the correctness of optimization methods. stop being a fucking dumbass.

>>11122451
Go for analysis. If you really wanna be valued in industry, then specifically probability theory. You will have Jane Street sucking your cock.

>>11122451
PDE’s, numerical analysis, gay homofaggot studies

>>11122461
>>11122464
I want to do government work. Not really interested in the financial sector.
>>11122455
Good meme

>>11119016
everyone who respond to this post, please take your worshipuddle to /his/
thank you
https://www.urbandictionary.com/define.php?term=cuddle%20puddle

>>11122470
If you want to do government work then I don't know what to tell you. What do you think mathematicians do in the government? At best you can be some economic advisor.

>>11122460
I don't get it, how can you prove that a constructive algorithm is correct nonconstructively

>>11122470
Probability, Stochastics models or PDE systems.

Look at Spring series math applied or HPE articles, mostly about solving PDE.

>>11122553
>What do you think mathematicians do in the government?
Generally speaking, the same as their counterparts in the private sector: solving applied math problems.
Except that these problems tend to be about evaluating the possible consequences of new regulations, rather than finding optimal solutions to maximize return.

>>11122451
anything in analysis, MAYBE geometry if you want to somehow into physics. stay away from algebra and foundations.

>>11122631
What about algebraic combinatorics? I double majored in Computer Science, I really enjoy combinatorics. Was thinking Analysis or Combinatorics as possibly avenues.

>>11122640
Tropical Geometry or Combinatorial optimization

>>11122611
I'm just thinking why the government would hire mathematicians. Finance hires because the technical skills are really up to that level, but the government? Even a statistics dropout could do those studies for them.

>>11122684
>I'm just thinking why the government would hire mathematicians
I can't speak for every government of course, but there are areas where the gap between private-sector and public-sector workers is smaller than the popular stereotypes would have you believe (to the point where revolving doors become a cause for concern).
Taxation is an obvious example: just as the big players churn their models to determine which country to stash their wealth in, governments that wish to retain them are effectively forced into doing the same calculations on their end (assuming that they are at least competent, as >>11122470 presumably does when asking about working there).

>>11119016
>Are you religious?
No, although I do believe in myself
>If no, then are you an atheist?
never bothered to define myself, but probably something along the lines of semi-spiritual atheism
>If no, then are you agnostic or something equivalent to it?
nah
>How do you see an ascetic life?
I do like to cater to the needs of ego

>>11122140
In highschool (second last year) we did basic induction proofs. We probably also did some geometry proofs before then. I also did some proofs of correctness in an algorithms subject in final year.

In uni every maths course I've ever taken has been proof based.

>>11122238
the standard axiomatisation of R doesn't need AC i think
>not for the ordered field part
>the Archimedean and Cantor axioms don't need it either
but there will be wierd things

>>11122140
Early high school in my case

>>11121518
>>11121523
This discussion seem bound to fail.

Applied mathematicans surely "use" the axiom of choice, i.e. they implicitly use the choice principle. Whether they get into a situation where what they do couldn't be translated to something constructive is another question
By the same token, applied mathematicans surely don't use "the axiom of choice", i.e. they don't do math and then make an arugment stating "by the axiom of choice..."

>>11121167
>laugh at you
I think it's more like they get angry.

>>11122460
Using Banach spaces doesn't mean you automatically use the axiom of choice - even if people studying Banach spaces like it.
Especially when you come down to using the theory to talking about numerical analysis, all theorems will have proves without choice.

>>11122587
If you use formal axioms to prove something "correct", you're in the formal framework already, and then - given your freely chosen axioms - it will be possible to prove a lot.
Whether there's a system that enables you to proving things correct and that system translating to "correct" in a fundamentally true and real world sense is another story.

>>11122640
If you like analysis and combinatorics you might be interested in looking into analytic combinatorics (very roughly speaking, performing complex analysis on combinatorial generating functions to get bounds or asymptotics on the behaviour of what they're counting). This has piles of applications, but it's most closely tied to algorithm analysis I think.
Algebraic combinatorics is very interesting but it's on the more useless end of things even as far as pure math as a whole goes. It's extremely useless by combinatorial standards.

That said, do not settle for a thesis topic because you think it's better for a job later. You will flop hard if you pick a thesis you don't find interesting enough to obsess over for years on end, and you're not locked out of industry by doing an abstract PhD. I know people who did their PhDs in absolute wank algebraic geometry and still got unsolicited job offers when they were graduating. People who are really good tend to be headhunted regardless of their precise specialty.

>>11122875
>>11123037
Dedekind cuts and equivalence classes of sequences are both fairly moderate.
Many constructive approaches (and/or theoretical type theories) will look like the former, where you first define the rationals [math] { \mathbb Q} [/math] and then look at predicates [math] { \mathbb Q} \to \{0, 1 \} [/math] that consistently cut [math] Q [/math]. E.g.

[math] f : { \mathbb Q} \to \{0, 1 \} [/math]
[math] f(q) := (q \le 2) [/math]

can be used to represent 2.
And

[math] g : { \mathbb Q} \to \{0, 1 \} [/math]
[math] g(q) := (q^3 < 200) [/math]

can be used to represent the cube root of twenty, 5.84804...

The set is then totally ordered by the consistency - any number x so that f(x) is true also has that g(x) is true, because g is bigger (further to the right) than f.
This ordering goes "from negative to positive infinity" on the number line.

What you need choice for is the well ordering of the reals, where you always have a least elements.
You can achieve this formally e.g. by ordering the whole set theoretical universe according to the formulas of sets (Gödel universe), and thus just everything is ordered and hence also the reals. But that's not a natural ordering.

The normal order [math] x\le y [/math] can also be defined as

[math] \exists z.\ x+z^2 = y [/math]

So along those lines, there are direct axiomatizations of the reals, e.g. that of Tarski.
https://en.wikipedia.org/wiki/Tarski%27s_axiomatization_of_the_reals

This is second order, however, while not much less appealing is the first-order theory of the real closed fields. Tarski showed that a huge bulk of geometry is exactly the same if you think of yourself as working with A real closed field
https://en.wikipedia.org/wiki/Real_closed_field

Anyway.
While [math] (x<y) \implies (x<z) \lor (z<y) [/math] is constructively true, the claim
[math] (x<y) \lor (x=y or y<x) [/math] is not decidable.
I.e. you might not want to claim things like
[math] (x<y) \lor \neg (x<y) [/math]

<2 and cube root of two-hundred, that is

>>11123071
David Chalmers lookin ass bitch

Dedekind cuts >>> Cauchy sequences

>>11123294
Cutting yourself >>>>>>>> constructing reals.

Do you guys think the field of reinforcement learning is (applied-)mathematically challenging enough?

>>11123393
>applied math
>challenging
ISHYGDTT

>>11122587
you're proving error bounds for finite dimensional approximations for infinite dimensional linear problems through declaring the existence of certain linear functionals. typically these are just auxilliary for your proof. sometimes they're more important.
when everything's separable, this isn't that crazy. probably just need countable choice. but L^infinity isn't separable.

>>11123037
>Especially when you come down to using the theory to talking about numerical analysis, all theorems will have proves without choice.
you don't know what you're talking about, this is explicitly wrong. literally look at the proof of any error interval for >>11123519 you moron, you use hahn banach constantly. just over and over again.
christ.

>>11122553
what a stupid post you absolute retard

Why yes I assume the existence of infinitely many Woodin cardinals, how could you tell?

>>11122611
>mfw I want to work at a job like this but I'm so retarded I can't find it on the fucking goverment job website

>>11123845
>he thinks you get good jobs by applying to public postings

There are [math]n[/math] obvious embeddings of [math]\Sigma_{n-1}[/math] into [math]\Sigma_n[/math]. Are these all the index [math]n[/math] subgroups?

>>11123538
>you don't know what you're talking about
That's only natural. He's a retarded CS-faggot larping as a mathematician.

>>11123977
>Are these all the index [math]n[/math] subgroups?
What have you tried?

>>11123991
>faggot
Why the homophobia?

>>11123977
Well, if you embed a group H into G, then the image of H is of order |H|. Moreover, if |G| = n! and |H|=(n-1)!, then |G:H|=|G|/|H|=n.

>finally find where I belong
>final thread edition

>>11124165
>>finally find where I belong
Mathematicians use "we", not "I".

> e = mc^2
> light has energy
> light has zero mass
> e = 0 * c^2
> yet e != 0

How

>>11124125
Don't bother responding if you don't have anything to contribute.
>>11124148
Yes, that is both not worth mentioning and implicit in my original post.

>>11124168
I'm sorry, I'll correct myself:

Given a universe where mathematicians refer to themselves singularly, rather than collectively, the following statement is an accurate portrayal of emotion:

>finally a thread where I belong

The proof is trivial, and left as an exercise for the reader.

In all seriousness, I'm an undergrad looking to progress into grad school for mathematics. Glad to find you guys! :D

Threadly reminder to work with physicists.

>>11124195
why do

you teens

type like

this?

>>11124165
It's not that I must, it's that I think it's best if I do.

>the "smart" girl in class got confused in the middle of factoring, of all things

>>11124270
have sex

I finished the syllabus for College Algebra (light green). I did some extra stuff like sequences (dark green).

Should I be good to jump into precalc?

>>11124306
>Should I be good to jump into precalc?
Why don't you try it and find out?

>>11124312
because I don't want to waste months of my life if I should take trig first

>>11124315
>>11124306
This is the precalc book btw

>>11123538
Firstly, using a theorem T (which is proven by a proof which uses choice AC) to prove a proposition P doesn't mean P needs AC to be proven. Your theorem at hand might be provable without it.

Also, why are you so aggressive. If you want to get into a dialog with people, don't call them moron.
Otherwise, learn not to be triggered by people who know less than you.

This is a formal matter, the claim could be stated formally. It might be boring to do, even if you find you don't want to invest the energy to clear this up mathematically, resorting for the third time to proclaim "people don't know what they talk about" won't make them not post shit in the next thread.

>>11124315
>>11124317
that book literally has trig in it you utter moron
>>11124525
never respond to one of my posts again you fucking troglodyte. it's absolutely humiliating to read your responses - i'm embarrassed to be having a "dialogue" with you and i cannot wait for it to end.
listen, if you knew even a SINGLE FUCKING THING about functional analysis, you'd know that it is OBVIOUSLY NOT DIFFICULT to take a theorem which states existence of some interval for some ridiculously high dimensional system and to use it to show existence of choice functions in arbitrary setups. like, that is a braindead obvious equivlance. stop bothering people with your mindless drivel.
>resorting for the third time to proclaim "people don't know what they talk about" won't make them not post shit in the next thread.
yeah, i don't know WHY IT'S NOT FUCKING WORKING, and i'll say it again, you SHITHEADS with your RIDICULOUS ANTI-CHOICE RHETORIC are NOT WELCOME IN /MG/. GO POST IN THE FUCKING ENGINEERING GENERAL.

>>11123977
If n != 6, then yes. Otherwise, there are some other weird examples

>>11124674
>never respond to one of my posts again you fucking troglodyte
how am I supposed to know it's you then?

What makes you people interested in mathematics? How frustrating is it? I'm a NEET looking for an easy hobby since I do nothing but browse the web all day.

>>11124317
ow u supposed tado ellipses if ya slopped it da last tome?

>>11124782
>What makes you people interested in mathematics?
Problem solving gives me d o p a m i n e
>How frustrating is it?
Very

>>11124767
You'll know by him being infinitely more intelligent and knowledgeable on maths than you'll ever be. If I were you, I wouldn't even bother spamming your """constructivist""" (or """intuitionist""", as your kind likes to be called) propaganda on here. Try >>>/g/ instead, it'll be far more fruitful if you spread this filth among your own kind.

>>11124525
>Firstly, using a theorem T (which is proven by a proof which uses choice AC) to prove a proposition P doesn't mean P needs AC to be proven. Your theorem at hand might be provable without it.
This is so deep! Do you mind if I use this as a basis for a paper? I'll properly credit you, of course. Your idea might revolutionize how we preach non-AC math to the so-called mathematicians who use AC for some unknown reason and dogmatically don't want to get rid of it.

>>11124674
You reek of an obnoxious know-it-all. You are quite lucky I am currently way more interested in analyzing Ruffini's writings than I am interested in analyzing yours.

Your kind begins to squirm in quite a funny way when they begin to realize that in some conversations their professional jargon means jack shit, and that literally every phrase they utter can be very effectively debunked, moreso with a vivid demonstration of glaring logical fallacies your "conclusions" rest upon.

It would be wise for you to remember my writing, here, style, and to remember it for later with the intention of never, ever cross my way, if I just so happen to fancy to post here - unless you yourself happen to fancy the notion of floors being thoroughly wiped with yourself.

-another-anon

>>11124200
I tried, they told me to fuck off while they jammed their dick into a Pulsed Laser Deposition System

>>11124873
What the fuck did you just fucking say about me, you little starting condition? I’ll have you know I graduated top of my class in the MIT, and I’ve been initiated in numerous secret techniques on Al-Gebra, and I have over 300 confirmed integrations. I am trained in gorilla mathematics and I’m the top math wiz in the entire set of US computational forces. You are nothing to me but just another equation. I will solve you the fuck out with precision the likes of which has never been seen before on this Earth, mark my fucking definitions. You think you can get away with simplifying that fraction that way over the Internet? Think again, factorial. As we speak I am contacting my secret network of underground mathematicians across the world and your domain is being traced right now so you better prepare for the tangent, maggot. The tangent that wipes out that little unknown variable you call your life.You’re fucking summed, sequence. I can be anywhere, anytime, and I can solve you in over seven hundred ways, and that’s just with my pen and paper. Not only am I extensively trained in calculating by hand, but I have access to the entire arsenal of the Texas Instruments Calculator Corps and I will use it to its full extent to wipe your miserable x's off the face of the page, you little inkstain. If only you could have known what unholy differentiation your little “trigonometric” problem was about to bring down upon you, maybe you would have held your exponential range. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn polynomial. I will prove fury all over you and you will drown in it. You’re solved dead, limit.

what's an explicit choice function for [math]\mathcal{P}(\{1,2\})[/math]? i'm so fucking dumb

>>11124924
never mind , i found one

>>11124926
yay good job!

>>11124930
thanks bro

>>11124782
it's not frustrating if you do maths by yourself but you do, don't you?

>>11123977
Yes, almost always. Let's have a look. For simplicity, I will denote [math]\mathfrak S_n[/math] by [math]G[/math].
If [math]H \le G[/math] has index n, then [math]G[/math] acts by left translation on [math]G/H[/math], a set of cardinal [math]n[/math].
Therefore, we get a morphism [math]\rho: G \to \mathfrak S(G/H)[/math].
We will prove that it is in fact an isomorphism. First, since both sides have order [math]n![/math], it is sufficient that we prove injectivity.
Now, the kernel of this action is the intersection [math]\bigcap_{g \in G} gHg^{-1}[/math]. Indeed, an element [math]x \in G[/math] acts trivially on [math]G/H[/math] if and only if, for each [math]g \in G[/math], [math]xgH = gH[/math], ie. [math] x \in gHg^{-1}[/math].
In particular, the kernel of the action is a normal subgroup of index at least [math]n[/math].
But the only subgroup of [math]\mathfrak S_n[/math] of index [math]\ge n[/math] is the trivial group (for [math]n \ge 5[/math], it follows from the simplicity of [math]\mathfrak A_n[/math] and the rest is checked by inspection).
Hence, [math]\rho[/math] is an isomorphism and maps [math]H[/math] to the stabilizer of the point [math]H \in G/H[/math].
Now, if [math]f: G/H \to \{1, 2, \dots, n\}[/math] is a bijection sending the point [math]H[/math] to [math]n[/math], then the induced isomorphism [math]f_*: \mathfrak S(G/H) \to \mathfrak S_n[/math] maps the stabilizer of [math]H[/math] to the stabilizer of [math]n[/math] in [math]\mathfrak S_n[/math], ie. the image of the standard embedding [math]\mathfrak S_{n-1} \to \mathfrak S_n[/math].
Finally, the composition [math]f_* \circ \rho: G \to G[/math] is an automorphism of [math]G[/math] mapping [math]H[/math] to [math]\mathrm{Stab}_G(n)[/math].

>>11124972
(cont.)
The key fact is that, if [math]n \ne 6[/math], then every automorphism of [math]G[/math] is interior (this is nontrivial).
Hence, if [math]n \ne 6[/math], there exists some [math]g \in G[/math] such that [math]f(x) = gxg^{-1}[/math] for each [math]x \in G[/math]. And therefore [math]H = g^{-1}Stab_G(n) g = Stab_G(g^{-1}(n))[/math], the image of another "obvious embedding".
If [math]n = 6[/math], then there exist some non obvious embeddings.
For example, it can be noted that [math]\mathfrak S_5[/math] has exacly 6 5-Sylow subgroups. The conjugacy action yields a morphism [math]\mathfrak S_5 \to \mathfrak S_6[/math]. Because the action of [math]\mathfrak S_5[/math] on its 5-Sylow is transitive (it is one of the Sylow theorems), the image of this morphism cannot be contained in the stabilizer of a point. Hence, this embedding is not one of the standard ones you talk about.

>>11124972
The important fact is that, if [math]n \ne 6[/math], then every automorphism of [math]G[/math] is interior.
Hence, if [math]n \ne 6[/math], there exists some [math]g \in G[/math] such that [math](f_*\circ \rho)(x) = gxg^{-1}[/math] for each [math]x \in G[/math]. And therefore [math]H = g^{-1}Stab_G(n) g = Stab_G(g(n))[/math], the image of another "obvious embedding".
If [math]n = 6[/math], then there exist some non obvious embeddings.
For example, it can be noted that [math]\mathfrak S_5[/math] has exacly 6 5-Sylow subgroups. The conjugacy action yields a morphism [math]\mathfrak S_5 \to \mathfrak S_6[/math]. Because the action of [math]\mathfrak S_5[/math] on its 5-Sylow is transitive (it is one of the Sylow theorems), the image of this morphism cannot be contained in the stabilizer of a point. Hence, this embedding is not one of the standard ones you talk about.

>>11124674
I know it has trig in it, cunt. It also has algebra in it, but for example it starts with linear equations in two variables which would be a lot harder to grasp without first starting in, and understanding, linear equations in one variable.

>>11124306
>College Algebra
Kek, that's baby level algebra, college algebra is theory of groups and rings, not that preborn level shit.

>>11125065
http://professorconfess.blogspot.com/2013/06/all-remedial-classes-in-one-place.html

Any new developments in mochizuki's IUTT? Is it really just a pile of masturbatory obscurantist theory with no application?

>>11125150
>Passing rates in College Algebra courses usually run a bit more than 50%, although not much more (at one state university, the rate went from 50% to above 85% from one semester to the next, due to extensive pressure and threats from administration to pass more students).
I would be shocked if 50% of my class passed. About 20% have withdrawn in the last 2 weeks

I'm working through Linear algebra done right, making sure that I can prove nearly any theorem presented. When I'm asked to provide a proof that the book it's self does not provide, how do I ensure its correct?

>>11125165
>When I'm asked to provide a proof that the book it's self does not provide, how do I ensure its correct?
I don't understand the question. It's correct if the proof is correct.

>always get supplementary angles and complimentary angles mixed up

>>11125190
Supplement: what you need because you're an unhealthy, fat virgin.
Compliment: what you won't get because you're an unhealthy, fat virgin.
Easy as that.

>>11125190
>Can't remember what surjective or injective it

>>11125165
>how do I ensure its correct?
Bei your own critic.

>>11124972
Man, fuck a number [math]6[/math].

>>11125217
Just bee urself :)

>>11124905
This is so over done. Embarrassing.

>>11125165
google fitch-style rules of logic + how to make new definitions and check them for their correctness.

>>11124924
If you know that a set can be ordered (wherever you got that information from), then "take the smallest w.r.t. the order" always works for a choice.

>>11125173
True, but is it easier to verify a proof then to reprove that it's correct?

>>11125160
I had to curve the college algebra class I taught because only 30% passed due to not wanting to fight administration on the issue. Imo math classes at the freshman level should never be curved to at least filter out the people who can't sit down and study a single subject for a bare minimum of 2 hours a day.

Let [math]\langle V,||\cdot ||\rangle[/math] be a normed space and [math](f_n)_{n\in \mathbb N}[/math] a sequence of bounded linear operators that converges to [math]f[/math] *in operator norm*. Suppose that [math]\lim_{n \to \infty} v_n = v[/math] for some sequence of vectors. Must then [math]\lim_{n \to \infty} ||f_n v_n -fv|| = 0[/math]?

Triangle inequality yields [math]||f_n v_n -fv|| \leq ||f_n v_n -fv_n || + ||fv_n - fv||[/math]. It's straightforward to show that [math]||fv_n -fv||[/math] tends to 0, but I'm struggling to show the same for the left summand. I've tried to find counterexamples too, considering all sorts of infinite dimensional / incomplete normed spaces and whacky linear operators on them, but to no avail.

Hints appreciated

>>11125600

Help!

>>11125334
No, I am serious here. Look at your own arguments and try if you can tear them apart, that is also how you learn.

>>11119016
>Do you love Emilia?
Yes I Do.

>>11125165
>>11125362
0 |__󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡󠛡 󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡󠛡󠛡 󠛡[assumption, want P iff not not P]
1 |󠛡 󠛡󠛡 󠛡󠛡󠛡 󠛡 󠛡󠛡󠛡󠛡 󠛡|__ P󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡 󠛡󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡[assumption, want not not P]
2 |󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡|󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡|__ not P󠛡 󠛡󠛡 󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡󠛡 󠛡󠛡 󠛡 󠛡󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡[assumption, for reductio]
3 |󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡|󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡|󠛡 󠛡󠛡 󠛡󠛡 󠛡contradiction󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡[contradiction introduction: 1, 2]
4 |󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡| not not P󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡 󠛡󠛡󠛡󠛡 󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡[negation introduction: 2]
󠛡 󠛡󠛡󠛡 󠛡 󠛡|
5 |󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡|__ not not P󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡[assumption, want P]
6 |󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡| P󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡 󠛡󠛡 󠛡󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡[negation elimination: 5]
󠛡 󠛡󠛡 󠛡󠛡 󠛡|
7 |󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡P iff not not P󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡 󠛡󠛡󠛡 󠛡󠛡 󠛡 󠛡󠛡󠛡 󠛡󠛡 [biconditional introduction: 1 - 4, 5 - 6]

>>11126018
Hopefully, maybe one day mathematicians will fast-forward to the 21st century...

Inductive syntax + binders, that's called the λ-calculus.

Therefore, use Coq to show your theorems and that you ain't afraid of cyberpunk mathematics.

where can I find more information on the elusive well-order of the reals?

>>11126094
But muh human verification

>>11126113
Some of it is here
https://math.stackexchange.com/questions/6501/is-there-a-known-well-ordering-of-the-reals

tl;dr
It's consistent with ZF that there is no formula for the well ordering (and so ZF doesn't let you write one down).
If you adopt the axiom of choice, then this still holds true: It's consistent with ZFC that there is no formula for for the well ordering. But in that case, the well ordering provably exists (in this unrealizable way).

To elaborate on the "positive" result in that thread: If you think of V as the class of all sets allowed by your axioms, then you might allow yourself some ordinal jumps and then within V take a look at the empty set and then all the sets for which you can at least give a first-order definition in terms of what you already have defined. That collection is called L and corresponds to what you can define in terms of pic related.
The axiom V=L amounts to saying that you just discard anything in V not captured by this L.
So in L, you can think of all sets being put in ordinal stages and also associated with some smallest formula. So, roughly, your complex set theoretical universe (L with V=L) is well ordered!
(So V=L also proves the axiom of chocie, because, roughly, you can use that overall order. L is by no means constructive, but at least has a definable flavour in principle.)
And since all sets are ordered in L, i.e. any element has a position in the overall order, any set is also ordered via this order. And since L is a model of ZFC, it has all mathematical objects that V_{w+w} has, i.e. all you might practically need, and in particular (any definition of) the reals. Naturally, apriori there's no reason to think 5.346*pi (some gigantic set if you e.g. use equivalence classes of Cauchy sequences to define this number) comes before 6357547*e^2 in this order of L. So it's not, like, some arithmetic ordering.

https://en.wikipedia.org/wiki/G%C3%B6del_operation
https://en.wikipedia.org/wiki/Constructible_universe

>>11126277
Roughly again, if that's not clear, L is well ordered because the sets all have formulas tied to them (the sets for which this is the case are exactly those of L) and so you can think about enumerting the formulas for them, and thus the sets itself.

>>11126277
But this is just for the reals of L.
Set theory can't regulate the size of 2^N against the side of ordinals. I.e. the quantity of subsets of N isn't something you can give a sensible upper limit to (if you adopt the continuum hypothesis as axiom, though, it's as small as it could legally be).
The conceivable reals of V might be quite different from the definable ones (in L)

>>11125165
Find someone knowledgeable to critique your proof.

>>11126364
So stack exchange

https://arxiv.org/pdf/1911.02400.pdf
>Proof of the Collatz Conjecture
>Agelos Kratimenos
>(Submitted on 4 Nov 2019)

>Collatz Conjecture is one of the most famous, for its simple form, proposed more than eighty years ago. This paper presents a full attempt to prove the affirmative answer to the question proposed by the conjecture. In the first section, we propose a number of definitions utilized later on the proof. In the second section, we discover the formula for a characteristic function. This formula describes the functionality of the paths taken for each number based on the Collatz Sequence. In the last section, we prove that every number will eventually reach 1, using the characteristic function.

>mfw dead on my feet
>>11124182
IIRC That's the approximation, not the full equation.
>>11126491
>>>/sci/sqt/ and quora also work, if it's babby linear algebra.
>>11126573
>greek name
Oh no.

>>11126583
Oh, yeah, here we go.
https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation
E^2 = (pc)^2 + (mc)^2
The mass vanishes, so it becomes E = pc.

>>11126573
seems like baloney

>>11126004
Make lugnica great again!

First for the Riemann hypothesis is false.

>>11126941
>first
You're not very good at this anon...

What are the prerequisites for learning set theory? I read it helps with everything else. I haven't done calculus yet but I'll start Strang's linear algebra at the end of the month

>>11126573
It's almost certainly not true, but I like believing that at some point in history by some fluke one of these "push symbols around randomly until the answer magically falls out" crank proofs was actually correct and no one will ever know because nobody wastes their time checking all of these.

>>11127044
>I read it helps with everything else.
I don't know where you read this but it's not really true. 99% of set theory is autism only interesting to set theorists. For anyone else, all you need is the most basic 1% of set theoretic definitions, and whatever set theory you need will be taught to you in piecemeal in other courses as it's needed.

Set theory doesn't have "prerequisites" in the literal sense of the word; an intro set theory book won't refer to necessary knowledge from outside the book.
But I probably wouldn't try to study it until after the first semester of analysis unless you're really motivated to for some reason. I don't think that thinking about completely abstract sets would be particularly enlightening (or interesting) for most people until they've done the set stuff at the beginning of a real analysis class.

>>11127044
>What are the prerequisites for learning set theory?
See theory consists of two parts. The most important foundation for modern mathematics that is usually taught in the first two weeks of any math degree and super extreme autism the field.

The first isn't hard and has basically no prerequisite, if you have a basic grasp of logic you are fine and the second requires you to have developed severe braindamage.

>>11127044
Not much. Predicate logic can help.
You need a tiny bit more than the basic only for topology and measure theory.

How could I stop comparing to myself to my peers when I'm reminded of my inferiority every time I discuss mathematics with them? I never have insight to offer and I always struggle to keep up with them. How am I supposed to be confident in myself as a mathematician? There seems to be nothing in this subject that I am good at.

>>11127353
Everyone can find a niche. Your brain is probably capable of fathoming at least one thing more accurately than theirs. Become a pro at that, then when you talk about your special brand of autism playtime they won't be able to keep up with you

>>11127353
Find out what they don't do, specialize in that, make them all feel dumb when you win the fields medal for topographically mapping the area around your anus to your benis

>>11127364
>when you win the fields medal for topographically mapping the area around your anus to your benis
kek

>>11127353
Enjoy math. Don't worry.

I'm trying to find a paper to submit a paper for the first time. Do you guys have some general tips for me?

Let's say I have two journals in mind with similar impact factor. The first one published x papers last year and the second one published 5x papers in the same period. So I have bigger chances of acceptance with the second one? Or am I just going crazy?

>>11127542
More detail please. IRB research paper?

>>11127353
Just do math for fun

I need to get better at basic math things again. By that I mean manipulating equations or therms, simplify things, basically being able to use all the rules for fractions, for potencys etc. to my advantage.
I dont know how exactly this type of knowledge is called, but is there a online course or book for recap all these things i never properly learned?

Aluffi for a first algebra book?

>>11127669
Precalculus, try Axler's book by the same name, you can skip sections you don't find useful.

>>11127671
The Summer before I entered grad school, I realized I knew basically no algebra (my undergrad used Hungerford - Abstract Algebra; no, that's not the good Hungerford), and I spent the summer reading Aluffi, doing every exercise. It worked well for me, I'd recommend it. But skip the chapter on homological algebra, it's not written nearly as well.

>>11127671
Totally first? Aluffi will assume a good bit more mathematical maturity beyond what most would have before taking their very basic groups/rings/fields. Are you asking to fill in, and have some mathematical background?
If the highest math you've done is some sort of linear algebra, probably go with Artin. It's more of a standard undergraduate text.

>>11127671
Read Bourbaki.

>[math]\sin^2(x) = \sin(x)^2[/math]
>[math]\sin^{-1}(x)\neq\sin(x)^{-1}[/math]
Whoever writes textbooks needs to be shot.
t. calculus TA

>>11127861
I've done Tao analysis I and linear algebra done wrong by Treil

>>11123294
Dedekind cuts are a meme. People approach irrationals with limits, not chopping the number line in two.

How do I use active recall in math to learn things?

>>11128251
Just use Total Recall.

>>11128267
got it, what's next?

>>11127935
The person writing the textbook didn't create the conventions (which existed long before the author was born).

Mathematical conventions are full of quirks and inconsistencies. Yet it's still much cleaner than the English language, and most of us manage to cope with that somehow.

>>11119004
>>11119138
Don't listen to this faggot, he's just jealous and probably gay.

>>11127608
It is a pure Math paper. In the end, I whored myself to a teacher for a recommendation to a shitty journal. Starting to get tired of this academic bullshit.

Suppose you have an unbounded supply of black and white balls. How many ways are there to arrange [math]2 \leq n[/math] balls in a row, such that (at least) two consecutive balls are black?

Thank you for being smarter than me.

>>11128599
Coding up

hasTwoBlacks[list_] := MemberQ[Table[list[[i]] + list[[i + 1]], {i, 1, Length@list - 1}], 2 b]
Table[Length@Select[Tuples[{w, b}, n], hasTwoBlacks], {n, 1, 15}]

in Mathematica returns
{0, 1, 3, 8, 19, 43, 94, 201, 423, 880, 1815, 3719, 7582, 15397, 31171}

and searching this on OEIS gives
https://oeis.org/A008466

>a(n) = 2^n - Fibonacci(n+2)

There are some references on the bottom of it, but none seem to spell it out nicely. I think the approach would be to create your formula by summing over all pairing positions (call it pivot pair) from left to right in the row, leaving the right of each pivot pair generic but restricting the left of each pivot pair to not have any pair.

>>11128563
He seemed sympathetic enough. I also need to lose weight again.

>>11128643
PS I now see plugging in three and four consecutives, etc., leads to 2^n minus the "Tribonacci numbers" and "Tetranacci numbers",...
https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Fibonacci_numbers_of_higher_order
So it's likely that the best way is to count the configurations that fail to have a pair and those are then Fibonaccis.

You can also consider the alphabet of more than two different colors and OEIS gote you covered. E.g., e.g., 3 colors and 3 consecutives
https://oeis.org/search?q=0%2C+0%2C+1%2C+5%2C+21%2C+81%2C+295%2C+1037%2C+3555%2C+11961&sort=&language=&go=Search

>>11119016
I'm an agnostic atheist. I don't know that there is no god or gods (agnostic), but there isn't sufficient evidence to make me believe in a god or gods (atheist) either.

Does it make sense to take a tenure position at a 'worse' school if you have multiple offers? eg. Terry Tao with UCLA vs say... Princeton.

>>11128549
No, quit acting retarded. It is entirely the fault of the textbook companies for choosing to stick with the [math]\sin^{-1}[/math] notation instead of using the now more common [math]\arcsin[/math]. There are already a dozen reasons why the people in these textbook cartels should be dragged out behind the barn and shot, you don't need to grab at straws to defend these wastes of oxygen.

>>11129171
Differences in "rank" between very top schools don't mean much to begin with, even to the average joe, and they mean even less once you've reached the point of your career where you have a substantial body of work and meaningful references instead of just "degree from X" like in undergrad.
For the .1% of rockstars who are good enough to be choosing between multiple offers at tier 1 schools, it's sure as hell not going to make a lick of difference to their career if they choose a better offer at the #7 school in the world instead of #4.

>>11129191
> choosing to stick with the [math]\sin^{-1}[/math] notation
Uh, that one's perfectly legitimate. It's using sin^2(x) to mean sin(x)^2 (when it should mean sin(sin(x))) that's the problem.

Also: path dependence is a real thing. You can shoot the textbook authors *after* we've dealt with the people still making staggered keyboards.

>>11127353
talk with them more, it's the only way to catch up
listen, ask about things you hear that interest you, and make an effort to understand
you'll start to catch up after a while, and suddenly other people will feel the way you do, but now about you.

>>11127940
Then sure, go for aluffi. You probably don't need hand holding. But don't expect to have any clue what's going on at first.

>>11128243
people approach reals with the least upper bound property (dedekind cuts)

>>11129599
I like the Dedekind reals more, because you can view them as simple black/while left/right predicate, i.e. decision predicate, i.e. characteristic functions, and then the cardinality {0,1}^Q becomes quite evident (as opposed to sequence definitions).
Nevertheless, I think to say people (normal mathematicans) approach them with the upper bound property in mind may be an overstatement. Maybe topologists do. Most will just reason about the reals with a simple closure property in mind that grants existence upon the well-definedness of a number. An it-just-werks kind of attitude: A well defined number without imaginary part is "just there, for sure".
I think in the future, people will go from decision predicate to the actual decision procedure and work with numbers in a more intricate framework.

Is the Inclusion–exclusion principle fascist?

Why does nobody properly govern the speech of the mathematicans.

>>11130250
>Why does nobody properly govern the speech of the mathematicans.
Because we have to do one thing after the other, speech police can't be everywhere at once.

>>11125165
linear algebra prof.

>>11125190
>always forget how to interpret necessary and sufficient conditions

>>11130853
Which kinda?
You either get one who teaches it to engineers and has no fucking clue about anything beyond how to multiply two matrices together or someone who can actually do linear algebra

my algebra teacher started talking to me about how great trigonometry is and talking about sine and cosine and chief krakatoa and I had no idea what the fuck she was talking about

>>11118998
"ergodic" is just a fancy word for "frequentist", aint it?

>>11131047
Ergodic is a property of a system, frequentist is a stream of philosophy of math.
So not sure what you mean. I suppose math coming out of frequentist thinking about statistics helps working out properties in ergodic theory.

>>11125165
see if you can find the question in math.StackExchange; even if it's correct you might find a shorter/more elegant proof. ask your prof only if he's a competent guy and if you're really unsure of the validity of your work.

Can we stop the rote memorization is bad meme? Why are alll mathematicians so anal about Math not being about memorization. Yes, it does entail a certain bit if memorization in order to understand the arbitrairy symbol pushing rules.

>>11125173
But it's not necessarily correct if you only _believe_ it's correct. Comparing your proof to the solution gives you peace of mind.

>>11127542
>>11128571
here's how things should go:
go to your teacher, ask him if it's worth publishing
if he doesn't like it, just give up
if it's worth publishing, he will check the paper and tell you where to publish
there's no shame in asking, especially if it's your first paper

Now that the thread's ending, I just wanted to say I'll miss you lads.

>>11131701
You too, bud. It was a pleasure shitposting with you. Sleep tight.

How do I become smart enough to make new math?

>>11119016
>Are you religious?
>If yes, which religion do you follow?
>If no, then are you an atheist?
>If no, then are you agnostic or something equivalent to it?
It depends on what you mean by "religious". I was raised a catholic and my mom would always bring me to church. I would always love go to church because there were other kids and they would give me bread and chocolate milk. I don't say with absolute certainty that there is a god or not but, however, I'm more inclined to believe there isn't. I can make any claim whatsoever that's basically unprovable and it would hold as much weight as the god argument. That being said, the fact that countless lives and thousands of years of literature pointing to a god seems odd. I wouldnt call it conclusive evidence but it makes you think. Also i dont really lean to a particular side because all the arguments i hear leveled against the opposite side are more a critique of large groups of people and not so much the actual theory behind the concept. Same thing happens with politics. The problem is not so much religion or new age atheism but rather the masses. The bulk of people is dumb and lazy, and would rather burn people or become close minded than even giving an inch to the other side.
>How do you see an ascetic life?
I dont know what that is.

>>11131939
Same guy. Just read what ascetic life is. I personally think that an ascetic lifestyle can lead to great acomplishments but that it isnt extremely neccesary. I dont know if i would be able to live in such a manner. I wasnt raised with much money and had already gone through hard stuff, which isnt meant to be a selfpitting comment, its just that that gives me less patience to deal with stuff. I wouldnt want to make my life any harder.

>>11126573
literally the first formula is wrong, kek

>>11131997
Lma fucking o

>>11131258
>Why are alll mathematicians so anal about Math not being about memorization.
Yes, obviously knowledge requires memorization of things.

>arbitrairy symbol pushing rules.
They are NOT arbitrary and you should at least know when to apply them and even better understand why they are true.

>>11131258
>Yes, it does entail a certain bit if memorization
Well no shit, retard

>>11131258
>prime numbers?
>yeah, bro! that's it! I like single diget numbers too!

How do I get better at math?

>>11133328
amphetamines

>>11131997
so it's all ogre

>>11133328
https://www.youtube.com/watch?v=SlCRfTmBSGs

>>11119016
I come here once in a while, I'm Catholic but not devote

k i know you guys are just gonna be bullies, but how do you study? like my book is open right now, how would you proceed?

for a trainwreck like myself:
>read chapter, interact with theorems/lemmas etc (i.e, try proving them, stretching them out like the little sluts they are, etc) and keep previous material in mind when doing so
>do scratchwork problems on blank printer paper, usually kept around in a gross pile anywhere from a week to a month
>write down final proof in composition notebook (so they stay together)
>flag any problems for review/retry on the laptop, also notes/references I'd like to keep around, especially for tricky problems n stuff
>repeat flagged problems next session

if the book doesn't have an answer key, i try and keep my final proofs on the laptop. do you guys keep the scratchwork? I feel like it's valuable in some sense, but idk.

for additional info, i do most my studying in a big fat AM chunk, then again after my nap around 3:30. any tips? I always feel like I'm a disorganized, inefficient mess

>>11133780
and when I get stuck on a problem and must resort to searching the solution, I try to only give myself tiny little breadcrumbs at a time. Sometimes I'll have the patience to be stuck for a whole week, other times I don't even last 15 minutes.

>>11133780
>>11133797
i listen to pink noise when i study, sometimes ambient (like Loscil) or other very subtle music like loop based stuff (like this: https://www.youtube.com/watch?v=0GKHaQ2MpuI))

>>11133780
>>11133797
>>11133803
and also, obviously when I'm hard stuck there's no other choice but to shitpost on here, irc and stack exchange. getting proofs reviewed is important

>>11133780
You study like you have a vagina.

>>11133861
well then give me some tips, that's very literally what I'm asking and why i typed this out

>>11133870
The "tip" implicit in that joke is that you're spending a lot of your time doing minimal-value busywork that makes your studying sound good, which is something I guarantee you most of the women in your department do (how many of the girls in your classes show up to lectures with a pencilcase that has multiple shades of highlighter in it?)
You could get at least a couple extra hours of math in per chapter if you cut out all the planning and transcribing and meticulous organizing of stuff and just focused your time on reading and thinking about the chapter and then solving the problems.

>>11133940
i agree. but this really only applies to the notebook, right? i only just started doing this after being fed up with searching through piles-of-shit scratchwork.

when i don't organize, it's hard to track what i needed to work on, or when i look back on it later, what supplementary material or thoughts were helpful. it really doesn't take long to add a line in a file on a computer saying "retry problem 13", "read more about y" or "this is like thing x". overall I very much agree with what you're saying, though, and trying to maximize the max-value work is what I'd like to go for. it's not like my notes are excessive or anything, and the flagged problems or whatever help increase my value work, i think

so, do you do no sort of organization in your studying? just open book, work, close book and repeat later? i did this for awhile, but things got a little unwieldy

>>11133960
I do essentially no formal (i.e. outside of my head) organization at all, but I'm aware I'm a little bit extreme in that regard. There's a different spot on the slider between total chaos and full-blown autism that works for each person, and since you're fairly far on the anal side at the moment and it's not working too well (else, why would you ask) it seems natural to try relaxing somewhat.

You're right, the biggest thing I'm referring to is the re-copying of finished proofs (I would need convincing that this isn't completely useless).
But depending on your course level, I think even the idea of flagging and repeating exercises isn't very useful. Spaced repetition is not the best way to approach abstract math. It's a good method for training _techniques_, because when you do the same thing over and over again your brain falls into a groove and starts doing it unconsciously. This is good for getting good at integrals, for example, but it's not very good for building concepts, because going through the motions of not understanding something will just get you really fast at not understanding it.
If you find a gap in understanding, there's no reason not to stop and address it right away while it's the freshest thing in your head rather than delaying fixing it until the next study session. I think this is fundamentally a better way of learning stuff, but it also gets rid of the redundancy in the middle of of "notice problem -> plan to address later -> address problem"

>>11133940
desu, most of what i wrote was my "idealized" form of studying; i don't really keep type up solutions like I mentioned, but when I'm trying my best to be organized I do, and I'll stop doing that in favor of just working. I'm just going to start keeping all my work in a composition notebook (including theorem and problem scratch work), but I'm still going to flag important tasks for later on the pc, along with keeping supplementary material and references in one place, as this is so fast and painless to do, and often very helpful for me. gg anon

>>11134004
when i was doing classes i was more like you and had no formal system either other than a reluctance to take notes in favor of active listening during lecture and active problem solving instead of copying stuff down. i've been on a weird organizational bender lately and it has not been helpful for studying in the least (it worked very well for managing my professional life, so i thought i could take the same concepts and see the same benefits here), i'm going to start cooling off it for this stuff now but it's been hard to let myself unorganize now because I've had this weird feeling it will pay off when i develop a very efficient smooth system, but i'm seeing more and more it's just cluttering my goal.

very helpful input about spaced repitition, thanks (this was also something that was more an "idealized" form of my studying habits than true, but i was planning on setting up a better system for this today, i will not now). i don't mean to get all weird on you, but i feel very uplifted and relieved now, like a great tension has been released.

>>11133780

i just open the book and start reading, front to back. if there's something i don't fully understand, i try to work it out on paper. sometimes i'll try to recall all the steps of a proof or several proofs in a chapter. sometimes i do exercises.

but i try not to avoid parts that i don't understand.

>>11133780
I liked the prose

>>11133803
>pink noise
Fuck this is patrician

>>11118998
Someone pls help with this problem:

Given:
[eqn]C(p) = \int \limits_{0}^{p} \cos{\big( \frac{\pi t^2}{2} \big)} dt[/eqn]
and
[eqn]S(p) = \int \limits_{0}^{p} \sin{\big( \frac{\pi t^2}{2} \big)} dt[/eqn]
prove using maclauring series and integration that:
[eqn]C(p) + jS(p) = \displaystyle \sum_{n=0}^{\infty} \frac{(j\pi/2)^np^{2n+1}}{n!(2n + 1)}[/eqn]

>>11134876
>Someone pls help with this problem:
>Given:
>C(p)=∫0pcos(πt22)dt
>and
>S(p)=∫0psin(πt22)dt
>prove using maclauring series and integration that:
>C(p)+jS(p)=∑n=0∞(jπ/2)np2n+1n!(2n+1)
What have you tried?

>>11134883
Pls no troll answers

How do I eve start? Im thinking of trying to write C and S as series but how the fuck do I even do that? Maybe (most likely) im just thick as a brick and not seeing something

>>11131258
It's just backlash against educators pushing memorization of pointless things like FOIL or the Reciprocal Derivative Rule.

>>11134876
see
>>11134939

>>11131754
You too, lad.
>>11134876
Please don't repost calc problems to /mg/, specially in the last thread.

Are there any good books on set functions?

>>11135308
No, those books were destroyed in the schism of 1998

>>11134876
are there any tricks to do w squaring it?

>>11134004
copying proofs is only good if you have a strong intuition between your mind and penpaper. im much better at writing and math on my phone because i use it more than keyboards or pen

/mg/pill me on motives

reminder godels ontolgical proof shows that angels and demons exist

>>11135555
godel was a hack in general. wasted quads.

>>11135555
proof?

>>11135535
is motive a mathematical term or like, youe motivation for life

bros... I started late on the math party. Is it true that you get worse at math as you age? I really want to get a PhD and work on making new maths.

>>11135585
>>11135589
Angels and demons are traditionally defined as good beings, that are naturally greater then humans, but not as good as maximally good beings such as god. ie angel is an object thats contains only positive properties or elements, but does not contain the essense of godlike ness. This means angels are contingent aswell

>>11135620
you didnt prove shit

>>11135608
you only get worse with age if you get stupider with age. now that bits up to you

>>11135626
consider subsets of any godlike objects. Angels are essentially "near misses" of god. Demons are "barley positive" etc. Depending on ones aesthetic views and assignments of positive and negative you can even identify how many Angels or demons exist.

Also the proof proves monotheism (though this has lots of proofs)

>>11135626
The interesting part as I said is that Angels and Demons don't exist by necessity, it is conceivable they dont exist in this world

brainlet here
trying to figure out where to even pickup lessons(mostly khan academy) on simplifying this:
x2 -3x +1 = 0
I think i can do
x2 +1 = 3x
so which one do I click on in pic that will help me further this? the end result is asking for x +1 over x = ?

>>11135922
that x2 is x squared

>>11135922
https://www.mathsisfun.com/algebra/factoring.html

Anyone coming to TMGRT2019 next week?

How did [eqn]x+40/100(8-x) = 90/100.8[/eqn] transformed into this equivalent equation [eqn]x+40/100.8 -40/100x = 90/100.8[/eqn] wich amounts to [eqn]60/100x = 50/100.8[/eqn] and well I know the result, it's [eqn]x = 400/60 = 20/3[/eqn], but what I wanna know is how that transformation occurred.

And that 100.8 is not a decimal. The 8 is multiplying the fractions. Just to makes sure, you never know.

>>11136497
> How did [eqn]x+40/100(8-x) = 90/100.8[/eqn] transformed into this equivalent equation [eqn]x+40/100.8 -40/100x = 90/100.8[/eqn]
Those two are not equivalent.

>>11119016
I am not religious. I am not an atheist. I am not agnostic. Ascetic life is the most healthy way to be, as studies have repeatedly shown that pursuit of pleasure as an endgoal is not successful. Sexual pleasure, in particular, diminishes your oxytocin sensitivity and damages your ability to form meaningful connections.

>>11122587
"I don't get it" is not a valid argument in mathematics.

>>11136975
Shit that's why I wasn't able to figure out this way. I reduced the fractions and got it right. But the book shows this way od solving it. I was able to figure but something was weird, I couldn't make sense of this method used