@robjohn Hmm... Yeah, sounds cool. But how would that be implemented in practice? :-).

@JonasTeuwen Not too hard, I have an actual digital encoder/decoder for tracing out the hilbert curves.

@robjohn You've made it?

@JonasTeuwen to get higher resolution, you just add one more part

@JonasTeuwen on paper.

hah I made a mathjax button

@robjohn Very cool. Do you have .pdf?

(or do you want to patent it?)

@JonasTeuwen I can probably make a PDF... remind me and I will make one.

@robjohn I'd like to see that, too. :)

ok kids... gonna go eat for 15 min

@JonasTeuwen I actually did visit a patent attorney about it, but it doesn't work with digital TV broadcast, so I didn't pursue it further.

@JonasTeuwen try replacing alt with title.

@ClarkKent does your blogging platform not have a way to store files?

@JM Yes! :-).

@robjohn Okay :-).

@robjohn But it can still be a cool toy for mathematicians!

@JonasTeuwen It would be :-)

@ClarkKent I don't know now... all the cool filehosts clammed up in anticipation of SOPA/PIPA... :(

the surviving ones look so seedy I wouldn't recommend them to an enemy.

@JonasTeuwen It worked?

@JM Yes!

@ClarkKent He is unaware of your superhero true identity?

@JM fa.its.tudelft.nl/~teuwen

@JonasTeuwen Looks good when I looked at the source... :)

@ClarkKent He was threatening you with Kryptonite?

"Are you threatening me???" A: "Maybe I am!"

That is the truth and nothing but the truth!

(said the unicorn)

@ClarkKent Is it, now?

@ClarkKent And there is a curve to prove it!

My sweat has a corroding property... My stylus is rusting!

@JonasTeuwen If you start getting chest pains, let us know so that we can RUN!

8-).

I just found my old unfinished paper on space filling curves in $\mathbb{R}^n$. I should finish it.

That has enough of the math in it to create the diagram again.

good morning: youtu.be/gvuWhPUSSn8

@JonasTeuwen Watch: youtube.com/watch?v=BQ9J_o7hI94

@BenjaminLim Time to go home now. I'll check it there!

it's correct. youtube bought youtu.be to make shorter links

guys, a bounded set on a metric, locally compact space is precompact?

False. Take d_b(x,y) = max(d(x,y),1). All of $\mathbb R$ is bounded under that metric, but it certainly isn't precompact

@kahen total boundness needed?

Speaking of which: I'm trying to wrap my brain around a proof of "if a group $G$ is locally compact, then it's paracompact". Starting with a precompact symmetric open $U$ nbhd of the identity, we construct $H = \bigcup_{n=1}^\infty U^n$, which is easily seen to be a clopen subgroup of $G$ by symmetry of $U$. But I don't see how it follows that $H$ is σ-compact using that $\overline U \subseteq U^2$ - how does that imply that each $U^n$ (or at least $U^2$, $U^4$, $U^8$, ...) is precompact?

back

@ClarkKent, a good part of general topology is the abstraction of situations that come up in practice—that is why there are many definitions: practice is complicated!

Could any of you fine people check if this is giving you a 500 error?

@JM No error for me.

@DavidK You're getting the PDF?

@ClarkKent, essentially all of a reasonable course on general topology is motivated by actual problems, those implications are actually things that are interesting in practice, or at least were. The problem is that it is just impossible to explain that context along with the topology.

It'd take years

@JM Yep

@DavidK Something's terribly wrong on my end, then. Thanks for checking!

Hello everybody!

Hi Dr. Nick!

@DavidK What?

@PeterTamaroff youtube.com/watch?v=YlmECL2ED2I&feature=related

@DavidK Oh! Never saw that one.

Any news?

Well, my topology professor won't tell us anything about the final exam that is on Thursday. Other than that, no.

Tsk. Can somebody be kind enough to download the article here for me?

(The AMS site has really been acting weird for me lately...)

@JM I'll try 8-).

@JM I'm on it.

What's the issue?

Oh, if it is easier for Peter, let him do it.

Done.

I'll give you a link to it.

@PeterTamaroff Gracias!

Here

@JM De nada!

@MarianoSuárezAlvarez Buenas!

For context: it's for this question.

@ClarkKent What is going on?

@ClarkKent Where is that transcript you're referring to?

@ClarkKent I can't find the transcript. Did he provide a link?

@PeterTamaroff Did you click on the left-pointing arrow in Clark's line?

@JM Yes.

@ClarkKent I want to see this transcript "I read the transcript and I don't really understand what you are feeling. "

@ClarkKent I suggested something similar to Kannappan earlier today.

@robjohn Do you have any context to provide? I'm worried about Kannappan.

@PeterTamaroff: You left this cryptic comment. Why was that?

@robjohn "The previous owner of the Mathematics chat Asaf Karagila" Iddidn't know the chat had an owen (no irony here, I'm really confused).

@PeterTamaroff No context really. I saw the transcript from earlier this morning and saw Kannappan saying he was going to delete his account, so I talked to him on Skype.

@robjohn That is really good from you. But why "owner of the chat"? What do you mean by that?

@PeterTamaroff There are owners of the chat rooms so that certain maintenance issues can be handled. There is not a whole lot that a room owner can do.

@robjohn Oh, right! I thought this room was self generated by the site!

@PeterTamaroff If you look here there are two owners listed.

I see. Good to know.

@ClarkKent not even close :-)

@ClarkKent Hahaha right, and succinctness too.

It's a coping mechanism for my hypochondriac dyslexia.

@ClarkKent just like that :-p

@ClarkKent =)

@ClarkKent Thanks. I have one important issue to deal with in MSE.

What to do with users that have as a username the surname of a well known mathematician?

Obivously Michael Hardy is legitimate, as an example. But some guys simple use Riemann, and even spell it wrongly.

Seems he fixed it.

Cauchy, Gauss

If I can bother any of you guys one more time: can you download this for me?

Hilbert

@JM Now what do I do with it?

I got it

@JM are you on skype?

@JM I'll give you the link now

@robjohn I don't have an account, sorry. :(

@PeterTamaroff You are too kind!

@JM It's free.

(Sorry, all the filehosts I know are down...)

@robjohn I used to, but I had neglected it for a bit and now I don't even remember what account name I used... :D

@JM Here

Maybe I'll get a new one one of these days.

@robjohn Did you have a videocall with Kannappan or chated?

@PeterTamaroff just chatted.

@PeterTamaroff Magnifico! Gracias!

@JM Whee are you from?

@JM I guess I could just get a dropbox account.

@ClarkKent I did tell I was on it.

@robjohn Dropbox works magnificently.

@ClarkKent Sorry... :(

I will have to look into this Dropbox, Peter... seems good.

I'll go for a while guys. See you later.

Okay, I'm on Dropbox.

Done for today. See you guys later!

@JM Bye!

@robjohn Can we take the squareroot of Diracs? The pointy things seem to converge when we take the limit 8-).

@ClarkKent Everybody is nuts! Except us. We are Batman and Superman.

I feel like an idiot for asking that question earlier... of course $U^2$ is precompact... $U^2 \subseteq \overline U^2$ and $\overline U^2$ is the continuous image of $\overline U \times \overline U$ under multiplication...

@kahen Ah, that is a good thing!

@JonasTeuwen you are the only two wearing spandex...

Of course that's sort of how it always is... you stare yourself blind on some miniscule detail before suddenly seeing the light and then you can't understand how you could ever think it was hard...

@kahen That's the cool thing about mathematics: -).

@robjohn Yes, but how... Sexy huh?

@JonasTeuwen I don't think so. I am trying to think of an argument why not.

They must have missed class that day...

@robjohn Cool. What's your username?

@PeterTamaroff username? all I gave was an email address, can I set up a user name, too?

@robjohn Well I guess the email is then the username. The good thing is we can create a folder and share it

@PeterTamaroff Yes; and user information is not displayed to others.

@robjohn The Fourier transform would map it to ... ? 8-).

@JonasTeuwen something that when convolved with itself would equal 1. I thought of that, but it is not satisfying.

@robjohn That would give some heuristic argument right?

@JonasTeuwen how?

@robjohn If you can complete it... 8-).

Hello!

@SalechAlhasov hey there!

The OP has accepted and unaccepted this answer twice. There have been no changes to the answer at all. Odd.

@ClarkKent There was an unpleasantness between Kannappan and Gigili. I saw bits of it, but I didn't follow the whole thing.

Again?

@robjohn, shalom! you got +1 from me as well to that problem... what program did you used to sketch that huge circle with triangles and dots(colored) inside?

@robjohn Maybe Adam is female? 8-).

@skullpatrol no, but that was the trigger for his leaving. I think he came back to mark his answers as CW before leaving.

@ClarkKent I think he was hoping that if he did that it wouldn't adversely affect others' reputations.

@ClarkKent The one the unaccepted robjohn's answer.

@JonasTeuwen tsk tsk

@robjohn (is joke)

Don't ban me! 8-).

@robjohn Does CW stand for "community wiki" ?

@skullpatrol yes

@robjohn thanx

BTW how was your birthday party?

@skullpatrol we had a nice dinner. Good Teriyaki Rib Eye and my wife made bread pudding :-)

Ah! Good old bread pudding. I'd love to have some... Must have been 10 years!

encrypted-tbn0.google.com/…

Careful I might have put some kryptonite in it :-D

@Ninefingers Welcome, Lord Mod. Is something amiss here?

@ClarkKent Is you're girl friend now a desperate house wife?

@FortuonPaendrag Nope. Maths chat is just on my favourites list and I clicked the "rejoin favourites button". Just pretend I'm a normal user :)

@Ninefingers Alas my lord, your name in blue you marks you as one of noble birth :)

@ClarkKent The images of kryptonite are boring ... :-D

@BillDubuque Hi.

@FortuonPaendrag Well... unfortunately in real life I am merely a peasant. Don't worry though, I leave the mod tools alone in rooms I'm not in frequently, unless it's blatantly obvious somebody needs duelling - ah, I mean, moderating!

Duel

choose your weapons

Sir

I choose... wait, are we restricted to medieval weapons?

no

anything goes

:-D

Hmmm...well the obvious choice has to be a really powerful nuke. I don't even need to aim it all that well then. Might end up killing myself too, but I'll still win ;)

Indeed, as once said "I don't know what exact weapons will be used in the third world war, but I do know that the fourth world war will be fought with sticks and stones."

@Ninefingers the first time your opponent had a duel, it finished sadly for him

@Ilya Talk to me, not about me, please :-D

@Ninefingers I have chosen the weapons

@skullpatrol another duel?

@ClarkKent It's a good thing that you live so long :-D

How can I get good at finding examples and counter-examples? It seems like I can usually figure out how to prove a statement, but then I can't find an example of the thing I proved.

@robjohn Yes, but the weapons are not of mass destruction ...

@Ilya Why is this skullpatrol still dueling? I thought you finished him in your duel? 8-). Is it a ghost?

@JonasTeuwen That was just a weak duel...

I admit: I am weak...

and I like to duel :-D

champagne anyone?

@DavidK What did you just prove?

Well I am speaking in a more general sense. That is, I always seem to struggle with finding examples and counter-examples, as opposed to proving statements. Similarly, I have a difficult time with problems that say "prove or disprove" unless I can quickly discern that the statement is true.

I think that's probably pretty general. I mean, I happen to carry around a few pathological functions in my pocket. When I try for a counterexample, I often rely on these

things like the topologist's sine curve, dirichlet's function, the irrational continuous dirichlet function, that terrible sine thing which is everywhere continuous but nowhere differentiable, that terrible fractal which is continuous but has a local max/min at every rational

and that's just analysis counterexamples

you do need examples of things that are not only counterexamples, too :)

that's true ;p Sometimes that's hard too

I recently saw a counterexample for something in algebraic topology that ruined many of my thoughts on cw approximation and the requirement that certain results have on things having the homotopy type of a cw complex

I guess I tend to approach problems with little consideration for how they might be applied (even in a purely mathematical context). So I don't often think about specific examples of the structures I'm studying at a given time, just how to prove the more generally stated theorems and propositions.

that's a deformation induced by the way we teach math

@MarianoSuárezAlvarez I am beginning to agree with this sentiment.

most math is taught without specific examples of structures being studied at a given time

people learn all sort of things about groups

and they know 3 examples

two of which are abelian

they can show there is no simple group of order 29174 but cannot exhibit a simple group

and so on

Is that an exaggeration, or have you really met such people? I mean groups seem like such an easy thing to present examples of.

I am not exaggerating much

Then again, I am more interested in algebraic than I am in analysis. so algebraic examples are more readily available for me I guess.

Math taught without examples is like teaching someone to swim without going into the water :-D

usually examples are restricted to counter examples

which is worse: teaching how to swim by showing you how to prepare aioli sauce

LOL

@MarianoSuárezAlvarez That's also an important skill. It goes well with baked potatoes.

yeah

You can think about that when you are drowning in the final exam ;-(

@skullpatrol Is this directed at me?

@DavidK No, just a lame attempt at humor :D

Entertainment is transforming bullshit in complete bullshit.

lol

encrypted-tbn1.google.com/…

@JonasTeuwen You make the most eyebrow-raise-worthy statements.

Thanks! I've been practicing a lot lately.

@MarianoSuárezAlvarez What?

Cf. math.stackexchange.com/questions/142825/…

I really think it is better to explain to new users what is wrong with their questions and let them fix them than fixing them ourselves

for precisely the same reason that is behind all the debate about the homework tag...

(apart from TeX, which is much harder to get correctly if you are new to it)

Probably, though Eric's comment isn't a bad substitute.

in any case, we can tolerate a badly written question for a couple of hours

@MarianoSuárezAlvarez The agents were approaching and he needed an exit!

When will the results of the mod election be known?

right after it is finished

which is...?

right when the election page tells you :D

look at the side bar

@skullpatrol Did you even check the website before you asked that question?

no :(

i just thought someone knew off hand

the internet is killing our memories

we just ask google

@MarianoSuárezAlvarez What reason do you refer to?

@skullpatrol 2000 UTC on the 15th.

@BrianMScott Thank you :D

I presume one of the reasons behind the homework-tag debate is the desire to have people do their own homework due to that being a strategy to maximize their learning

I feel fairly confident in saying I've learned a lot by asking for help...

I don't care if they prefer to remain dumbasses.

@ZhenLin Yes, but you actually want to learn something.

So you would analyse the answer, I suppose. Not just take it for granted and hand that in.

but, @ZhenLin, getting that help does not equal getting complete solutions—that's behind the homework-tag thing

@ZhenLin And I suspect that some of the help that you got just pointed you in the right direction rather than solving your problem for you.

I don't think there is a problem with getting a complete solution, you can still learn a lot from that!

But it requires some discipline.

my only point is that the same argument can be made for letting users fix their own questions

@MarianoSuárezAlvarez Yes, I see. What with that gun pointed at his head, he'll have some especially effective reinforced learning.

I prefer answering questions than fixing them

:)

@JonasTeuwen Which is why I'd rather post a good hint, if I can come up with one, and only later post a complete solution.

@MarianoSuárezAlvarez Yes, but then you can also argue that a full answer can also be useful for other users :-).

I prefer hints as I lack discipline 8-).

I would argue that it's more educational to see a complete, detailed solution with heuristics.

I prefer to just give hints because I'm too lazy to figure out all the details.

I tend to answer only to the person asking the question

If I can't come up with a good hint, my preference is to post a very complete solution. (I think that Arturo has mentioned that he also tends to these two extremes.)

I don't have a problem with answers for the general good—but I don't write them

@ZhenLin Depends; if someone can get it just from a hint, the exercise in doing so is very beneficial. If not, then the kind of answer that you describe seems to me the most useful.

@BrianMScott I don't think too much about it actually 8-). I often just write something that should help... Should think about it more.

@Jonas Your thesis looks so scary with all those integrals! :O But, congratulations!

@ZhenLin You might enjoy JDH's answer.

Okay, so I was teaching complex analysis... They had to compute the Laurent series of some function around $i$ and after partial fractions they actually had the term $(z - i)^{-1}$. A girl asked me... "how do I find the Laurent series of this part?"

@BrianMScott Well, sometimes what needs hinting depends on the person! For example, in this answer I thought (1) was so obvious that I didn't need to do more than state what needed proving. Turns out that needed its own hint.

@JonasTeuwen We're in different situations: I've been doing it for decades, so I've lots of practice at it, and I'm not taking time from anything else, since I'm retired.

@BrianMScott :-). I'm here more to learn actually something myself and if I can help others in the process, that's cool.

@MarianoSuárezAlvarez Do you think answers are of more value to the OP than to the community? Ah, I see you've partly answered already.

I like it when people write answers that are also relevant for others!

I answer the OP's question

@BillDubuque I think that he's thowing the baby out with the bath. The obvious response is to encourage better hints.

@BillDubuque Yes, I saw that. I already upvoted it.