2:02 PM
@UserX: In your last comment, I thank you for not referencing Wikipedia.
Seriously people, we are not the Wikipedia worshipers cult. Get better sources.

@Nick That said, Wikipedia has been the best source of information in my life.

@Chris'ssis Isn't there a non integrable singularity in the form of a pole on the interval of integration?

@JasperLoy: Mine too. Wikipedia has created some kind of monopoly.

I always get nervous while posting answers on complex numbers, because there will always be someone marching along, saying "BRANCHES" loudly, downvoting it :(

@RandomVariable Do you refer at $e^{-W(1)}$?

2:08 PM
@Chris'ssis Yes.

@VibhavPant: Hey, that's my tagline. Who has been using it? I should sue them.

@RandomVariable Trying to find something at high school level.
See here
0

What is the easiest way to test the convergence of $$\int_0^{\infty} \frac{\sin(x)}{x+\log(x)} \ dx$$ Is it possible to use the high school tools for that?

@Chris'ssis: Is that even closed form? Clossable... able to be closed... ah, I suck with terminology.

I gave up the essay. Can't believe how retarded linguistic teachers and authors can be
They write articles about scientific matters with simply no idea on the subject and then make you to agree with them on an essay. I refuse to participate in this madness.

@JasperLoy True.

2:18 PM
@Chris'ssis lol you waited all these hours and created a question just to get the same suggestion as mine about 1-2 hours ago.

@Sawarnik My undergrad paper was only 25 pages long, compared to others' which were about 100 pages long, lol.

@UserX I don't wait for nothing, but I work here on some hard proofs.

@JasperLoy Nice. What was it on?

@Sawarnik It was on Lebesgue integrable functions.

@UserX that is a mistake for trying to get into med school
you need debating skills

2:20 PM

@IceBoy what do you mean? Do you suggest medicine is not a science? Oh... the authors of this are beyond delusional and unscientific, they're supporting conspiracy theories and unbased results.

@UserX it is applied biochemistry, no?

@IceBoy the main reason I'll pursue the career of the anesthesiologist specialty is because I hate dealing with retards. And most people are retards.

a master debater can debate any side of any argument

@UserX There are many stupid and evil people in this world, it's true.

2:24 PM
@IceBoy: That sounds very 144

I don't intend to become a masterbater(pun intended)
That's a politician.

@JasperLoy: No one is the later, just too twisted up in the former.

A master debater by your definition sounds like the exact opposite of a communist.

like a lawyer
law school is not that different from med school

It definitely is.

2:26 PM
the entrance exams are similar

@IceBoy: You have never been to either a law school nor med school, have you?

This is included in a formal article by a linguistics major; (we should boycott GMOs because they'll cause genetic disorders for us in the future)

@robjohn is it okay to steal someone's name on math stack? For example if someone makes his profile name as Rob John and use the picture that your using?

@RegDwight whatever

2:30 PM
@UserX all I'm saying is don't lose easy marks by giving up on the essay part my friend :-)
just fake it

@TheArtist: There are copyright laws, I think, that protect a person's online individuality. If not, then you better be lobbying for it. Otherwise you'll have to deal with Sherlock and Holmes. Know what I'm saying? (This sentence titled as "Nick's debating skills" is licensed CC BY-SA 4.0)

Hi again.

Hi pal

@UserX You mean Master Blaster? ;)

@Nick :p
What's the best way to study for a math exam? I have 1 more week left for my math exams to start :/

2:36 PM
For a moment I thought we have Andre Nicolas here, but it turns out that its the troll artist, sigh.

@Sawarnik nice one ;)

@TheArtist I should ignore you again.

@TheArtist: Depends on what level of exam. In highschool the method is this: Derive Formulas , Remember Formulas, Apply formulas, Practice Practice Practice

@IceBoy O really? :O

@Sawarnik Seriously now what did I do? :o I said nice one for thinking im Andre

2:38 PM
12 mins ago, by Ice Boy
the entrance exams are similar

lol, my question here was downvoted again ...

@Nick Why Wikipedia is a bad site?

@Nick Thanks nick :)

@Chris'ssis: That downvote was definitely a high schooler who couldn't do the problem.

@Nick LOLLLLL :D

2:40 PM
@Nick lol

Btw, not me. I was an upvote. Don't look at me.

@UserX Can we be friends on FB? :)
@Nick Me too!
@Nick Sherlock and Holmes? haha

@Sawarnik: Mr. Kaushal, I don't see you asking me to be your friend on FB.

@Nick lol, I am not Kaushik :P

@Sawarnik: Yes, those are the names of my pinkies.

2:43 PM
@Nick You most probably are.
:p

@Sawarnik: Apologies, it was a typo.

lol

@Sawarnik: Hey, you've hanged out with @Balarka for a long time, what can you tell me about quintics?

@Nick Sorry, nothing.
But what you want to know? :P

@Sawarnik: Solving method for $x^5 + x^4 - 12x^3 - 21x^3 + x + 5 = 0$
not the ugly solution, just the method.

2:47 PM
@BalarkaSen ^

@Sawarnik: He has much much better things to do.

Hello

@Nick Then get hold of Chris'sis, she has Mathematica.
Doesn't it give the method as well?

Anyone, If you have a serious longform answer, then I'd love to read it.
This question was recently asked on main
2

$$x^5+x^4-12x^3-21x^2+x+5=0$$ I think it can be solved by trigonometric ways but how?

2:51 PM
@Chris'ssis Does that not fall under Dirichlet's test?

Wolfram doesn't give an exact solution though.

The Galois group (over $\mathbb{Q})$ is $\mathbb{Z}_5$, so it is solvable with radicals. — Travis 5 mins ago

So I doubt.
@Nick Oh well.

@Sawarnik: :D Ah, maybe I'll get Galois theory someday.

2:53 PM
@TheArtist Appearing to be a mod is definitely not acceptable. It is also definitely not acceptable to impersonate someone.
15 hours ago, by Weapon of Choice
> Under no circumstances will Subscriber use the Network or the Service to [...] (c) create a false identity or to impersonate another person,

@robjohn Wll, I think it might be used.

@robjohn But I will definitely not have a diamond, so what's the special problem?
@Nick haha
maybe, i would someday too.

@Sawarnik I've heard the community managers tell us that it is not acceptable for someone to have the same name or avatar as a moderator. I don't know if there is any written rule that would back that up, but it seems like a good rule of thumb.

why delete?

@Sawarnik And I will have the same profile for you, except for a small extra full stop in an "About Me". Problems?

2:59 PM

People might just think that the moderator has resigned as a moderator, and hence, it will create confusions. So, no same name, especially not for the moderator.

@robjohn On needs to carefully treat the point $e^{-W(1)}$ before anything else ... See also @DanielFischer's comment on main

And gave away 99% of his rep as bounties.

@Sawarnik This actually happened with a user, so....

@JayeshBadwaik I ll get very intelligent then, so no problems :D :D

3:00 PM
@Sawarnik He is no longer a part of MSE, so I cannot give you a link.

Hmm, ok :|

@Chris'ssis Yes, I forgot that the denominator went to $0$ there. That would require a Cauchy Principal Value. Otherwise, the integral diverges there.

@Nick Not all quintics can be solved by radicals.

Maybe when I earn enough rep, I'll give away lots of bounties on every christmas to the jolliest of heartwarming answers on MSE.

@Chris'ssis to which question?

3:02 PM

@Nick What is the enough rep mark? :P

But that one apparently has cyclic Galois group, @Nick

@JayeshBadwaik: haven't seen you in a while. Hey there :-)

@Sawarnik: ... mhh, more than @robjohn ?

@nick if you're interested about quintics, move on to the number theory chat. i'm going to explain some of those in plain elementary highschool language

3:03 PM
@Nick That increases everyday.

@robjohn Hey Rob! Hi. :-D Yeah, Grad school is keeping me pretty busy. How are you doing now-a-days?

Anyway, you will never overtake that :P
@Chris'ssis Do you why @r9m 's blog is deleted?

Ermagash, Robert Israel; the only guy that outranks robjohn just answered that question I linked to earlier. Ermagash!

@Sawarnik I have no idea what is @r9m's blog. He showed me once a blog, but then he deleted it.

@Chris'ssis It contained a lot of integral stuff, some big articles.
It also had one geometry problem I loved.
But why did he delete such nice blog? :O

3:07 PM
@Nick It's the garde

Fields are actually related to fences in some way, but that is also a modern branch of mathematics.

Stacks, bundles ... wood, stick?

@Sawarnik Sheaf.

@As regards your comment on main, still, it's nothing said about that point

@Hippalectryon: En garde!

3:13 PM
Why is Maddox on the starred board -__-
2

@Chris'ssis A simple pole, so if you take the principal value, it's harmless.

@Chris'ssis Cauchy principle value jumps around the simple pole by making a little hole at the contour, in complex analytic talk.
So you're not really integrating but jumping around that point to "avoid" it ;)

@rob john thanks for the info :) Does this only apply to moderators and people with real pictures? What about my name , which isn't my real name. Anyone could call himself "the artist" , so is this valid? That one can copy another's identity as long as you don't have his/her real picture or like U know

@Hippalectryon: What's Maddox and what happened to @TheGame ? You lose?

@Nick >:c
@Nick My usual name is Hippalectryon, I changed to The Game once and because of the 30 days delay I couldn't change back

3:20 PM
@TheArtist As I said, I don't know if there are any written rules about all of this, as it is a moving target. People change their usernames all the time, no one knows who anyone really is, etc.
@Hippalectryon You can always ask a mod if there is something that needs to be changed. Not simply whimsical name changing.

@Hippalectryon: Well, long story short the reason that it's on the starboard is this: @UserX said the pun corresponding to master debater and someone flagged it thereby causing a disturbance in the MSEforce which caused @RegDwigнt to come into the room and reply to that message.

@robjohn You should have told me that earlier :c I waited a month till i could change my name back :)

@BalarkaSen In my post I talk about a proof at high school level.

3:26 PM
@Chris'ssis Can you define "high school level"?

@DanielFischer: An answer that I can reproduce!

a level between elementary school and university :P

@DanielFischer At my school, math without limits

I find the $$\lim_{\epsilon \to 0} \int_a^{c + \epsilon} + \int_{c - \epsilon}^b$$ idea pretty high-school.

Beginner's calculus level.

3:29 PM
@Alizter Man, no limits? Algebraic geometry, category theory, ...?

@BalarkaSen: I want to go to that highschool.

@DanielFischer I talk to my pure teacher about groups sometimes.

@Nick Romania and Hungaria would be just what you are looking for.

@Alizter Peer groups, presumably.

@DanielFischer Doch. Finite groupen.

3:30 PM
Infinitely venerated peer groups?
PUNPUNPUNPPNUNPUNUPUN

terrible german

Guten Taag, want some der tea, ja?

Nein. Ich musse meine hausaufgaben machen.
no wonder I got a B
Joke I have no homework. We have a break now.

@DanielFischer If you asked that a teacher in high school how would he/she respond to that? I admit that the high school stuff might be slightly different in each country.

@Chris'ssis Slightly is wrong. It's vastly different. And even within one country the differences can be huge.

3:37 PM
@Chris'ssis: Immensely different. If you want to measure the education standards of the population of an entire country, go to a financially weak high school there. Those students determine the future of that nation and of the world.

@DanielFischer Even within one city the differences can be huge.

@RandomVariable You mean there are cities with more than one school?

for two schools school1 and school2 in the metric space of schools, $\sup d(\text{school}_1, \text{school}_2) = d(\text{Romania}, \text{India})$

Well, even in the same school the differences can be pretty large.

@DanielFischer: I live in a city with more than 20 decent high schools.
Even in the same class, the differences can be very large

3:42 PM
Fermat descent.

If you want me to be an expert in these kind of things, you're completely wrong, I'm not an expert, but I can look around at the countries around my country and see how things are. I mainly refer at the stuff that is taught, not at how deep they teach you the stuff that is recommended to be taught (here the differences can be huge between any two high schools).

@Chris'ssis Nobody can be an expert for all countries. I'm just saying that "high school level" isn't well-defined.

Hi @BalarkaSen

@DanielFischer Aren't we talking about high schools? Granted, I didn't sleep at all last night. So we might be talking about cats for all I know.

@RandomVariable We're on the internet, everything here is about cats.

3:48 PM
@DanielFischer: lolcats, thundercats, potato cats, they're everywhere!

4:07 PM
@DanielFischer: My age is one of the roots of $x^2 + 88x + 1207 = 0$ . Guess which one.

@Nick Wow, $-71$ years. I can't wait until you're born.

Me neither :D

I wonder what we can say about

@DanielFischer Haha.
@Nick Will you expand sin(B+A/2) for me?

I think this question desperately needs more answers. Any takers?

4:13 PM
$$\lim_{n\to\infty}\sqrt{n}\int_0^{\pi/2}\sin^n(x) \underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots+\sqrt{2+\cos(x)}}}}}_{n - \text{radicals}} \ dx$$

@Sawarnik: $\sin(\frac{A}{2})\cos(\frac{B}{2}) + \cos(\frac{A}{2})\sin(\frac{B}{2})$

Thanks.
@DanielFischer Wait, the Dr. isn't there yet :O

@Sawarnik: Wait did you mean $\sin(\frac{A+B}{2})$ or $\sin(A + \frac{B}{2})$? I gave you an expansion of the former.

@Chris'ssis can you link the integral with sinx/x+logx ?

10

What is the easiest way to test the convergence of $$\int_0^{\infty} \frac{\sin(x)}{x+\log(x)} \ dx$$ Is it possible to only use the high school tools for that?

4:17 PM
Thanks

@Nick :O
But I get the idea :)

@Sawarnik: You forgot that? Can you try deriving it? Also, I can give you the Taylor series expansion of it too if you want?

No need :P

I'm inclined to say that $$\lim_{n\to\infty}\sqrt{n}\int_0^{\pi/2}\sin^n(x) \underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots+\sqrt{2+\cos(x)}}}}}_{n - \text{radicals}} \ dx=\sqrt{2 \pi}$$ am I right?

@DanielFischer: Will you attend my birth in $2085$? If you don't come, I won't be coming to your funeral, fyi.

4:23 PM
@Nick That's a deal. I'll see whether you are at my funeral, and if so, come to your birth.

Agreed
@DanielFischer: How do I make a number sleep using latex on this site?

@Nick What do you mean by "make a number sleep"?

like $8 \to \infty$ ... I want to kick a number onto the ground.

Ah, rotate. Hmm, it don't know whether a package providing that is available here.

@DanielFischer: I wanted to provide a funny answer to the last question you linked to.
The joke would be along the lines of the following one:

4:33 PM
I'm working with a complex number math library, where a complex number is represented by an object with two properties: real and imag, where real represents a real number, and imag represents the coefficient in front of the imaginary number.

Will it be fair to say that if imag is set to 0, then the object represents a real number, e.g. $a + i0$, where $a$ is the number represented by real?

@Chris'ssis I've computed the Cauchy PV of your integral

@robjohn Nice, let me check that.

@Chris'ssis Checking it numerically seems to agree :-)

Here's a different angle on my question. So let's say we had the following expression: $a + ib$

If $b$ is $0$, then is the above expression considered to be in the set of real numbers, or is it still in the set of complex numbers? I'm asking because I'm about to say to someone that $a +i0$ is a real number, but I might be horribly wrong about that.

@Nick My birth year is one of the roots of $x^2-2014 x+29985$.

4:49 PM
@SalehenRahman what does i*0 equal?

@SalehenRahman $a+i0$ is a real number but $ib$ is purely imaginary. (It exists just a terrible name).

@IceBoy $0$ I presume.
@Alizter thanks!

@IceBoy: $i*0 = i^4 +i^2 = i^3 + i$

@SalehenRahman then you are correct since a + 0 = a

@IceBoy thanks!

4:52 PM
@Nickm What are you on?
How did you just cancel $i$? That breaks the equality

@Nick Will you do some geometry?

@Alizter: Who said I cancelled $i$ ? i*0 is always there.

@Nick forget it.

@Sawarnik: Ofcourse I will. But I'm watching the dictator episode of house.
@Alizter: k.

5:07 PM
@Nick Sure. Here is it:

(???)

$l_a, l_b, l_c$ are the angle bisectors a triangle with sides $a,b,c$. Prove that the triangle is equilateral if this is true:
$$\frac{bc}{l_a^2}+\frac{ac}{l_b^2}+\frac{ab}{l_c^2}=\frac94$$
@Nick

I just reviewed an edit where the editor had swapped the sides of all the equations. How pointless.

@Alizter lol...for the 2 points?

@Sawarnik Probably.

5:14 PM
@Alizter: a + b = c can sometimes be better expressed as c = a + b. They have slightly different interpretations.

Piano.

@Nick It this case there was no reason. In fact, it was worse.

Ting-tang-tung.

@Alizter: Was that the only edit?

@Nick Yes.

5:15 PM
wow, reject :/

Obviously^
But you know what, when I used to review, such trivial edits got accepted before I could reject.

Hmm.
@Nick Do you have any ideas? Well, you didn't even check it for equilateral, the condition is actually:
$$\frac{l_a^2}{bc}+\frac{l_b^2}{ac}+\frac{l_c^2}{ab}=\frac94$$
which becomes: $al_a^2+bl_b^2+cl_c^2=\frac94 abc$ :/
or: $al_a^2+bl_b^2+cl_c^2=9R\Delta$ .. what am I supposed to with that? @Nick
@Nick @Nick @Nick

5:30 PM
@Nick The cop-out would be $3$ and $\omega$.

Welcome back @RegDwigнt

@Nick @Nick

@DanielFischer: What copout ?

@Nick

@Sawarnik @Sawarnik @Sawarnik @Sawarnik I have no idea. Brain shutoff.

5:33 PM
@Nick Oh.
I posted the question though.

@Nick You don't need a package to rotate then.

@Sawarnik: Sorry, I don't get your notations and stuff. I'm tired, I have school tomorrow and Chase just killed an African dictator which is a worse tragedy than when Kutner shot himself. I'm overwhelmed.

@Nick haha...school tomorrow :P .. i have holidays :D ... ok :( .. hmm.

I know that for every two elements $x,y$ from Banach algebra $A$ is true that $\sigma(xy)\cup \{0\} = \sigma(yx) \cup \{0\}$, where $\sigma$ is spectrum of some element. I am wondering why we need to add $\{0\}$, that is, how to find two elements $x,y \in A$ for which is true that $\sigma(xy) \neq \sigma (yx)$?

@DanielFischer: Sure, $3 \to \omega$ and $8 \to \infty$. Now who else can we knock over?

5:39 PM
$1\to \rightharpoonup$

This is interesting.
I want to knock over $0$ and $i$

@IceBoy yes, hello. I've been noticing this chat is easier on my browser these days. It used to take forever to load MathJax, but now it's a breeze just like the other rooms.

5:55 PM
@RegDwigнt it still freezes mine :(

Interesting.
As in, earlier today I was in FF under Ubuntu, and now I'm in Chrome under Vista, so it's not even to do with that.

I need clarification