Mathematics - 2014-10-24 (page 2 of 3)

Nick

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.

Jasper Loy

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

Random Variable

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

Nick

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

Vibhav Pant

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

Chris's sis

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

Random Variable

2:08 PM

@Chris'ssis Yes.

Nick

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

Chris's sis

@RandomVariable Trying to find something at high school level.

See here

0

Q: Test for convergence $\int_0^{\infty} \frac{\sin(x)}{x+\log(x)} \ dx$

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?

Nick

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

UserX

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.

Sawarnik

@JasperLoy True.

UserX

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.

Jasper Loy

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

Chris's sis

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

Sawarnik

@JasperLoy Nice. What was it on?

Jasper Loy

@Sawarnik It was on Lebesgue integrable functions.

Ice Boy

@UserX that is a mistake for trying to get into med school

you need debating skills

Nick

2:20 PM

UserX

@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.

Ice Boy

@UserX it is applied biochemistry, no?

UserX

@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.

Ice Boy

a master debater can debate any side of any argument

Jasper Loy

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

Nick

2:24 PM

@IceBoy: That sounds very 144

UserX

I don't intend to become a masterbater(pun intended)

That's a politician.

Nick

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

UserX

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

Ice Boy

like a lawyer

law school is not that different from med school

UserX

It definitely is.

Ice Boy

2:26 PM

the entrance exams are similar

Nick

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

RegDwigнt

@UserX Nobody cares if your puns were intended

6

UserX

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)

The Artist

@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?

UserX

@RegDwight whatever

Ice Boy

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

Nick

@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)

Sawarnik

Hi again.

Ice Boy

Hi pal

Sawarnik

@UserX You mean Master Blaster? ;)

The Artist

@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 :/

Sawarnik

2:36 PM

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

The Artist

Any advice ?

@Sawarnik nice one ;)

Sawarnik

@TheArtist I should ignore you again.

Nick

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

Sawarnik

@IceBoy O really? :O

The Artist

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

Ice Boy

2:38 PM

12 mins ago, by Ice Boy

the entrance exams are similar

Chris's sis

lol, my question here was downvoted again ...

math.stackexchange.com/questions/989145/…

Sawarnik

@Nick Why Wikipedia is a bad site?

The Artist

@Nick Thanks nick :)

Nick

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

Chris's sis

@Nick LOLLLLL :D

Sawarnik

2:40 PM

@Nick lol

Nick

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

Sawarnik

@UserX Can we be friends on FB? :)

@Nick Me too!

@Nick Sherlock and Holmes? haha

Nick

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

Sawarnik

@Nick lol, I am not Kaushik :P

Nick

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

Sawarnik

2:43 PM

@Nick You most probably are.

:p

Nick

@Sawarnik: Apologies, it was a typo.

Sawarnik

lol

Nick

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

Sawarnik

@Nick Sorry, nothing.

But what you want to know? :P

Nick

@Sawarnik: Solving method for $x^5 + x^4 - 12x^3 - 21x^3 + x + 5 = 0$

not the ugly solution, just the method.

Sawarnik

2:47 PM

@BalarkaSen ^

Nick

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

Ice Boy

Hi @JayeshBadwaik

Jayesh Badwaik

Hello

Sawarnik

@Nick Then get hold of Chris'sis, she has Mathematica.

Doesn't it give the method as well?

Nick

Anyone, If you have a serious longform answer, then I'd love to read it.

This question was recently asked on main

2

Q: Solve this tough fifth degree equation.

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

trigonometry

Please put in a solution.

robjohn

2:51 PM

@Chris'ssis Does that not fall under Dirichlet's test?

Sawarnik

Wolfram doesn't give an exact solution though.

Nick

@Sawarnik: The comments say:

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

Sawarnik

So I doubt.

@Nick Oh well.

Nick

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

Sawarnik

@Nick lol...but wait...you have already tried to read that?

robjohn

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,

Chris's sis

@robjohn Wll, I think it might be used.

Sawarnik

@robjohn But I will definitely not have a diamond, so what's the special problem?

@Nick haha

maybe, i would someday too.

robjohn

@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.

Sawarnik

why delete?

Jayesh Badwaik

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

Sawarnik

2:59 PM

@JayeshBadwaik None at all :D

Jayesh Badwaik

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.

Chris's sis

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

Sawarnik

And gave away 99% of his rep as bounties.

Jayesh Badwaik

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

Sawarnik

@JayeshBadwaik :O Whom?

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

Jayesh Badwaik

3:00 PM

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

Sawarnik

Hmm, ok :|

robjohn

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

Balarka Sen

@Nick Not all quintics can be solved by radicals.

Nick

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

robjohn

@Chris'ssis to which question?

Chris's sis

3:02 PM

@robjohn math.stackexchange.com/questions/989145/…

Sawarnik

@Nick What is the enough rep mark? :P

Balarka Sen

But that one apparently has cyclic Galois group, @Nick

robjohn

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

Nick

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

Balarka Sen

@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

Sawarnik

3:03 PM

@Nick That increases everyday.

Jayesh Badwaik

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

Sawarnik

Anyway, you will never overtake that :P

@Chris'ssis Do you why @r9m 's blog is deleted?

Nick

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

Chris's sis

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

Sawarnik

@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

Hippalectryon

3:07 PM

@Nick It's the garde

Balarka Sen

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

Sawarnik

Stacks, bundles ... wood, stick?

Balarka Sen

@Sawarnik Sheaf.

Chris's sis

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

Nick

@Hippalectryon: En garde!

Hippalectryon

3:13 PM

Why is Maddox on the starred board -__-

2

Daniel Fischer

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

Balarka Sen

@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 ;)

The Artist

@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

Nick

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

Hippalectryon

@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

@Nick Maddox chat.stackexchange.com/transcript/message/18305950#18305950

robjohn

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.

Nick

@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.

Hippalectryon

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

Alizter

@DanielFischer Look what I found. Maybe it is related?

Chris's sis

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

Hippalectryon

Aha

Daniel Fischer

3:26 PM

@Chris'ssis Can you define "high school level"?

Nick

@DanielFischer: An answer that I can reproduce!

Ice Boy

a level between elementary school and university :P

Alizter

@DanielFischer At my school, math without limits

Balarka Sen

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

Nick

Beginner's calculus level.

Daniel Fischer

3:29 PM

@Alizter Man, no limits? Algebraic geometry, category theory, ...?

Nick

@BalarkaSen: I want to go to that highschool.

Alizter

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

Balarka Sen

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

Daniel Fischer

@Alizter Peer groups, presumably.

Alizter

@DanielFischer Doch. Finite groupen.

Balarka Sen

3:30 PM

Infinitely venerated peer groups?

PUNPUNPUNPPNUNPUNUPUN

Alizter

terrible german

Nick

Guten Taag, want some der tea, ja?

Alizter

Nein. Ich musse meine hausaufgaben machen.

no wonder I got a B

Joke I have no homework. We have a break now.

Chris's sis

@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.

Daniel Fischer

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

Nick

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.

Random Variable

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

Daniel Fischer

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

Balarka Sen

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

Daniel Fischer

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

Nick

@DanielFischer: I live in a city with more than 20 decent high schools.

Even in the same class, the differences can be very large

Balarka Sen

3:42 PM

Fermat descent.

Chris's sis

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).

Daniel Fischer

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

Sawarnik

Hi @BalarkaSen

Random Variable

@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.

Daniel Fischer

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

Nick

3:48 PM

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

Nick

4:07 PM

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

Daniel Fischer

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

Nick

Me neither :D

Chris's sis

I wonder what we can say about

Sawarnik

@DanielFischer Haha.

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

Daniel Fischer

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

Chris's sis

4:13 PM

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

Nick

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

Sawarnik

Thanks.

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

Nick

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

UserX

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

Chris's sis

10

Q: Test for convergence $\int_0^{\infty} \frac{\sin(x)}{x+\log(x)} \ dx$

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?

calculus real-analysis integration improper-integrals

UserX

4:17 PM

Thanks

Sawarnik

@Nick :O

I asked you about the other one.

But I get the idea :)

Nick

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

Sawarnik

No need :P

Chris's sis

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?

Nick

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

Daniel Fischer

4:23 PM

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

Nick

Agreed

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

Daniel Fischer

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

Nick

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

Daniel Fischer

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

Nick

@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:

Salehen Rahman

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`?

robjohn

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

Chris's sis

@robjohn Nice, let me check that.

robjohn

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

Salehen Rahman

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.

Sawarnik

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

Ice Boy

4:49 PM

@SalehenRahman what does i*0 equal?

Alizter

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

Salehen Rahman

@IceBoy $0$ I presume.

@Alizter thanks!

Nick

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

Ice Boy

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

Salehen Rahman

@IceBoy thanks!

Alizter

4:52 PM

@Nickm What are you on?

How did you just cancel $i$? That breaks the equality

Ice Boy

@SalehenRahman A real number a can be regarded as a complex number a + 0i whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi whose real part is zero. It is common to write a for a + 0i and bi for 0 + bi.

Sawarnik

@Nick Will you do some geometry?

Nick

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

Alizter

@Nick forget it.

Nick

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

@Alizter: k.

Sawarnik

5:07 PM

@Nick Sure. Here is it:

Nick

(???)

Sawarnik

$l_a, l_b, l_c$ 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

Alizter

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

Sawarnik

@Alizter lol...for the 2 points?

Alizter

@Sawarnik Probably.

Nick

5:14 PM

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

Sawarnik

Piano.

Alizter

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

Sawarnik

Ting-tang-tung.

Nick

@Alizter: Was that the only edit?

Alizter

@Nick Yes.

Nick

5:15 PM

wow, reject :/

Sawarnik

Obviously^

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

Nick

@Sawarnik: Ask your question on main. Don't be embarrassed, you'll get quicker answers.

Sawarnik

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

Daniel Fischer

5:30 PM

@Nick The cop-out would be $3$ and $\omega$.

Ice Boy

Welcome back @RegDwigнt

Sawarnik

math.stackexchange.com/questions/989362/… @Nick

@Nick @Nick

Nick

@DanielFischer: What copout ?

Sawarnik

@Nick

Nick

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

Sawarnik

5:33 PM

@Nick Oh.

I posted the question though.

Daniel Fischer

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

Nick

@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.

Sawarnik

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

Cortizol

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 $\sigma(xy) \neq \sigma (yx)$?

Nick

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

Daniel Fischer

5:39 PM

$1\to \rightharpoonup$

Sawarnik

This is interesting.

I want to knock over $0$ and $i$

RegDwigнt

@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.

Ice Boy

5:55 PM

@RegDwigнt it still freezes mine :(

RegDwigнt

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.

UserX

I need clarification

Ice Boy

about?

UserX

What's the most intuitive, elementary, introductory etc. to read? Set theory, elementary set theory etc.