/mg/ = /math/ general: ebil Gowers bogeyman edition

gee there sure was a lot of math in the last thread

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Can we have one /mg/ without animeposting, depression and butthurt spergs?

My favorite theorem is Lagrange's Four Squares theorem. What's your favorite number theorem in number theory, anons?

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>>9046804
>Lagrange's Four Squares theorem
There's some recent conjectural generalizations:
every natural [math] n [/math] can be written [math] n=x^2+y^2+z^2+w^2 [/math] with [math] x+3y+5z [/math] a square
every natural [math] n [/math] can be written [math] n=x^2+y^2+z^2+w^2 [/math] with [math] x [/math] and [math] x+24y [/math] squares (true up to 10^10)

Kind of surprising finding such structure inside the solutions imo

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>aliens somewhere have solved Riemann hypothesis
>we live on planet brainlet

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>Classical conformal field theory is defined as a conformal field theory where the conformal weights of all primary fields vanish. In this case, conformal field theory is nothing but group theory.

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Heh, you think you know about Mathematics?

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>>9047046
Heh... nothing personnel... undergrad.

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>>9046804
>What's your favorite number theorem in number theory, anons?
number theory mixing with geometry is nice

elliptic curves, singular k3 surfaces and rigid calabi-yau threefolds over [math] \mathbb{Q} [/math] are all modular

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>>9046804
>What's your favorite number theorem in number theory, anons?
Let [math]\zeta_{k_1\dots k_n} = \sum_{m_1 < \dots < m_n}\frac{1}{m_1^{k_1} \dots m_n^{k_n}}[/math] be the multiple zeta function, then [math]\zeta_{1,2} = \zeta_3[/math].

>>9047046
>>9047057
I still think his advice to start with an interesting mathematical curiosity and fill in prerequisites from there is pretty good t b h.

>>9047123
Who is he? What prerequisites? Advice?

>>9046640
What's /mg/'s opinion of hyperbollic geometry? I decided to do my undergrad "thesis" on it after reading Geometry of Surfaces by Stilwell. The distinct models are pretty cool, and being able to recreate so many different geometries in [math]\mathbb{H}^{3}[/math] is breddy nice.
>>9047091
Would you recommend number theory to someone who's very interested in geometry? For the moment I don't think very much of it because it look a bit meh to me, but if there's interesting geometric interplay I may get something out of it, I don't know.

>>9047127
Qiaochu Yuan, graduate student at UC Berkeley. I'm referring to his SE answer here: https://math.stackexchange.com/questions/181387/motivation-and-methods-for-self-study/181410#181410

He's pretty much a meme though. Probably browses this site.

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Mathfags, tell me: if you know the values of a+b, c, and the hypotenuse, is it possible to find the value of b? This is not homework, don't worry

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>>9047132
>Would you recommend number theory to someone who's very interested in geometry?
In my experience number theorists seem more up to the idea of diving into geometry than the other way around, they just have very distinct aesthetics. Maybe it's easier to find interesting number theoretic problems in geometry than geometric problems from number theory. Anyway pic related is easy reading (not easy math, but mostly conjectures and theorems without proofs), sort of a blueprint for a lot of work done in arithmetic geometry from the last 30 years (+ probably the next 100 years)

>>9047148
I don't think so. I think you can keep a+b, c and the hypotenuse the same but change a and b.

I.e. if you change that picture to a+ (something small) and b - (same something small) you get the same triangle

>>9047132
>What's /mg/'s opinion of hyperbolic geometry?
It's fucking nice, m8. I was introduced via Wildberger's series on Universal Hyperbolic Geometry.

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>>9047148
I'm gonna go with 'maybe' because i don't have time to play with these variables more.

>>9047132
If you like hyperbolic geometry and number theory than dynamical systems/ergodic theory is probably the route you wanna take.
>>9047007
From what I've seen a hell of a lot of solid state physics (at least at the level of studying crystals and metals) basically boils down to group theory so looking at cft as a tool to describing condensed matter systems becoming group theory when looking at basic crystalline structures may not far fetched I suppose.
>>9047148
No, consider the following, let a+b=12, c=5, and the hypotenuse be 13, then two possible solutions for (a,b) are (2.10) or (5,7), in fact there are infinite positive real numbers (a,b) s.t a+b=12, basically being on the line (a, 12-a) for 0<=a<=12.
>>9046804
Connes proved that the riemann hypothesis is equivalent to a certain trace formula, then further made the connection to statistical mechanics (though thanks to random matrix theory people already knew that the distribution was pseudo random). In general connes has done some interesting work connecting number theory and physics via noncommutative geometry.

>>9047134
Why is he a meme exactly?

>>9047271
>Why is he a meme exactly?
Because he's only known for posting on stackexchange a lot

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>>9046640
>leave math to me

Currently reading Differential Equations, by Shepley L. Ross. Really enjoying it, especially after I switched from digital to physical copy.

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>>9047384
>discord

>>9046640
Man, Gowers even looks like a villain. How do we stop this motherfucker?

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Le obligatory suicide anime post face LOL! I must say Atiyah's book on K-theory is really easy to read, I like it.

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>>9046640
>preparing for a calculus II final
>Have to study lineal differential equations and bernoulli's little shit
>Khan Academy DE section ends with separation and exact DEs

OH SHIT WHAT DO I DO

>>9046804
>What's your favorite number theorem in number theory, anons?
Do the Sylow theorems count? (I'm not into number theory.)

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>>9047465
>Do the Sylow theorems count? (I'm not into number theory.)
No.

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>>9047252
>From what I've seen a hell of a lot of solid state physics (at least at the level of studying crystals and metals) basically boils down to group theory so looking at cft as a tool to describing condensed matter systems becoming group theory when looking at basic crystalline structures may not far fetched I suppose.
Actually the equivalence comes from the operator algebra. If the conformal dimensions of all the primary operators are 0 then the fusion relations basically just form a presentation for some group. Crystal symmetries aren't universal while conformal invariance is, so the former really isn't really what's at play here.

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I WANT MY MEME LIST

RATE MY MEME LIST

YOU DEPRESSED FAGGOTS BETTER LISTEN TO ME RIGHT NOW IM NOT GOING AWAY

MUH BOOOKKKKSSSSS

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You know, Scholze is an awful lecturer. I have to watch this on 2x. He spends too much time repeating what he's already written down, with minimal exposition.

https://www.youtube.com/watch?v=TU39h4rDJAs

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>>9047733
He also spends too much time looking at the blackboard. Scholze my man, if you're reading this, engage with your audience more. There no point to the lecture if it's just a paper by dictation.

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Given this relation, what properties does a function
f have to satisfy so that
[eqn]S=\{(x,f(x)|x\in dom(f)\}[/eqn]
is a maximal chain? Clearly f must be monotonically
increasing, but must f be onto [math]\mathbb R[/math]?

Example: if f is the identity for all reals, then S is a max
chain. Proof: try to add (a,b) with a < b, then choose
c so a<c<b, then neither (a,b)~(c,c) nor (c,c)~(a,b) so
(a,b) is isolated; or have a>b and choose so a>c>b.

What assumptions are necessary to generalize this?

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>>9047785
>[math]\mathbb{R}[/math]
No such thing.

How long does it take to have your article reviewed?
I submitted a paper to a journal 2 months ago via an online submission form, and received no information yet (except for an automated email)
Was is so bad they didnt even reply?

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>>9046962
not even our best Big Ashkenazi Brain can compete holy shit

>>9046962
>>9047911
>reddit images
>>>/r/eddit/

>>9046962
>we
Speak for yourself, subhuman.

>>9046640
brainlet here, can you write the absolute value function without it being a piecewise function? I don't care how deep down the math rabbit hole you need to go to do it, I'm not pretending to understand the solution, just want to know if it's possible.

>>9047916
sqrt(x^2)

Help me with my algebra excercise: "for every positive integer [math]n[/math] construct a group containing two elements [math]g, h[/math] such that [math]|g|=2,|h|=2, |gh|=n[/math]"
For [math]n \geq 2[/math] it's simple:
Let's take a dihedral group [math]D_{2n}[/math] generated by [math]x^2 =
e, y^n = e, yx = xy^{n-1}[/math]
[math]g = yx, h = x[/math]
[math]g^2 = yx yx = yx^2y^{n-1} = y^n = e \implies |g| = 2[/math]
[math]h^2 = xx = e \implies |h| = 2[/math]
[math]gh = yxx = y, |gh| = n[/math]
But what should I do with the case [math]n = 1[/math]
If I try to make a multiplication table for a group to satisfy this condition:
[math]g^2 = e, h^2 = e, gh = e[/math]
such table would violate cancellation rule. The problem would be solved if [math]g = h[/math] is the same element yet I'm not sure I'm allowed to do this. What should I do?

The cube fitting problem from the previous thread could easily be solved once you find a way to count how many squares fit into a circle, but then I don't know if there's a slick way to simplify the resulting sum in a slicker way. Any thoughts?

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How do I answer this? I'm unsure as to what a Cp value is, or how I can use them to determine the answers to the questions.

Please help this poor brainlet

>>9047904
It can take a few months depending on the journal. If none of the editors are interested, even more. I know some guys who had their papers in review for more than 2 years.

>>9047952
Read your notes dummy. How should we know what Cp is? (It's probably Mallows' [math] C_p [/math] statistic though, just a hunch.)

>>9047935
You've provided and proved an answer for n>1. You've provided and proved an answer for n=1. You're done, kiddo.

And even if you weren't sure your answer for n=1 was legit, you've proved that no other answer is possible. So, you've check your answer as well.

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>>9047948
that alone is not a trivial problem, hell packing cubes into a cube is not even trivial.
assuming that you can get to the optimal 3d packaging from stacking up optimal 2d packages is also foolish

>>9047882
I'd be just as happy if you could do it for [math]\mathbb Q[/math]

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I am glad that people took my bait and started to work on the packing problem. Don't give up anon!
Packing problems are awesome.
https://www.quantamagazine.org/sphere-packing-solved-in-higher-dimensions-20160330/

>>9048012
Don't be a killjoy. Splitting the problem on rows like that can at least give you a lower bound on the number of cubes you can fit.
>>9047948
By the way, the horizontal cross section is a circle only for paraboloids of revolution.

— — — — — — — —

0. Remedial Mathematics
Khan Academy

— — — —

>1. The Prerequisites of University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
How to Prove It - D. J. Velleman

— — — —

Pick One Path:

>2a. Introduction to Applied Mathematics (Some Proofs)
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
<go do your STEM lol>

>2b. Introduction to Pure Mathematics (Proof-Based)
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter
<go do your pure maths lol>

>2c. The Mixed Approach
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter
<go do whatever you want lol>

— — — —

>3. Foundations for Advanced Pure Mathematics
Linear Algebra - K. M. Hoffman & Ray Kunze
Analysis I & II - Terence Tao
Visual Complex Analysis - Tristan Needham
Algebra - Michael Artin
<feel free to branch off into any specialization>

— — — — — — — —
Is this legit? I'm an EE freshmen but I don't want to be a total brainlet ;_;

>>9048037
Visualizing R^2 as a Cartesian plane, the relation (a,b) ~ (c,d) simply requires that (a,b) lie below and to the left of (c,d), with both inequalities being non-strict.

So you shouldn't need any more conditions beyond f:R->R being monotone (with f(a)=a for a<0). For example, f(x) = min{x,0} should work.

>>9048152
>I'm an EE freshmen but I don't want to be a total brainlet
Impossible.

>>9048152
You won't

>>9048152
Get this crap outta here, no one cares about your meme list. Weren't you supposed to be a chemistry major anyway?

>>9048188
>meme
>>>/r/eddit/

>>9048152
>Analysis
Analysis needs to be banned.

>>9048195
Why?

>>9048195
t. bitter sophomore

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Algebraic * > *.

>>9048204
Because it relies heavily on nonexistent garbage.
>>9048211
>t.
>>>/b/

>>9048219
>it relies heavily on nonexistent garbage
The empty set?

>>9048219
>nonexistent garbage
go on

>>9048227
Not just the empty "set".
>>9048228
What were you trying to say here?

>>9048232
I was wondering what *you* were trying to say in your previous post.

>>9048235
I was just saying that analysis needs to be forbidden.

>>9048237
I know it's bait, but I have nothing better to do, so I'll ask why and what you mean by "nonexistent garbage"

>>9048243
The empty "set", or any other "set" for that matter.

The only ontologically problematic concept in set theory is the empty set, which is vacuous. How can nothing exist when obviously something does? It is much easier to accept infinities than nothingness.

>>9048245
What sort of math do you do that doesn't rely on sets ?

>>9048219
>Because it relies heavily on nonexistent garbage.

I kind of agree with this anon. There is such thing as constructive mathematics which states that all mathematics is computable(this is about computation theory, arithmetics is irrelevant) implying that we should throw away all the uncomputable mathematics(which is anon said "nonexistent garbage"). For example, actual infinity is uncomputable which potential is just fine. Excluded middle shouldn't be taken as an axiom and used in general case(in intuitionistic type theory by Per Martin-Löf it is a theorem). Axiom of choice is garbage as well.
To sum up, mathematics should get rid of all undecidable problems(read about this on wiki) and uncomputable garbage, otherwise it's just FAITH, not science

>>9048250
>The only ontologically problematic concept in set theory is the empty set
Set theory itself is a "problematic concept".
>>9048252
I didn't claim that my math doesn't rely on sets.

>>9048253
>There is such thing as constructive mathematics
Which is consistent with set theory, which means it's garbage as well.

>>9048253
Nice false dichotomy you have there.

>>9048254
So why does relying on sets make analysis more deserving of being banned ?

>>9048253
>There is such thing as constructive mathematics which states that all mathematics is computable
Wrong.

>>9048253
Type theory, especially HoTT is just fine, though.

>>9048259
It relies on them heavily.

>>9048253
>mathematics should get rid of all undecidable problems
I agree. Mathematics should be complete, consistent and decidable.

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Inaccessible cardinals exist. Deal with it.

>>9048266
Can you be more specific ?

>>9048270
Analysis relies heavily on "sets". This is already pretty specific.

>>9048269
Of course they do, set theory is inconsistent.

>>9048271
You didn't explain what you mean by "analysis" or "heavily".

>>9048277
By "analysis" I mean "analysis". By "heavily" I mean "heavily".

>>9048280
>>9048276
>>9048271
>>9048266
>>9048254
you literally have nothing to say aside from "SETS ARE ICKY EWWWW"

>>9048253
>mathematics should get rid of all undecidable problems
Which "set theory" already does. You would have known if you weren't such a retard.

>>9048280
And can you characterize how it makes heavier use of set theory than linear algebra ?

>>9048286
I'm pretty sure "set theory is inconsistent" and "SETS ARE ICKY EWWWW" are different statements.

>>9048276
Which set theory? Tarski–Grothendieck set theory? Prove it.

>>9048289
Do you even know what "heavily" means?

>>9048293
>Which set theory?
ZF is definitely inconsistent.
>Tarski–Grothendieck set theory? Prove it.
I'm currently working on that. You'll have to wait.

>>9048291
they're literally the same if you have nothing to say about them. you keep parroting it and I don't even think you know what it means. which of the axioms do you have a fucking problem with?

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Stop feeding the troll please.

>>9048304
>ZF is definitely inconsistent.
elaborate.

>>9048305
>which of the axioms do you have a fucking problem with?
It's not currently known precisely which axiom causes ZF to be inconsistent. We are working on it.
>>9048309
There is nothing to elaborate on.

>>9048305
Not him. I don't like the axiom schema of specification. I also can't stand the axiom of choice. And anything you can use to arrive at the empty set.
Whether infinite sets exist or not is something that remains to be ascertained but we know for a fact that something exists, therefore no-thing doesn't.

>>9048315
Why is the "empty set" "nothing" though? It's just a "set" with no members.

>>9048298
Do you ?

>>9048324
I believe I do. Also, can you stop using French punctuation please?

>>9048315
So your problem with set theory is that you're schizophrenic

>>9048325
Well, please enlighten me. No, I am French.

>>9048331
>Well, please enlighten me
How should I enlighten you?
>No, I am French.
You aren't typing in French right now though.

>>9048188
but i'm not the guy that created the list, anon.

Should've quoted him instead.

>>9048321
You're appealing to the axiom schema of specification again, without even realising it. Not everything you can define can also exist. Just because you proclaim something to exist doesn't mean it does exist.
This is the oldest and most persistent philosophical error in history. The assumed actualisation of fictitious beings/modes of beings.

>>9048338
>How should I enlighten you?
On your use of the word heavily.

>>9048313
Inconsistency can only be defined relative to an ambient theory, so if your ambient theory is ZFC (for example) then ZF is trivially consistent.
Of course you can only conclude that if you assume ZFC to be consistent, but if you aren't willing to do that then you have no business using ZFC as a metatheory in the first place.

If you prefer using PA as your metatheory, I recall reading somewhere that it's bi-interpretable with ZF where the axiom of infinity is replaced with its negation, which is completely unsurprising.

>>9048315
Set theory has its problems, but they lie with the axiom of regularity, rather than specification.
t. Mochizuki

>>9048344
>You're appealing to the axiom schema of specification again
Nope. I don't believe in "set" theory.
>Just because you proclaim something to exist doesn't mean it does exist
I'm saying that the existence of a "set" with no "members" is pretty easy to accept. It's not the same as accepting the existence of "nothing".

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What is a good theory that would allow me to refute the axiom of choice?

>>9048347
The axiom of regularity too is bizarre, but it's not the only one. The axiom schema of specification is the most egregious example of bullshit though.
It is equivalent to saying that every work of fiction has ontological actuality, that it exists somewhere in a non-fictional way.

The wiser course is arguing to axioms, not arguing from axioms.

>>9048352
>Nope. I don't believe in "set" theory.
Then why the fuck are you even talking?
Never reply to me again.

>>9048356
AC is independent of ZF. There are models of ZF without choice.

>>9048357
>The wiser course is arguing to axioms, not arguing from axioms.
if you think these axioms aren't the result of a huge body of math and mathematicians agreeing that they're the "right" ones then you're retarded

>>9048360
Yes, but I want to actually prove its negation.

>>9048359
>Then why the fuck are you even talking?
I'm merely pointing out that the empty "set" isn't the same thing as "nothing".
>Never reply to me again.
Why is that?

>>9048365
In which context? In ZFC the negation is false because choice is true.

>>9048363
You have no idea what you're talking about. Most mathematics in use doesn't require the full ZF system.

>>9048369
Are you replying to the wrong post? If you think these axioms aren't the result of a huge body of math and mathematicians agreeing that they're the "right" ones then you're retarded.

>>9048363
>truth is decided by consensus
>>>/lit/
And never come back.

>>9048374
no one's talking about truth
what the fuck do you think "truth" means anyway, you fucking popsci imbecile?

>>9048372
You have no idea what you're talking about. Most mathematics in use doesn't require the full ZF system.

>>9048368
>In which context?
I'm asking for a context where I can prove its negation.

>>9048377
read the post again and your reply, and notice that your reply says nothing about the post aside from a generic "no"

>>9048379
The point.

Your head.

>>9048378
ZF+negation of choice

>>9048378
None? For the family of sets {{0}, {1}} there exists the set {0,1} in any reasonable theory.

>>9048381
as long as you don't elaborate I'll keep assuming you're just retarded. "all math uses the full ZFC" has nothing to do with what I said

>>9048382
shut the fuck up

>>9048326
low blow

>>9048382
Did you even read my post?
>>9048383
Are you saying there is no theory which can prove the negation of AC?

>>9048392
Not any theory where the sets {{0}, {1}} and {0,1} exist. It would have to be a theory so different from ZF that choice wouldn't even make sense to state.

>>9048385
It has everything to do with what you said you brain-dead ass-wipe. The body of math propped up around these axioms has very little to do with the overwhelming majority of mathematics as it is used by mathematicians. The whole exercise was done for its own sake. Mathematicians didn't agree on anything. Most mathematicians don't care about such set theoretical considerations in the first place.
Not that it matters anyway, since truth is not decided by consensus.

Now fuck off.

>>9048389
What did you expect exactly ?

>>9048395
Another imbecile who has no idea what he's talking about. The axiom of choice is only necessary as a postulate when you're trying to make selections from infinite sets. You don't need it for finite sets.

>>9048395
You're retarded.

>>9048402
The fact that you need it or not has nothing to do with what its negation implies, moron. Theories where it's false exist, theories where it never works can't exist.

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>>9048402
>infinite sets
No such thing.

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>>9048392
I'm neither of those, so don't blame them for this, but the independence of (not-)AC from ZF means you can have both ZFC and ZFnC.

What you would like to find is a claim P that implies the negation of the axiom of choice. Such a claim is, ofc, independent of ZF, or else not-AC wouldn't be. Therefore, you can add this P as your axiom, giving you some set theory ZFP whose axioms are the Zermelo-Fraenkel axioms and the claim P. The easiest way to do this would be to choose P=not-AC, but you can find a stronger claim too.

Also, check constructivistic logic.

>>9048412
I couldn't care less about your discussion with that troll. I'm just pointing out you have no idea what you're talking about. The the sets {{0}, {1}} and {0,1} have nothing to do with the axiom of choice.

>>9048397
>Not that it matters anyway
aka "I know the shit I'm blurting out is just my opinion so in case you ignore it I'll still pretend to be right"

everyone and their mothers uses ZFC. applications of zorn's lemma are incredibly common in algebra. so what, they just happened to think of zorn's lemma independently, and no one cares about the axioms?

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>Witten/Ashkenazi memes in the physics thread
>Wilberger/Ultrafinitism memes in the math thread
What the fuck is wrong with you people?

>>9048412
I'm not sure you understand what a negation is

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>>9048402
>implying its necessary for infinite sets

>>9048421
>I didn't read so forgive me for being an idiot
The sets {{0}, {1}} and {0,1} are an example that you can't have choice being false every time, jackass.

>>9048422
>everyone and their mothers uses ZFC
You. Have. No. Idea. What. You. Are. Talking. About.

>>9048430
anything to say about how common choice is in algebra or are you going to ignore that because you're dumb?

>>9048429
Stop posting about shit you know nothing about please. It's obvious you have no idea what the axiom of choice entails and are just grabbing onto the word "choice" like an idiot.

>>9048429
can a set be equal to an element?is there a difference?

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>>9048417
>but the independence of (not-)AC from ZF means you can have both ZFC and ZFnC
I know, but don't I need to explicitly add an axiom which states that AC is false?
>Therefore, you can add this P as your axiom
I want to prove the negation of AC from the other axioms. The theory doesn't have to be ZF.

>constructivistic logic
It doesn't refute LEM or AC. I need a theory which allows me to prove the negation of choice, I don't care about LEM that much.

>>9048431
Stop posting already.

>>9048432
Since you're so much of a brainlet I'll explain it to you. Take the set {{0}, {1}}. The axiom of choice being true in this particular instance means the set {0,1} exists. If you want it to be false in every instance then the set {0,1} can't exist.

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>>9048429
The negation of AC says that there is atleast one case in which the choice isn't ok. Finite sets are not a contradiction https://en.wikipedia.org/wiki/Axiom_of_choice#Restriction_to_finite_sets
>The statement of the axiom of choice does not specify whether the collection of nonempty sets is finite or infinite, and thus implies that every finite collection of nonempty sets has a choice function. However, that particular case is a theorem of Zermelo–Fraenkel set theory without the axiom of choice (ZF); it is easily proved by mathematical induction.

>>9048422
NGB is better for some purposes, as it has proper definitions for classes and stuff.

>>9048436
You are making this hard.

>>9048438
glad to see you have nothing to say about shit and were just trying to parrot your imbecile opinions freshly pulled out of your dumb ass. here's a jewel so you can remember and show everyone how retarded you are:

>The axiom schema of specification is the most egregious example of bullshit though. It is equivalent to saying that every work of fiction has ontological actuality, that it exists somewhere in a non-fictional way.

>>9048440
I mentioned there are many systems where choice is false, he insisted he "wanted to prove the negation". I assumed this meant he wanted a theory where it was false in every instance.

>>9048426
If you want the cartesian product of any collection of non-empty sets to be non-empty, then yes, the AC is necessary.

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I know that ZF and ZFC are consistent, but is ZF with Negated AC also consistent?

>>9048442
All i'm reading from you is huff and puff. Fuck off. You're brain-dead. That was an analogy you troglodyte. Kill yourself and spare humanity of your imbecility.

>>9048449
AC is independent of ZF.

>>9048449
https://en.wikipedia.org/wiki/Axiom_of_determinacy

>>9048450
>The axiom schema of specification is the most egregious example of bullshit though. It is equivalent to saying that every work of fiction has ontological actuality, that it exists somewhere in a non-fictional way.

>>9048449
>I know that ZF and ZFC are consistent
ZF and ZFC prove their own consistency, so no.

>>9048439
The axiom of choice has nothing to do with being able to form a set of picks from other sets when the sets are finite. It is independent of such considerations. You can assume the opposite of the axiom of choice and you can still have {1,0} from {{0}, {1}}.

>>9048454
Elaborate?

>>9048454
I already know you have no idea what you're talking about. No need to continue exhibiting your ignorance.

>>9048458
I'll do it even more slowly this time.

An equivalent postulation of the axiom of choice is that "every product of non empty sets is non empty". The product of the sets {0} and {1} contains, in any reasonable theory, the set {0,1}. If you want some kind of "anti-choice" axiom, a strong negation of choice, that says it's false in every instance, then the product of {0} and {1} must be empty and so the set {0,1} must not exist.

>>9048459
it's a retarded platitude with no substance behind it

>>9048463
>The axiom schema of specification is the most egregious example of bullshit though. It is equivalent to saying that every work of fiction has ontological actuality, that it exists somewhere in a non-fictional way.

>>9048465
YOU DON'T NEED TO TELL ME WHAT THE AXIOM OF CHOICE IS OR WHAT ARE ITS EQUIVALENT FORMULATIONS! I already pointed that out >>9048447

THE AXIOM OF CHOICE CAN BE ASSUMED FALSE AND YOU CAN STILL HAVE NON EMPTY PRODUCTS OF NON-EMPTY SETS WHEN YOU'RE ONLY DEALING WITH FINITE PRODUCTS!

STOP POSTING YOU GODDAMN CRETIN!

>>9048468
Elaborate?

>>9048470
chill man. you can also have the axiom of choice be false and have non empty products of infinite non empty sets. like the infinite product {1}{2}{3}{4}... will be N.

>>9048480
>infinite non empty sets.
No such thing.

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yo am i the only pleb that goes regularly on /sci yet hardly knows the fuck bidmas is

>>9048484
>thing
No such thing.

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>this thread is SCHOLZED

>>9048468
It's an analogy you pile of retardation.
>There exists a set whose members are precisely those objects that satisfy the predicate P.

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>>9048497
>tfw you will never have his babies

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>>9048532
And why would you want them?

>>9048012
>that alone is not a trivial problem
Never said it was, but it seems much much simpler.
>assuming that you can get to the optimal 3d packaging from stacking up optimal 2d packages is also foolish
Yeah, you're right. Didn't really think this one through, didn't I? :D
>>9048118
>By the way, the horizontal cross section is a circle only for paraboloids of revolution.
True, I didn't remember correctly the problem. This is just a thought I had on the bus.

>>9048103
>I am glad that people took my bait and started to work on the packing problem. Don't give up anon!
>Packing problems are awesome.
I sweat to fucking God if it's an unsolved problem I'm going to be very pissed.

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Is ZF consistent with the negation of the axiom of "infinity"?

>>9048933
ZF includes axiom of infinity, so I imagine you're asking if the rest of the ZF axioms are consistent with not axiom of infinity. They should be, otherwise it'd be a theorem, not an axiom.

>>9048933
ZF proves the existence of HF (the hereditarily finite sets), which is a model of ZF with the negation of the axiom of infinity.

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>>9048152
>he posted it AGAIN

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Dieudonné's 5 year 'How to be a Mathematician, not a mathematician' plan (published as "A Letter from
Dieudonne")

>1st year (Elementary algebraic geometry)
Borel and Bass - Linear algebraic groups (first part)
Cartan-Chevalley Seminar 1955
Chevalley Seminar 1956 'Classification des groups algébriques'
Mumford - Introduction to algebraic geometry (chapter 1)
Semple and Roth's - Algebraic geometry
Serre - Faisceaux algébriques cohérents (cohomology parts)
Serre - Géométrie Algébrique et Géométrie Analytique
van der Waerden - Algebraische Geometrie

>2nd year
Borel and Bass - Linear algebraic groups (the rest)
Borel-Tits - Groupes réductifs
Serre - Groupes algébriques et corps de classes

>3rd year
Borel-Harishchandra - Arithmetic subgroups of algebraic groups
Borel - Introduction aux groupes arithmétiques
Weil - Adeles and algebraic groups
Seminaire Borel-Serre - Complex multiplication notes

>4th year
Mumford - Introduction to algebraic geometry (chapters 2-3)
Read Elements de géométrie algébrique until Mumford's 'Abelian varieties' makes sense
Mumford - Geometric invariant theory
Serre - Algèbre locale
Samuel Ergebnisse - Méthodes d'algèbre abstraite en géométrie algébrique

>5th year
Abelian varieties over finite fields, formal groups
Automorphic funtions, modular functions
Jacquet-Langlands theory
Algebraic geometry of surfaces
Advances theory of schemes (Grothendieck topologies, étale cohomology...)

Is there a better name for "real" numbers?

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>>9049208
> Is there a better name for "real" numbers?
the Archimedean completion of [math] \mathbb{Q} [/math]

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>>9049208
imaginary numbers

>>9048497
>cute girls cannot talk about maths
https://www.quantamagazine.org/authors/erica-klarreich/

>>9049244
what a self righteous cunt. holy shit.

>>9049273
>what a self righteous cunt. holy shit.
>>>/r9k/

So, what meme post is best 4 learning math?>>9049088 or
>>9048152 ?
although i dont know why the latter gets so much angry (you), care to explain?

>>9049283
brie is the one who sexualized herself. This makes no sense in context.

>>9049290
>meme post
>>>/r/eddit/

>>9049208
Why don't we just call them "numbers"? The reals are the purest of all numbers and are deserving of the name.

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>>9049406
>The reals are the purest of all numbers

>>9049407
>>9049294

>>9049562
Who are you quoting?

>>9049563
>>9049290

>>9048933
ZF proves you are a fucking anime faggot and you should stop posting these pedophile cartoons.

>>9049698
>ZF proves you are a fucking anime faggot and you should stop posting these pedophile cartoons.
>>>/reddit/

>>9048864
Why? Unsolved problems are the best problems available. You get to try all new stuff, and potentially be the first to solve it! Even if you don't solve it you can publish a paper on it if you get some significant approximations!

>>9049698
see >>9049701
Redditry isn't welcome here.

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>>9049701
>>9049719

>>9049722
>>9049719

>>9049795
I think you are a faggot, not just because of your pathetic anime drawings, but because you are irritating in general.

Jesus, what the fuck guys? I would hope the next thread won't have people taking obvious bait again, but I'd be stupid to expect anything else at this point.

>>9049818
The redditors are on the loose today.
see >>9049719

>>9048497
>>9048532
>Scholze is married to a gypsy
What the fuck was he thinking???

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>>9049894

>>9049208
We've decided a few months ago to call imaginary numbers "co-reals".

>>9047904
>>9047964
Mochizuki's IUT papers are still locked in review. It's been 4 years. What is the longest a paper was held in review before it was published?

>>9049936
>What is the longest a paper was held in review before it was published?
does Galois's work count? a few decades I think

I was trying around a bit with the collatz conjecture. It seems that the maximum cycle length below a number is
[eqn]C(x)=\pi^{e+1}*x^{\pi-3}[/eqn]
Dunno why though. It's just an empirical result.

>>9049958
sequence length I mean, not cycle.

>>9049958
SO BEAUTIFUL NUMBERS

Why shouldn't I switch to math?

>>9049958
go into more details

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>>9049958
>collatz conjecture
I have already solved it. You shouldn't even bother.

>>9048424
>the physics thread
What are you talking about?

>>9050066
Go ahead, but I hope you don't end up as most of the guys here.
Enjoy it.

It has been proven that the continuum hypothesis cannot be proven or disproven in ZFC set theory.

So why do some mathematicians apparently still believe that the continuum hypothesis is true or false?

how can a statement be considered true if you know it cannot be proven to be true and false?

what do these mathematicians think that it means for something to be true but unproveable?

>>9050274
Because ZFC system =/= mathematical truth.

Model theory, logic, set theory and the like doesn't seem to be /mg/'s forte.

>>9050278
a statement can only be matheamtically true after you have decided on what axioms you're using.

is it true that the interior angels of a triangle always add up to 180 degrees?

well until you decide whether you're using euclidian axioms or non-eucidian axioms you can't say whether it is true.

am I misunderstanding you? what do you mean? At the moment it sounds like you're talking nonsense and don't know anything about maths

>>9050291
>a statement can only be matheamtically true after you have decided on what axioms you're using.
Wrong.

>>9050291
>At the moment it sounds like you're talking nonsense and don't know anything about maths
The heights of irony.
Provable =/= true.
A provable statement is true if an only if the axioms it depends on are true. How do you determine if the axioms are true?
You might want to have the least familiarity with the topic before you spout nonsense.
>>9050288

https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem

After suffering through the first two chapters of Hatcher's algebraic topology this semester (I hate this book with a passion, hidden hypothesis and too much geometric intuition for my tase) I'm thinking of going through Rotman's Introduction to Algebraic Topology. Thoughts?

Also, for anyone interested specifically in topology, what are some cool theorems to look forward to during Rotman? I've seen the proof for Jordan's separation/Brouwer/Hairy Ball already.

>>9050274
>>9050278
ZFC is know to be inconsistent.

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>>9050378

>>9050378
I can't wait to see the paper, congrats on your eventual fields medal anon.

>>9050505
>implying Fields medals are still awarded for merit

>>9050522
I had forgotten they just award them to four random mathematicians now.

>>9050555
>implying that if the choices are not meritocratic then they are random

>>9050262
how do most of the guys here end up?

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Has anyone read this?

https://www.amazon.com/Colonel-L%C3%A1grimas-Carlos-Fonseca-Su%C3%A1rez/dp/1632061031

>Holed away in a cabin in the Pyrenees, the world-famous and enigmatic mathematician Alexander Grothendieck is working furiously on a final project. But what exactly is this monumental, mysterious undertaking? Why did this man, one of the greatest geniuses of the century, a politically militant man himself, suddenly decide to abandon politics and society altogether? As the reader pursues the answer to these questions, two layered narratives emerge. One is a series of unforgettable characters that have transfixed the mathematician’s imagination: Chana Abramov, a woman obsessed with painting the same Mexican volcano a thousand times, Vladimir Vostokov, an anarchist in battle with technological modernity, and Maximiliano Cienfuegos, a simple man who will nonetheless become the symbol for the Colonel’s as well as Europe’s restless political conscience. The other is the protagonist’s life story: a picaresque journey that traverses the 20th century: from the Russia of the October Revolution to the Mexico of the anarchic 1920s, from the Spanish Civil War to Vietnam, all the way back to France and from there to the Caribbean islands. Out of this Borgesian web emerges a tragicomic allegory for the political arch of the past century, one that began addicted to political action and ended up hooked on big data.

>>9050740
Depressed and suicidal.

>>9050312
> if the axioms it depends on are true.

ok, which set of axioms are "true" , euclidian geometry or non-euclidian geometry?

axioms aren't "true" you ignoramus.

there is no one true set of axioms.

there's no such thing as an axiom or set of axioms being true.

an axiom or set of axioms could be mutually inconsistent or self-contradictory or invalid for some other reason.

but assuming none of these things are the case, like with euclidian geometry axioms vs non-euclidian geometry axioms, there is no way to say that one is more true than the other.

So the statement "the interior angles of a triangle always add up to 180 degrees" is either true if you've chosen euclidian geometry axioms or untrue if you've chosen non-euclidian geometry axioms.

until you've chosen your axioms you can'tsay whether or not it is true.

if you're pretending to be a retard then good job, I'm annoyed at what a retard you are.
>>9050308
>>a statement can only be matheamtically true after you have decided on what axioms you're using.
>Wrong.
Wrong

I've just given you an example of why I'm right, moron

>>9050844
you don't know what you're talking about.
>spacing
>>>/r/eddit

>>9050288
yeah, bring back animeposting pls

>>9050856
so you're clearly unable to refute my argument because I'm right.

fuck off retard

>>9050872
Your only argument seems to be mimicking the posting style of other anons upthread. If tired diatribes about non-euclidean geometry is all you can offer, you're clearly out of your depth here. Read less popsci garbage.

What is mathematical proof is an open philosophical question. You can start with Putnam's essay with the same title.
With that caveat in mind, you can then move on to Chang and Keisler's Model Theory and Takeuti's Proof Theory textbooks, to get a hang on what axioms and proofs are all about.

>>9050943
>What is mathematical proof
What is mathematical truth"

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How do you deal with racism in the mathematical workplace?

>>9051552
Go away /pol/bait

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>>9051552
>monkey in Brazil
>isn't eaten

>>9051552
I don't because black people aren't smart enough to be mathematicians.

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>>9051552
see >>9051710

>>9050872
>so you're clearly unable to refute my argument because I'm right.
Someone not being able to refute an argument doesn't mean it's """right""". And he actually refuted your retardation.

>>9051552
I don't. Except very few Asians mathematics in my university is pure white. (In my first semester there were some Sandniggers/pooinloos, but they left pretty quickly)

>>9051552
I don't, because I am the racist.
Deal with it.

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where are the guys who post math exercises

>>9050943
>If tired diatribes about non-euclidean geometry is all you can offer, you're clearly out of your depth here.

And yet you haven't been able to refute it whatsoever. All you're able to do is mud slingand call it names like a "a tired diatribe".

if your position is correct then tell me which set of axioms is "true" , euclidian or non-euclidian geometry.

you can't because you're wrong.
all you're able to do is impotently name drop. if any of those tomes contained an argument demonstrating how I'm wrong then you'd be able to summarise it here.

but at no point have you offered any argument even attempting to refute me.

transparently weak.
>>9051896
that never happened. If you think it did then show me where.

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>>9052165
It isn't an either-or question. They're axiomatic models for different geometrical structures.
(Stop posting. You're a clueless retard.)

>>9052113
I seem to be awful at picking exercises so I stopped posting any.

>>9052229
And yet before you claimed
>A provable statement is true if an only if the axioms it depends on are true.


but now you're agreeing with me that
>a statement can only be matheamtically true after you have decided on what axioms you're using.

>is it true that the interior angels of a triangle always add up to 180 degrees?

>well until you decide whether you're using euclidian axioms or non-eucidian axioms you can't say whether it is true.

Well done for wasting time and eventually back-peddling to agree with what I said to begin with.

dishonest and mentally feeble

>>9052266
It seems that you're not only mathematically illiterate. (Pro-tip: I'm not agreeing with you at all.)

For the second time, so that any brainlet may get it: provable [math] \neq [/math] true. A statement is provable in a model if it follows from the axioms. A provable statement is true [math] if\ and\ only\ if [/math] the axioms of that model are true.

>>9052273
no , you've back-peddled but don't want to admit that you're agreeing with me.

before you disagreed when I said
>a statement can only be matheamtically true after you have decided on what axioms you're using.

>is it true that the interior angels of a triangle always add up to 180 degrees?

>well until you decide whether you're using euclidian axioms or non-eucidian axioms you can't say whether it is true.

and you disagreed by saying
>A provable statement is true if an only if the axioms it depends on are true.

implying , laughably, that somehow either euclidian or non-euclidian geometry was more "true" than the other, or that one was true and the other was false.

but now after finally being challenged directly several times you've finally presented something mathematically relevent and admitted
>It isn't an either-or question. They're axiomatic models for different geometrical structures.

This entire argument you've been unable to provide any reasoning for how my statements are wrong, and when you do provide some reasoning , it back peddles and contradicts what you disagreed with me on earlier in the discussion.

Good job. bravo.

>>9052276
axioms can't be true. that's a type error you dipshit. axioms can be invalid if they're mutually contradictory or some other fundamental errors, but among axioms or sets of axioms you can't say which are are true or false.

in mathematics people arbitrarily choose (valid) axioms then start proving statements which are true within those axioms.

that's what it means for something to be true in maths.

Did you really go to a university and study mathematics and yet end up with no idea how it works?

What an amazing waste of your time.

>>9052287
* but among axioms or sets of axioms which are valid

>>9052281
I still disagree, it's just that you can't even [math] read [/math]. This:
>a statement can only be matheamtically true after you have decided on what axioms you're using.
is "not even wrong". Like I said, what it means for some mathematical construct/idea/theorem to be true is an open philosophical question.
Personally, I am a principled Platonist (which I believe is the only sensible position to take): I actively subscribe to the view that the existence and truth of mathematical objects is independent of the models used to describe them.
Regardless of what it means for something to be true though, that is orthogonal with it being provable. See >>9050315

>>9052287
Stop posting already.
Fucking buffoon.

>>9052165
>>9052266
>>9052281
>>9052287
>all

>this

>reddit

>spacing

>>9052291
lol at this point you're basically an infant having a tantrum
>Personally I believe in the existence and truth of mathematical objects is independent of the models used to describe them.

Go worship some fairy tales

You originally claimed in reference to the continuum hypothesis
>Because ZFC system =/= mathematical truth.
implying that mathematical statements like for example "There is no set whose cardinality is strictly between that of the integers and the real numbers." or "the interior angles of a triangle add up to 180 degrees" are true or false independent of or outside of the axioms of the system you have decided to work in.

Which is obviously wrong and garbage and I correctly stated that it is wrong and explained how with an example
>a statement can only be matheamtically true after you have decided on what axioms you're using.

>is it true that the interior angels of a triangle always add up to 180 degrees?

>well until you decide whether you're using euclidian axioms or non-eucidian axioms you can't say whether it is true.

At this point you're backpeddling and your argument is in freefall as you're now being forced to admit that statements you previously disagreed with are not wrong (while using the weasle words "not even " to make teh allegation that something is invalid or nonsensical without the need to back it up) and then having to appeal to woolly , vague nonsense like
> what it means for some mathematical construct/idea/theorem to be true is an open philosophical question.
for lack of an argument.

lol, what a butthurt retard
very embarrassing
>>9052292
typical non-argument from a frustrated man who doesn't want to admit that he is wrong and has no counter argument.

I'm self-teaching myself some calculus, and am reading Keisler's "Elementary Calculus: an infinitesimal approach". I like the idea of infinitesimals, so I'm pretty excited. I hope the book is good.

>>9052301
>true or false independent of or outside of the axioms of the system you have decided to work in.
Exactly. Proof is a syntactical matter. Truth is a semantical one.
I don't know how to put it in simpler terms than this.
You're utterly clueless. I already gave you some pointers that would help with your lacunae. but you continue to argue like troglodyte about shit you don't understand.

>>9052307
As to the fucking triangles, a triangle in the euclidean plane is a different mathematical object from a triangle in the hyperbolic plane. Their existence and the truth of the various theorems about them are independent from one another. You try to profit from a semantic ambiguity (the fact that the term "triangle" is used in the case of both objects) but the only thing you succeed at is showing that you have no fucking clue what you're talking about.

But I already said as much before.

>>9052307
Gosh if you're really insisting on repeating the moronic claim that whether "the interior angles of a triangle add up to 180 degrees" is true or false is independent of or outside of the axioms of the system you have decided to work in then I can simpy demonstrate again that this is wrong and garbage.

is it true that the interior angels of a triangle always add up to 180 degrees?

It's true in euclidian geometry , a set of axioms, and it is untrue in non-euclidian geometry a different set of axioms.

so in order to claim that the statement has some transcendental , real, most-valid truth value beyond and independent of the set of axioms which it disagrees with, then what you're basically saying is that the foundation of your argument is that you have imagined your own one-true universe where real, valid mathematics is where it happens that only one of either euclidian or non-euclidian geometry is allowed, the one you agree with.

so basically you're a spastic who can't accept that mathematics is about making up rules then deriving results. and no set of rules is more "true" than any other.

absolute fucking moron

>>9052327
God I hate arguing with stupid blowhards.
>is it true that the interior angels of a triangle always add up to 180 degrees?
it depends on how you define a triangle.
>It's true in euclidian geometry
It can also be false in euclidean geometry, if, for example, you define a triangle as a set of 3 points (not all of which lie on a geodesic curve) and the geodesic curve segments connecting them on a hyperbolic surface in the three dimensional euclidean space.

So basically, you're clueless imbecile.

>>9052324
the definition of a triangle is exactly the same in both euclidian geometry and non-euclidian geometry, you dishonest charlatan.

So no, they are not different objects, they are versions of the same object with different properties depending on whether you include the axiom "If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles." or not

So the statement "the interior angels of a triangle always add up to 180 degrees" is always well defined but whether it is true or not DEPENDS ENTIRELY ON WHICH AXIOMS YOU HAVE DECIDED TO INCLUDE OR ASSUME

IN NO OTHER SENSE is the statement "the interior angels of a triangle always add up to 180 degrees" true or false.

There is no one true , most valid set of axioms that exists somewhere which is the final judge and magically decides whether a statement is true or not outside of the axioms that we humans have decided to work in.

That is just a figmant of your teenage imagination.

This entire hissyfit is the result of you being butthurt that mathematicians don't subscribe to your personal religious belief.

>>9052353
You are an idiot.
>>9052351

>>9052351
in a 3 dimensional euclidian space a geodesic, the shortest path between two points, is a straight line so no, triangles in euclidian spaces always have internal angles that add up to 180 degrees.

What you havetried to audaciously do is do non-euclidian geometry then call it euclidian at the end.

you're such a dishonest moron lmao

>>9052356
>>9052351
https://en.wikipedia.org/wiki/Sum_of_angles_of_a_triangle
>In Euclidean geometry, the triangle postulate states that the sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate.[1]
>Eric W. Weisstein (2003). CRC concise encyclopedia of mathematics (2nd ed.). p. 2147. ISBN 1-58488-347-2. The parallel postulate is equivalent to the Equidistance postulate, Playfair axiom, Proclus axiom, the Triangle postulate and the Pythagorean theorem.

> tfw you will never be so retarded that you try to argue that triangles in euclidian space might have interior angles that add up to 180 degrees

>>9052365
Why are you still posting you clueless ape? Every time you make one of your stupid posts the level of discourse in the thread goes down.
/mg/ is shit enough as it is without your stupid ass shitting all over the place.

>>9052369
A geodesic curve on a surface is a line only if the surface has curvature 0 everywhere, i.e. if it is an euclidean plane.

>>9052373
meant for >>9052365

>>9052370
hahaha great counter argument.

you're lashing out because your moronic counter example was exposed as totally invalid.

>>9052373
exactly, hence why a triangle in a euclidian space has angles that add up to 180 degrees, because the geodesics will be straight lines hence why >>9052351 is wrong.

>>9052381
If you define a triangle as per >>9052351 then yes, the sum of its interior angles will not add up to 180 even in euclidean geometry.

>hence why a triangle in a euclidian space has angles that add up to 180 degrees, because the geodesics will be straight lines
You clearly do not know what a geodesic is. A geodesic curve on a sphere is not a straight line, you fucking moron. Nor is it a straight line on a hyperbolic surface.

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>>9052381
Please tell me you're trolling.

>>9052327
>>9052353
>spacing
>>>/r/eddit

>>9052388
your example is simply doing 2d non-euclidian plane geometry and then saying "but this hyperbolic surface which we are doing 2D non-euclidian geometry on is inside a euclidian space". It's only because you are introducing the contived requirement that the geodesics be restricted to go through a hyperbolic surface that the geodesics are not straight lines, which they would be in any unrestricted euclidian space since a geodesic is the shortest path between two points. I admit I did not notice the hyperbolic surface requirement you introduced to your contrived redefinition , but it does not matter to the main argument.

besides which , this diversion makes no difference to me being correct in the main argument.

triangles have a standard definition in both euclidian and non-euclidian geometry and in this standard definition the truth value of the statement "the interior angles of a triangle always add up to 180" is true when you have decided to use euclidian geometry as your axiom system and false when you have decided to use noneuclidian geometry as your axiom system.

so >>9052327
is correct
mathematical statements, e.g. the interior angles of a triangle always add up to 180 degrees, are not true or false independent of what axiom system you have decided to work in.

now just take the L you stupid, butthurt loser

I know you must feel embarrassed and frustrated and ashamed about studying maths and being so wrong and ignorant about something so simple but the solution is to educate yourself rather than lashing out.

>>9052404
My example is clearly "doing" euclidean geometry as it only requires the axioms for a 3-dimensional euclidean space.
The fact that you can interpret that construction as a model for geometry in the hyperbolic plane is part of my point.

Write less, think more.

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>>9052404
>I know you must feel embarrassed and frustrated and ashamed
p.s. embarassed is synonymous with ashamed

>>9052411

your example doesn't have a point, because it doesn't do anything to contradict or refute the main argument

triangles have a standard definition in both euclidian and non-euclidian geometry and in this standard definition the truth value of the statement "the interior angles of a triangle always add up to 180" is true when you have decided to use euclidian geometry as your axiom system and false when you have decided to use noneuclidian geometry as your axiom system.

so >>9052327 (You)
is correct
mathematical statements, e.g. the interior angles of a triangle always add up to 180 degrees, are not true or false independent of what axiom system you have decided to work in.


so changing the meaning of triangle so that the lines forming the triangle have to be geodesics on a curved surface is irrelevent.

>>9052431
>your example doesn't have a point, because it doesn't do anything to contradict or refute the main argument
It directly refutes the argument that what the measure of the interior angles of a triangle add up to depends on the axioms you use, since the construction is done in an euclidean space.
And it directly illustrates that a triangle in the euclidean plane and a triangle in the hyperbolic plane are different mathematical objects, by way of a model of a hyperbolic triangle in an euclidean space.

A definition is a definition. Are you saying that it is not true that for the object I constructed, the measure of its interior angles does not add up to [math] \pi [/math] radians? Or are you saying that it isn't a triangle?
Sadly, you're wrong on both counts. And regardless, now you're arguing that what the sum of the measure of the interior angles of a triangle is depends on the definition of triangle, which was my point in the first place!

You're just sad at this point, give it a rest. Study more so you'll know what you're talking about next time.

>>9052450
I have correctly said
> the truth value of the statement "the interior angles of a triangle always add up to 180" is true when you have decided to use euclidian geometry as your axiom system and false when you have decided to use noneuclidian geometry as your axiom system.

To which you have said "aha but if I change the meaning of triangle so that it means that the lines forming the triangle have to be geodesics on a curved surface then it is not true that in euclidian geometry axioms a triangle's interior angles always add up to 180 degrees"

But this refutes nothing because that is not what triangle means.

if you want to change the meaning of words then you might as well say "but what if euclidian now means hyperbolic ? now in euclidian geometry it is untrue that the interior angles of a triangle always add up to 180 degrees".

in both euclidian and non- euclidian geometry the standard definition of triangle is the same

the only difference is that in euclidian geometry there is an extra axiom which ensures that the interior angles of a triangle add up to 180 degrees such that the statement is true in euclidian geometry and false in non-euclidian geometry.

you're really just making up nonsense non-arguments.

desperate and pathetic, transparent.

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>>9052471
Nothing more on the matter need be said. You're obviously a mathematically illiterate buffoon who should move his ass back to >>>/g/ ASAP.

>>9052431
>>9052471
>reddit spacing
>>>/r/eddit

>>9052485
no other nonsense arguments to make huh?

just resorting to empty name calling because everything you've said has been refuted and you have no counter argument.

I agree that nothing more needs to be said by me because I'm correct.

I'm glad if you'll finally shut the fuck up and take the L

>>9052509
>>9052495

Hello, /mg/. I know you like noob questions, so could you verify my proof please.
I have to proof for odd integer[math]\ n > 1[/math] if [math]gcd(r, 2n) = 1[/math] then [math]gcd(\frac{r-n}{2}, n) = 1[/math]
Firstly, [math]gcd(r, 2n) = 1 \implies r[/math] is odd
There are some integers [math]a, b[/math] such that
[math]ar + 2bn = 1[/math]
[math]ar - an + 2bn + an = 1[/math]
[math]a(r-n) + n(2b + a) = 1[/math]
Since both [math]r[/math] and [math]n[/math] are odd [math]r-a[/math] is even:
[math]2a(\frac{r-n}{2}) + n(2n+a)=1 [/math]
Hence, [math]gcd(\frac{r-n}{2}, n) = 1[/math]

>>9052864
everything's good except you just typoed

>Since both r and n are odd r−n is even:
and
>2a[(r-n)/2]+n(2b+a)=1

solution to

f(x)^f(x) = x ?

t. can't into latex

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>>9053419
1^1=1

>>9053447
What is f(x) then
you only gave 1 set of solutions

>>9053480
Ever heard of a constant function?

>>9053419
>>9053480
You might want to define the domain and range of [math] f [/math] before you ask such things.

>>9053480
f(x) = ln(x)/W(ln(x))

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>>9051552
I don't because I'm self taught master race.

2017 IMO results are up

>>9054228
Why is Germany so fucking shit at the IMO?

>>9054310
Shit tier math education I would guess.
(One state recently had a scandal where in the mock exam for their "highschool diploma" the average barely passed)

I would also say that very little focus is set on helping good students, I live in Germany and math class was a huge fucking joke throughout "highschool" I never felt challenged in any way (I am a brainlet) and I was not the only one.

There is also endless repeating of the same stuff so that the brainlets can understand it, coupled (atleast in my state) with a shit tier elective system which makes people with no interest in a subject still take the """advanced""" courses.

In my classes there was also very little logical thinking (except when the teacher diverted from what he is supposed to teach).

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>>9054228
The following are the [math] \mathbb{qt}\pi [/math]ies who got at least bronze, i.e. the girls you should find and (if all else fails) kidnap and rape if you want your kids to be both smart [math] and [/math] pretty cute:

[math] \mathcal{Amanda}\ \mathcal{Vanegas} [/math]
(I could not find a higher quality image.)

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>>9054456
[math] \mathcal{Anna}\ \mathcal{Mustata} [/math]

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>>9054458
[math] \mathcal{Jelena}\ \mathcal{Ivančić} [/math]

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>>9054460
[math] \mathcal{Zsuzsanna}\ \mathcal{Baran} [/math]

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Honourable mention for our resident /math/ematician [math] \mathcal{Alice}\ \mathcal{Ryhl} [/math].

>only 7 points
Good job, [math] brainlette [/math]!

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I kept trying, but I could not find any (reliable) photos of the girl from Korea (these people should choose more distinctive names for fuck's sake).
Cutest overall is probably [math] \mathcal{Alexandra}\ \mathcal{Timofte} [/math] (but she only got 15 points in total).

The rest are as fugly as expected.

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>>9054458
>Anna Mustata 3 years ago
gross

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>>9054508
>>9054533
>2 gold medals, 1 bronze
I found my mathfu

>>9054468
I'm seeing 9 points total and 7 on the first problem, not that it makes a huge difference.

Only 2 (Linus Cooper and Mikhail Ivanov) participants were able to solve this problem, and another 2 (Joe Benton and Pavel Hudec) gave partial solutions. Can you do better /mg/?

A hunter and an invisible rabbit play a game in the Euclidean plane. The rabbit’s starting point, [math] A_0 [/math], and the hunter's starting point, [math] B_0 [/math], are the same. After [math] n - 1 [/math] rounds of the game, the rabbit is at point [math] A_{n-1} [/math] and the hunter is at point [math] B_{n-1} [/math].
In the [math] n^{\text{th}} [/math] round of the game, three things occur in order:

(i) The rabbit moves invisibly to a point [math] A_n [/math] such that the distance between [math] A_{n-1} and [math] A_n [/math] is
exactly [math] 1 [/math].
(ii) A tracking device reports a point [math] P_n [/math] to the hunter. The only guarantee provided by the tracking device to the hunter is that the distance between [math] P_n [/math] and [math] A_n [/math] is at most [math] 1 [/math].
(iii) The hunter moves visibly to a point [math] B_n [/math] such that the distance between [math] B_{n-1} [/math] and [math] B_n [/math] is exactly [math] 1 [/math].

Is it always possible, no matter how the rabbit moves, and no matter what points are reported
by the tracking device, for the hunter to choose her moves so that after [math] 10^9 [/math] rounds she can ensure that the distance between her and the rabbit is at most [math] 100 [/math]?

>>9054545
I think the page updated in the meantime or it had some display error when I checked. So she probably guessed a couple true results with no proof.

>>9054533
She looks noticeably better now. A bit of exercise and better hygiene is all she needs. Probably the fugliest of the girls I posted but the other contestants are way more hideous. They either look like deformed trolls or men with long hair.

>>9054468
Cute.

>>9054508
Is it just me or are the rumanian teams at the IMO among some of the most well-adjusted people there, usually? Even the monsters like Manolescu who got a perfect score at every IMO he participated in comes off as pretty, you know, neurotypical.

Why is that?

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>>9054543
I raise you pic related
>4 gold medals, 1 silver

>>9054547
>Euclidean plane
No such thing.

>>9054668
See
>>9048269

>>9054697
see >>9054668

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>>9054456
>>9054458
>>9054460
>>9054462
>>9054468
>>9054508
>>9054533
>>9054543
>>9054623

Why are math girls so ugly?

>>9054456
damn what a cutie

>>9055015
IMO contestants are usually plain or ugly/weird looking

Brainlet here, I have been studying eigenfaces and face identification, and I think I understand the theory, but can somebody please show an example calculation step by step of how to use it with 2x2 matrices and real numbers, so that I can check that do I understand it.