Mathematics

J. M.

12:00 AM

Why yes, that is a dupe. Let me look around...

Hmm...

Srivatsan

Extra triangle constraint

J. M.

and this is a bit more general.

Srivatsan

the cutting sticks conjecture is still open, right?

@JM How is it general, J.M.?

J. M.

On second thought... cutting sticks isn't an exact fit... I didn't see the n(n+1)/2 at once.

robjohn

1:01 AM

@JM The bounty generated a lot of attempts, though.

They just shouldn't let teenagers integrate around contours without a license.

Henning Makholm

I think my license has expired ... what on earth is going on there?

J. M.

Yeesh...

robjohn

1:22 AM

@HenningMakholm In his question or my answer?

Henning Makholm

Mostly in his question -- but I'm afraid that's only because I haven't really tried to understand your answer yet.

I dimly remember something about evaluating doubly-infinite integrals by completing the real axis into a contour and summing over residues for the enclosed poles. But that depended on the "new" part of the contour being far away where the integrand had faded away. What happens near the 0 end of the integral here?

hmm.. setting xi=exp(2pi/5) I can see that f(xi*z)=xi^2 f(z), so we can integrate outwards along the real axis, around a large arc at some large radius, and come back to 0 along a ray from direction xi. The total of this will be (1-xi^2) times the integral, plus a term for the arc that falls away as the inverse square of the radius. Right.

robjohn

@HenningMakholm The integral is being taken around an infinite "wedge". The incoming piece is z=e^{2\pi i/5}x and the outgoing piece is z=x.

@HenningMakholm almost, there is a factor of e^{2\pi i/5} from the dz as well. so (1-xi^3)

Henning Makholm

@robjohn Yes, saw that in the comments. Got it now.

Benjamin Lim

@HenningMakholm A certain user posted 3 questions in the space of one hour, all in the imperative.....

robjohn

@HenningMakholm My answer sort of anticipated the OP needing to ask questions. That actually helps in that he has to think about the problem a bit more, and in that I don't need to lose his attention in one long monologue.

Benjamin Lim

1:36 AM

@robjohn What do you mean about needing a license to do contous integration?

Henning Makholm

@BenjaminLim The imperative is unproblematic. The problem is asking a question that just consists of an exercise with no thoughts of the OP's own. To criticize the symptom (the imperative mood) rather than the cause (no independent effort) makes it unnecessarily hard for the OP to figure out what he's doing wrong and what he should be doing instead.

robjohn

@BenjaminLim It was just a joke... The question was posed in a much more derogatory way, but then was changed.

Benjamin Lim

You have said more precisely what I wanted to say. It is true that the OP has not put any effort into the questions

robjohn

@BenjaminLim The original title of the question was Does wolframalpha approximate definite integrals badly or did I just calculate badly?

At least he offered the possibility that he was in error.

Henning Makholm

We use the imperative all the time in mathematics. "Let f(x)=x^2+e^x" is an imperative. "Consider the following function" is an imperative. "Differentiate both sides of the equation and then divide by g(y)" is an imperative.

Benjamin Lim

1:39 AM

@robjohn I don't understand what is derogatory about the original title?

@HenningMakholm You're right. I think I wanted to say what the OP posted was as if he was ordering people to do the homework without him trying, like what you said.

robjohn

@BenjaminLim When I saw Does wolframalpha approximate definite integrals badly I felt it derogatory.

Henning Makholm

Right. But I wish people would focus more on "without him trying" than on "ordering" when they leave such comments.

Benjamin Lim

Yeah. I like coming on stackexchange because I know people can correct me when I'm wrong.

robjohn

@HenningMakholm Indeed. I don't see the purpose of criticizing the imperative. That gives me the impression that we are a bunch of prima donnas.

Benjamin Lim

@robjohn Next time I will only focus on the OP not trying. You mean you felt it degraded wolfram alpha?

robjohn

1:44 AM

@BenjaminLim not degraded, just a bit of disrespect. It was only enough to make the joke about driving=contour integration

Henning Makholm

@Benjamin, there is some prior discussion (and links to a longer discussion here) on this matter in the "Imperative questions" room. Unfortunately nothing concrete ever really came of it.

Benjamin Lim

I will take a look

robjohn

@Benjamin: don't get me wrong, I don't think that Wolfram is infallible.

Benjamin Lim

I know what you mean. It is not infallible, sometimes when evaluating integrals it gives complicated answers when the integral is actually simple

robjohn

@BenjaminLim That is very true.

Benjamin Lim

1:46 AM

@robjohn @HenningMakholm I will go for lunch now. See you guys!

robjohn

@BenjaminLim I have had some people ask me why they got the answer wrong because the answer from Mathematica looked so different.

Henning Makholm

Do chatrooms decay if nobody speak in them for some time? Perhaps it would be worth it starting a meta question on the imperative matter just for archiving purposes.

robjohn

@HenningMakholm Oh, no. WolframAlpha particle decay of chatrooms... Film at 11!

Henning Makholm

Um.. random association game?

robjohn

Word association football

I have to take my dog to the park. bbl

Was Film at 11 a foreign phrase?

@Henning: In the US, at least, it is a joke phrase to imply fake importance. It comes from the news stations leading people to watch the late night news. They announce something and then say "Film at 11"

Henning Makholm

1:54 AM

I'm aware of "film at 11", but the alpha particle decay seemed a bit random.

(Though of course, that is how radioactivity works).

robjohn

@HenningMakholm I was just positing a type of decay since you were wondering about chatroom decay.

See you in a bit.

J. M.

@HenningMakholm Nope. As long as there are x number of messages in it, it won't disappear. On the other hand, they do get archived (can't post in it anymore) after y days of inactivity. (where x and y are written somewhere in meta.SO).

Henning Makholm

Okay. Here, I think: meta.stackoverflow.com/questions/104677/chatroom-deleted

Which says that the threshold is 15 messages by at least 2 users. Should be safe, then.

J. M.

Great.

Srivatsan

2:17 AM

I think the OP misunderstood our insistence of manners... =)

Henning Makholm

A propos of the discussion just above ...

Srivatsan

I took back my downvote because I realised I did not understand your answer, @J.M. =)

Will put it back when I get it...

Henning Makholm

I write a nice answer to VVV, and in return he threatens me with armored fighting vehicles...

2

Srivatsan

2:33 AM

Well, I was going to post a comment about blue Rudin, but the name seems somewhat standard. Like baby Rudin. E.g., abebooks.com/Principles-Mathematical-Analysis-1964-blue-Rudin/…

J. M.

3:04 AM

@Srivatsan What? I was out (and terribly distracted.)

(If this keeps up, I might have to take the day off.)

robjohn

@HenningMakholm He threatened me with the same attack force.

I am lame at getting the correct link

Matt

Hey guys can I get your input on a proof?

robjohn

@Matt which proof?

Matt

imgur.com/8wFIb

This one I did

Im not sure my use of modus ponens is valid

nor negation for that matter

Srivatsan

3:23 AM

@JM Sorry, I felt I understood, but on second thought I did not. Sorry about that... =)

Henning Makholm

@Matt, why not just use p|ab => p|a or p|b?

Srivatsan

I too find it hard to concentrate today. (Watching a movie now =)) // I might go through the answer tomorrow...

Matt

@HenningMakholm This is just how I thought to do it

J. M.

@Srivatsan Which one? I'm currently repairing at least two answers I was writing when I got interrupted...

Srivatsan

The Dirichlet convolution one.

I even wrote a comment nitpicking about something. I deleted it realising that I might be the one who got it all wrong, after all =)

J. M.

3:27 AM

Ah. I'm giving the entire gory details just so nobody can complain it was too brief.

Srivatsan

Aw, good for me then.

Henning Makholm

@Matt, is this for a course in formal logic? Otherwise I'd say you're putting too much emphasis on the mechanics of logical reasoning. It dwarfs the actual number theoretic content of the proof.

For the idea you're using, I would just say something like: By the FTA, let p1^e1 .. pn^en be the prime factorization of a. Then the prime factorization of a² is p1^2e1...pn^2en, so one of the p_i's must be 7 and the exponent 2e_i must be nonzero. Thus e_i is also nonzero. Since 7 occurs in the prime factorization of a with nonzero exponent, 7 divides a. QED.

Matt

3:44 AM

@HenningMakholm yep, its for a discrete math class, im using all my new tools :P

mixedmath

Henning - "Tanks - Battleships!"

that was very funny

Henning Makholm

@Matt Looking a bit further at it, I don't quite think it holds together. It looks like you're keeping some quantifiers on p_i and e_i implicit, and that just won't do when you're trying to be formal about things.

As the proof reads, it looks like you're defining the p_i's and e_i's to be the prime factorization of a. THen you're letting P be the claim a =/=7^e1*p2^e2*..., which is true if and only if p1 happens to be different from 7 -- and Q be a^2=/=7^2e1*p2^2e2*..., which is true if and only if p1 happens to be different from 7.

Matt

ok

So all I know is that 7 definitely divides a^2

J. M.

I hope I haven't forgotten anything...

Matt

So basically what im trying to say by a^2=7^2e1p1^2e1...

is that 7 is a factor of a^2

which must be true if it divides

Henning Makholm

3:56 AM

You probably meant to let P be the statement "there exists e1,e2,... and p2,p3,.... such that a=7^e1*p2^e2" -- but you're not allowed to let the "there exists" be silent. Your argument will be unintelligible then.

Matt

So how would I express this?

Srivatsan

@JM My +1. I certainly did not see the answer at all, so I am glad I pushed you to expand the answer... =)

Thanks for the effort, b.t.w.

J. M.

...and people wonder why number theory gives me headaches... :D

Henning Makholm

@Matt, I don't immediately see a good way to get through if you start by factoring a^2. It seems to end up superfluous no matter how we proceed.

J. M.

(no problem, and thanks for the +1, @Sri.)

Matt

4:00 AM

@HenningMakholm , Hm, ill have to ask the instrutor, thanks for the input, g2g!

Srivatsan

4:17 AM

I am afraid we might drive away a fraction of the new users by our insistence on manners and showing work.

J. M.

"our insistence on manners and showing work." - if it means less crap, so be it...

Srivatsan

One more of those questions: math.stackexchange.com/questions/83835/probability-inequalities

Yes, I am not saying it's a bad thing.

Srivatsan

4:28 AM

@JM I actually agree more with Andrew Stacey's comment below the post.

"If you really don`t want that much low quality questions filter China and India."

I found that comment hilarious... =)

J. M.

That's a bit below the belt, I'd say...

Srivatsan

Yes, it is. But since I am "from India", I have the right to enjoy it nevertheless. =)

J. M.

A programmer and a photographer? Then not likely...

Srivatsan

I want to ask the op why they are solving algebra homework. =)

Henning Makholm

I did.

Srivatsan

4:43 AM

Ok. I am happy as long as I didn't have to ask =) . I even upvoted your comment, Henning...

@J.M. can you correct the "actully" now that you touched the post?

Thanks...

J. M.

Done.

Srivatsan

Thanks, J.M. // I would've done it but I was hoping you might catch up with the 5-min edit window. All is well though...

J. M.

I don't feel like cooking today. I'm eating out. See you guys later.

Srivatsan

Enjoy your lunch, @JM.

Mike Spivey

5:49 AM

@JM Thanks for that link. I hadn't realized that the penalty for downvoting questions had been removed.

yayu

@sri that china and india comment was not by andrew stacey but by some user named zdravko.

a bit sad but true though

Asaf Karagila

7:11 AM

Top of the morrow, idle chat mob.

Matt

7:57 AM

Same to you : P

Zhen Lin

8:44 AM

My laptop failed mysteriously and catastrophically. And I thought I was going to get some Ph.D. application bureaucracy done this weekend...

QED

yep computers

Transcript for

$Mathematics$ Mathematics