I just can't believe what gets votes. Can this answer be worth 14 votes?

Don't get me wrong, I would have given a very similar answer, I am just surprised at the amount of effort vs the number of votes.

odd

@QED Not really. We've been discussing the phenomenon that people will only vote on the things they understand and more people understand the simpler things, and the things that take more work are understood by fewer people, so they get fewer votes.

That's for sure

I hope it doesn't discourage people from writing good answers to difficult questions though

I don't think they write the answers for the votes.

I know I still write answers that take too long to do. :-)

I wonder where I could read something interesting about circle of convergence

if a power series has a radius of convergence then it can either converge or not on the edge of the circle: I bet there are some weird patterns that can show up around the edge (other than boring stuff like a finite number of points missing)

fractals perhaps

Take a look at Lacunary Functions.

That would be a place to start.

Gotta take the dog for a walk. bbl

Oh that's brilliant, thanks!

bye

@anon Yes indeed. : dx.doi.org/10.1016/S0377-0427(02)00644-1

@robjohn hm. sorry about that :)

@robjohn If this question is worth 32 and its answers 25, resp. 24, then probably yes.

Well, this one was short. So, hi everybody!

And bye everybody!

@QED Maybe this is of interest.

thanks

@Srivatsan: would you mind adding the word "compact" in the title of the post you just edited?

@tb: can you vote on an answer to a closed question?

@tb compact Hausdorff?

@robjohn Yes, you can. What am I missing? You could've voted and found out, no?

@Srivatsan yeah, that's my Bourbaki education speaking.

@Srivatsan Ah, so it only prevents new answers...

@Srivatsan I wasn't trying to vote, I was just noting that a new vote came on an answer to a closed problem...

@robjohn The idea of closing a question is to collect the answers in one place and to link them together. Editing, commenting and voting are still possible. There is the concept of locking a post, which makes it read only and disables everything else. It rarely happens.

@robjohn Oh, makes sense. [Then the answer to your question is even clearer :)]

@tb ok, that answers my question :-)

Yes, that's the longer, correct-er answer. =)

This meta thread links to a question that was locked (before it was deleted) because of the uproar in the comments.

That's the only example I can think of right away. The infinite monkeys question was locked for some time, too. As I said, it happens very rarely.

@Srivatsan thanks for editing, it's much better this way.

Oh, Adam Smith.

@tb Sure, np.

Was this about the guy who admitted he was asking for help on a take-home?

exactly.

Hm. Maybe I'll re-read this. I do think such a question is completely indefensible, though.

@tb Aw, I can all that question now. =)

@DylanMoreland I think I agree. On the other hand, I'm not sure I like the message: just don't say where your problem comes from and you won't have any problems. The formulations of some of the comments was way out of place in my opinion.

Well, sure.

I remember the kid saying, "well, at least I was honest"

which was pretty ballsy

A professor I know did catch this happening with one of his take-home exams, on this site. He was livid.

The precise formulation was: You seem to advocate lying. You're basically encouraging me to exclude details. It's a "take-home test" - don't you think our teacher expects us to look up answers to questions we don't understand? It's basically just an excuse for us to do "homework."

It's a tough issue.

Although it's hard for me to accept, "well, you won't catch everyone, especially if they're clever about it" as a reason to not perform the policing you're able to do.

@DylanMoreland Well, that's like what I said. =) I don't remember what the kid said.

It ties in with the discussion of yesterday. What to do? I don't know. The problem is that there is no way for us to tell. I would guess the vast majority of questions are assignments of sorts. I think I'm pretty much of the same opinion as the one JDH expresses here.

I was with him until the last paragraph.

Giving people answers on a silver platter is not something so venerable as "collaboration".

Well, does JDH advocate giving complete, beautiful answers to all questions even if they are HW?

Have you ever been to a really satisfying set of office hours? I feel like that's the ideal experience here.

I had a difference of opinions with him on that issue, too in the comments here.

@Srivatsan Yes. He's also opposed to giving partial answers or outlines even if the OP explicitly asks for not having the full solution given away.

@tb I guess that's a stand, nothing right or wrong.

In fact, I do think that will make the site a better place in the long run. Might not be useful for the OP though.

Sure. On the other hand, I like good outlines and hints at least as much as full-blown solutions.

Yes, agreed. Often full-blown solutions do not add much to insight.

Funny that this thing came up today. One second; let me pull out an answer that I posted today.

See my answer here: math.stackexchange.com/questions/88689/….

My first hint was a hint, then I wanted to post the full solution anyway for some reason.

He has a point that only one person asks the question and yet hundreds will read the solutions.

But if I'm responding to A's question then it's hard for me to not put A's interest at the fore.

Ah well. This will never get resolved.

@DylanMoreland But I guess each of the ones who is reading will put in effort to understand the answer, no?

So why can't we assume that the future reader will also try to crack the hint?

@DylanMoreland Exactly. That's what I tried to do in the thread linked to above. Give a hint that basically tells you what to do and if you think about it for five minutes you should be able to fill in the details. Then explain what you can do with it, some nice consequences. I don't think there's anything wrong with that and decreases the utility of the site.

It's as hopeless as a Skullpatrol koan.

I like the exercise or proof sketch style answers. Will teach the reader to break down the problem into steps.

I'll take a look at both.

@Srivatsan I saw it earlier, but only in its finalized form. Good job, I think. One thing you could have pointed out is that the map f -> M_f gives an isometric C*-algebra homomorphism from L^\infty to B(H). This is a crucial ingredient for the formulation of the spectral theorem in its measurable functional calculus form.

I can point it out, but I should know or realise it first =).

Let me look for a good reference.

Maybe that's the way to go, Theo: have a sequence of tasks that amount to painting by numbers.

I am reading what you said. tb.

@tb - what's H?

And, the last statement is a little over my head. What's "in its measurable functional calculus form"?

We're receiving many edit suggestions replacing \rightarrow with \Rightarrow in this answer: math.stackexchange.com/a/88579/13425. I just rejected one now. I know one was already rejected in the evening.

Here it is, see also here and the section IV.4.

Dup? math.stackexchange.com/questions/88767

@Srivatsan Yeah, I rejected such a suggestion earlier. These minor notation quibbles are completely ridiculous, IMO

@Srivatsan H=L^2[0,1]

Well, I have a feeling some people think it's wrong to use -> instead of =>. Or it's just a quibble.

Some people think it's the other way around.

Yeah, if I prefer one to the other (and I do), then I will use that one in my post. I can't suggest edits to other people's posts, right?

No you can't. You could leave a comment explaining your preference.

(or you could use another browser and suggest an edit anonymously :))

Yes. That's why I think perhaps those users are under the impression that the notation is a typo.

What's up with Baire today?

And why do people make such a fuss about it? It's really nothing but a pimped nested interval theorem.

@tb - Ya, I see people (at MSE/MO) regarding Baire and Tychanoff as inherently deep topological statements.

Perhaps not deep, but at least "inherently topological"

If deep = "requires some choice" then yes, maybe.

But I seem to have a skewed view on what's a deep theorem, recently.

This springs up in the threads that discuss Fürstenberg's proof of infinitude of primes, e.g.

But that's a cheat :)

Is that the "topological" proof?

May be a cheat, but I am just focusing on the "topological" thing right now. :)

I feel like it's pretty misleading. I wouldn't want people to get the idea that that train went anywhere.

What's misleading?

there is no such thing as a deep theorem

it's just personal taste

same like an emotional movie, someone might find it trivial

I just remember someone on MO thinking that this would be a good avenue for proving results in number theory.

And as far as I can tell that's just not true.

Yes. As Nate put it: Someone is abusing the language of topology, e.g. Fürstenberg's "topological" proof of the infinitude of the primes. See also is Fürstenberg's topology useful?

(I don't know what I wanted to say. :))

:)

I don't know. I certainly don't understand the objection to the proof, or the claim that certain things could be or could not be "inherently topological". :)

But I don't have nothing more to add.

the objection is that the proof is exactly the same as the other proof, except it's be rewritten in a weird language

so people don't like it because it's nothing new

NARQ?

Right. I think Brian Conrad brought up the contrasting example of Euler's proof of the infinitude of primes.

I think you have this comment in mind

I can wholeheartedly agree with Pete Clark in that whole comment thread :)

Agreed.

would like to hear about "real" examples though

real examples of what?

making use of the profinite topology on Z to get some number theory out

Sometimes I'm amazed of what is considered research level on MO.

@QED The profinite completion of Z is the absolute Galois group of F_p. That's number theory.

@tb I don't quite follow this :). Why don't you post it as a comment under my answer?

And it pops up a lot in class field theory.

I don't get the impression that it proves anything hard for you, but it's there and it places restrictions on things.

@Srivatsan: Since you posted what is essentially the answer to the min-cost matching for bipartite graphs question I thought you might be interested in my comment on it. It's at the bottom.

@MikeSpivey Oh, yes, I noticed the comment, Mike. Thanks for updating me though.

(I was kind of pissed that entering the keywords in the title in google gives the relevant references without too much pain. :))

I haven't read your blogpost yet. I will do so more leisurely.

@Srivatsan Yeah, that happens frequently on this site. :)

@Srivatsan Okay, done.

@tb Thanks, tb.

I upvoted the comment, even though -- of course -- I still don't understand it.

@MikeSpivey Well, one more thing. I was thinking of setting a bounty for your latest question asking for a combinatorial interpretation for an identity.

Wanted to tell you first.

Have to go now, they're closing the coffee shop here. See you, Mike.

See you, all.

See you @Srivatsan

@Srivatsan That would be fine. It's currently the highest-voted unanswered question in the combinatorics tag. And see you!

@Mike, Thanks. I'll make up my mind (on the bounty amount and stuff) tomorrow.

@Srivatsan: Just so you know, it would have been fine with me if you had put a bounty on it without mentioning it to me first.

hi all

Hi Alexei.

hello

@AlexeiAverchenko what on earth was that comment?

Hi btw.

Good way to start things off.

you used two different symbols for the trivial group :)

in one chain

i've never seen this done in my entire life :D

But in the first instance, it is including into an additive group.

Sure, because I think of Z as the additive group of integers, and it's pretty common. It also emphasizes the fact that we have a short exact sequence of non-abelian groups.

It's pretty common when you see central extensions.

While the diffeomorphism group of S^1 is a group having the identity 1 as neutral element, so it makes sense to denote its neutral element by 1. Doesn't it?

@AlexeiAverchenko See e.g. here

God... how I hate Tuesday mornings.

alright :)

came back! :)

@AsafKaragila So, you work on Sundays, and hate Tuesday mornings? This surprises me... :)

@Srivatsan Saw that. So you found another coffee shop?

No, caught a bus and landed up in my office.

@tb On Tuesday I wake up at 7, and I am going shopping with my dad. I only start the university at 12, though.

@AsafKaragila Every tuesday, or this tuesday?

@Srivatsan Every.

Can someone tell me how to phrase "it is not the case that g is zero a.e." better?

TG replied Darij :-D

This is one of my favorite recent comments. :)

@Srivatsan, that's fine

Hey Stupid !, :-D

@MikeSpivey I somehow saw that one coming :)

Or at least something to that effect.

@AsafKaragila Oh gosh.

@tb Me too, me too :)

@MikeSpivey That's a bit much. It was a well-intentioned comment by Patrick.

Splice was polite, yes.

Don't get me wrong -- it's funny!

@DylanMoreland It felt a bit weird to me. Just the very fact that Splice wrote such a nice answer means that they is not a random person.

@DylanMoreland I think it was well-intentioned. I'm not knocking Patrick. It's just a funny exchange.

It was weird. I'll give you that.

@MikeSpivey Oh, I didn't mean it was too much on your part.

who is splice?

Everyone is doing fine.

@tb Why can't you find the dupe before I fix all of the TeX.

I guess my alarms should have gone off on that one, though.

@AsafKaragila I'm with Ryan on this.

@tb Ryan? He didn't post on that thread.

@tb Just so you know, Jonas made a comment on your comment in my answer.

@AsafKaragila He just did.

That's clever math.stackexchange.com/a/88782/16697

@Srivatsan Thanks, I was thinking of mentioning this, but the overkill here prevented me from doing so.

@tb Oh. I am also with him on that. I always find it amusing when he complains about how his threads are closed... and then the thread gets closed.

Either way, I'll be back in about two hours.

See you.

@DylanMoreland I'll try my best in the future :)

:)

thanks , i would like to get the proof please :D

Happily, someone has provided it.

Oh, yes! Adding [Elliptic Type] makes this question waaaay better...

@tb That made me laugh. :)

They did at least respond (sort of) to your request about what kind of PDE... :)

Do you think I should reconsider my downvote? :)

@tb That's your call. :) I haven't downvoted, but I agree that it's an overly broad question. Too bad Willie isn't here. This is his area, isn't it?

@MikeSpivey I voted down after the addition because I found it rather ridiculous. It definitely is Willie's area, yes. I don't see anything more one could say than look at Evans and Gilbarg-Trudinger.

I'll add a comment to that effect.

So I've never asked a question on the site. Is it impossible to vote up an answer that you've accepted?

Because I see accepted answers with zero upvotes, and that doesn't make sense.

No, of course it isn't. But unregistered users can't vote, they can only accept answers.

Ohhhh.

I learned something.

Thanks Theo. I should have read the site docs, probably.

But there are also registered users that have strange voting habits. I answered about 6 or 7 quite non-trivial questions of one person and the only vote cast by that person was on another question.

Another reason could be this: if a user has low accept rate, then we pester them into accepting answers. But no one is questioned for having low upvotes or downvotes.

@tb Well, another question of yours or someone else's?

@Srivatsan I just see that this person has 1 vote cast overall and it was on a question.

Oh, sorry. I didn't remember that this info was available.

@DylanMoreland I'm not entirely sure why this is so. I think the (flawed) assumption is this: people are eager to vote and it is a means of motivating people to register. J.M. and I discussed this yesterday. There are badges for an inordinate amount of accepted answers without votes: Tenacious and Unsung hero. David Mitra is pretty close to the golden badge.

Ah, right.

@DylanMoreland And if a user has < 15 rep, they can't vote, either. All they can do is accept.

@MikeSpivey At least they should be allowed to vote on their questions, I think.

Well, a reasonably good question should earn three upvotes. I don't think that's hard to obtain. It should also motivate others to vote on questions.

A couple of the tags I pay attention to - like linear programming - aren't popular with the site as a whole. Questions in these tags don't even get many views, much less upvotes. It's not uncommon to have one person ask a single LP question - even a decent one - and not get 15 rep. I'm sure there are other tags for which this is the case, too.

Even if it's not an LP question, I found this one pretty nice. I was rather astounded that both question and answer only got three votes.

@tb: Thanks. :)

I'm actually happy when any of my answers on some optimization-related question gets three votes. :)

It's late here. Good night, folks.

I think this question now deserves to be re-opened.

i cast my vote.

@robjohn Actually, it seems that the posts are shown only once for review, so systematic use of the review pages should produce the desired effect already.

@Srivatsan Thanks

I have a quick reference request: does exercise 18 in chapter 3 of Big Rudin indeed trivialize this year's putnam A3? (for the putnam problem, see here: artofproblemsolving.com/Forum/viewtopic.php?f=80&t=449984)

I don't have access to a big Rudin, but I'm curious, because that's what I heard.

I am referencing here the comment at the end of the solution by "ns2675"

I don't understand what you mean by "trivialize". The statement is given there and it's just an abstract way of looking at the exercise.

@Srivatsan Zev's reopened it now.

I haven't taken graduate level real analysis yet. Is the solution of the problem really sort of obvious to someone who has, like is claimed?

I don't think it's any more obvious than the exercise, but I'd assume that anyone knowing a bit about L^p spaces knows this. That doesn't mean it's obvious.

It is, however, a standard exercise in this form. Or at least the slightly easier variant saying that the p-norms converge to the infty-norm.

Is higher real analysis generally useful like this for doing these sorts of tricky putnam problems? Or was this just a one time trick thing?

I don't know. I had the impression last time you asked about Putnam (the first time I ever looked at these problems) that many of the questions are explicit instances of well-known abstract results. But, as I said back then, I don't really follow Putnam, so I can't tell for sure.

what a curious comment!

@Potato: did you see my responses re: for $r>-\frac{1}{\log(1-\epsilon)}$ and $x\in[0,1-\epsilon]$, $rx^r f(x)$ is decreasing pointwise?

@Srivatsan Hm. I saw that, too, and "I was, like, whatever." (Liam Lynch)

My first bounty. :-)

@Srivatsan Good luck!

Thanks.

Ello.

@tb At least I got an "Investor" badge in return. =)

@Matt hey Matt.

Hi Matt

Now what's this?!

@tb Do you know what a deer without eyes is called?

tb: You haven't seen that yet? I had a great time when I first saw that post.

@robjohn This bookmark is really handy also for instances where the site fails to render :)

I flagged it for removal.

@Matt No, but I bet you'll tell me soon :)

@tb No eye deer. (Read: no idea)

Oh, my dear.

oh. Gave the wrong answer then :)

It's almost as good as: what's yellow and complete?

Hm....

I like this one better (classic!): what's purple and commutes?

@Srivatsan Abelian grape.

@Matt If you didn't know the other answer, I can tell you.

But you just have to think along the same lines...

@Srivatsan I'm working on it. It'll either be a lemon or a banana. Right?

Right. :-)

Do good math jokes exist? Based on the answers above, no.

@tb Nice :-) where does the site fail, for instance?

@Srivatsan I guess banana doesn't really rhyme with anything, so it'll be lemon. Right?

@Matt What does lemon rhyme with?

Don't know yet!

But complete suggests it's a space...

I've never heard of lemon space.

@robjohn Go here, scroll to the bottom of the page and go to page 2. MathJaX won't render.

@tb If you reload it will.

@Matt Clicking the bookmarklet is faster :)

@tb Yeah I haven't managed to make my extension button trigger the js...

@tb Banana space?

@Matt Bananach space.

Oh.

@robjohn Another instance is in the review windows if you have several things open already, it sometimes happens that MathJaX doesn't render. After reloading the site won't display those posts again, so the bookmarklet is extremely convenient there.

@tb Indeed. It seems to work there because nothing is using \[ or \] for displaymath. I had to disable those because something about the way chat handles the [ and ] characters made [0,1] render as $0,1$

@Matt I didn't claim it was funny :)

@robjohn displaymath = \displaystyle?

@tb displayMath is what MathJax calls the stuff rendered with $$...$$. The stuff rendered with $...$ is called inlineMath.

Okay, I see. Makes more sense.

Test: $$F(x) = \int_{0}^x e^{t}\,dt$$

@robjohn Now I'm confused :)

In LaTeX, $$...$$ is the same as \[...\] but not with the bookmark.

@tb why? It looks fine to me.

Test 2: \[F(x) = \int_{0}^x e^t\,dt\]

[F(x) = \int_{0}^x e^{t}\,dt]

Your first test renders, the second doesn't

@robjohn Okay. I see. On the main site they use \\[...\\]

\[...\] won't render either.

Hmm... maybe the original bookmarklet had a mistake...

test: \[\Gamma\] [0,1]

Ah... I fixed it. It now handles the square brackets properly... now I need to update the pastebin copy...

@tb: reload your bookmark from pastebin and the \\[ and \\] should now work, too.

@robjohn Did you update it or did you post a new one?

@robjohn perfect! :) Thanks a lot for this!

Yay! Finally. Made my extension button work.

It now needs to update with new events.

Engineering is so painful.

I have no idea how to do that yet.

@Matt Did you get the newest version from pastebin?

@robjohn No. Going to now.

$$ \frac{1}{42}$$

\[x\in[0,1]\]

@robjohn: It would be great if you could post the bookmarklet together with a short description of how to install it as an answer here. It doesn't look as if the supreme powers of SO are thinking about implementing it, and having a bookmarklet allowing us to trigger compilation manually is certainly much better than nothing.

And also much better than the codecogs PITA

@tb I will post there. :-)

Now debugging the js : (

@robjohn: a short description how to install it and how to use it would be great. I mean to explain that dollars are allowed as delimiters, [ ] are not (this is the state now, right?) and maybe some other details that might be important for using it.

It was a great idea to do this, just wanted to thank you for your work.

I mean \[ \].

@robjohn Yes, I did see your responses. They were helpful, thank you.

I'm beginning to understand ghost candy!

Ghost Candy? Is this a ghost of a stripper from Vegas?

What does that mean?

@AsafKaragila 'sup with your recent obsession with strippers?

I have no such obsession... it was merely pointed out that strippers from Vegas are essential to mathematics. Also, Zhen keeps mentioning names which are very fit for strippers.

@tb: meta.math.stackexchange.com/a/3297

@robjohn great, thanks, +1'ed

@tb: Suites spectrales.

MathJax Support For The Chat!!

@ZhenLin I knew I was missing the link. That's a joke in Eisenbud, right?

Indeed.

I'm reviewing for my complex final and everything is starting to come together and click nicely. This is a wonderful feeling.

While we're talking about strippers: The spectral sequence is like the mini-skirt; it shows what is interesting while hiding the essential. from here

So what change am I supposed to see after creating the bookmark?

@Srivatsan This should be rendered after clicking the bookmark: $$F(x) = \int_{0}^x e^{t}\,dt$$

"Once installed, activating the bookmark will render" - what does activate mean?

@Srivatsan clicking it

@Asaf: I keep forgetting it's $\LaTeX$

Yes, you do. :-)

@Asaf: was adding this godforsaken ugliness really necessary? :) I can't fathom how somebody with otherwise good taste could come up with that crap.

@tb: It's not like I bumped a year old post just to correct a typo :-)

@rob: Perhaps you can just post the script into the answer?

@AsafKaragila yes but edits are supposed to be improvements

@AsafKaragila I guess code will keep things right...

@tb: Once J.M. edited a post of mine and changed a display mode \dfrac{1}{2} into \frac12 just because it was in form of his TeX style. The outcome wasn't even changed by that. (I think he may have also corrected some typo, but still... the TeX edits were unneeded.)

@AsafKaragila you know my stance on this...

@tb This is an overkill, but some people really abuse braces.

(check the revision history, of course)

@Srivatsan how can you abuse braces?

@tb No need, I already know the history.

@tb {\put{every{thing{in{braces}}}}

LaTeX \neq Lisp.

Or...