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17:01
@robjohn It must have been pain. Why don't you consider TeXing these up and putting them up as pdf or ps
@KannappanSampath When I have time. For now, it is simpler to leave them be :-)
I did TeX one page...
I see and you got tired?!!?
@robjohn Oh, no. I have a suspicion that plain text will be back in vogue in a few years. =)
@Srivatsan Why?
@robjohn Smileys have become punctuation marks these days. :/
17:04
@Srivatsan I did that because a friend from Apple wanted to solve the quartic.
@robjohn And he refused to read the text file? =)
I am just joking, rob. I hope you preserve the text file in any case; that's all.
@Srivatsan No, but the text file was a bit harder to read and I wanted to put some MathJax on my site.
@robjohn What is your site?
@Srivatsan Was it for my message?
@Srivatsan Definitely, I will keep the ascii-art pages
@Srivatsan the site that those pages are on.
17:07
@KannappanSampath No, one of my previous comments was meant to be a joke, but I am not sure it was perceived as such. Hence the comment.
I used it to stuff things that I could reference from sci.math
@Srivatsan I didn't see the smiley at first. I kind of figured you were kidding, but i asked, just in case.
@robjohn whim.org is a cool name =) .
(Is it short for anything? Why would you name a computer/site like that?)
@Srivatsan Thanks :-) I came up with it during a fire drill at Apple.
@robjohn Yes, I actually added the smiley later. In my third edit.
@Srivatsan West Hills Institute of Math
I live in West Hills
17:10
@robjohn You know/have interest in astronomy as well?
@Srivatsan I like astronomy and astrophotography.
@robjohn Cool, man. Surprising it didn't come up in chat before.
@Srivatsan It did at one point, but it was a small digression
And what is this "institute"? What does "it" do?
Are you a one-man institute?
=)
@Srivatsan It is a fictitious organization beyond the math on the website
17:13
[Hope you don't mind me asking too many questions.]
@Srivatsan so I guess I am a uninstitute :-)
@robjohn behind or beyond?
"uni" as in one
@Srivatsan as in the only institute is the math on the website
By the way, why did you choose to do it in text in the first place? I am not sure I have the patience. (I am thinking I should do one up by hand-writing all my stuff and putting them up. =))
Surely TeX has been around for a while, and I presume you knew about it. (Question: you TeXed your thesis, didn't you?)
@Srivatsan When I started on sci.math, there was no LaTeX, or TeX even. Then sci.math was a text only newsgroup
17:17
@robjohn I don't understand the timeline. TeX has been around since the eighties at least, no? Perhaps even the seventies?
According to Brian, TeX has been around since 80's atleast!
@Srivatsan You're right, but I had never used TeX, so I guess I was unaware of it
And, according to him, Arturo has been using it since then, while he was a teenager!
Then my question about your thesis becomes even more interesting. You type-wrote it? =)
I started doing math papers using special fonts on the Mac
It provided what I needed until I got CMacTeX years later
which is a LaTeX engine, but I guess it does TeX, too
17:20
@KannappanSampath That's perhaps not too surprising. I would've typed out some stuff when I was nineteen. (As a counterpoint, times have changes, TeX is more ubiquitous today and all that.)
Today, you'd be odd not to use LaTeX
@robjohn "Special fonts" -- That sounds fancy.
@robjohn ...which is a good reason to not use it. :-)
@Srivatsan There was a Symbols font on the Mac very early, similar to the one on the PC these days
Is anyone here aware of a Technique that you can use to get information like number of people registered from a page that uses Google docs for maintaining forms?
No. (I cannot even parse your question properly.)
@robjohn: Coming back to your writeup on pi cot (pi z), in your second section about the alternating harmonic series, why are you allowed to split the series up?
17:25
@Srivatsan Think in the PV sense...
In general, one cannot split a series.
Oh I see, PV does have advantages then.
It is $2\sum\limits_{k=-N}^N\frac{1}{2k}-\sum\limits_{k=-2N}^{2N}\frac{1}{k}$
@robjohn Yes, I see that now, thanks.
That gives the alternating series to $2N$
I understand.
There are many a fake-proof of $1=0$ based on similarly manipulating the series $\sum \limits_{n=1}^{\infty} \frac{(-1)^{n-1}}{n}$.
17:29
That is the same thing I used in this answer
@Srivatsan but not doing it in the proper way.
@robjohn Yes, that is the difference between PV and sum. (And I did say fake-proof.. =))
I will tell you why I was interested/bugged by this a few months back.
Okay :-)
In my calculus class, we saw the definition of PV. It is of course not hard to follow once you understand the distinction between the value of an integral/sum and the Cauchy PV; and I was comfortable with these things.
But we were not shown a single even remotely useful application of the PV, so I filed it away as not-useful.
That was not good of the instructor.
@robjohn Yes, but it is an engineering calculus course. The key is to keep your expectations low. :=)
Only last year did I come across this once again: in this notes of T. Tao on random matrices. See page 192.
17:38
@Srivatsan Where do you study? (if you think it is not too personal)
@KannappanSampath Currently? // to myself: Of course, currently. What else does "do" mean!?
Yes, assuming you once told me that you're an IIT-M alumni!
@KannappanSampath Ha, that is a big secret. These CMU people will come after me if I let it out.
@Srivatsan Yes. However, when studying Harmonic analysis and singular integrals, you do a lot of PV integrals.
@Srivatsan I was also puzzled but I thought, you wanted to make sure you answer the right question.
17:41
@robjohn Yes, I have done none of that (as you might know already).
And, your home page link will be much appreciated! You don't have a G+ account; I see no way I can follow you!!!
@KannappanSampath No, I prefer it that way currently.
Hello!
@robjohn Did you see the book? The trouble is: while the book gives a lot of intuition and perspective an all that jazz, a significant fraction of it is left at an informal level, with the expectation that a person who has done a PDE/analysis/harmonic analysis course (for instance) will be able to fill up the details.
Fair enough. In the present case, pages 191-193(?) is some kind of mystery to me. In particular, I did not understand why the PV of that integral just popped out of nowhere.
Could someone show me the steps to found the domain of this function?
http://www4b.wolframalpha.com/Calculate/MSP/MSP56151a01hi4g75fba66600005412cgab2h2eb1bd?MSPStoreType=image/gif&s=5&w=135&h=46

(the logarithm has 1/2 as base, but wolfram don't want collaborate xD)
17:44
@Srivatsan Most of the stuff I see from Terry is on his blog, and that is quite informal, though he does fill in details when needed.
@robjohn Yes, but "when needed" is relative. I feel like telling him "All this makes one fine hint, but it's a little far from a proof, I am afraid." :-)
@Srivatsan one person's hint is another's proof :-)
@robjohn Of course. I am not complaining; it just shows a few gaping holes in my knowledge.
Now I am curious: why did he get a principal value there?
Of course, here you have to deal with many levels of knowledge and so it is hard to know what level of detail to include
Lemme look
@robjohn Yes, totally. I do understand if he expects the reader to have some knowledge. It's unreasonable to expect a book to be completely self-contained.
17:51
@unNaturhal Please post questions that require miniscule details on the main site!
@KannappanSampath Miniscule details? Or minute details?
@Srivatsan seems fine to me this time. =)
@KannappanSampath Sure. But could you explain what you meant?
@Srivatsan Tiniest details, missing them could mean nothing, but still needs consideration.
For instance, I might have some condition that gives a redundant inequality. So, If I missed it, I am still fine but only this time!
@unNaturhal I can tell you how to proceed; but if you want detailed steps/hint/answer, then you could take it to the main site as Kannappan already suggested..
You now know what to do be considered a pure mathematician.
18:00
@Srivatsan The principal value is actually a bit odd, because there he means to delete an interval symmetric around $x$, not $0$.
It would be better to rewrite the integral as
@robjohn PV "about" x, perhaps? Since the singularity is at $x$ this time, isn't it?
$\int_{\mathbb{R}}\log|y|f(x-y)\;\mathrm{d}y$
Then the deleted interval is around $0$
But then the differentiation doesn't make as much sense.
So the principal value is taken around $x$ in the first integral, so that the differentiation makes sense
Oh, I see. You will get some extra terms from differentiating $f(x-y)$, right?
Yes, but not if you move the x back to the $\log$
Aw, that is an interesting point: if the position of the singularity is a function of $x$, won't that contribute something to the derivative? That is transparent when you write it the way you wrote, but his expression seems wrong.
@robjohn Won't you get $f'(x-y)$ terms? What happens to those?
18:05
Hang on...
Sure, take your time.
$$
\begin{align}
\frac{\mathrm{d}}{\mathrm{d}x}\int_{\mathbb{R}}\log|x-y|f(y)\;\mathrm{d}y
&=\frac{\mathrm{d}}{\mathrm{d}x}\lim_{\epsilon\to0}\int_{\mathbb{R}\setminus[x-\epsilon,x+\epsilon]}\log|x-y|f(y)\;\mathrm{d}y\\
&=\lim_{\epsilon\to0}\int_{\mathbb{R}\setminus[x-\epsilon,x+\epsilon]}\frac{1}{x-y}f(y)\;\mathrm{d}y\\
&+\log(\epsilon)(f(x-\epsilon)-f(x+\epsilon))\\
&=PV\int_{\mathbb{R}}\frac{1}{x-y}f(y)\;\mathrm{d}y\
\end{align}
$$
Oops, the second step is after differentiation
Too late to delete the oops
Taking the derivative of the limits just evaluates the integrand.
One second.
and if $f$ is smooth, $\log(\epsilon)(f(x-\epsilon)-f(x+\epsilon))$ will go to $0$
$Lip(\alpha)$ is smooth enough :-)
however, this is not elementary enough that I would have left it out.
But he is Terry Tao
18:22
$Lip(\alpha)$ -- where did that come from?
Is it given that the function is so and so smooth?
$\lim\limits_{\epsilon\to0}\log(\epsilon)(f(x-\epsilon)-f(x+\epsilon))=0$
if $f\in\mathrm{Lip}(\alpha)$ for $\alpha>0$
@Srivatsan I would assume that $\rho$ has some smoothness requirement in the paper
Hmm, it is a probability measure
@robjohn Let's say there is. I couldn't figure it out based on the nearby pages. He has been using this notation for a long time at this point, and from the top of my head, I don't where to look to find all the assumptions on $\rho$.
a discontinuity in $f$ could cause a problem.
Working formally, and assuming that $\rho$ is a probability measure that minimises $(2.138)$, argue that
@robjohn This section is titled "Mean fi eld approximation", so I am guessing sweeping such assumptions under the rug might be "allowed".
And how is he able to differentiate an inequality?
@Srivatsan which inequality?
18:32
Grr, sorry! I misread it now.
Ok, one more question: $\int_{\mathbb{R}}\log|x-y|f(y)\;\mathrm{d}y$ is interpreted in the PV sense also, right?
@Srivatsan It doesn't need to be, if it is a Lebesgue integral
There, the integral around $0$ vanishes
Why? Why is this better than $\lim_{\epsilon \to 0}\int_{\mathbb{R}\setminus[x-\epsilon, x+2\epsilon]}\log|x-y|f(y)\;\mathrm{d}y$?
(Does this question even make sense to ask?)
I broke it into PV so that I wasn't sweeping anything under the rug.
@Srivatsan Do you see that removing the interval doesn't matter?
That the integral of log converges around 0.
18:37
@robjohn I agree that what you wrote is correct. But it seems to me that you interpreted the LHS in the PV sense, and that leads to the PV as the answer. So: there's the chance that if I interpret it differently, say $\lim_{\epsilon \to 0}\int_{\mathbb{R}\setminus[x-\epsilon, x+2\epsilon]}\log|x-y|f(y)\;\mathrm{d}y$, then you will get an analogous modified-PV as the answer. So my question is: at what point did we choose to put in the PV interpretation and not the modified-PV one?
@robjohn Can you show this?
Ah, the $\log(\epsilon)$ on one side would be different than the $\log(2\epsilon)$ on the other.
...?
=)
and you'd get $\lim\limits_{\epsilon\to0}\log(\epsilon)(f(x-\epsilon)-f(x+\epsilon)-\log(2)f(x+\epsilon))$
@robjohn - which doesn't go to zero! Is that what you are getting at?
The error term for the limits of integration when differentiating
So that is why he chose the PV
@Srivatsan Yes
18:40
@robjohn Such clairvoyance is annoying. :/
Some one should tell Asaf when he comes that the movie he suggested me to watch is just awesome!!!
@KannappanSampath Why don't you tell it yourself? Both of you will be around in chat, right?
@Asaf, you were seen 10s ago by the server, if you're still around, here's my thanks!
Darn, took too long. You'd get $\lim\limits_{\epsilon\to0}\log(\epsilon)(f(x-\epsilon)-f(x+\epsilon))-\log(2)f(x+\epsilon)$
18:42
Hey look, Bill's here! Hi @BillDubuque.
I recently got home.
Hi everyone.
Which movie? Kung Pow?
Hi @Asaf.
@Srivatsan which would be $\log(2)f(x)$
18:42
Hi N.
@Bill good morning (?)
@AsafKaragila Yes that same exact movie !! =)
@BillDubuque Hi
Yeah, it's a good movie.
@robjohn Not sure if he can respond. (Reps and stuff.)
@Srivatsan They haven't fixed that yet?
18:43
What's to "fix"?
@Srivatsan I thought they were going to restore his account or something. I don't know; I just saw something in the logs this morning
But, I've seen that you can create a room in which you can forcibly allow someone to speak irrespective of reps and stuff! Not sure if it will work!
I just realised: is there a way for a suspended user to "contest" their suspension in meta? I think there is some lower bound on the reps needed.
@KannappanSampath Why do you assume BD wants to speak with you? :=)
I didn't assume BD wants to speak with me, but just wanted to bring such thing to light!
@robjohn Why do we get this? I think you will get $f(x+2\epsilon)$.
18:46
@Srivatsan I guess I am wholly in error. I thought some mistake had been made with Bill's account and that mods were going to fix it.
@robjohn Well, nothing like that came up as far as I can tell. (And I was here in chat almost all the time.)
I think they should allow the OP to comment anywhere in their questions. I do not see the point in blocking the OP from commenting just because they have <50 reputation points. If I am to request this feature, should I post in meta.math or meta.SO?
Here we go...
$$
\begin{align}
\frac{\mathrm{d}}{\mathrm{d}x}\int_{\mathbb{R}}\log|x-y|f(y)\;\mathrm{d}y
&=\frac{\mathrm{d}}{\mathrm{d}x}\lim_{\epsilon\to0}\int_{\mathbb{R}\setminus[x-\epsilon,x+2\epsilon]}\log|x-y|f(y)\;\mathrm{d}y\\
&=\lim_{\epsilon\to0}\int_{\mathbb{R}\setminus[x-\epsilon,x+2\epsilon]}\frac{1}{x-y}f(y)\;\mathrm{d}y\\
&+\log(\epsilon)f(x-\epsilon)-\log(2\epsilon)f(x+2\epsilon)\\
&=PV^{\;\prime}\int_{\mathbb{R}}\frac{1}{x-y}f(y)\;\mathrm{d}y\\
&-\log(2)f(x)
\end{align}
$$
where PV' is the modified PV to be half on the left from on the right
One extra paranthesis in the second step in the second summand?
@robjohn Ok, thanks. This is certainly messier, but do you see anything wrong in this interpretation?
(Of course, the answer to this could very well depend on the first 190 pages of the book =); so you might not know the underlying context/subtext.)
No. And it would give good answers, as long as everyone used that definition of PV
@robjohn Ha, that is good to know.
18:55
There might be worse consequences for higher derivatives, but in this particular case, it is okay.
But things usually work out more nicely with the standard definition of PV.
I see.
So, to file things away for me: there is some inbuilt arbitrariness that percolates downstream; but in general, things work out more nicely with the standard definition of the PV.
(I just copied your comment :).)
Pretty much. That, and it is easy for people to grasp the symmetric deletion so it makes it good as a standard.
@robjohn How do I cite your bookmarklet for chat?
Request citation!
@KannappanSampath Where do you want to cite it?
19:03
Rob Johnson, ChatJax 2011.
I am using the name Asaf gave it.
@robjohn in a meta thread about mathjax not rendering the review posts!
@KannappanSampath Why don't you just link to Rob's meta post?
I think that I complained about that already.
@KannappanSampath Oh, just point them to the post
It's still below 30 votes :-)
Thank You @robjohn
19:05
@robjohn It's anyway famous by now. Everyone except Mariano knows and uses it.
@Srivatsan I always wanted to name something in mathematics. It seems that I at least named something in math.SE ;-)
@AsafKaragila It's a cool name.
My upper chamber often posts a message: TO LET !!
I agree.
@Srivatsan He uses the other bookmarklets to disable the immediate LaTeX conversion when writing a question/answer
19:07
@robjohn It's like taking a stool hardener and a laxative and see who's gonna win.
2
@AsafKaragila Ouch!
@robjohn It's a Family Guy joke.
@AsafKaragila Since most laxatives only promote peristalsis...
From "Road to Germany", Mort says that he did that.
@robjohn Fun.
@AsafKaragila That's why the "Ouch!"
19:09
I assume there should be a PV for dimensions > 1. Is it defined in the following way?
$$
\lim_{\varepsilon \to 0+} \iint \cdots \int_{\mathbb{R}^n \smallsetminus B(0, \varepsilon)} f(x) dx
$$
@Srivatsan I don't know if the sphere or cube is standard. I would think the cube, but you'd probably have to specify which.
@robjohn Good point. I didn't think of that, but let's ignore that bit for now.
@Srivatsan Fine with me :-)
Looks like we lost Bill.
=) Not like I am going to do something nontrivial with it anyway. =)
@Srivatsan I think that it is useful in Singular Integrals and such
And I think they use the sphere there
Gotta get back to work. bbl
19:17
Sure. Thank you for your time. See you around!
19:37
Does it matter if it is a cube or ball in the Euclidean case?
@JonasTeuwen I would be surprised if it didn't matter.
You would be surprised if it didn't matter whether it is a cube or sphere?
It did seem kind of sensitive to the "shape" of the object we are cutting out.
Oh, that integral.
That's usually a sphere.
Covering arguments are easiers with cubes :-).
@JonasTeuwen I've seen Stein use both cubes and spheres
19:40
@JonasTeuwen I don't get it: in that case, why would I pick spheres?
Yes, because in the Euclidean case the norms are kinda equivalent.
@Srivatsan When dealing with spherical harmonics, the sphere is easier to use.
Hm, that makes sense (that there are applications that favor spheres over cubes).
Isn't your PV integral just $$\lim_{\varepsilon \downarrow 0} \int_{|x| \geqslant \varepsilon} f(x) \, \mathrm{d}x?$$
@JonasTeuwen Ah, but we were looking at a case where $[-\epsilon,\epsilon]$ and $[-\epsilon,2\epsilon]$, which are equivalent in the same way that all norms are equivalent, that gave different answers.
19:43
It think it does matter if you take the Gaussian measure with $\mathbf{R}^d$ because the doubling property fails. I should think about that.
Oh.
@JonasTeuwen and the diagonal and sides of some cubes differ by more (in higher dimensions)
Usually it is the symmetry that cancels things out, but I know in certain arguments, the assumption is made that some functions integrate to 0 over each sphere
And in those arguments I know that deleting the sphere is important
@robjohn Can you point me to some standard basic books? I assume we are talking about harmonic analysis or some such topic..
@Srivatsan Singular Integrals and Differentiability Properties of Functions by Stein is a good starting point with lots of references (to pretty old material since the book itself was written in 1971).
It's also good because I have a copy and can see what's up if you have a question :-)
Ah :=)
(sigh Why do such old books cost a ton?)
19:58
Ah, I didn't notice that it is $65
@robjohn Nevermind that. I might possibly try to check it out from the library.
I just want a feel for the topic though.
@Srivatsan That is a less expensive route :-)
That's a nice book. But it is quite hard for a first glimpse at harmonic analysis, I'd say.
@JonasTeuwen maybe. It was my first book, but then, I'm an analyst at heart.
@robjohn Or some old bookstore? Not for this book in particular, but in general, I want to make a visit and grab some cheap old stuff (if any fits that description).
20:01
I wrote my BSc about a corollary of a theorem in that book.
@Srivatsan I would definitely promote an old bookstore.
@robjohn Did you think it was easy to understand?
(It was my first book too)
@JonasTeuwen I thought it was reasonable, not a book that spoon-feeds you, but I could follow it. Of course I was taking a couple of courses from Stein at the time.
@JonasTeuwen I wish I could read that :-)
(On the other hand, I am trying to do too many things at a time. Should probably focus on this or that.)
@robjohn Why not?
@Srivatsan Oh, I looked at the beginning and did not see that the inside was written in English :-)
20:07
@Srivatsan He probably can’t read the Nederlands. But it’s actually in English.
@BrianMScott Precisely!
George: What is Holland?
Jerry (also wearing a moustache): What do you mean, 'what is it?' It's a country right next to Belgium.
George: No, that's the Netherlands.
Jerry: Holland *is* the Netherlands.
George: Then who are the Dutch?
I am reminded of this now (I am talking about the message I just deleted).
But it is nothing special, I have written out the first three chapters of that book and in the last chapter I have proven something which was of course already known but which I did not know.
@JonasTeuwen What do you mean, 'I wrote the first three chapters of the book?'
I took the first three chapters out of Stein's book and have filled in the details and have written the report about that.
20:12
Are you serious or kidding?
Mind: I didn't know functional analysis or measure theory at the time!
Oh that makes sense. Sorry, I haven't seen the book, so didn't know what to expect. =)
@JonasTeuwen How did you pick your topic? I'm asking because I thought I had picked a topic but now I'm having second thoughts because I think the prof is a creep and I'm not sure whether it's important at all to like the supervisor or not.
It is not so verbose.
@JonasTeuwen That is quite an impressive feat.
20:13
Well, I have picked the supervisor which I liked and then he suggested a topic.
Which was quite ambitious given my knowledge at the time. But I did ask for that.
Then I'm potentially doing it wrong.
Bill Dubuque wrote me and asked me to tell the chat group that he is not here because Willie Wong has suspended his math.SE account for 30 days. Willie says that Bill was being impolite in some comment, but Bill thinks that it may have to do with a personal grudge (because Bill has criticized Willie's moderation on many occasions).
Well, for a BSc project it might not be that important but for larger things it surely is. Anyway, I'd suggest you pick a professor that you like (and that you are interested in his field).
Well, it is also the case that what's right for one could be quite bad for another.
Willie Wong doesn't seem like someone holding personal grudges like that.
20:15
Bill says that he probably won't return. I wrote back: "I hope you decide to return. Math.SE would be better if you did. I don't know how bad your relationship with Willie is, but I would hope that some neutral ground could be found."
@robjohn Tell him that I read the comments and that I was wondering why he was so angry about someone posting a wrong answer.
I picked Mary Ellen because she was the only general/set-theoretic topologist at Madison. Fortunately, I also liked her. Oddly enough, I probably talked more mathematics, even about my dissertation, with Ken Kunen.
@Srivatsan Do you mean that for some people a bad supervisor it not a bad thing? 8-).
@MattN He can probably read what you say here, but he cannot respond.
I hope he returns, he often gives very good answers.
20:17
@JonasTeuwen Some people could grow independent of the advisor. I am not sure if it's ok to have an evil advisor, but I think I do know people whose advisors are hands-off (and hence not directly helpful).
Okay, that might be true. It was only a suggestion based on my experience :-).
@JonasTeuwen In general I think that his answers are often more useful to other answerers than to the asker.
@Srivatsan Well this one here is probably not evil. It's hard to explain but someone about him disturbs me.
@JonasTeuwen Yes, he is a great asset here.
@BrianMScott Yes, but I don't see that as a problem. MSE is also some kind of problem/answer database to me.
20:18
@Srivatsan Mine was hands off, but that was exactly what I wanted.
There is a difference between not liking the supervisor and having one "hands off".
Absolutely.
@JonasTeuwen Yes, I was going to post something to that effect next :=)
Mine is quite "hands off", but when I have a question he always has/makes the time.
Maybe I shouldn't say that, he probably doesn't feel that way about the "hands off" thing 8-).
He thinks he is hands on? =)
20:21
Depends on the student.
I don't really need it since I want to figure out things by myself first. Only if everything else fails I go to him :-).
I wouldn't expect someone to justify the application of de Morgan's law in an analysis thesis. =) Is it that detailed? (In that case, I might find it helpful to me.. :D)
(Jonas, I was referring to your BSc thesis.)
Hmm, I had never written something like that so I might be too verbose at some points and too little at others.
My MSc thesis is already much better 8-).
@BrianMScott Regarding the "closure question": before you left you told me to give him the easier direction. I'm not sure my proof is right but if it is then both directions are equally easy.
@MattN where was that?
They’re both pretty easy, but I think that the direction that you originally gave is slightly the easier of the two.
20:29
Ok : )
I've given both now. Although on close inspection he seems to be of the lazy kind...
Thanks.
@Srivatsan Beat me to it.
@MattN I saw that you’d given both. (I was the first upvote.)
@BrianMScott Yay! Nice. Thank you! : )
20:32
hey guys, I'm pretty sure the result from this integral
http://www3.wolframalpha.com/Calculate/MSP/MSP48391a01iadf315e225d00005a0h9hh7cg014a6c?MSPStoreType=image/gif&s=40&w=265&h=36
is $-\frac{cos(x)}{4}$
http://www3.wolframalpha.com/input/?i=integrate+1%2F2sin%282x%29
at wolframalpha I'm getting a different result: $-\frac{cos(x)}{4} -1/4$. Is this residual $-1/4$ a part of the constant?
@robjohn Actually, one final comment (posted by B in reply to the upvoted comment from P) has been deleted -- presumably by the mods. That might have tipped the scales. (Don't remember what it said.)
@Srivatsan Could be.
@Clash W|A gives $-\frac14\cos 2x-\frac14+C$ as an alternate form, which is correct: $\cos 2x=2\cos^2 x-1$.
@BrianMScott but if I integrate using trigonometric identities I get $-\frac{cos(2x)}{4}$ (without the residual $-1/4$).. does this make any difference or is part of the constant?
@Srivatsan Interesting. Did he get suspended for that or is there something deleted?
20:39
@Clash It’s part of the constant. You’ll often find, when dealing with trig functions, that two antiderivatives differ by a constant.
@BrianMScott alright, many thanks brian! :)
21:11
@JonasTeuwen There is no official news on why he was suspended, so we are just guessing. That thread was the last one BD was active in. As far as I remember, all the comments except one are intact. The reply from Bill to Paul's comment has been deleted; I don't recall what it said.
@JonasTeuwen And by the way, this might be interest: chat.stackexchange.com/transcript/message/3100596#3100596
Yes, I have read that. So basically we are just guessing. I'll refrain from having an opinion on this then 8-).
Bill's absence will be felt for two reasons:
(a) His "hints", even though terse, are enlightening once one gets to understanding them.
(b) More than anyone else, he has been rallying for some social issues as well:
(i) The everyday running of the site should be handled by the community rather than the moderators, to the extent possible.
(ii) Rather than close all questions that are ill-posed, "experts" could use their knowledge and expertise to help the poster arrive at an answerable question.
21:26
@Srivatsan Those are all good points. I hope he decides to come back.
Hm, I can't believe David is already at 12k already. I am inviting bets on how many more days it will take him to overtake me.
@Srivatsan Which David?
Mitra.
@Srivatsan Two months?!
No way it'll take him that long!
21:34
Depends a lot on what kinds of questions come along.
I would give it $28\pm1$ days
@Srivatsan
How come your future-predictor is so precise? =)
@Srivatsan How do you know it's precise?
I am guessing after all!
@KannappanSampath You specify an interval of 2 days. It's as precise as it gets in Stackland.
@KannappanSampath You’re confusing precision with accuracy. Your guess is very precise, but it may not be very accurate.
21:37
Ah, I didn't realise that could be the issue.
Oh, Yes! It makes more sense now!
Let's see! If my prediction turns out right, @Srivatsan will turn a Nelson's eye towards my messages!!?
Rough analogy: Imagine a dart-throwing experiment. Precise but not accurate would mean you keep hitting the same place, but that is nowhere close to the bull's eye. Accurate but not precise would mean that you hit the bull's eye from time to time, but you are not consistent in which spot you are hitting.
I would say rather that ‘accurate but not precise’ means that the mean position of your throws is very close to the centre of the target, but the standard deviation is large. Oh, I added your example to the half-of-the-integers question.
Are people here aware of protests by the mathematical research community by and large to Elsevier?
@BrianMScott Hm, that sounds better. :)
21:43
Looking forward to Gowers's response to David Clark.
@BrianMScott Have you seen this Demotivators picture? =)
@BrianMScott Thanks. And I like the way you explained it; it's pretty much how I wanted to say it. My phrasing of that example is a kludge. :/
@Srivatsan I have now. :-) (It took a while to download.)
Oh, it loads quickly for me.
But you’re not on dialup!
21:52
Bill Dubuque must come back!!!
(shouts after reading the message from Bill through Rob)
I guess we are seeing a "Let's hope Bill comes back" message posted every few minutes. =)
@Srivatsan No, he's only been here two months! and he has 12k!
@robjohn Yes, you should be alarmed. It'll be me tomorrow, and you the day after. =)
@Srivatsan I've been here six months and I only just got 15k. :-(
@Srivatsan He's averaging about 200 points a day.
@robjohn I was a tad quicker. :-) // I hope you didn't mind that comment. :D
21:57
I had to check, but it appears that I’ve been here for seven months.
@Srivatsan You've been here 6 months and have 13888... what do you mean?
Did anyone recently peep into my profile?
@robjohn I was a tad quicker in my comment. Hey, I am not competing with you for reps! :D
@Srivatsan Well, I have not been able to do as much here lately due to work issues, so you could pass me soon.

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