/sci/ - Science & Math

>>12011389
>Elliptic curves

>>12011399
Based

What do you do when you are working on your research, and stumble upon a problem (worth a lemma) from a different branch that you are not familiar with?
Read books, do exercise, learn relevant ideas just to prove a lemma? This might take 6 months.
Consult other people in that field?
It's my situation right now

>>12011407
step 1: google
step 2: ask your colleagues

>>12011399
I don't get this. Are you praising elliptic curves or making fun of it?

Is /mg/ formalist, Platonist, intuitionist, or something else?

>>12011435
Platonist

>>12011435
Platonist.
formalists are autists and intuitionists are antisemites

>>12011435
I don't give a shit about philosophy. I prefer to do math.

>>12011474
Math is philosophy.

>>12011477
Math is the opposite of philosophy. Math uses logical deduction to show that some statements are in fact true. Philosophy on the other hand is just bullshitting about how you cannot know nothing and everything is subjective and truth doesn't exist.

>>12011435
Stoic.

>>12011489
You sound exactly like someone who had never read a philosophy book, and all of the ideas about philosophy you got is from /sci/.

>>12011489

>>12011496
I have read enough philosophy books. The only philosophy worth mentioning has been settled in the 19th century. After the year 1900 philosophy became obsolete thanks to progress in math and science.

>>12011399

>>12011435
i am INTERNATIONAL MATH OLYMPIST
I DAB ON UR PHILOSOPHICAL DILLEMAS
UR TOO DUMB 4 COMBINATORICS HENCE STOP DREAMING ABOUT INFINITE SETS

>>12011505
Then how can you say philosophy is the opposite of math. I don't get it. What did you even read?
Earlier you said that in philosophy,and truth doesn't exist. But if you read about most schools of philosophy, they always establish a set of axioms and build everything else around it. Logical reasoning is still there.
Also, no one was really arguing about modern philosophy. I agree that it's garbage but that doesn't mean all old philosophy = worthless.

Anyone feels like you can do math better when you do them in cycles?
There are some problems that I got stuck with for a week or two. When I visited it a few months later, I was able to do it instantly.
It's weird. I guess for my case, doing math is like an upward spiraling staircase.

>>12011542
That's called life, anon.

>>12011549
Well I thought it was just me. If that's the case I would have changed my workflow for the better. Earlier this year I was continuously agonizing over some problems for weeks to no avail.

Why are peer reviews so fucking slow? Maybe somebody should pay them so they speed up. I hate this retarded system.

>>12011435
Childhood is when you idolize Brouwer. Adulthood is when you realize that Hilbert make more sense.

>>12011389
does someone know where I can find a list of the [math]H_k(K(Z,3)) [/math] that is a bit longer? I know that they're computed entirely in H. Cartan's seminar but it's very hard to read for me because I don't know french

>know 3 people from undergrad that went to accelerated math high schools, did competitive mathematics, got perfect grades etc.
>all 3 now work as software developers. They never published a single paper.
>me, a literal midwit, is chugging along with my PhD. 4 published papers so far.
Is being a midwit key to being a math researcher?

>>12011712
Yes.

>>12011435
formalist
anything else isnt math by definition

>>12011712
Unironically yes. It's really more about commitment and curiosity then being an academic drone. These people become frail when they realize research isn't vomiting the textbook up on paper.

>>12011712
Midwit + having enough grit.

>>12011800
Gritwit
Where’s my Reddit gold

>>12011804

>>12011712
What field do you work on?
My belief is that there are fields in which I can never contribute because I'm a brainlet.

>>12011810
Algebra

>>12011826
Nice.

>>12011489
>>12011505
You sound like you have no idea what philosophy even is

>>12012123
>you sound like you have no idea what philosophy even is
>never expounds on what it is
>just shits on other people
>acts like a retard
>thinks hes diogenes
>he does it for free
how many times are you going to make this same post

>>12011525
There's as much logic in philosophy as there is in law, which is to say that philosophers and lawyers consider themselves logical but they don't do anything close to rigorous logic most of the time.

>>12012134
I'm not the other guy, calm down geez, you're gonna pop something

Whats the favorite branch of math of someone who is jacked and good at sports? Is it combinatorics?

>>12012173
Algebra

>>12012173
Stats. Those sports guys are always talking about their favorite sports guy's stats

>>12011505
>After the year 1900 philosophy became obsolete thanks to progress in math and science.
Not even wrong

>>12011435
half a step between intuitionist and Platonist

I am a brainlet high school dropout and I'm trying to build an air conditioner out of a table fan and bottled water. I'm using a 2 liter bottle of coke replaced with water and it calls for 1 cup of rock salt and 5 cups of water. How many tablespoons of table salt equals 1 cup of rock salt?

>>12012154
what about my post seems aggravated to you?

>>12012241
What have you tried?

c. 212 B.C.: Do not disturb my circles.

c. 2012 A.D.: Do not disturb my picking of mushrooms.

>>12012295
I wonder how successfull that session was.

>>12012274
Not him, but the "does it for free" part.
Any mention of doing it for free outside of the janitorial staff context makes me think of some sort of anger.
You just sound mildly angry to me, however.

>>12012295
Assuming you're posting this because of the recent video of that scottish fag, I need to say that it was really really bad.

>>12012314
i just think does it for free sounds funny

talk about RH

>>12012365
It's not my fault you're a nigger

>>12012350
It does, yes.

talk about time cube

>>12012429
Tooker, I am the one running your simulation. You can break free if you can get ALL the simulacra to accept your proof that RH is false. This is the test we give to newborns to see if they are worthy of living in our society.

>>12012429
Take your meds.

>>12012331

I'm unaware of what you're referring to. I just became aware of the (years old) mushroom thing the other day and I found the repeated use of (do not) "disturb" to be amusing.

>>12012445
I am the one who put you in the position where I would know to brutally defile your blessings at the appointed hour. All those little children you've been farming, and the adult progeny with their own children now? That's basically the vice I'm going to put your balls in. I did that to you.

>>12012365
Rh yes. Curvature over imaginary identity state space converges over the maximal of the nullification and identity principles. Eg 1/2

>>12012546
I'm referring to https://www.youtube.com/watch?v=FWS2mnXrHkA
Prepare to die inside, uninformed and plainly wrong don't even begin to describe how shitty this one is. Also prepare for point-care.

>>12012594

Since it's so awful, I just won't watch it. Why would you recommend something awful to me?

>>12011505
don't forget religion, that sucks as well
science can do everything

>>12012606
I don't recommend watching it, just posting for reference I was making.
And yeah, the mushroom thing is fun. But to b honest with you probably fake imo.

>>12011435
In general, /mg/ is maths

>>12011664
seniority is when you learn to proofread your posts on /mg/

>>12012365
Tooky, what is this image supposed to tell me

>>12012711
My name is Tooker.

Incidentally, the nagger at the desk of this hotel today made sure to accidentally call me Took.

Anyone here ever had an oral exam?
>inb4 you know exactly what inb4

>>12012721
>>12012721
Uh huh. Very good tooksie

Kooky
Tooky

>>12012724
The US doesn't do oral exams for undergrad.

>>12012771
So everything is a written exam? What about graduate courses?

>>12012727
I suppose that person, or the person who sent that android, doesn't think their whole family is going to get killed for it.

>>12012786
>hurrrr
>durrrrr
>pfhhft
>ngeehh

>>12011389

>>12012783
Everything is written in undergrad and most everything is written in grad, too, but before I got my master's I had to do an oral exam for each of my courses that was administered by the respective professor. That was it though.

>>12011435
Formalist with a practically motivated preference for rejecting LEM.

>>12012718
Tooker, I enjoy your posts and respect you as a person.

>>12011389
wtf is this
anime?

>>12011435
master grade

>>12012812
:(

Please actually try to learn. You're missing out on cool stuff.

>>12012991

>>12013210
kek

>[math]\forall x \exists y P(x,y) \wedge \forall z Q(y,z) \implies \ldots [/math]
>Too hard to read, use natural language instead
>the square of the sum of x and y is equal to the sum over all divisors z of y of...
>Too hard to read, use symbolic language instead

What explains the difference in standards? Both algebraists and logicians say this, so it can't be a preference for one field over the other.

>>12011489
>Math uses logical deduction to show that some statements are in fact true.
completely false.

>>12011712
>publishing shows my true level
the state of zoomers

The difference is that some people bet all their money on being able to convince everyone that a certain person is retarded but they don't have a vested interest in 3rd parties' opinions of other 3rd parties.

>>12012173
Homos dont like maths. Homos like orgies, because homos are men with a female brain.

>>12012144
>consider themselves logical but they don't do anything close to rigorous logic most of the time.
Learn history of logic please, you'll learn why ''rigorous'' logic was invented and when.

>>12011435
Formalist in the streets, platonist in the sheets.

>>12012724
Yes, my first analysis course was oral exam only. Galois Theory was oral exam only. Very hard to bullshit your way through it if you do not know the material.

Has anyone here read Elementary Geometry from an Advanced Standpoint? I am interested to see how to define a function on R^3 that satisfies the postulates of "angular measure", is it really as the author makes it out to be?

More generally does the "angle" defined by an inner product on a 3-d vector space satisfy these postulates?

>>12013593
there's no definite answer. knowing how to balance between natural and symbolic language in a given context is just a skill that you develop over time

>>12013593
>Logical symbols bad
That's it.

>>12013712
I'm a mathematician, I know what rigor is for. Just because astrologists say they study the heavenly bodies doesn't mean they're doing astronomy.

What do I need to know before working through Lang's Algebra?

>>12014663
According to Lang himself in the preface, you just need to know basic linear algebra and polynomials. High school maths is obviously implicit.
The kind of person who could actually pull off Lang as a first algebra text isn't the kind of person who'd ask what are the prerequisites, tho, so in your case, you should follow Lang's recommendation of working through his Undergraduate Algebra.

>>12014663
You can’t do it alone, you will need at least one person to teach/study with.

>>12011435
erm... intuitionist? platonism is aesthetic but all i can intuit is that what i can sense is real, including senses of abstractions. if something exists, it is a form. if it is a form, it exists. there cant be nonexistent forms. seems like a intuition-constrained platonism to me

>>12014790
i guess what i mean is, can there be non-sensed things that exist (senses including abstract senses)? it doesnt seem meaningful to me. all the future is either predicted or surprise/magic/unobserved function

platonism seems unattainable and wishful, is there any reason besides aesthetic? also the dimension/space of forms would have contradictions imo

>>12013593
>he doesn't define all of his logical primitives in the introduction, and write the rest of the paper entirely in these symbols
NGMI

>>12014405
Post the pages or whatever
What are the postulates?

Hey /mg/ anons, I'm doing my first pass through Analysis. Is it crucial to master the concepts regarding Dedekind cuts and proving the laws of arithmetic with them or can I circle back to them later in a second pass? I'm getting really bogged down by the terseness of it all and want to quickly get to calculus-like concepts

>>12011435
Antifoundationalist

>>12014909
The construction of the real number system only matters to set theorists. Anyways, you can do it easier by Cauchy sequences on Q.

>>12014921
Thanks anon. I've got upcoming chapters on limits and sequences before continuous functions, I'm guessing limits is a good place to jump in seriously then?

Is there a general theory that explains inversion symmetries for PDE? e.g time inversion of the heat equation/brownian motion, and the kelvin/conformal transformation for the Laplace/wave equation.

https://static.wikia.nocookie.net/4chanlit/images/9/99/1589315802071.png/revision/latest?cb=20200513215816

or

https://static.wikia.nocookie.net/4chanlit/images/2/2e/15-36-45-1514290698220.png/revision/latest?cb=20181126191732


I am an absolute brainlet who got top percintile scores in math during high school and now haven't taken any math beyond that for last 10 years.
Best friend is a math major though and he is inspiring me to begin learning it again since he is going for his PhD and doesn't want me to not understand his work.

>>12014947
>>>/wsr/

What does it mean for mathematical techniques to become 'old-fashioned'?

I'm asking because I'm thinking of picking up 'Elements of Pure and Applied Mathematics' by Harry Lass and one review describes it as explaining 50-year old math using 100-year old techniques. Is it brainlet cope or can you seriously go wrong learning 'old' techniques?

>>12014958
From one hobbyist mathematician to another, I wish you all the best anon

>>12014960
Yeah you can go wrong in at least a couple ways. You won't understand modern work as easily if all the terminology and notation you pick up is ancient. You also won't understand what you learn as well. Progress in math has a lot to do with finding cleaner, easier, more general techniques for understanding a wide variety of phenomena. You can rederive some stuff using older methods once you know it, but the real understanding of the situation has been lost at that point.

>>12014966
Cool, thanks anon. Dropped that one then

>>12014796
>implying aesthetics aren't enough of a reason

>>12014958

>>12014989
Soul

>>12014947
last = remainder of N/4
2nd last = remainder of N/16
3rd last = remainder of N/64

>>12014904
>>12014405
Ok, also needs to satisfy the SAS condition for triangle congruence.

>>12015005
It's literally just the angle you're already familiar with in the 2D plane spanned by the two vectors.

>>12015013
Sorry I thought you said "the inner product". Obviously you'd have to verify those axioms for any other inner product.

>>12014966
Just curious, could you point me to an example of a new cleaner, general technique vs it's old counterpart? I'm comfortable with analysis and set theory if there's any nuggets in there

>>12014962
Thanks, do you have any tips?

>>12014989
Also thanks, this looks about the same but maybe better, I will try it out.

>>12014958
I'll let someone else do the recs but man do I hate the titles in the second pic. I understand why they wouldn't want to spouse stuff like LA and analysis like "real" big boy math but they make stuff sound so boring.
Only thing I'd say is take a random precalc book or khan academy classes for the basic shit instead of trying to do it rigurously or whatever.

>>12014989
Is Alfohrs really that good?

>>12015032
Honestly I'm finding my feet in this world so I'd be the last person to advise you on formal stuff, other anons here are better equipped.

I will say though, the practice meme really is true. Treat it as though you're practicing an instrument. Continually going over the same things over and over again until you're comfortable with it is much better than skim reading and barely grasping definitions. Application seems to be key (again, seems to be, I'm no genius).

Also, I'm of the philosophy that if I don't understand a concept in one book after a while, I find another interpretation and see what I've missed. Sometimes taking a break from maths also helps solidify concepts when you come back to the bit you're stuck on. The 'fresh pair of eyes' meme really rings true.

Lastly, don't be disheartened by others. I think as hobbyists we're especially prone to this because there's people around you who are taking this study formally and you're just in your room poring over books. Forget them. Maths is about practice anyways and as long as the pure pleasure of being able to 'hear the music' of this world is enough to keep you going, you'll be set for great things (be it great understanding, or something greater).

Good luck and I'll see you at infinity

>>12015013
>>12015020
Yes I know in my heart that [math]\arccos{\frac{v \cdot w}{|v| |w|}}[/math] should work, I assume that's what you mean. I am just wondering if someone has a rigorous proof that the postulates hold for this given either a geometric or analytic definition of arccos.

>>12015052
It's a safe choice. There's so many complex analysis textbooks out there. If you have access to a library, I would just go there and start reading some books until I find one that I like.

>>12015030
Look at the history of factorization of polynomials for a good example of this. Also, if you go far enough back concepts aren't even defined despite being used. The real numbers in the modern sense weren't even discussed until the late 19th century. Everything before was just vague handwaving.

>>12013703
in my department probably 50% of the grad students are gay

>>12015272
What is in the fountain water at your uni?

>>12015329
Estrogen...

>>12015329
Fluoride

is godels incompleteness theorem a proof of platonism?

>>12015401
Gödel himself denied that they alone proved Platonism, but he was a mathematical Platonic himself.

>>12015409
i agree that they alone dont prove platonism
but i think it brings you pretty close
>there are true statements that cant be proven
>thus there are truth values that cant be perceived
>thus truth/reality exceeds perception
the only thing is, an unperceived set with the trait true is still perceived as a set itself with the exterior trait true. does this cause the interior to be undifferentiated and non-platonic, or does it subsume Forms into perception somehow?

>>12015419
You'd probably enjoy reading this.
https://plato.stanford.edu/entries/goedel-incompleteness/#GdeBenMecPla

>Godel, Escher, Bach
is it any good?

>>12015515
If you're into philosophy, math, logic, and linguistics, then yes; but it's certainly not an easy or short read. It's something you've got to actually put some effort and time into.

>>12015469
is this trying to say that godel believed in platonism because he believed human mind surpassed any machine? i dont see the connection
whats special about diophantines btw

>>12015419
>>there are true statements that can’t be proven
The incompleteness theorem only states that there are statements that are undecideable (can’t be proven). It’s only because you’re already a Platonist that you think they are underlyingly true. Also a formalist could argue that because there are undecideable statements, there is no platonic truth and you have to formally append the statement or its negation as an axiom.

>>12015616
Also I know historically formalists like Hilbert were more likely to believe that every statement was decideable like hilberts program. I’m just being an argumentative bastard

"there exists vector in space such that...."
means, either in the future you will write a vector with this property
or you wont

"there doesnt exist vector"
you wont write a vector with such property

this is platonic existence projected into deterministic, non platonic reality

>>12015665
interesting that the "wont" possibility appears in both
kind of like an omnipresent 0 component of all xor truth statements referring to what will happen in the future

Not sure if I'm being retarded here, but is there a name for this concept?

I have a list of nonnegative numbers [math](a_1, \ldots, a_n)[/math] and some fixed positive [math]\mu[/math]. I want to then choose another set of nonnegative numbers, [math](b_1, \ldots, b_n)[/math] such that [math]\sum_i a_i b_i = \mu[/math], but with the caveat that each [math]b_i \leq 1[/math]. The goal is to use as few [math]b_i[/math]'s a possible.

Now this is a stupidly simple optimization problem, you just take the [math]b_i[/math]'s which correspond to the largest [math]a_i[/math]'s until you reach the given [math]\mu[/math]. I'm just looking for a name for this thing, or if it's a problem that comes up in some context.

>>12015690
[math] \cos(\alpha) |a| = \sum_i a_i b_i \frac{1}{|b|} = \frac{\mu}{|b|} [/math]
where alpha is the angle between a and b.

>>12015700
a and b arent vectors?

>>12015705
what does that mean
you clearly can embed them as is in R^n

>>12015708
is the angle between them 0 always? or are you talking about arbitrary vectors of norm a,b

>>12011461
>antisemites

Based

>>12015708
wait i misread sorry different a and b got confused

>>12015690
>>12015700
Let me rephrase, I'm looking to minimize the number of nonnegative [math]b_i[/math]'s. So the full problem is
[eqn]\text{minimize} \quad\|b\|_0\\
\text{subject to} \quad a^T b = \mu, \|b\|_\infty \leq 1[/eqn]
where [math]\|b\|_0 = |\{i : b_i \neq 0 \}|[/math].

>>12015714
You have [math]\mu[/math] and [math]a[/math] and compute [math]\alpha:=\arccos(\mu/|a|)[/math], which corresponds to the angle between your array a and a unit normed b.

>>12015720
minimize the number of nonzero b_i's *

>>12015665
Did you run out of clozapine today?

Is there any application of number theiry outside of algebra? Sone creepy old guy once told me about connections to statistics an prob theory, but I couldn't understand him

dear anon who i used a ? mark at when i said "a and b arent vectors?"

sorry for using a question mark in a rude way, rudeness is bad and im sorry. also sorry for speaking hastily without properly reading your message
i hope you didnt feel bad because i was rude and if you did, im sorry and take it back and dont want you to feel bad

>>12015753
Based. Niceness is the future

>>12015727
Computer science and cryptography.

>>12015419
there are not true statements that cant be proven
there are only consistent statements that cant be proven
a statement is true iff and only iff it can be proven
fuck godel

>>12013694
Now this is cope

>>12015824
whats the difference between consistent and true? do you mean consistent relative to other statements but not axioms?

Has anyone here done their master's/PhD overseas? If so, is it something you'd recommend?

>>12015887
a set of axioms is consistent if for any statement x you cannot prove x and - x
a statement is consistent with a set of axioms if appending the statement to the axioms is itself a consistent set of axioms

>>12014915
I am the unique (up to isomorphism)

>>12015329
Atrazine

>>12015824
Gödel is arguably the greatest logician of all time, only Frege can be argued to be greater.

>>12015924
Currently doing mine in the UK. I think it's nice. Just find a good supervisor with lots of contacts and funding.

>>12015968
How involved is the process?

>>12016042
What do you mean? Applying? Getting started? Actually doing the studying?

>>12016127
The application process. Are there are a lot of hoops you need to jump through or is it pretty straight forward?

>>12016134
I just sent emails to several places, then one of my recipients said he has money but he wants to see my qualifications and to have an interview via Skype. I sent my diploma (make sure you have an official translation if your uni's language does not match that of the country you are applying to) and then he sent me his contact info. We talked for maybe an hour and after a few days he sent me a message asking if I would like to join him. That's all it took before Brexit from a Union country to the UK. Nowadays there may be some extra inconveniences for EU citizens, but at least it used to be extremely easy. Oh and you may need a language test with a score sufficiently high.

>>12016166
Oh and you need letters of recommendation.

>>12016166
>>12016183
Thanks!

>>12016183
how well did you know your referees?

>>12016206
You are welcome!

>>12016215
The algebra & topology department was really small, so there were basically only 3 lecturers. I used one for my bachelor's thesis and another for my master's thesis as the supervisors. I also prepared some fancy questions to ask them every now and then to seem like I knew my stuff and to leave an impression in their minds. I can't say I would have known them too well, but we would just have casual chit chat after the actual business was taken care of, especially with the master's thesis supervisor, if there was still time left in the schedule. Just make sure you don't seem arrogant, but still give the impression that you are interested and know more than is required, then you will get nice letters. Bigger departments will probably be more difficult with so many students. Maybe post-lecture questions on something related to what you have been doing on the lectures, but still something you will definitely have had to find out on yourself.

>>12016238
>if there was still time left in the schedule
For the scheduled meeting, that is. Sorry I'm a bit sleepy.

>>12016238
ty my guy
I finished undergrad a couple years ago and remember chatting with my academic advisor on occasion but he has now retired. Hopefully he remembers, or can pretend to remember me when I apply for an MSc then use my current manager as the other ref. Most of the modules I took had 50-300 students in and I regret not interacting with the professors (at the time I figured most things out on my own/with other people, thought that they would have little time). Although a lot of places ask for two academic, I hope they will be a bit more forgiving for someone working.

>>12016279
No problem! 2 letters seems to be the most common, at least in Europe. I hope you can somehow manage to get those two, and get the position you are after. You could try contacting a prof telling them that your interest in academia sparked a bit later and ask for advice on how to train yourself to be a postgrad candidate (warning: this may be a horrible idea!) or something like that. Somehow show them your interest and maybe even a bit of this regret of yours in order to convince them that you are worth recommending. Anyhow, time to sleep. Good luck!

/gnmg/

>>12012134
Nobody here is responsible for your faggotry but you. If you get shit on here, how about reassessing your simplistic beliefs yourself.

>>12016330
Night, lad.

If I'm going to be honest with you guys; I have no idea what you guys are talking about but still browse this general.

>>12016489
Cheers.

>>12016330
Nighty night.
>>12016489
Same.

>>12016489
Ask a question, guarantee you there are dumber people here than you

>>12016489
Why?
But also, same

>>12015824
>a statement is true iff and only iff it can be proven
This is just blatantly false

formal math = absolute rigor based upon symbols and quantized "meaning". creates discrete thinking.


Schitzophrenia = No rigor whatsoever. Continous meaning with alot of crazy. Gets stuck in triangle relations with no concrete causality.

Geometry = a balance between both

Has anyone here studied representation theory? It's the only undergrad algebra course being offered by my uni's dept next semester besides the basic year long sequence.

Seems like a boring subject prima facie and have heard as much from other students who took the class (however, it was with a different professor)

>>12016845
Representation theory is fucking cool.

t. did first half of Serre with my friends

>>12015329
dihydrogen monoxide

>>12016659
I'm stealing this one

>>12016845
Representation theory is super cool, especially in the context of Lie theory. I recommend Hall's book on it.

>>12016886
>>12016934
Glad to hear it. The course is using this text which seems like a good sign.

>>12016343
i wasnt the anon he was talking too
im just sick and tired of philosphy pseuds like yourself never backing up anything they say
why is it that you guys are the most likely out of anyone to just throw ad hocs, christ

>>12016657
>This is just blatantly false
Only if you can prove that.

>>12017012
provability and falsehood are not the same

>>12017012
Prove it.

>>12017070
yes they are

>>12015924
If you like to speak continuously a foreign language for several years, yes, otherwise it sucks.

>>12015665
>I love to use classical maths.
cringe af

Looking for a nice axiomatization of Set for my (pre)sheaves, I've come up with the following axiom schema (ignoring the bound-variable tedium):

For any definable relation R(x,y) and small set D, there is an axiom
[math](\forall x \in D \exists y: R) \implies \exists C (\forall x \in D \exists !y \in C: R)[/math]

In other words, if R is entire on its domain D, then there is a small C over which R is the rule of assignment for a well-defined function (or more precisely, anafunction).

Has this axiom schema been studied before? I feel like it should have, especially from the constructivist literature, but nothing really comes to mind.

>>12017076
Aren't grad level courses in Europe usually done in English?

>>12017089
I don't know any category theory. But in descriptive set theory this is called uniformization property. That is, every binary relation has a selector. The uniformization for various projective sets is implied by large cardinals. If I remember correctly the existence of n many Woodin cardinals implies uniformization for Pi_{2n+1} sets, though its been a while. The periodicity theorems are the characterization of this, Kechris's Classical Descriptive Set Theory has these results. Of course uniformization is trivial if AC holds. But that is why it is important to descriptive set theorists, since they care about determinancy where AC fails.

>>12017089
>Looking for a nice axiomatization of Set for my (pre)sheaves, I've come up with the following axiom schema (ignoring the bound-variable tedium):
is this not what lawvere did in his phd thesis

>>12017114
They are done in the local language, but they try to hype themselves as international courses, so some courses are done in english, more so in meme private schools where brainlets pay to get their diploma, like any non scientific schools.

>>12017284
>is this not what lawvere did in his phd thesis
Sure, but that's for algebraic theories only, and the usual approach of interpreting nonalgebraic relations as equivalence classes of monomorphisms, while mathematically illuminating, is unsuitable for foundational purposes since it merely shifts the problem to interpretation of the equivalence relation. For example, I don't see it shedding much light on the property of wellfoundedness, and how it relates to induction.
>>12017254
>I don't know any category theory
Well, I don't know any set theory, so everything works out nicely! From skimming through Kechris (and Moschovakis, as per his recommendation for effective descriptive set theory) it sounds like exactly what I'm after. Thanks for the pointers!
(Since Moschovakis is also the key reference for the Wiki article on effective DST, I assume it's still the standard textbook?)

/gmmg/

>>12017114
>>12017289
It varies. We had most officially in English but some were done locally. When there were no foreigners around, the lecturer would switch the language.

>>12016489
Totally not this haha...

>>12016979
Serre is good for that stuff.

>>12016932
Please do. Retards outing themselves as thoughtless vessels for charismatic lunatics and vacuous sociopaths is always a good thing for the rest of the world.

>>12011712
>>12011733
>>12011810
>>12013694
All the really smart competitive math/programmers I knew ended up working as researchers or quants for tech and finance firms. A few guys from my program ended up as assistant professors, still trying to get tenure. And one or two of them ended up working for the government as cryptographers, probably the best thing you can do at that point. It's a sad life.

>mathematical maturity

>>12017583
great post. cool frog!

>>12017589
he's right

>>12017589
he's right

>>12017089
What's the colon notation?
Looks like a stronger Axiom Of Dependent Choice to me.

>>12017726
>>12017745
How is he right when he didn't say anything? Am I supposed to reconstruct some deep insight from
>>mathematical maturity
and a disappointed-looking frog image?

>>12017752
I guess it's more of a /lit/ and /tv/ style thing, but it's just picking up some trope and expressing how it's tiresome/overused/lazy/obnoxious or just too common

E.g. make the face every time I read a paper with
>we propose a unified mathematical framework for

Then again, it's not to say that those phrases don't have their place or >mathematical maturity should be represented with something else. It's just making fun of tropes.

https://tvtropes.org/pmwiki/pmwiki.php/Main/CheckPlease
https://tvtropes.org/pmwiki/pmwiki.php/Main/GroinAttack
https://tvtropes.org/pmwiki/pmwiki.php/Main/BeautifulAllAlong
https://tvtropes.org/pmwiki/pmwiki.php/Main/BadassBookworm
https://tvtropes.org/pmwiki/pmwiki.php/Main/InsufferableGenius
or just
https://tvtropes.org/pmwiki/pmwiki.php/main/tsundere

>>12011435
Ultraformalist. Numbers do not exist until we construct them. The truth of theories like real numbers or infinitesimals is irrelevant, the only constraint is consistency. As for usefulness of math toward our perceptions, the only constraints are predictive power and consistency.

Discovering the joy of math after graduating, after job, after girlfriend -- awful ordering.

>>12011489
t. Some teenage brainlet who has never taken an actual math class at university and has never opened a philosophy book

Guess what anon? You're a retard. People who are actually intelligent appreciate a wide variety of academic subjects, and math and philosophy in particular have historically been very close. In recent decades the overlap has mainly been around game theory, social choice theory, formal languages/automata, logic/proof theory, constructive mathematics, and reverse mathematics. If you claim to be interested in math, then I'd expect you to at least be aware of stuff like constructive analysis.

https://en.wikipedia.org/wiki/Harvey_Friedman

if you do a proof only once, are you sure you know the theorem, or do you have to keep doing the proof to know the theorem and as soon as you stop, you lose the knowledge of the theorem?

>>12017012
Godel literally proved it.

>>12017357
There is no really self contained book on EDST. I never learned it from Moschovakis, I find the notation pretty dated, its like 40 years old now. What are your goals? If it is to understand structural properties of sets of reals, probably Mansfield and Weitkampt's Recursive Aspects of DST is your best bet, it is also has pretty bad notation but the theory is built in a beautiful way. Depending on how much recursion theory you know Yu and Chong Recursion Theory book is also pretty good introduction to EDST from a recursion theorists standpoint, there is a lot of forcing in this book though. Su Gao's Invariant DST has an introductory section on EDST, no real proofs are given. If you ever do learn more set theory ie forcing, EDST is the primary place forcing is used for constructions, not just consistency results. The argument goes that you make some generic extension where the object you want actually exists, then use the descriptive complexity of the object to conclude it must already existed in the ground model.

>>12018280
While I certainly don't hold this belief myself, there are many mathematicians who would consider most of those areas not properly belong to mathematics or not be of much real interest. You're being a little aggressive in setting up your personal program as something everyone should know.

>>12018309
I forgot my last sentence, if you learn forcing, then the book you want is Miller, Descriptive Set Theory and Forcing: How to Prove Theorems about Borel Sets the Hard Way. This book is awesome. Also Andrew Marks has some notes from a course EDSt, I think its just google search his name and EDST.

>>12017075
Provability and falsehood are very different concepts. Look up Godel's incompleteness theorem.

>>12018362
what exactly do you mean by "falsehood" ? a statement is semantically true if and only if it is provable

>>12018305
>>12018362
thats literally not what godel fucking proved
he shows that there exist statements which cannot be proven or disproven in a sufficiently strong system
so he showed there exist independent statements. If a statement is independent, it is not true nor false in the system
it is independent
these are not complicated words

>>12018382
>if a statement isn't provable it's independent
Proof?

>>12016657
????????? wtf man

>>12018313
I never made any claim that anon should know those subjects. I wouldn't expect anon to have an in-depth knowledge of constructive mathematics or game theory. However, if he's claiming to be a mathfag, then he would definitely be aware of something like game theory, even if all they know is that it was pioneered by von Neumann.

You seem to have missed the whole upshot of my post, which should have been fairly clear given the context. In fact, it was the anon I was responding to who made the autistic assumption about an entire field of knowledge (namely philosophy). He claims that the entire field of philosophy hasn't contributed anything in 200 years. I disagreed with this claim, and as evidence I cited subjects like constructive analysis and game theory. I never made any claim that he should have an in-depth knowledge of either of these subject. Nor do I, as you suggest, study any of these subjects. I'm in an applied math program and will be graduating in a few months. I hope to go to grad school for applied math a I want to work on Ramsey Theory and/or mathematical biology, so you're suggestion that these are personal interests of mine is nonsensical. Do honestly think that there are professional mathematicians or professional scientist or social scientists in any field that haven't heard of game theory? I would argue that its one of the most iconic intellectual developments of the 20th century.

>>12018378
>what exactly do you mean by "falsehood" ? a statement is semantically true if and only if it is provable

Nope. A statement is "true" if its reflection is provable in the meta-theory. Outside of logic we only tend to work in only one encompassing logical system, so that provability is confused with "truth", but just as provability, ultimately truth is also a relative notion.

>>12018412
I'll ask again, what do you mean by "falsehood" (or "truth") ? because true iff provable is a basic result of mathematical logic

>>12018400
If a statement isnt provable or disprovable then its independent, by definition

>>12018378
This is not exactly the Godel completeness theorem. A sentence [math]\varphi[/math] is provable from a theory T iff for every model M of T then M satisfies [math]\varphi[/math]. The truth value of a sentence depends on the model. A theory can say a sentence is true in the class of its models if it proves it, but just because M is model of T, and M satisfies a sentence in the language of T doesnt mean that T proves that sentence.

What's the point of you guys discussion?
There's already a word for provable, namely provable.
Just say "Platonically true" for the useless notion of true and satisfiable for the model one.

>>12018362
>Look up Godel's incompleteness theorem.

One consequence of Gödel's theorem is that "truth" is an ill-defined concept. The pop-sci phrasing that "in any reasonable deduction system, there are true statements that are not provable" is actually retarded.

The correct phrasing is that in any reasonable system, there are independent statements, including consistency of that system. No need to invoke some random notion of "truth", which is only relative to the ambient meta-theory and just adds to the confusion.

Math is not about truth, it's about provability. For the former, please refer to your local schizo or pedophile priest.

>>12018412
YOU may work in a meta theory, but I have no preference at all for taking Continuum as true or its negation as true

>>12018435
Are you retarded? ZFC is one such meta-theory and it doesn't take sides.

>>12018418
>elementary arithmetic's consistence is either independent from elementary arithmetic or false
Kill me.

>>12018440

Anon-kun, I am afraid that...

>>12018382
A theorem can't prove a definition, brainlet, and everything else that you said just recapitulates my own claims. You sound like you assume I'm ignorant of Godel's proof, but I am not. Godels incompleteness theorem proceeds by applying a Cantor Diagonalization argument to the system of Peano Arithmetic. A formulae phi is shown to exist such that phi is true if and only if there does not exist any natural number n such that n encodes a proof in Peano arithmetic of the statement phi. He does this through his coding method of Godel numbering. The diagonalization component of the argument is identical to Cantor's except in that Godel showed that there can be no integer n corresponding to the PA formula phi, whereas Cantor shows that there can be no integer k corresponding the decimal expansion he is able to construct.

The statement phi ends up being true in the system of PA, but unprovable. Introductory textbooks will generally even include a remark to address the question "but can't we just add phi to PA as an axiom?", and they of course explain that adding phi to the axioms of PA lust means that we have a new diagonal formula phi' that is not provable.

>>12018378
There are statements that are true under one interpretation and false under another interpretation of the symbols of a theory. For instance, many of the properties of hyperbolic geometries are inconsistent with the properties of Euclidean geometries. A set of axioms and a proof system are just tools for performing operations on sets of formula. Whether that system of reasoning has applications to actual concrete interpretations of the language is another question. For most purposes Euclidean geometry appears to be true, but at the same time, non-Euclidean geometries are not inconsistent despite not describing the geometry of everyday experience, and in fact hyperbolic geometries can even be modeled internally in Euclidean space using Poincare discs (and other models too).

>>12018474
>The statement phi ends up being true in the system of PA

Sorry for being picky, but read literally this is wrong.

Logical systems like PA don't give a shit about truth, they only tell whether a formula is provable or not. To claim that something is true means that somehow you can translate a PA statement into a meta-theoretical statement, and assuming furthemore that PA is consistent, then the statement is provable in the meta.

For the sake of the argument, let's recall that PA can be embedded into ZFC. We will pick the latter as our meta-theory, and PA as the object theory to which we will apply Gödel's theorem. It gives you a PA formula [math]\phi[/math] s.t. neither PA proves [math]\phi[/math] nor PA proves [math]\neg\phi[/math].

Now, ZFC proves PA is consistent, so you can lift [math]\phi[/math] into a different statement [math]\hat\phi[/math] which is the reflection of the PA formula as a ZFC formula. Since you have access to more proving power you can show that [math]\hat\phi[/math] is provable in ZFC, i.e. "true" in your parlance. But once again this is relative to your metatheory. You could have well have taken an exotic meta in which PA is inconsistent.

>>12018408
Please do not be upset. I do not care to debate it with you further, but you came off as someone working in logic/philosophy who has a chip on their shoulder about it not being considered "real math".

>>12018430
>The pop-sci phrasing that "in any reasonable deduction system, there are true statements that are not provable" is actually retarded.

I think the best way to read that phrasing is via a common use notion of LEM in the metalogic.
As in
>There are statements [math] G [/math] so that neither [math] G [/math] nor [math] \neg G [/math] are provable, and one of them "must be truth."

The point of disagreement can maybe be highlighted with a more concrete example.
Let
[math] P(m_1,m_2) [/math] denote the statement
>The pair of 15 × 15 matrices with integer entries, [math] m_1 [/math] and [math] m_2 [/math], can be multiplied in some order (e.g. [math] m_1\cdot m_2\cdot m_1\cdot m_2\cdot m_1\cdot m_1 [/math] would be one such product) such that the result is the zero matrix.

This is known to be computationally undecidable (mortal matrix problem).
I.e. there cannot be an algorithm that, given any two matrices, returns the correct answer to the claim.
So presented any pair of matrices, we're sadly not in the situation to promise to eventually be able to report that they can be multiplied to 0 or that they can't be multiplied to 0.

We can consider the claim that P is decidable for all matrices, i.e.

[math] \forall m_1. \forall m_2. P(m_1,m_2) \lor \neg P(m_1,m_2) [/math]

and this can also be written with just one universal quantifier over the naturals, since we just need to code 2*15^2 naturals with 1, i.e. this is effectively just a statement of the form

[math] \forall n. Q(n) \lor \neg P(n) [/math].

is trivially provable in Peano Arithmetic via Excluded middle but it's not anymore if you drop it (i.e. do Heyting arithmetic).

Now what about the common language sentence
>The pair of 15 × 15 matrices with integer entries can either be multiplied in some order so that the result is the zero matrix, or it can't.

If we judge this to be true, you use an apparently sensible notion of "truth" that however escapes provability.

[math] \forall n. Q(n) \lor \neg Q(n) [/math].

∀n. Q(n) ∨ ¬Q(n)

Another sentence to consider may be

>EACH pair of 15 × 15 matrices with integer entries can either be multiplied in some order so that the result is the zero matrix, or it can't.

>>12018474
>you assume I'm ignorant of Godel's proof, but I am not
>true in the system of PA
I am not that anon, but this is wrong, and it one of the main reasons this whole discussion is peepeepoopoo. Nothing is true in PA, because PA cannot talk about truth. Truth happens in models, PA is a first order theory. The Godel sentence is constructed so that it is true in the standard model of the natural numbers. That is where the whole "there exists true but unprovable statement" comes from.

To summarize it in other words,

the theory proves that there's numbers corresponding to statements [math] G [/math] and [math] \neg G [/math], such that those two each can't be proven. PA also proves [math] G\lor \neg G [/math]. The common language reading of that in the metaloigc would be
>Either "G" is true or "not G" is true (G is false) or both are true (inconsistency), but both aren't provable (unless inconsistency).

I think that's the common "true" people invoke.

Logic faggots ruined another thread.

>even though its not provable its still true cuz if i work in a different theory i can prove it
>no, of course you cant prove it in PA, but if you work in an extension of PA you can, so its true
if you extend to another theory to prove it, then youve still accepted that truth is the same as provability, you just proved it somewhere else

>>12018097
Based based based based based

bros... i did maths today... i had fun... bros...

>>12016562
Asking questions gets you nowhere on this site. The way to find information is to be wrong and smug about it, that way people dogpile you to call you a retard

>>12018716
For you, anon:
On syntax:
https://web.math.princeton.edu/~nelson/papers/s.pdf
All papers by Nelson:
https://web.math.princeton.edu/~nelson/papers/

"As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct."

>>12018097
Doesn't sound ultra to me tbqh. I think consistency is a vastly overrated feature. If I let out the formalist in me, an inconsistent theory is sure as good as a consistent one. I one and can provide a sequent ending in the string of letters "[math] \neg(A\land \neg A) [/math]" and in one I can't. Shouldn't bother an ultra-finitist. Literally the only difference between an inconsistent theory and a consistent one, apart from what they can prove, is that the majority of people don't find inconsistent theories interesting. That's but a meta-meta-mathematical property.

>>12018097
Doesn't sound ultra to me tbqh. I think consistency is a vastly overrated feature.
If I let out the formalist in me, an inconsistent theory is sure as good as a consistent one.
In one and can provide a sequent ending in the string of letters "¬(A∧¬A)" and in one I can't. Shouldn't bother an "ultra-formalist".
Literally the only difference between an inconsistent theory and a consistent one, apart from what they can prove, is that the majority of people don't find inconsistent theories interesting. That's but a meta-meta-mathematical property.

>>12019028
>the majority of people don't find inconsistent theories interesting
Turing-complete programming languages are, per the Curry-Howard correspondence, inconsistent logical systems. It would be a far shot to say that nobody cares about them.

>>12019105
>Turing-complete programming languages are, per the Curry-Howard correspondence
I don't follow

>>12019140
Curry-Howard tells you that type systems for programming languages correspond to deduction systems in logic. A type is the same as a formula, and a program of a given type is a proof for the corresponding formula.

The original example is simply-typed λ-calculus corresponding to intuitionistic natural deduction, but there are gazillions of well-known examples, scaling to rich logical systems.

https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

Now, if you pick a type system rich enough to do maths such as the calculus of constructions, and you add to it a fixpoint combinator, it does two things: first, it makes it Turing-complete, and second, it makes it inconsistent. Turing-completeness is easy to check, and inconsistency is just because a loop that never returns has an arbitrary type, so in particular you have a proof of false.

Yet, this is the ultimate constructivist realm, since by definition you're manipulating a programming language. Actually it's even part of what I'd call "Girard's program" to get rid of logical systems altogether and replace them with empirically-based experiments defined in some well-behaved programming language to work around the limitations of Gödel's incompleteness theorem.

>>12019028
>can provide a sequent ending in the string of letters "¬(A∧¬A)"
I find paraconsistent logic wholly interesting, but that doesn't count.
Indeed, consistency preference is up to the person. I find co-trivialness boring in itself, but I actually like analyzing inconsistent theories to see what makes them inconsistent.
For example, the zero product property (0*x=0) and an unconstrained inverse property (x/x=1) in a field algebra are inconsistent. To resolve this, limit the inverse property (x!=0 -> x/x=1), or replace the zero property and inverse property entirely to get a wheel algebra or meadow algebra, inventing a symbol for 1/0 and 0/0 in the process.

To me, ultraformalism is distinguished from normal formalism like so:
1. A rejection of Hilbert's platonist origins in Cantor's work [1],
2. A rejection that large number notations terminate to a unary notation (often phrased as a rejection that large numbers exist [2], and a rejection of the full induction axiom [3]). I'd rather split notions of number that line up more closely with the computational properties of their notation.
Calling it "ultra" is splitting hairs, though, so I suppose you're right.

Note that I reject ultrafinitist notions of a largest number (like Wildberger), or that real number notations like 1=0.99999... always lack a formal meaning (Zeilberger) [4]. There is cool research into "feasibly consistent" theories, though [5]. Those being very interesting inconsistent theories, my post has gone full-circle.

[1] https://web.math.princeton.edu/~nelson/papers/hm.pdf
[2] https://web.math.princeton.edu/~nelson/papers/e.pdf
[3] https://web.math.princeton.edu/~nelson/books/pa.pdf
[4] https://sites.math.rutgers.edu/~zeilberg/Opinion146.html
[5] https://link.springer.com/chapter/10.1007%2F3-540-60178-3_78

>>12019105
People care about them, but not as logical system via their type system. I'm not shook that the bottom type has an `undefined` inhabitant, even if it's ugly.
Are you Σ5 by any chance?

>>12019245
>Are you Σ5 by any chance?
Nope.

did someone post a /mg/ disc*rd a couple days ago or was that a fever dream

How immediate should be stuff like this?

>>12019322
That did happen, but it wasn't an /mg/ discord, it was just a random discord that was apparently also posted on /x/, and Nikolaj was there.

>>12019329
Compute the derivative and look at specific values of the function.

Algebraic Geometry is the /x/ of 20th century math.

>>12019365
are those gottingen lecture notes still /mg/s preferred intro to AG

>>12019365

Look to my coming on the first light of the fifth day, at dawn look to the east.

>>12019373
A geometer is never late, nor is he early. He arrives precisely when he means to!

>>12019329
Showing 2 values is easy, that's just intermediate value theorem. Plug in random values for [math]f(x)=xsinx+cosx-x^2[/math] and test for a sign change.
Showing exactly 2 is a bit harder. Obtain all local extrema (min and max) via derivative of [math]f(x)=xsinx+cosx-x^2[/math], compute f() for each value, and then apply intermediate value theorem by testing for a sign change.

>>12019414
>Showing exactly 2 is a bit harder
It's fairly trivial. The derivative is always positive for x < 0 and always positive for x > 0, and the function equals 1 in 0, so there you go.

>>12019329
>>12019414
>>12019358
Just notice that the extremum are located at x=0 and at all the extremum of cosine. So after the first maximum at pi/2 (symmetrically -pi2) the function will be bounded by f(x)=|x|<x^2 after the two first extremum

>>12011435
I'm an engineer

>>12019451
Based materialist.

>>12019371
which one?

>>12019450
>>12019414
>>12019358
Thank you all, and I guess I got my answer anyways, but I was really asking how tough stuff like that was supposed to be when first taking calculus. I only had an inkling of an idea of what to do on that for a good while, it kinda sucked

>>12019523
https://youtu.be/uqwC41RDPyg

>>12019525
kys redditor

>rip a textbook from libgen
>skim it for a short time
>find it interesting
>save it in some folder to self-teach later
>never look at it again
>rinse and repeat
who else does this?

>>12019545
This but I actually read it

>>12019490
i'm sure they were linked in /mg/, I had them open in my browser for months
I feel like a fool now I can't find them, it may possibly have been a different german, or even dutch university but still written in english

>>12019646
Not him but I thought I had bookmarked them, but aparantly nope. I think it was a German University, but not Göttingen.

>>12019525
Well I sorta liked that but my question stands

>>12019523
When you’re first taking calculus it’s normal for it to be a little tough

>>12018537
and truth in logic is Tarski's idea of truth, which is not truth.

>>12011399
Sex

>>12011560
Work on problems in parallel

How do I teach myself real analysis quickly? My current strategy as a beginner is to write down and memorize all the definitions, theorems and lemmas in my introduction to analysis book to use them in proofs later.

>>12015055
Bro you are a good guy

>>12020519
Page by page day by day

>>12015055
Reddit fuck off

https://homepage.univie.ac.at/herwig.hauser/bildergalerie/gallery.html
for me, its crixxi

>>12019678
was it these from Bonn?
https://www.math.uni-bonn.de/people/ja/alggeoI/notes.pdf

>>12015329
Tiddy pills

Does anyone know a cool book on the finite simple group of order 168 (i.e. [math]PSL(2,7)[/math])?

>>12020565
Have a (You)

>>12020714
Go back to your home site fucking faggot

>>12020736
is faggot and bromance the same?


i mustve mistook faggot and bromance

Is everyone fucking dead?

>>12021633
I'm shy and thinking.

>>12021633
My supervisor doesn't let me shitpost on Tuesdays

>>12021633
I'm working, you're supposed to amuse me when I take a break.

>>12021633
Elliptic curves

>>12021633
No, I simply can't prove it yet.

>>12021633
Yes.

>>12020519
This is the brainlet way of learning. Just do all the exercises.

>>12022397
Works for the first chapter. But then you have to start developing a tool set of techniques, and SCAMPER plus jotting a gist helps consolidate the memory and helps understand better.

>>12022403
*comprehend
because understanding comes at the exercises.

inf understanding = comprehension.

Is there a simple way to see that a subgroup of a finitely generated abelian group is finitely generated, without using the fundamental theorem?

>>12021633
My supervisor only let's me shitpost on Tuesday

>>12021633
fall term already started for the category theory undergrad fags

What is the largest natural number in English langiuage that is exactly two syllabes long?

>>12022959
Some Xillion, I would assume.

>>12022959
Do you have to say the “a” before a hundred and other numbers like it, cause if not I think it would be “trillion” if you pronounced it like a retard

>>12022959
Googol is defined as [math]10^{100}[/math]
If you are want to cheat a bit, than say Graham's.
If you are into esoterica, them [math]TREE(twelve)[/math] is technically two syllabes long.

>>12011399
Bsasded

does someone have this picture that goes like this
>could you fill water in the hole
>which hole?!

which picture?

I've been trying to solve: [math]\int x \ln (\frac{x}{e^x}) dx [/math]

I don't understand the approach they have taken in the solution. in particular, rewriting [math]x[/math] as [math]\frac{1}{x}[/math]. what am i missing?

>>12023754
That looks a bit fucky. Take the derivative of the RHS.

>>12023754
The solution is wrong. You are right about x being rewritten as 1/x.

>>12022959
Rayo’s

>>12023754
Where is the image from? The “solution” is blatantly wrong. Also cheers for not just gobbling a solution and assuming it’s correct, if you weren’t thinking it through you never would have known they were wrong

>>12023977
thanks. it's from this set of 50 questions (which were good practice overall): http://archives.math.utk.edu/visual.calculus/4/integrals.2/index.html
i spent an inordinate amount of time on this one and was torn between abandoning it and satisfying my curiosity by posting it here
grateful to be assured i had not missed a trick and it was, in fact, wrong!

what type of bread does /mg/ have with their morning coffee?

>>12024763
Sourdough, buttered.

>>12024763
I don't eat breakfast, I don't eat bread, I don't drink coffee.