8:00 PM
When I think that music today would fright people on ~1500, the ideal of a fixed set of rules for music dies - I'm able to hear and like beyond this fixed set of rules.

I like Erik Satie,too.

Same for beauty - the same fixed set of rules, and people try to force a digsuting legitimacy on this. "Beauty is X, no other element could be added to this group"

@GustavoBandeira People are stupid.
Some more than others...

14 mins ago, by MeAndMath
..

@GustavoBandeira what?what's wrong?
You asked what feeling the song gave me.

8:05 PM
Yeah, that's the second possible meaning I thought. =)
brb
bath

ok.

I'm clean! Yay!

@GustavoBandeira DAmn,you're fast!

@MeAndMath Lol

too noisy...

8:13 PM
It reminded me that.
Haha
I like a WIDE range of sounds.
@WillHunting LOOK THIS

@GustavoBandeira That's an interesting equation. I have many example, yet it seems hard to prove.

@PeterTamaroff Haha.
Peter Trollaroff
4

Justin bieber annoys me...
Restart annoys me...Michel Teló,Gustavo Lima ...

@MeAndMath btw, I played Satie's #1 gnossiene last semester.

@GustavoBandeira Cool!

8:16 PM
@MeAndMath But you like Gustavo Bandeira, right?

@GustavoBandeira yes

Have you ever heard Carlos Gardel?

Nope.
I thought he was a brazilian nationalist.

My greatgrandmother sang this song!And danced!

8:19 PM
@GustavoBandeira You should put yourself on fire.

Oh, I confused him with Carlos Gomes.;
@PeterTamaroff =D

@PeterTamaroff He's a legend!

I've hit 13k =D

@MeAndMath Almost.

8:23 PM
@MeAndMath My father used to hear this song, but it was interpretated by some brazilian singer.

That is the right choice

@PeterTamaroff lol

@PeterTamaroff Didn't want to be rude :(

Ok, I gtg. Girlfriend is waiting, I'm gonna travel ~260KM to see her.

@GustavoBandeira What a romantic.

8:24 PM
@MeAndMath Peter is the troll set - all the trolling elements are inside him, relax.

@GustavoBandeira What patience...

Peter is the infinte sum of the trolling numbers - which are trolli-dimensional numbers.
gtg
cya

good trip.

When can a sum and integral be interchanged?
This seems to imply only sums with positive terms can be interchanged with integrals.
However, in this post, an interchange is done without the sum having only positive terms.

8:45 PM
Keywords: uniform convergence, fubini's theorem, interchange of limits. Google away.

@anon :)

@PeterTamaroffdo you know anything about continuum hypothesis?

@MeAndMath The hypothesis is that $\aleph_0\leq 2^{\aleph_0}$ is a "tight"inequality, correct @anon?

@anon Does the sum of the function have to have uniform convergence in order for the order of integration and summation to be switched? That is what seems to be implied here.

@PeterTamaroff yes

9:01 PM
@MeAndMath Ok, so?

@PeterTamaroff This problem wasn't solved yet,isn't it?
what's its implications?

@PeterTamaroff Where?

I'm on the train.

@GustavoBandeira Wow

@MeAndMath It is a "hypothesis" really, and I think it has been proved indepedent of the ZF axios, meaning one can insert it as an axiom, or insert it's negation, and things will go well.
@anon Could you correct me if I'm wrong?

9:05 PM
@GustavoBandeira is she mathematician?

Nope.

@GustavoBandeira how boring.

@MeAndMath You seem to have a case of mathiction.
@MeAndMath Not everything in life is maths!

Should I date only mathematicians?

I think it is...

9:07 PM
If this is the case, I'm gonna be gay and date Peter. <3

@GustavoBandeira Ultimate troll mode: [on]
I'm not a mathematician, also!

Hello, Pitty. ;-)

I can't imagine myself living ,dating whatever,with someone who is not mathematician , or scientist...

@GustavoBandeira Lately I've been referring to people with questions on chat to non existent theorems. Like, someone asks about groups, and I go "That falls down easily with Schuzenheimers Theorem".

9:10 PM
@MeAndMath Spot on!

Well, that's the MSE function: If you don't date a mathematician, you come here. :-)

@PeterTamaroff What does "majorant on some D" mean?

I would not give up on math , for anything in this world!

@GustavoBandeira Also, if an engineer has a problem, I usually suggest to try "turning it off and back on".

@PeterTamaroff nope.

9:11 PM
@Argon majorant on some domain $D$
@MeAndMath Bronies?

If a genius appeared to me asking:You want the love of your life or Fields medal?
I would say Fields!

@MeAndMath Well, that is OK. There is "no love of your life". Except for Freddy. He can always have it.

I would say "potatoes".

Math is the first love of my life.Don't think anyone would understand me.

@GustavoBandeira Make them sweet.

9:15 PM
With gorgonzola?

@GustavoBandeira You have a passion for cheese don'tcha? I love camembert.

YES!

@PeterTamaroff Sorry for bothering you, but what is a majorant over $D$? The internet has revealed very little.

@GustavoBandeira I had a collegue who said that I was a really bizarre girl...

9:22 PM
Haha, why?
(if I stop answering, its lack of mobile internet)

@Argon OK. You're not bothering.

@GustavoBandeira i WONDER WHY..

My girlfriend`s uncle said I have schizophrenia, check my site, on my profile.

@GustavoBandeira Paranoid uncle is paranoid.

9:25 PM
@GustavoBandeira Eu,hein...Se ele me conhece,então...

Well, you like math, weird enough.

@PeterTamaroff Could one think of a majorant as an upper bound?
of sorts

@GustavoBandeira My analysis prof said that I was too obsessed...

@MeAndMath Because you are.

@PeterTamaroff is there anything wrong with it?

9:28 PM
@Argon Careful with the wording: Given a series of functions, we say that a convergent series of positive numbers such that $|f_k(x)|<a_k$ for each $k$ is a majorant for $$f(x)=\sum_{k=0}^\infty f_k(x)$$. Say this is true in some subset $S$ of the reals. Then we say $f$ is majorant on $S$
@MeAndMath Extremma are problematic

@PeterTamaroff I just wanted to be better.And more inteligent...I'm not good enough..

@MeAndMath Better in what sense?

@PeterTamaroff better...brilliant.

@PeterTamaroff Do you mean $\forall x \in S$?

@Argon I didn't mean it, I said it =)
@MeAndMath NOT ENOUGH DATA

9:34 PM
I'm here.

@GustavoBandeira But not there.

@GustavoBandeira Say it.

@PeterTamaroff So $a_k$ is a majorant for $f(x)$ and $f(x)$ is a majorant on $S$?

@GustavoBandeira is anyone else in your family a mathematician?

@Argon Yes. Not there are many majorants.

9:43 PM
Not

Note?

@Argon Yes.

My father liked math, but he knew only elementary math.

@GustavoBandeira you are the only one

@GustavoBandeira Well, one doesn't need to understand the ABC conjecture to like math.

9:45 PM
Yes. We have engineers in the family.

@GustavoBandeira same here.
I discovered that ,in my family about ages ago,there was a physicist and a priest mathematician in Italy.About in the eighteenth century.

So if there exists a sequence of numbers $|f_k(x)| < b_k$ so that $\sum_{k=0}^\infty b_k < \infty$ for $x \in D$ then the sum and the integral can be interchanged if the bounds of the integral are in $D$?

Mathematicians are rare in Brazil. People only want to study the most easily monetizable stuff.

@GustavoBandeira Totally.

I guess Brazil is composed of 33% of medics, 33% of lawyers and 33% of engineers. :-)

9:49 PM
@Argon Essentially. You can read about that in Apostol's Calc I. He proves all that.

@GustavoBandeira none of them working correctly

YES! XD
The cool part is the mathematical reputation if engineers....
Of engineers.

@PeterTamaroff What do you mean when you say $\lim f_n$?

@GustavoBandeira yes!na minha universidade eles tem o estereótipo carinhoso de serem fags.

Haha, é assim: a matéria mais odiada na escola é matemática, dos três cursos que citei, o que mais se aproxima é engenharia, como é o mais próximo disso, eles recebem a fama, já que não existe matemático pra mostrar o contrário.

9:56 PM
@GustavoBandeira É!Eu não gosto de engenheiros...showoffs...

Eu tenho uma hipótese: parece que pra entrar no curso de engenharia, o aluno não pode ter a capacidade reformular algo além do que é dado a ele.

@GustavoBandeira there are people there who've evidently paid for tickets. Why?

Rob? What you mean?

@Argon $$\lim_{n\to\infty}f_n(x)$$
@Argon Are you really a noble gas?
2

10:00 PM
@GustavoBandeira Just my comment on the video you linked :-)

Does anyone here do any abstract algebra?

@PeterTamaroff I was waiting for him/her to say something that I could comment "How noble"

@achacttn Why would you wanna do it?

@PeterTamaroff It's pretty sexy
4

@achacttn LOL

10:02 PM
The topology one? I guess you replied that comment "lets go straight the point" or something like that

@achacttn <3

@achacttn what about $\color{red}{\text{abs}}\text{tract alge}\color{red}{\text{bra}}$ would be sexy?

@robjohn One does not simply take the bra from algebra.

Hell....no chat jax on android... :-(

@GustavoBandeira you lose :-)

10:05 PM
@GustavoBandeira robojohn just highlighted 'abs' from abstract and 'bra' from algebra

@GustavoBandeira I have Android and LaTeX renders cool.
At least on main.

@PeterTamaroff but not on chat

@robjohn Someone has some work to do...

I have an algebra exam in 1.5 hours
no permitted materials :(

Rob, can't you jack this? :-D

10:07 PM
How does one remember all these theorems

@PeterTamaroff :-p

@PeterTamaroff :)

What theorems? What topics?

@Argon Is that a yes or a no?

@EdGorcenski Mainly group theory

10:08 PM
@achacttn it is better to remember principles rather than theorems, I think

Hack #

(Sylow theorems are probably an exception)

@PeterTamaroff The name is a concatenation of my first and last name.

I wonder... does everyone here just have like the proofs for theorems memorized
able to be recalled at any time

@JohnSenior yes, but like the addition and times tables, theorems can make the application of those principles go much faster.

10:09 PM
A truncated version at least

In physics, you can sort of fumble around with equations and derive things from first principles
in mathematics, if you don't have exact definitions for theorems and propositions and such... good luck trying to figure anything out :(

@JohnSenior I taught my son to add on his fingers when he was very young. He decided that he did not need to learn the addition tables, and then the multiplication tables since he knew how to get the answer. He suffered through and ended up hating math.

@Argon Arthemis?

@PeterTamaroff Haha, no. Aaron - truncated

@robjohn to be fair, math isn't for everybody :p

10:11 PM
@Argon Well, that is a cool name too.

@robjohn very true - just than when I was learning maths at high school I had a real aversion to learning anything "by rote" - I always worked things out from the definitions

@achacttn That is true, but he is smart and knows how to apply the ideas. He may not have become a mathematician, but I don't think he would have hated it so much.

I derived the formulas for trig functions so many times that eventually I knew them all anyway :)

@JohnSenior I like doing this too. Is it the same for you as it is for me, that once you understand and know how to derive it, you sort of forget about it and take it for granted

@JohnSenior practice, practice, practice...

10:13 PM
@robjohn yep - exactly

@robjohn What does your son do now?

@PeterTamaroff haha... but 9gag? >:O

@achacttn He is in college majoring in game design.
@achacttn my son sends me things from 9gag from time to time.

@robjohn Are you a math professor or something? o_O

10:16 PM
@achacttn He is!

@achacttn I used to be at UCLA for a couple of years after grad school. Then I went to work for Apple.

@PeterTamaroff That's pretty cool ~
@robjohn Ah awesome! What do you actually do at Apple?

@robjohn What do you think about Apple's Thermonuclear War on patents?

@PeterTamaroff Good that the galaxy S3 made it out alive !

@achacttn well, I am back at UCLA, but writing software now. I used to work on graphics software while at Apple (QuickDraw GX)

10:18 PM
@achacttn I have a Sony Ericssion XPERIA. It kicks ass.

@PeterTamaroff Eh? What are they doing now? They just got $1 billion in a patent suit against Samsung. @robjohn See this Tell me what you think. @robjohn If you write software for graphics engines... what math exactly did you do in grad school? (Sorry for spamming with questions, just curious) well, used to @achacttn I did harmonic/fourier analysis in grad school. @robjohn Ah~. I'll be doing a waves and optics course in my second year, I heard it's basically all fourier analysis 10:26 PM @Robjohn didn't know this topic if do extensive. Was so extensive # @PeterTamaroff It is a matter of levels. Next time you prove a theorem, think of what you are really doing. Mostly putting together ideas you've learned from others, adding a bit of your own innovation. @robjohn Interesting. @robjohn absolutely right @robjohn even guys like Gauss fit into that category - just that they added quite a bit more of their innovation than I ever do :)))) @JohnSenior Some inventions are big and others are an incremental process (OK - vastly more than I ...) 10:34 PM @robjohn Wouldn't that apply to any scientific field though? In the beginning, we are all in school reading a textbook full of discoveries made by other people... @GustavoBandeira você já chegou aonde estava indo? @achacttn That is what I am saying... the computer industry included. @robjohn Yet, there is an unfair game going on. Patenting the "slide to unlock" seems moronic. @PeterTamaroff I know lots of people who think that all patents are moronic. @robjohn Actually, I think all human development (mathematical or otherwise) is incremental - just the size of the increments varies a bit ... 10:36 PM @robjohn Well, I don't think ALL are, but many of them are. @robjohn What is your opinion on patents in general? @robjohn It is something utterly selfish. @achacttn technology benefits since people are more motivated to invent if they can patent their inventions. @robjohn Wouldn't that benefit be 'decreased' in a sense if the patent restricts that technology being used more freely? @achacttn However, there are some who will invent whether compensated or not. @achacttn It restricts the use, not the invention... and patents are only temporary. 10:40 PM @robjohn I did not know this. Are all patents temporary? @achacttn I believe so. The term of a patent is the maximum period during which it can be maintained into force. It is usually expressed in number of years either starting from the filing date of the patent application or from the date of grant of the patent. In most patent laws, renewal annuities or maintenance fees have to be regularly paid in order to keep the patent in force. Otherwise the patent lapses before its term. The term of a patent or specific "claims" in a patent may also be curtailed by judgment of a court, as where a claim or patent is held "invalid" under the relevant law, and thus no longer enfo... @robjohn Hm.. so patents are not temporary if the renewal annuities are paid? @achacttn or the court curtails them. @MeandMath Não, o ônibus sai às 20 @achacttn and it varies from place to place and perhaps even from situation to situation. 10:45 PM @GustavoBandeira tá quase saindo,então. Sim. Depois eu tenho uma coisa pra te mostrar. @GustavoBandeira mostre. Sim, mas depois, tá no computador. @GustavoBandeira qual o conteúdo? sobre o que é? @achacttn I don't know if this can be done forever. At least in the US Constitution it is said that the protection is to be temporary. See here 10:49 PM @robjohn I will bookmark and read after my exam, thanks É pseudo matemática, deve ser uma idéia completamente demente. XD @achacttn I missed that... when and in what is your exam? @robjohn in 50 minutes. On abstract algebra @achacttn Oh... good luck! @robjohn Group theory (a lot of linear algebra examples), plus a little bit on prime fields @robjohn Thanks! 11:07 PM Hey @robjohn What was your field in mathematics again? @N3buchadnezzar harmonic and fourier analysis (with some$\Psi$DO thrown in) =) I have started learning some fourier analysis, and this semester we also have a introductory course in functional analysis. It is fun 11:21 PM @robjohn You are missing a$\mathrm{d}\lambda$in your integral here math.stackexchange.com/questions/187729/… (3.6) @N3buchadnezzar I am not integrating with respect to$\lambda$@N3buchadnezzar are you sure - I think the integral is wrt$\phi$, isn't it? @robjohn Yeah! I saw it now, it is a tad late here. Really awesome solution @N3buchadnezzar Thanks. It is one of those answers that came to me in the shower :-) I would perhaps have placed the fraction in front of the integral to absolutely avoid confusion when dealing with dofuses such as me. $${\color{red}-} \frac{\lambda \pi/8}{1+\lambda^2} + \frac{1}{2} \int_0^\infty \ldots$$ 11:28 PM @N3buchadnezzar I thought of that, but I worried that moving it might also cause confusion. Furthermore, where it is, I can simply change the - to a + to get the similar answer for$\cos$@N3buchadnezzar Of course the - can be changed to a + there, too I moved the$\mathrm{d}\phi$up into the numerator. Perhaps moving it back to the end of the integrand would make the separation clearer. @robjohn Yeah, at the moment it blends in too well. I often move the integration constant up, but usually only when the integral is the last part. Or when the numerator only contains a constant. Answers like this wants me to finish my integration booklet even more. Alas university coursework is too time consuming. Basically a collection of as many fun and interesting integrals with solutions as possible. @N3buchadnezzar moving the increment down makes 3.7 and 3.8 look worse. If it gets moved in 3.6, would that be clearer? That is the step where the constant term is pulled out. @robjohn Moving it in 3.6 would suffice =) @N3buchadnezzar done. 11:43 PM 222 days on MSE @robjohn You said you came up with this in the shower, what was the reasoning behind looking at this particular integral? @N3buchadnezzar Since the answer was$\sqrt{\frac\pi8}$, I figured that something similar to the way one could show$\int_{-\infty}^\infty e^{-x^2}\,\mathrm{d}x=\sqrt{\pi}$would work Yeah, the gaussian trick of squaring and adding a dummy variable. Then you added$\sin(x^2)$, and messed around with the coefficient until you obtained the desired output. clever =) @N3buchadnezzar actually you don't add a dummy variable, you square the integral which can be written as a double integral$e^{-x^2}\,e^{-y^2}=e^{-x^2-y^2}$suggests the conversion to polar then$\mathrm{d}x\,\mathrm{d}y=r\,\mathrm{d}r\,\mathrm{d}\phi$seals the deal$(\int_R \exp(-x^2)dx)^2=(\int_R \exp(-x^2)dx)(\int_R \exp(-x^2)dx) = (\int_R \exp(-x^2)dx)(\int_R \exp(-y^2)dy) = \int_{R^2} \exp(-x^2-y^2) \,dx \,dy $Seems to me like one adds the dummy variable$y$, to be able to obtain$e^{-(x^2+y^2)}$11:58 PM No, you change the$x$to a$y$to keep them straight in the double integral, but yes, both$x$and$y\$ are dummy variables

@robjohn Rob, could you clarify something?

@PeterTamaroff that depends on you, grasshopper...

@robjohn And the last transition is justified since the exponential function is analytic on R, right?