/mg/ - maths general

[Anonymous No.11407699]

*blocks your path* edition

[Anonymous No.11407702]

previous:
>>11396004

[Anonymous No.11407716]

Reminder that Cantor's Diagonal Argument is complete rubbish, since it relies on intuitive resolving of undefined behaviours.

[Anonymous No.11407723]

Also reminder that 0.999999... only equals one when defined as such. There is no inherent fundamental that requires it so.

[Anonymous No.11407725]

>>11407716
>>11407723
how's high school?

[Anonymous No.11407729]

>>11407725
You cannot intellectually refute what I just said. Instead you choose the path of ignorance.

Why?

Pride? Stupidity?

[Anonymous No.11407733]

>>11407716
>intuitive resolving of undefined behaviours.
Such as?

[Anonymous No.11407735]

>>11407723
but why does it even matter though, it's all definitions in the end anyway

[Anonymous No.11407737]

Reminder that
>>11407716
>>11407723
is a retard

[Anonymous No.11407744]

>>11407723
Sum of x(k) from k = 0 to inf = Limit of sum of x(k) from k=0 to n as n-> inf

Where do you see 0.999... being defined as 1?

[Anonymous No.11407753]

>>11407723
0.9999... being not equal to one would imply the existence of an infinitesimal within the real numbers, and the set is there fore not Archimedian. fuck off to /x/

[Anonymous No.11407758]

I asked in the last thread but only got a partial answer. How the fuck does one show an arbitrary function is continuous on its entire domain? My intuition tells me that induction would not be an appropriate method for this, but I'm not sure of an alternative.

[Anonymous No.11407764]

>>11407733
* Population and enumeration of the set under test.

* Order of operations - there's no reason the complementary sequence has to be synthesised after the set's enumeration step.

>>11407737
Cope. I'm 160+IQ

>>11407753
>Here's how I've defined my numbers. No other definitions allowed.
Literally brainlet tier.

>>11407744
Summing to infinity is supposed to define a recursive operation as a distinct identity? Try harder midwit.

[Anonymous No.11407767]

>>11407764
>Here's how I've defined my numbers. No other definitions allowed.
>Literally brainlet tier.
If we're not talking about the reals, then the question is rather meaningless isn't it

[Anonymous No.11407770]

ugg want know how me count stone if keep break stone into part stone

[Anonymous No.11407772]

>>11407767
What question is that, brainlet? I'm fishing for disagreement over a very reasonable statement...and you took the bait. Literally outing yourself as a very dumb boy. Don't ever come here again.

[Anonymous No.11407773]

>>11407770
UGG BREAK STONE IN HALF

UGG HAVE TWO STONE BUT IN TOTAL STILL ONE STONE

UGG KEEP BREAKING STONE SMALLER

UGG THINK STONE PIECES KEEP GET SMALLER UNTIL NOTHING

STONE MADE OUT OF NOTHING???

[Anonymous No.11407778]

>math is about physical things
oh sweet summer child...

[Anonymous No.11407779]

>>11407764
>* Population and enumeration of the set under test.
What about it?

>* Order of operations - there's no reason the complementary sequence has to be synthesised after the set's enumeration step.
It doesn't have to... but it can be. Do you even have a point?

>Summing to infinity is supposed to define a recursive operation as a distinct identity?
Where do you see a recursive operation?

[Anonymous No.11407781]

>>11407772
mods pls

[Anonymous No.11407784]

>>11407758
If you're the polynomials guy. If [math] f [/math] and [math] g [/math] are continuous functions, then so are [math] f+g [/math], [math]f*g[/math] and [math]f/g[/math] if [math] g(x) \neq 0 [/math] [math] \forall x [/math]. Can you figure out the rest, or do you need another breadcrumb?

[Anonymous No.11407786]

>>11407773
UGG HAVE STONE
UGG BREAK STONE 2
UGG 2 STONE EQUAL 1 STONE
UGG 2=1
*publish paper*

[Anonymous No.11407793]

If you've btfo math so hard that you've basically undid the last 300 years of progress, how about announcing it to the world via the news, social media, or any reputable university? Clearly, we're all wrong and you're right and need to be set straight.

[Anonymous No.11407796]

>>11407784
No the polynomials part, I totally understand. Suppose [math]f \text{is just an arbitrary real valued function on some domain} D.[/math] From what I understand about continuity, showing this function is continuous on some point [math] x_0 \in D[/math] is straightfoward. Now, how do I generalize to ALL [math] x_0 \in D[/math]?

[Anonymous No.11407797]

>>11407779
>What about it?
Its fixed nature. The writer assumed it is a static and closed process, thus his methods are complete for all enumeration processes. This is false.

>It doesn't have to... but it can be. Do you even have a point?
Then define it as such. The argument leaves it as a sole incident, with no note of the mutability.

>Where do you see a recursive operation?
Assuming a finite base, 10/3 will always be a recursive calculation.

[Anonymous No.11407803]

>>11407796
dammit. didn't close the \text{} brace. my apologies

[Anonymous No.11407809]

>>11407793
ugg no care about progress of discipline
ugg need publish paper for tenure

[Anonymous No.11407826]

>>11407796
Well, either you could try and prove that it IS continuous on any arbitrary point in its domain, which would be tough, OR (since I'm working through baby rudin right now for a class) theorem 4.8 of pma states: A mapping [math] f [/math] of a metric space [math] X [/math] into a metric space [math] Y [/math] is continuous on [math] X [/math] if and only if [math] f^{-1}(V) [/math] is open in [math] X [/math] for every open set [math] V [/math] in [math] Y [/math]

>>11407803
Eh its latex, it happens, don't worry about it. As long as I can read it.

[Anonymous No.11407834]

>>11407796
You make a delta function which, get this, takes epsilon and x as it's arguments.

[Anonymous No.11407841]

>>11407797
>Its fixed nature. The writer assumed it is a static and closed process, thus his methods are complete for all enumeration processes. This is false.
That's the entire point of the proof, it's a proof by contradiction that shows there are infinite sets that cannot be enumerated.

>Then define it as such. The argument leaves it as a sole incident, with no note of the mutability.
Oh, I get it, you're a schizo spouting gibberish.

>Assuming a finite base, 10/3 will always be a recursive calculation.
It's a number, not a calculation. Also, this doesn't explain where there is a recursive operation in the definition.

[Anonymous No.11407843]

Why do so many engineering and CS majors get filtered by integral calculus?

[Anonymous No.11407851]

>>11407843
Anyone can do a derivative
My dog can do a derivative
Your Wife's son can do a derivative
Integration however is a god damn art

[Anonymous No.11407857]

>>11407826
Interesting. I figured induction wouldn't be enough because you could easily devise a function, say a rational function, with a single point of discontinuity on an open interval, and thus breaking induction. Based on what you're saying though, in the rational function example, would that mean you have one such set [math]V[/math] in [math]Y[/math]where you don't get an open set [math]f^{-1}(V)\in X[/math]?

>>11407834
Please elaborate. I'm still pretty new to this stuff

[Anonymous No.11407860]

>>11407843
All analytic functions can be easily differentiated, but it's not so straightfoward going the other way.

[Anonymous No.11407874]

>>11407841
>shows there are infinite sets that cannot be enumerated.
Wrong bucko. A set is not defined by the sequencing of its enumeration - only by the contents.

>Oh, I get it, you're a schizo spouting gibberish.
Low IQ answer because you cannot refute the Truth.

>It's a number
Really broseph? Tell me what that number is, I'll wait.
Oh nevermind, you can only express it as the result of a calculation.

You have been thoroughly BTFO by a superior mind. Please terminate your existence.

[Anonymous No.11407889]

>>11407874
>A set is not defined by the sequencing of its enumeration - only by the contents.
Where did I say it was? Fucking illiterate schizo.

>Low IQ answer because you cannot refute the Truth.
Schizo response.

>Really broseph? Tell me what that number is, I'll wait.
10/3

[Anonymous No.11407891]

Are you guys still arguing about 0.999...?
I told you, neither 0.999... or 1 are actually numbers. They're human-created representations of a single point on the number line. The confusion and argument comes from our representation method being shitty and doesn't reflect the underlying properties of the real numbers.

[Anonymous No.11407892]

>Abstract Algebra
Professor is famous for being one of the hardests here, he studied ib Harvard
>Analysis
Professor has a famous for being good but also hard
>Calculus III
Professor is a cutie blond with big boobs
>ODE
Professor is a bald

What do you guys think of the subjects I'll do this semester? I'm still struggling with proofs, need to practice How to Prove It before classes start

[Anonymous No.11407893]

>>11407891
>I told you, neither 0.999... or 1 are actually numbers.
Wrong, try again.

[Anonymous No.11407894]

>>11407891
more like one incel keeps spamming it and everyone else foolishly gives it attention.

[Anonymous No.11407895]

>>11407892
How are you taking analysis without learning vector/multivariable calculus?

[Anonymous No.11407897]

>>11407892
>struggling with proofs and going into Analysis/Abstract.
WHEW. You're in for a rough time bud.

[Anonymous No.11407899]

>>11407893
He's right though, brainlets who can't abstract will deny because they're too dumb to understand

[Anonymous No.11407904]

>>11407889
>Where did I say it was? Fucking illiterate schizo.
So we agree that for all sets tested by the diagonal argument, they can be enumerated differently- thus without note or definition the argument falls through? I'm glad you agree with me, kid.

>10/3
So the result of a calculation? Congratulations bro, you're now just humiliating yourself.

[Anonymous No.11407908]

Quick rundown on elliptic functions that Abel and Jacobi worked on?

[Anonymous No.11407910]

>>11407895
It's not required in my uni, I'm going to do Analysis I which is Real Analysis, vector calculus is only required for Analysis II
>>11407897
I still have 20 days to learn proofs, I'm using how to prove it

[Anonymous No.11407911]

>>11407899
>He's right though
Wrong, try again.

[Anonymous No.11407912]

>>11407910
>I still have 20 days to learn proofs, I'm using how to prove it
Then shut the fuck up, grab a book on how to prove shit (based on what you're doing preferably one that has an emphasis on set theory) and get going

[Anonymous No.11407915]

>>11407894
I'm actually extremely attractive and get pussy every odd gym sesh I attend. I would consider myself a 9/10. With my career and income- 10/10.

>>11407891
Finally, perhaps there is some intelligence on /mg/. Just as I originally said, their distinction is either defined as so or not so.

Why is the only non-brainlet here using an anime avatar? I'm disgusted.

[Anonymous No.11407921]

>>11407915
Math is inherently anime.

[Anonymous No.11407922]

>>11407912
Thanks, I'm gonna make it this semester, ladt semester I failed a lot of classes due to procrastination buy this time I'm confident, we're all gonna fucking make it brah

[Anonymous No.11407926]

>>11407922
Define 'a lot'.

[Anonymous No.11407929]

>>11407926
5. But I didn't study for any of them, I would make it otherwise

[Anonymous No.11407931]

>>11407904
>So we agree that for all sets tested by the diagonal argument, they can be enumerated differently- thus without note or definition the argument falls through?
How can I agree with schizo gibberish like this? You're not actually saying anything. It doesn't matter how they are enumerated, there will always be a member of the set complementary to each diagonal of the enumeration. Therefore they can't be enumerated.

>So the result of a calculation?
Every number is a result of infinite calculations, doesn't mean they are defined by calculation. It's hard to tell since your posts are full of schizo gibberish, but you appear to be arguing that because 10/3 is an infinite repeating decimal, then 10/3 is "recursive." 10/3 is not repeating or infinite in other bases. So your argument is completely arbitrary.

kys schizo

[Anonymous No.11407933]

>>11407908
>Bernoulli bow to the Abel and Jacobi
>in contact with aliens
>rumoured to possess transcendental abilities
>controls AMS with an iron fist
>owns think tanks and banks all over the world
>direct descendants of the ancient non-euclidean line
>will bankroll the first cities in function space
>own basically every finite difference program research facility on Earth
>first designer babies will be Abel and Jacobi Babies
>both Abel and Jacobi said to have 200+ IQ
>ancient Indian scriptures tell of two angels who will descend upon the Earth and will bring an era of enlightenment and unprecedented mathematical progress with them
>They own Operations research labs around the world
>You likely have Abel and Jacobi structures inside you right now
>The Abel and Jacobi are in regular communication with the Mathematicians Euler and Gauss, forwarding the word of God to the Academic Church
>They learned fluent French in under a week
>Nation states entrust their gold reserves with the two. There's no gold in Ft. Knox, only Ft. Abel and Jacobi
>The two are 67 years old, from the space-time reference point of the base human.
>In reality, they are elliptical temporal beings existing in all points of time and space from the ivp bang to the end of the boundary
>The two will guide humanity into a new age of wisdom, peace and Putnam problems

[Anonymous No.11407936]

>>11407931
So I'll choose to enumerate whatever the complementary sequence is after it has been synthesised, so it will always feature the set. Problem, brother?

>doesn't mean they are defined by calculation.
So post the number out in full. Go on. If it is defined by its own numeric identity, you'll have no trouble writing it out for me. Remember: no operators (+ - / * ), because that would be a calculation.
I'll wait.

[Anonymous No.11407938]

>>11407933
Finally a good fucking post.

[Anonymous No.11407942]

>>11407933
Holy based.

[Anonymous No.11407952]

>>will bankroll the first cities in function space

[Anonymous No.11407957]

>>11407933
>can produce quality math shitposts
>can't publish a math paper
>can't find a job
can one of you 115+ IQ folk please put me out of my misery?

[Anonymous No.11407967]

>>11407936
>So I'll choose to enumerate whatever the complementary sequence is after it has been synthesised
Then there will be a new member containing the complement of the diagonal of that member. Dumb schizo. No matter how much you add, you will never enumerate the whole set.

>So post the number out in full.
What does "in full" mean? A number is a number regardless of its decimal form. Here is the number in base 3:

10.1

There's the "whole number," same as 10/3

[Anonymous No.11407977]

>>11407933
>Abel and Jacobi
>AMS

[Anonymous No.11407980]

Apologize.

[Anonymous No.11407981]

Why do topologychads keep winning???

[Anonymous No.11407982]

>>11407977
American Mathematical Society

[Anonymous No.11407983]

>>11407796
Find a function delta(epsilon, x_0) that works for a given point x_0 with a given precision epsilon.
This is usually hard to do, which is why people usually don't do it. But sometimes your function will be uniformly continuous, so you can pick the same delta(epsilon) working for every x_0. And even if it isn't a lot of times it will be uniformly continuous on a bunch of sets, and the union of these sets will cover everything in D.

[Anonymous No.11407987]

>>11407860
>all analytic functions
what? we're talking about power series now?
>can be easily differentiated
i agree, of course. how else would one differentiate a power series?
>but it's not so straightforward going the other way
what? you don't know how to integrate a power series?

[Anonymous No.11407989]

>>11407982
>Jacobi died in 1851
>AMS founded in 1888

[Anonymous No.11407990]

>>11407981
isn't topology slowly dying research wise?

[Anonymous No.11407993]

>>11407989
he didn't die, retart.

[Anonymous No.11407995]

>>11407989
Why, thank you, you're the only one who realized it was all a joke, thanks for sharing this illuminating and not obvious thought with us, you truly are god you know, what will be your next huge discovery, milord?

[Anonymous No.11407999]

>>11407857
Yep, isolated points/singletons aren't open, so with the right choice of open set, you'd get a whatever set unioned with the single point, which wouldn't be open. For instance: say [math] f:R\rightarrow R \text{ where } f(x)=x^2 \text{ when } x \neq 4 \text{ and } f(x)=4 \text{ when } x=4. [/math]. Then take [math] V=(0,9) [/math]. Then [math] f^{-1}(V)=(0,2) \cup [4,4] [/math]. Therefore [math] f [/math] isn't continuous. Induction would only work on functions with the naturals as their domain.

The other guy is just saying do the proof of continuity at a point for any arbitrary point.

[Anonymous No.11408002]

>>11407967
>No matter how much you add, you will never enumerate the whole set.
Actually, brainlet, the argument was about proving bijection with the natural numbers. Recursion does not preclude bijection. Better yet, the idea was that the complementary sequence is never enumerated, which is a very silly thing to unintentionally define.

>What does "in full" mean?

Why, every single digit of course! You told me that it's a number, not a calculation (>>11407841), thus you should be able reference this number using just digits.

Remember: no cross bases. If you use it as its own base, you are merely deferring the calculation to the base thus you are not referencing the number if you cannot also write the base out in full.

[Anonymous No.11408007]

Would /mg/'s quality improve or not if all anime posters were expunged?

[Anonymous No.11408008]

>>11408007
>Would /mg/'s quality improve or not if all anime posters were expunged?
You'd be expunging the quality posters.

[Anonymous No.11408009]

>>11407995
Yikes I was just kidding hun, don't take it personally

[Anonymous No.11408035]

>>11408009
No, you were autistically criticizing a joke as if it were serious, now go fuck yourself

[Anonymous No.11408041]

>>11408008
Quality posting and avatarfagging with a cartoon are mutually exclusive, anon.

[Anonymous No.11408046]

[math] \not \ \and [/math]

[Anonymous No.11408050]

>>11407980
I'm sorry for being such a brainlet Mochizuki-Sensei please don't roast my understanding of elliptic curves

[Anonymous No.11408052]

>>11408035
Ok whatever you say hun.

[Anonymous No.11408068]

>>11408046
How to I write the logical connective in LaTeX? What about the 'and' and 'or' connectives? I thought it was something like \not, \and, \or

[Anonymous No.11408071]

>>11408052
Shut it

[Anonymous No.11408073]

>>11408071

[Anonymous No.11408075]

>>11408068
https://lmgtfy.com/?q=latex+logic+symbols

[Anonymous No.11408076]

>>11408002
>Actually, brainlet, the argument was about proving bijection with the natural numbers.
Which is enumeration, you illiterate mongoloid schizo.

>Recursion does not preclude bijection.
Recursion has nothing to do with any of this, you illiterate mongoloid schizo.

>Better yet, the idea was that the complementary sequence is never enumerated, which is a very silly thing to unintentionally define.
Nice gibberish, you illiterate mongoloid schizo.

>Why, every single digit of course!
Why are digits in decimal important?

>You told me that it's a number, not a calculation (>>11407841 (You)), thus you should be able reference this number using just digits.
I did, not that it proves anything. 10.1 is 10/3 in base 3 digits.

>Remember: no cross bases.
Because?

>If you use it as its own base, you are merely deferring the calculation to the base thus you are not referencing the number if you cannot also write the base out in full.
What calculation? You haven't explained any of your arbitrary demands, you illiterate mongoloid schizo.

[Anonymous No.11408078]

>>11408075
Based and, dare I say, redpilled.

[Anonymous No.11408080]

>>11408073
Holy fuck, you can't shut up can you? You wanna have the last laugh, is this it? What a child you are. I'm not letting you get the last post here.

[Anonymous No.11408084]

@11408080

[Anonymous No.11408085]

>>11408068
[math]\land[/math], [math]\lor[/math], [math]\neg[/math]

[Anonymous No.11408090]

>>11408084
Fuck u

[Anonymous No.11408093]

>>11407999
>isolated points/singletons aren't open
it's worth saying that it depends on your choice of topology

[Anonymous No.11408094]

>>11408085
How?

[Anonymous No.11408099]

>>11408094

[Anonymous No.11408115]

>>11408099
I'm on mobile

[Anonymous No.11408117]

>>11408115
>Phoneposter
You have to go back.

[Anonymous No.11408122]

>>11408117
Oh, I'm sorry that I was born in a shitty third world country and am too poor to fix my 10 year old notebook, it's all my fault, go fuck yourself

[Anonymous No.11408133]

>>11408122
grow up

[Anonymous No.11408144]

>>11408122
>I was born in a shitty third world country
So Mississippi?

[Anonymous No.11408145]

>>11408144
America is the greatest country on earth.

[Anonymous No.11408146]

Reminder that Springer are petty and overprice all of their subpar books

[Anonymous No.11408149]

>>11408144
Alabama

[Anonymous No.11408154]

>>11408093
Yes yes, can't forget that.

[Anonymous No.11408155]

>>11408146
Name one (1) better math text producer than Springer.

[Anonymous No.11408157]

>>11408155
AMS

[Anonymous No.11408160]

>>11408076
>Which is enumeration, you illiterate mongoloid schizo.

Stop reading there. "You will never enumerate the whole set" does not preclude bijection. Uncountable set can still be bijective.

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

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

Educate yourself, brainlet.

[Anonymous No.11408161]

>>11408155
Oxford Press
Cambridge Press
AMS
Princeton
Birkhause
Mir Moscow
There are more that I'm not remembering right now, all of them are better quality than Springer shit

[Anonymous No.11408162]

>>11408155
>Name one (1) better math text producer than Springer.
Name one (1) worse math text producer than Springer.

[Anonymous No.11408164]

>>11408161
>Birkhause
Birkhauser's just a Springer imprint though
and CUP is pretty much as bad as Springer when it comes to print quality these days, although they do seem to at least still proofread most of their books before printing

[Anonymous No.11408166]

>>11408162
>>11408161

[Anonymous No.11408168]

Why do we hate Springer, again?

[Anonymous No.11408171]

>>11408164
Yeah, I fucked up, I've only seen one book by Birkhauser but it felt better than the average springer yellow books.

CUP is bad? I have two books from them and they're honestly light years above Springer in quality, even their paper is made of the highest quality, but those are famous books in their respective areas, I don't know how it is for smaller books.

[Anonymous No.11408172]

What is an exact value of [math]\pi ^{\pi ^{\pi ^{\pi }}}[/math]?

[Anonymous No.11408175]

>>11408160
>"You will never enumerate the whole set" does not preclude bijection.
Bijection with the natural numbers? Of course it does, because the enumeration is a bijection between the natural numbers and the members of the set, you illiterate mongoloid schizo.

[Anonymous No.11408176]

>>11408172
[math]\pi ^{\pi ^{\pi ^{\pi }}}[/math]

[Anonymous No.11408177]

>>11408172
3^3^3^3

[Anonymous No.11408179]

>>11407716
You're using a thesaurus to say you dont understand the axiom of choice

[Anonymous No.11408181]

>>11408176
This.

[Anonymous No.11408182]

>>11408172
>Define [math] \pi [/math] as 3
It's 3^3^3^3

[Anonymous No.11408183]

>>11408172
You can't express it with a decimal expansion, if that's what you're asking

[Anonymous No.11408186]

>>11408160
The illiterate mongoloid schizo deleted his post, here it is in all of it's retarded glory:

>>11408076 (You)
>Which is enumeration, you illiterate mongoloid schizo.

Stop reading there. "You will never enumerate the whole set" does not preclude bijection. Uncountable set can still be bijective.

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

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

Educate yourself, brainlet.

[Anonymous No.11408194]

What would the major ramifications be if the Riemann hypothesis was disproven?

[Anonymous No.11408196]

>>11408194
None.
Tooker already disproved it and nothing happened.

[Anonymous No.11408198]

>>11407699
I wanna get a math minor. Anyone have suggestions for must-take classes?

[Anonymous No.11408200]

>>11408168
99% of their hardbacks are print-on-demand garbage. Absolutely atrocious physical quality, and yet they charge pretty much the same prices as the AMS charges for real, properly printed books with sewn bindings and quality paper.
Books published in major series (GTM etc.) have shit editing standards nowadays, and books outside of a major series are essentially a self-publishing platform. They receive literally no editing and will accept any garbled pajeet trash as long as it's vaguely mathematically correct.

[Anonymous No.11408203]

>>11408198
Abstract algebra
Vector calculus
Some sort of analysis course
Linear algebra
PDEs

[Anonymous No.11408204]

>>11408194
It would destroy entire new fields of mathematics that were developed assuming it was real, especially in number theory. We're talking about works of lifetimes being thrown entirely ibto the trash

[Anonymous No.11408206]

>>11408203
thank you!! <3

[Anonymous No.11408212]

>>11408164
>Modern Birkhauser Classics
>proudly says the books are entirely uncorrected
I hate this.

[Anonymous No.11408226]

>>11408200
This so much, thank you for saying it, they can't keep getting away with it.

I have Axler's LADR and it's the only book I've seen from then that has a decent quality, and I think that's just because Axler is one of the editors or the UTM series.

[Anonymous No.11408227]

>>11408175
>>11408186
I deleted that one because I realise my version of uncountable differs from the conventional definition, partly due to flawed arguments such as our current topic. So I'll agree that my terminology was incorrect.

However, it is clear that with the correct enumeration steps, the diagonal argument is false, since it operates on the premise that choosing a complementary sequence breaks the bijective index, since, with the steps chosen as part of the argument, in order to feature the complementary sequence, an out-of-order operation is required, assuming the populating mechanism can only be traversed as defined.

You saying "You will never enumerate the whole set" has a double meaning. Enumeration as its computation definition, and I am correct- bijection can be preserved. Enumeration as its "countable" condition, and my argument no longer holds. But- it's countable condition is dependant on what I am refuting.

Bijection holds with the diagonal argument, with the correct sequencing of enumeration and population.

[Anonymous No.11408230]

>>11408226
How is Axler's book, anyways? It seems pretty divisive.

[Anonymous No.11408234]

>>11408183
But why? Computers are too weak? Wolfram|Alpha gives powers of 10 representation [math]10^ {10^ {17.82364533941695}}[/math]

[Anonymous No.11408235]

>>11408230
It's garbage,

[Anonymous No.11408238]

>>11408234
>1 KB, 129x22

[Anonymous No.11408244]

>>11408230
It's the most divisive book in math apparently, but that's just because it refuses to build LA using determinants, it's still a pretty elegant construction of Linear Algebra though, but it might be more useful for pure mathematicians and people not bound by conventions.

To me, the way to study LA is
>Axler>Hoffman>Roman

There's also Halmos' book, but I never read it.

[Anonymous No.11408246]

>>11408227
>However, it is clear that with the correct enumeration steps, the diagonal argument is false, since it operates on the premise that choosing a complementary sequence breaks the bijective index, since, with the steps chosen as part of the argument, in order to feature the complementary sequence, an out-of-order operation is required, assuming the populating mechanism can only be traversed as defined.
All this schizo gibberish and no argument. What's wrong with the steps? Saying that it can be done differently does not affect the proof as it's done.

>You saying "You will never enumerate the whole set" has a double meaning. Enumeration as its computation definition, and I am correct- bijection can be preserved.
What does computation have to do with anything? It's a mathematical proof.

All these posts and the only thing you've "refuted" is your claim to understanding Cantor's diagonal argument.

[Anonymous No.11408253]

>>11408244
Is it good if I'm looking for a more abstract approach to LA, then?

[Anonymous No.11408254]

>>11408246
Seems like you'll never know the truth, brainlet. Stay primitive :^)

[Anonymous No.11408258]

>>11408226
>and I think that's just because Axler is one of the editors or the UTM series.
It's not that, it's just because it's one of the most popular books they publish. You can find proper copies of stuff like Proofs from the Book without too much hassle too.
I believe most Springer books still do get a tiny traditional printing (I have a handful of fairly obscure new texts with real bindings on them and great print quality even on the on colour(!) diagrams), but very popular books actually get a nontrivial print run.

>>11408230
It's a good book, well-written, but it's also a huge meme. Avoiding determinants is not even close to the radical restructuring of the course he's marketed it as so successfully. It just changes a couple proofs to more conceptual methods and the rest of the book is just bog-standard LA.

[Anonymous No.11408264]

>>11408253
Yes, you will understand the structures behind LA without relying on determinants, the problems are all proof-based, read the introduction for more info on Axler's method.

[Anonymous No.11408266]

>>11408254
Seems like you have no argument, schizo. What a surprise.

[Anonymous No.11408271]

>>11408258
>fairly obscure new texts
I'm interested in know what are those texts

[Anonymous No.11408276]

>>11408266
There's like 3 pages of argument you failed to understand, brainlet. I feel bad for you.

[Anonymous No.11408281]

>Why yes, I do use Cramer's rule instead of Gaussian elimination when solving systems of linear equations. What made it so obvious?

[Anonymous No.11408287]

>>11408281
>Still solving Linear Systems
How's middle school going?

[Anonymous No.11408288]

>>11408276
What did I fail to understand? Everything you've said has been refuted.

[Anonymous No.11408293]

>>11408281
>why yes, I solve systems of linear equations by googling "solver of linear equation", opening some link and plugging in the values, how could you tell?

[Anonymous No.11408294]

>>11408271
I bought volumes I+II of these on a whim a couple years ago after reading the MAA review complaining they were too hard, and the copies I got were both impeccably printed.
I also have a few combinatorics monographs from the last 5 years that I think have a fairly small niche and are still nice.

[Anonymous No.11408304]

>>11408294
based Gorodentsev

[Anonymous No.11408305]

>>11408288
Calling someone a "schizo" isn't a refutation, Anon.

[Anonymous No.11408308]

>Calling someone a "schizo" isn't a refutation, Anon.

[Anonymous No.11408313]

>Calling someone a "schizo" isn't a refutation, Anon.

[Anonymous No.11408314]

>>11408294
Whoa, nice book, I was looking for a good and modern introduction to Algebra, you think this will suit me?

[Anonymous No.11408320]

>>11408294
>Each chapter contains both “exercises” that are imbedded in the text, and “problems” that are collected at the end of each chapter. The latter tend to be more substantial, and often develop topics and well-known results that are not covered in the book. For example, one problem essentially leads the student through a proof of the Weddeburn-Artin theorem. Some problems are simply unreasonable; one, for example, calls for a compass-straightedge construction of a regular 17-gon. Hints for some, but not all, of the problems appear at the end of the book.

[Anonymous No.11408322]

>>11408305
Point to one thing I didn't refute, schizo.

[Anonymous No.11408325]

But my world is simply connected.

[Anonymous No.11408328]

>>11408313
>>11408322
>>Reddit

[Anonymous No.11408334]

>>11408328

[Anonymous No.11408339]

>>11408314
No
There's a lot of cool unique shit inside, and it's really fun to read if you already took an algebra course, but the structure is fucking bizarre and nothing like a normal algebra book. There are also way too many fuck-you problems in the sets without any indication that they're not really doable.

[Anonymous No.11408341]

>>11408334
Go back to your primate brothers on /rmath or wathever the fuck

[Anonymous No.11408351]

>>11408339
>they're not really doable.
What do you mean? They're literally impossible problems or just really hard?

[Anonymous No.11408371]

>>11408351
Of course there aren't _literally_ impossible problems in a textbook. They're just sometimes randomly unreasonably hard.

[Anonymous No.11408376]

>>11408371
Can you post an example? I'm curious.

[Anonymous No.11408381]

>>11408376
read the thread >>11408320

[Anonymous No.11408382]

>>11408381
Gauss did that at age 19.

[Anonymous No.11408391]

>>11408382
Yeah, if that brainlet did that, we can do it as well.

[Anonymous No.11408444]

>>11408234
The decimal expansion would have an infinitely long representation. Therefore, any finite string of digits you use to represent the number will be an approximation, which is by definition not exact.

[Anonymous No.11408448]

Just bought this. Did i make the right choice? What can i expect?

[Anonymous No.11408449]

>>11408444
By your logic e^iπ shouldn't be an exact number as well.

[Anonymous No.11408451]

>>11408448
For CA you should start with Zill then go to Alfohrs then Conway

[Anonymous No.11408457]

>>11408449
e^iπ isn't even an irrational number. Who let you on this fucking board?

[Anonymous No.11408460]

>okay, so I want to build up my CV which means I need to start publishing math papers. But I don't have a PHD and I have only one contact in Academia and I can't afford to lose him on trying to shotgun random results his direction and convincing him I'm a crank
>To do this, what I'll do is Avoid all crank endgoals. So if the problem is one of the Hilbert problems, Millennium problems, or any other problems that have any kind of prize/prestige attached to them, avoid them like the fucking plague or I might self-delude myself into thinking I have a serious proof
>Start browsing Number Theory in arxiv
>Neat! I understand a large chunk of the material, let me start playing with some of the definitions in the pap-
>Suddenly
>"Robins Inequality if proved, proves Riemann"
>Drop paper
>Pick another paper in NT
>okay lets try this again. Now I know what harmonic seq-
>"Now, via Robin's inequality, if proved gives u-"
>repeat 4 more times
Welp, time to try a different field.

[Anonymous No.11408476]

>>11408457
>excuses
You said that an irrational number to the power of another irrational number can't be an exact number, but I just refuted your stupid claim because e^iπ is an exact number.

[Anonymous No.11408481]

>>11408068
http://detexify.kirelabs.org/classify.html

[Anonymous No.11408485]

>>11408481
Is this a gigastacey?

[Anonymous No.11408513]

>>11408476
Are you retarded? pi^pi^pi^pi is still irrational. Your counterexample isn't really a counterexample because you didn't give an irrational number. Get off this board, highschooler

[Anonymous No.11408520]

>>11408513
>pi^pi^pi^pi is still irrational
prove it

[Anonymous No.11408530]

>>11408513
Holy fucking shit, you're either too dumb or is just refusing to understand what I said and is trying to bait me.

OF FUCKING COURSE pi^pi^pi^pi is irrational, but you used that fact to say that every number that is like pi^pi^pi^pi, or in other words, that every irrational number to the power of another irrational number can't be exact, it can only be an approximation and this is wrong because there is e^iπ which is an irrational number to the power of another irrational number and it has an exact value, It's not an approximation.

I tried to be as handholding as I could with that explanation, is this clear enough for you, you chimpanzee?

[Anonymous No.11408540]

>>11408530
>but you used that fact to say that every number that is like pi^pi^pi^pi
Please show me where I said this lmao

[Anonymous No.11408546]

>>11408530
>>11408540
Like, I really don't think you can read. pi^pi^pi^pi is irrational. All irrational numbers do not have an exact decimal expansion. Simple as that. I said nothing about powers.

[Anonymous No.11408550]

>>11408540
Well, you could have said that from the beginning instead of deliberately calling me things because you couldn't understand a single sentence

[Anonymous No.11408557]

>>11408550
You deserve it brainlet. Learn how to read before doing math

[Anonymous No.11408558]

>>11408546
Yes, but that don't mean that every irrational number to the power of another is irrational

[Anonymous No.11408563]

>>11408558
This claim was NEVER made.

[Anonymous No.11408575]

>>11408557
Seek mental help and a private english teacher, it will do wonders to you

[Anonymous No.11408578]

>>11408563
Yeah, neither was my claim that pi^pi^pi^pi isn't irrational, but because you can't read you just assumed that.

[Anonymous No.11408586]

>>11408578
Please show a direct quote of this

[Anonymous No.11408599]

>>11408586
okay

[Anonymous No.11408601]

>>11408575
chad schizophrenia vs virgin mental stability

[Anonymous No.11408609]

>>11408599
based

[Anonymous No.11408610]

>>11408586
Here >>11408513
Here>>11408457
You assumed I said pi^pi^pi^pi isn't Irrational and then you assumed I said e^iπ is irrational, idk where you took that from but I wasn't saying any of that, you either can't read or is just trolling

[Anonymous No.11408611]

>>11408599
Holy based.

[Anonymous No.11408614]

>>11408610
I don't know what argument you even tried to disprove with e^iπ then

[Anonymous No.11408617]

what are you mongs even arguing about

[Anonymous No.11408619]

>>11408617
fair enough

[Anonymous No.11408621]

>>11408617
Now do tau^pi.

[Anonymous No.11408622]

>>11408614
I thought you were claiming that an irrational number to the power of another irrational number is an irrational number and then I used e^iπ to disprove your claim, I think I already explained that like 4 times here man, what's wrong with you really? Admit you were wrong and rude and just move on

[Anonymous No.11408628]

>>11408622
>I thought you were claiming that an irrational number to the power of another irrational number is an irrational number
The only one here being a retard was you. This claim was never made and you acted like it was. Holy fucking shit anon seek help

[Anonymous No.11408642]

>>11408628
Yeah, ok, I misread but then you made another shitshow mosreading my misread somehow, you start claiming that I was saying pi^pi^pi^pi is not irrational and that e^iπ is irrational, so yor misread was way worse than mime, therefore you're the one in need of more help here

[Anonymous No.11408650]

>>11408642
how's senior year of HS going anon

[Anonymous No.11408666]

>>11408599
Absolutely based

[Anonymous No.11408681]

>>11408650
How's the Zoo going, chimpanzee?

[Anonymous No.11408684]

>>11408681

you: >waaah you were mean to me, apologize

also you: >CHIMPANZEE

[Anonymous No.11408686]

>the state of """""debate""""" on /mg/

[Anonymous No.11408687]

Maybe I should answer in your language, that way you might understand a sentence

Uaaaa uaahaauuuaa uaaaahhaa

[Anonymous No.11408696]

>>11408684
AGAIN, you can't read a sentence, I'm more and more convinced that you're an actual primate.

Where is the post where I asked you to apologize, I said you were rude and a troglodyte. If you say what you want, you'll listen to what you don't want to listen.

[Anonymous No.11408706]

>people are now making fun of our resident caveman ugg
Leave Ugg alone, he does well enough counting rocks

[Anonymous No.11408715]

>>11408696
>Admit you were wrong and rude and just move on

[Anonymous No.11408716]

>>11408617
how the fuck is it not known whether that'is irrational or not?? I thought mathematicians were supposed to be smart. Im honestly super disappointed.

[Anonymous No.11408728]

>>11408715
Admitting being wrong is not the same as apologizing. I'm outta this shit for today, congratulations.

Oh, now I know how you can communicate, https://youtu.be/NBFBbFcixRY give my regards to Katja.

[Anonymous No.11408788]

>>11408716
if the attendants of /mg/ were really smart we would NOT fucking be here

[Anonymous No.11408808]

>>11408788
Misha Verbitsky posts here. He's not smart, huh?

/math/ is the most intelligent board and subboard.

[Anonymous No.11408817]

>>11408808
>/math/ is the most intelligent board and subboard.
That would be /v/.

[Anonymous No.11408822]

>>11408808
then why don't you go suck Misha's cock for an answer?

[Anonymous No.11408830]

>let [math]F : T \rightarrow T^*[/math] be the classical functor which sends a topological space [math]A[/math] to the topological space with base point [math](A, x_0)[/math]
>let [math]G : T^* \rightarrow T[/math] be the forgetful functor
>we define the discrete space with [math]\alpha[/math] points as [math]GF^{\alpha}( \emptyset )[/math]

[Anonymous No.11408832]

>>11408822
Heh, being this jealous, I live in the same city as him so I have to opportunity to meet him one day and even ask him to be my doctoral advisor in the future, how does that makes you feel?

[Anonymous No.11408845]

>>11408832
Aren't you the LARPer who was talking about a middle school teacher on Tinder? Something tells me to take this post with a grain of salt.

[Anonymous No.11408848]

>>11408832
>have you done the curriculum?
>n-no but I was hoping th-
>talk to me once you're done with the curriculum

[Anonymous No.11408863]

Pi Wrong?

[Anonymous No.11408867]

>>11408845
That was real though, she didn't answer me until now unfortunately, maybe I asked for her whatsapp too early

[Anonymous No.11408896]

>>11408867
>That was real though
Whatever helps you sleep at night.

[Anonymous No.11408909]

Threadly reminder to work with physicists.

[Anonymous No.11408915]

Why do normies know Newton but not Lagrange or Hamilton?

[Anonymous No.11408928]

>>11408915
Maybe because Newton created physics from scratch?

[Anonymous No.11408938]

>>11408915
because muh laws of motion are onions tier. They wouldn't even know what the word "operator" means much less the work of Hamilton or Lagrange

[Anonymous No.11408944]

>>11408928
Which were later made obsolete by Lagrange and Hamilton.

[Anonymous No.11408946]

>>11408832
>>11408848
and then they kissed

[Anonymous No.11408950]

>>11408944
Yeah, it was needed two people and hundreds of years to make Newton's work obsolete. His achievement is much more impressive imo.

[Anonymous No.11408959]

>>11408950
I'm not trying to discredit Newton. I just don't understand why he receives such a disproportionate amount of credit for classical mechanics, when his findings are outdated and, if we're being honest, Lagrange was definitely more accomplished than Newton.

[Anonymous No.11408979]

>>11408959
Didn't I tell you already? Newton singlehandedly created physics, what he did is way more impressive than Lagrange, especially considering all he had was philosophy and Galileo.

Also, your question is stupid, who'll be more remembered, Plato or Wittgenstein? The former of course, but the latter is infinitely more important for modern philosophy.

[Anonymous No.11409005]

ugg throw rock
ugg if throw rock strong enough rock go longer
ugg can ugg throw rock so it never fall???

[Anonymous No.11409022]

>>11409005
Based Ugg.

[Anonymous No.11409024]

^

Why don't the mods ban that guy already? I guess anything is allowed in this thread nowadays.

[Anonymous No.11409070]

>>11408979
>Newton singlehandedly created physics
Truth.

[Anonymous No.11409125]

How long did it take you guys to be comfortable with math in general? Do you just keep learning new things forever or is it possible to reach the 'boundary' of knowledge without being a genius and start contributing to math?

I know it's a dumb question but I'm feeling hopeless.

[Anonymous No.11409134]

>>11409125
How long have you been at it? The guys who are reaching the boundaries are not generalists - they're ultrafocused on a specific field and that's where they're producing new results.

What are your goals? Do you want to be a generalist, or do you want to study something specific and bring something new to the table?

[Anonymous No.11409143]

>>11409125
Depends on field you chose to work on. If it's a famous one like Dynamical System you'll only reach modern research problems in post-doctorate. If it's Graph Theory or applied shit it's much faster.

[Anonymous No.11409155]

>>11409134
>>11409143
I'm nothing, just finished highschool and was gonna do CS. I was just curious, wanted a perspective. I've always wanted to go deeper in math but I feel I'm too dumb, always felt dumber and slower than my peers because I look too much into dumb problems, always trying to understand why while everyone resolved everything mechanically without asking questions and moving on.

[Anonymous No.11409159]

>>11409143
Speaking of, do you have any idea how is the situation with rep theory nowadays?

[Anonymous No.11409170]

>>11409143
Are there any real world applications of graph theory or is it mostly pure?

[Anonymous No.11409176]

>>11409155
Indeed, understanding takes some time, and education systems seem preoccupied with getting people to memorize the trick to do things. I'm guessing you finished HS with a Calculus class, no?

[Anonymous No.11409198]

>>11409159
Representation Theory? I know teo guys who work on it, but it's far from my area of expertise so I can't say much, but it does look like a lot of people are working with it these days.
>>11409170
The game of Chess is just applied graph theory, for instance.

[Anonymous No.11409261]

>>11409170
Tons of applications in CS.
But I think it was the sort of field where some parts have applications and parts don't, like say, Riemannian Geometry.
>>11409198
Really? I had the impression it had beyond autistic requirements nowadays.
Nice.

[Anonymous No.11409284]

>Pick Mathematics to major in because I want to study game theory
>Turns out economists have taken over the discipline

[Anonymous No.11409289]

>>11407796
My nigga, the function is continuous on its entire domain iff it is continuous at each in it. So it suffices to show that it is continuous at an arbitrary point in it

[Anonymous No.11409295]

>>11409284
>economists have taken over the discipline
>when game theory was basically always strongly linked to economics, and is essentially a generalization of Walrasian microeconomics
You really didn't think this one through.

[Anonymous No.11409296]

>>11409284
Economists invented the discipline

[Anonymous No.11409297]

>>11408915
>>11408959
Because everyone learns Newton's law in high school, but only physics and math majors ever hear about Lagrange and Hamilton.
>>11409159
Depends on what you mean by "rep theory". I know a guy who works on Soergel bimodules and disproved a conjecture by Kazhdan and Lusztig, but I barely understand the area so I'll link you to this instead: https://mathoverflow.net/questions/138310/what-to-do-now-that-lusztigs-and-james-conjectures-have-been-shown-to-be-false
As the other anon said, lots of people working on it which means there's still tons of problems to solve and horizons to explore.

[Anonymous No.11409304]

Is Poincare the most important figure in topology?

[Anonymous No.11409310]

>>11409284
Pass as many courses in analysis, probability theory and measure theory as you can and then study mathematical economics: https://impa.br/wp-content/uploads/2017/04/PM_08.pdf

[Anonymous No.11409312]

>>11408080
>caring so much about what an autistic 2hu fag does on a math general in an anime website

[Anonymous No.11409314]

>>11409304
Nope, it's Grothendieck.

[Anonymous No.11409315]

>>11409297
Why don't highschools teach Lagrangian mechanics instead?

[Anonymous No.11409317]

Divide is such a messy operation, I'm starting to wonder whether it should really be used in pure mathematics at all

[Anonymous No.11409321]

>>11409312
>an anime website

[Anonymous No.11409322]

>>11409304
Absolutely. You basically can't even begin to argue it was actually someone else.

[Anonymous No.11409326]

>>11409322
>>11409314

[Anonymous No.11409355]

>>11409310
dont give the smooth brain any ideas anon

[Anonymous No.11409364]

>>11409304
I'd say Pontjagyn

[Anonymous No.11409384]

Redpill me on 17. I'm talking the really esoteric stuff.

[Anonymous No.11409388]

>>11409384
It's the third Fermat prime.

[Anonymous No.11409394]

>>11409388
thats impossible... I killed them all...

[Anonymous No.11409400]

>>11409394
All whopping five of them.

[Anonymous No.11409410]

>>11409364
It's Potryagin you dumb fuck

[Anonymous No.11409435]

>>11408198
Category Theory
Logic
Abstract Algebra
Topology
Complex Analysis

If you're going for a minor, go for the good stuff. You won't get anything usable out of PDEs unless you specialize in them.

[Anonymous No.11409441]

>>11409435
>Topology is useful, but PDEs aren't

[Anonymous No.11409449]

>>11409388
I read the wikipedia page too, asshole. I need more

[Anonymous No.11409458]

>>11409449
>He needed to Wikipedia Fermat primes
Never gonna make it.

[Anonymous No.11409466]

>>11409458
I meant the wiki page for 17, not the fucking Fermat primes. I bet you haven't even read the page for every number on wikipedia. This is entry level shit, come on.

[Anonymous No.11409473]

>>11409435
How the hell did you even think on that list? It's like you've just thrown a bunch of subjects into it without even knowing about them

[Anonymous No.11409478]

Do Hilbert spaces have applications outside of quantum physics?

[Anonymous No.11409479]

>>11409435
>takes CA
>fails cuz it req RA
fugg :DDD

[Anonymous No.11409483]

>>11409466
Anon, I wrote them.

[Anonymous No.11409498]

>>11409478
Yes.
>PDEs on [math]H^1[/math]
>unitary [math]*[/math]-reps of [math]C^*[/math]-algebras
>covariant reps of group algebras [math]L^1(G)[/math]
>irreps of affine Lie's
>

[Anonymous No.11409505]

>>11409483
That's nice, but I still need the deep knowledge on this number, preferably from a mathematician who specializes in 17.

[Anonymous No.11409508]

>>11409498
What's going on in this picture?

[Anonymous No.11409514]

>>11409508
Old woman on life support

[Anonymous No.11409531]

>>11409478
It's the basis of several modern mathatical fields

[Anonymous No.11409542]

>>11409384
It is the seventeenth number in the infinite sequence of numbers consisting only of number 17.

[Anonymous No.11409545]

>>11409542
Prove it.

[Anonymous No.11409548]

do you guys have actual master degrees or are you learning through pure autism?

[Anonymous No.11409549]

>>11409545
That's literally impossible.

[Anonymous No.11409557]

Rudin is a meme

[Anonymous No.11409559]

>Klein bottle

[Anonymous No.11409710]

>>11409548
both

[Anonymous No.11409895]

>>11409557
what about Super Rudin?

[Anonymous No.11409896]

>>11409559
Cope

[Anonymous No.11409920]

>>11409384
without 17 we would not be able to count to 20

[Anonymous No.11409924]

>>11409920
Sure we can, using Hilbert's Hotel, we merely need cordon off room 17 and move every resident from 17 onwards n+1 rooms (So 17 would move to 18, 18 would move to 19 ect..)

[Anonymous No.11410055]

Just started my MSc and I'm having a panic attack about my future.
I am not Ph.d material, so I need to find a job, but I feel unemployable. Lots of jobs here in Germany seem to demand strong programming skills, which I do not really have. All I know is MATLAB. I could pick up C++/Java but I'd require training.
Cannot become a teacher because that requires a different degree.
Also not keen on my future being an office drone serving some monster corporation but I got no other option, it seems.
My dream was to be a professor at some small university or community college, but I am too stupid even for that.
Anyone got some words of advice or encouragement?

[Anonymous No.11410114]

>>11410055
Drop the Community College dream, they're about as bad as High schools now (if not worse because someone can go 15 years without touching a math problem and they'll be expected to start precalculus from essentially nothing)

[Anonymous No.11410223]

>>11409304
yes

[Anonymous No.11410429]

Stats question:
8.1. An urn contains 4 red and 3 white pieces. Identify the sample space Ω and the distribution P for the experiment given by drawing two pieces from the urn. Let X be the number of red pieces drawn. Find the distribution of X and Y = 2X - 1. How is the function X: Ω R defined?

Can someone help me with this? The question just seems so ambiguous. I've found P(X = 0,1,2) but i don't see what to do next

[Anonymous No.11410500]

>>11408007
Yes, but only because the retarded children who shit up the thread form a proper subset of all anime posters.

[Anonymous No.11410501]

>>11409478
Yeah. Hilbert spaces are extremely important for applied maths fields like inverse problems and regularization or integral equations.
>>11409548
Pure autism.

[Anonymous No.11410505]

>>11409310
will I have go probably go through functional analysis?

[Anonymous No.11410556]

Why is Stokes' and Gauss' Theorems so fucking hard aaaaaa I can't get my head around this shit

[Anonymous No.11410636]

if I have two maps [math]f, g: (X, x_0) \to (Y, y_0)[/math] that are homotopic via a homotopy that does NOT preserve basepoints, do they induce the same maps on higher homotopy groups?

[Anonymous No.11410971]

>>11410636
Only if [math]f,g(x_0)[/math] lie in the same path connected component as [math]y_0[/math]. Let [math]p,q[/math] be such a path then [math]f_*(\pi(X,x_0)) \cong p^{-1}\pi(Y,f(x_0))p \cong q^{-1}\pi(Y,g(x_0))q \cong \pi(Y,y_0)[/math]

[Anonymous No.11411018]

>>11410636
I don't think so.

[Anonymous No.11411028]

>>11411018
Oh, right, higher homotopy, not the fundamental group.
No idea. Probably not.

[Anonymous No.11411039]

What's the difference between a Banach and Sobolev space?

[Anonymous No.11411068]

>>11411039
Learn what a weak derivative is, then the definition of a Sobolev space follows easily.

Basically in laymen terms, it is a space that is not complete in the usual sense, but is complete in a weaker sense because of an alternate weaker definition of a derivative.

[Anonymous No.11411146]

>>11410505
Might be useful to understand PDEs.
>>11411039
A Banach space is a complete normed vector space, and a Sobolev space is a Banach space of functions that have a "weak derivative". For instance, in an interval [math]I=(a,b)[/math] we can define [math]W^{1,2}(I)=\left\{u\in L^2(I):~ \exists g\in L^2(I): \forall v\in C^1(I): \int_I u(x)v'(x)\,dx=-\int_I g(x)v(x)\,dx \right\}[/math]. Note the similarity with the "integration by parts" for usual differentiable functions. Here [math]g[/math] is the weak derivative of [math]u[/math] and [math]W^{1,2}(I)[/math] is a Banach space, and in fact it happens to be a Hilbert space with the inner product [math]\langle f,g \rangle_{L^2}+\langle f',g' \rangle_{L^2}[/math] where [math]f',g'[/math] are resp. the weak derivatives of [math]f,g[/math].

[Anonymous No.11411148]

>>11410556
>stuff out equals thing in

[Anonymous No.11411162]

>>11411146
PDEs aren't "useful."
>>11411146
False. Your test function space "C^1(I)" must also include a condition of compact support, or some kind of vanishing at the endpoints, or else your little "integration by parts" restriction would require a boundary term.

[Anonymous No.11411163]

any combinatorics bros here
shit is comfy desu

[Anonymous No.11411174]

>>11411163
took a combinatorics course prev semester.
it was indeed quite comfy - will go back to it after this semester as some of the topics piqued my interest

[Anonymous No.11411175]

>>11411162
The entire world is modeled using PDEs.

[Anonymous No.11411186]

>>11411163
>>11411174
How are we defining 'comfy' here?

[Anonymous No.11411191]

>>11411186
Doesn't require much thinking

[Anonymous No.11411196]

>>11411186
problems are cute
still get to use fancy algebra
but also draw pictures

[Anonymous No.11411202]

>>11411186
to me it's the beautiful simplicity of it combined with deeply pragmatic problems and many interesting results.
what also gets me is that even the simplest problems can surprise you.

[Anonymous No.11411229]

>>11408909
Mathematicians need physicists and physicists need mathematicians, otherwise we can't survive, we're united by the ribbons of fate, one will die without the other, that's the structure of the world.

[Anonymous No.11411244]

>>11411229
Not necessarily, assume [math]\delta \geq |x| \geq 0[/math] where x is the number of mathematicians....

[Anonymous No.11411246]

>>11411162
>PDEs aren't "useful."
cope

[Anonymous No.11411274]

>>11411186
i don't know about "comfy" but I feel like it's a more honest field than others
I sometimes read papers about functional analysis and dynamical systems, and a lot of them go like this:
>introduce some definitions over 10 pages
>prove some basic things about these definitions
>cite some other papers, we generalise the notion of xxx from the paper of yyy, obviously no one will ever need this generalization
basically people often fill whole papers never doing anything hard, they just learn a shitton of theory and then regurgitate without adding anything
On the other hand, there is almost no place for such retarded shit in combinatorics

[Anonymous No.11411280]

>>11411274
What is the most dishonest field of mathematics?

[Anonymous No.11411288]

>>11411280
Statistics (if you even still consider it a field of mathematics)

[Anonymous No.11411292]

>>11411288
100% this

[Anonymous No.11411596]

>>11410971
I think you misread my >>11410636 post

>>11411018
aren't f and g the same map?

[Anonymous No.11411635]

>>11411280
Computer science

[Anonymous No.11411673]

>>11411280
Lie theory.

[Anonymous No.11411708]

>>11411175
>>11411246
As a dedicated PDE theorist, you two are disgusting wretches. PDEs are NOT "useful."

[Anonymous No.11411735]

Does anybody know of a general theory of variance and bias for estimators? Especially one that makes it obvious how one might go about reducing variance and bias for a given estimator.

[Anonymous No.11411786]

>Complex analysis
>Partial differential equations
>Differential geometry

[Anonymous No.11411819]

>>11408830
such a functor F doesn't exist

[Anonymous No.11411828]

>>11411673
kek

[Anonymous No.11411837]

>>11411673
Underrated.

[Anonymous No.11411962]

How does one avoid Plagiarism mathematics papers?

Example:
I have done math research which derived results from a set of papers. I have properly cited them all and given proofs for all necessary results. I then submit them for consideration.

However, unknown to me, my results were already published say, 6 months ago, despite the fact I arrived at the results independently. What about the case where I my set of cations is nearly equivalent to the paper that was got published 6 months before me? What if the citations were for the most part different? What will be the repercussions and how do I avoid this?

[Anonymous No.11412166]

Dummit and Foote or Herstein?

https://www.strawpoll.me/19434002

[Anonymous No.11412193]

>>11409435
>category theory
fun subject but not super well understood by undergrads until after they've had a year long sequence in abstract algebra
>logic
I agree
>abstract algebra
I agree, but only if you do a full year survey from groups, symmetry, representation, rings, fields, algebraic geometry, galois theory, etc.. Otherwise you're fucking around with abstract structures for a semester while zoomed into a small, clean, neat bit of the whole picture, which is what algebra in undergrad is all about
>topology
I agree, but not before any sort of analysis course / in the same semester as an analysis course that features heavy use of rudin
>complex analysis
not before foundational real analysis

This is a list of subjects I like, but it's skewed heavily towards theory building subjects. If the guy you're responding to is going for a minor, he should probably get a class like combinatorics or graph theory down his belt - still pure, but in undergrad it's based heavily on solving problems.

[Anonymous No.11412198]

>>11412166
>103 votes
What the hell, are there that many lurkers on /math/?

[Anonymous No.11412315]

>>11412166
Herstien seems like a half assed Dummit and Foote to me. Am I missing something?

[Anonymous No.11412400]

>>11407987
>analytic functions
I guess he means https://en.wikipedia.org/wiki/Closed-form_expression#Analytic_expression

[Anonymous No.11412409]

>>11412315
The thing I hate about Herstein is his pre-historic notation, someone should update that shit, it's symbol for equivalence classes is Cl() wtf

[Anonymous No.11412489]

>>11412198
>>>/vr/6222678
>103 votes
strawpoll must be doing something strange

[Anonymous No.11412556]

>>11412489
Holy fucking shit
>The actual state of /vr/

[Anonymous No.11412594]

>>11412556
Still better than /v/.

[Anonymous No.11412652]

New thread when?