No, it is always good to not spam this room with non-sense. And if a feeling that you did exactly that crosses your mind, an immediate apology is in order!!

@KannappanSampath I prefer this to the Langlands program :)

@tb Heh.

Well, I'll change the gravatar.

I'm thinking of changing that to SF

Now this spammer has arrived here

I tend to look at answers by new users and this one made little to no sense.

(but not downvote-worthy)

I review posts periodically.

@tb Should I encode a nicer message?

I thought this one reflects my interest.

As you wish :) I find unlocking geek codes funnier than Langlands but there's nothing wrong with the latter.

tmi^ I guess.

There was nothing wrong with that :)

I'm slightly less ambitious, though...

@tb I get it-- another way of saying--you're too ambitious! :)

@KannappanSampath no, not at all. I'm not ambitious enough :)

Jasper starts dancing again :)

Right. I'll ask him the next time he is here.

(about...you know what.)

...his dance? He's stabilized again.

@Jasper Can you enlighten us about this phenomenon of leaving and entering the chat room in quick succession, rechristened as "dancing"?

@JasperLoy But that explains only the first part--that of leaving--there are two others as you see--the entering--and--the quick succession. :) Thank you for that piece of info, though.

OK. I see. So, the shift between the two happens at the speed of light, then. :)

Well, no more boring. I get that. Thank you.

Time to have something for the night. BBL.

Good afternoon everyone. I have a question about Math.SE's history, more specifically about its early beginnings; is there anyone here who might be able to help me with that?

I'm currently active on CS.SE, and we're wondering what Math.SE did during public beta to increase the size of its community

Indeed :) We have quite a few users who're very capable of answering just about all the questions asked so far, but we're missing the influx of questions

What is CS.se?

Computer Science, cs.stackexchange.com

I don't know if anyone of the regulars here was part of public beta (I don't think so). But maybe you find something here. I think there was quite a bit of influence via mathoverflow.

I am banned from posting in there because I havent answered enough questions I think, that might be a start

in CS I think

@robjohn, do you remember this?

'Ello @tb.

@Jordan you can not comment if you have not enough rep, but you can answer and pose questions. Nobody took action so it was that way, that is how the system works.

I cant post questions

'Ello @Gigili! I didn't see you answer a question yesterday. Did you get involved in some shooting?

@Jordan Have you made an account for CS.SE?

@Jordan Are you logged in the site? I can't find you in the user list

maybe I am thinking of the other programming ones

I was thinking of programmers and SO

@tb I postponed the event until today, so watch out!

I'd answer a question about 2+2, or 2+3 at most.

@Jordan You are banned there? Should we keep you on our radar, then? ;)

No, the people over there are just incredibly sensitive elitists

I asked too many simple questions, they laughed at me ,called me an idiot and told me that everyone else got through the simple stuff without help so I have to as well

Not quite in that language, but it was implied

@Jordan Did they delete the questions? I see only one on programmers.SE.

a few were deleted, but the one that caused all the controversy was the one trying to get tech support sort of

It was in chat, I don' really care I just don't like those people

@Jordan The Visual Studio one is a bad question. YOu don't even say what specifically went wrong.

I know that is because they closed or deleted the question I asked before that

so I was really frustrated and just posted that

Ok, I was just desperate, I had spent a lot of time trying to fix the problem

@JasperLoy Right. FOR NO REASON.

@Gigili crosses fingers that someone asks about $1+1 =2$

I came back but will be off for a while.

@KannappanSampath well, sometimes you also get upvotes FOR NO REASON...

I can never get the correct second derivative... trying to do $\frac{3x-3}{2\sqrt{x}}$

I am not good at anything :P

@Jordan do the first derivative carefully: simplify it before you proceed.

I mean I just cant get what wolfram is getting

What do you get for the first derivative?

And what do you get for the second one?

for the numerator I am getting $6x^\frac{1}{2} - 3x^\frac{1}{2} - 3x^\frac{-1}{2}$

that expression was the first derivative, I am not working towards the second

I can succesfully get the first derivative

And the denominator?

4x

(a sign seems wrong in your numerator)

oh it is +3x at the end

So this is $\frac{3 \sqrt x + 3/\sqrt{x}}{4x}$.

I would extend by $\sqrt{x}$ because that would look a bit cleaner.

I dont understand

I got 6x -3x +3x

Wait. You have $3 x^{1/2} + 3 x^{-1/2}$ in the numerator.

yes

This is the same as $3 \sqrt{x} + 3/ \sqrt{x}$.

how

$x^{1/2} = \sqrt{x}$.

oh nevermind I see that, I was just confused for 6x went

$x^{-1/2} = 1/x^{1/2} = 1/\sqrt{x}$.

Now I would do: $\displaystyle \frac{3 \sqrt x + 3/\sqrt{x}}{4x} \cdot \frac{\sqrt{x}}{\sqrt{x}} = \frac{3x + 3}{4x^{3/2}}$.

how did you know to do that?

that is the answer wolfram gets

I always try to get rid of as many square roots as possible.

(by extending fractions and the like)

I always forget when to use those kinds of tricks and manipulations

You could also rewrite the whole thing as $\frac{3}{4} \left(\frac{x^{1/2}}{x} + \frac{x^{-1/2}}{x}\right) = \frac{3}{4} \left( \frac{1}{x^{1/2}} + \frac{1}{x^{3/2}}\right) = \frac{3}{4} \left(x^{-1/2} + x^{-3/2}\right)$

Always play with the formulas until they look manageable.

The last one seems quite easy to handle, doesn't it?

hmm

What I always do seems right, but it gives wrong answers

Can you work with the last expression and derive it?

maybe

I think it is $\frac{-3}{8}x^\frac{-1}{2} - \frac{9}{8}x^-3$

Well, I agree with upvotes too. @tb. blushes

@Jordan: not quite, but almost. $\frac{3}{4}\left( - \frac{1}{2} x^{-3/2} - \frac{3}{2} x^{-5/2}\right) = - \frac{3}{8} (x^{-3/2} + 3 x^{-5/2})$.

Now you can pull out $x^{-5/2}$ and put it into the denominator to get

$\displaystyle - \frac{3 (x + 3)}{8 x^{5/2}}$

I dont quite understand pulling that out

I guess you factored it out and since it was negative it could be rewritten on the bottom?

Exactly. An intermediate step would be $-\frac{3}{8}(x + 3) x^{-5/2} = -\frac{3}{8}(x + 3) \frac{1}{x^{5/2}}$.

Then write everything as one fraction.

Can i ask something?

Sure, just ask.

you take all x'es and test among all b's if ...

So, the elements b of a are sets themselves. They have elements x. The union is the collection of all those x'es.

But b only ranges over the elements of a.

no, this doesn't look good. Let's consider a specific example.

a = { {1,2,3}, {1,2}, {5} }

then your b's are {1,2,3}, {1,2}, {5}

and the union of a is { 1,2,3,5 }

or slightly more involved: a = { { 1, {2,3} } , {1, 3 } }

then the union is { 1, 3, {2, 3} }

What's the name of this operation: {{1,2}} -> {1,2}

?

It's the union!

Nope.

your set is a = {{1,2}}

I mean... Let me try to express.

then b runs through (the only element of a) b = {1,2}

and now Ua = {x | x in b} = {1, 2}

The union makes this process? ({{1,2}} ->{1,2})

Bizarre.

Never knew that

That's what union does: you have a collection of sets and you collect together their elements. Informally: you delete the second level of parentheses and cross out the duplicates.

{{1,2}, {1,3}} -> { 1, 2, 1, 3 } -> {1,2,3}

Got it.

I'm curious about something.

I guess it have no value, since it's an element, am i right?

It doesn't have a value. It "runs through" all the elements of a

Yes, that's what you do in examples: but you don't have a set theoretic operation that allows you to do this. The union axiom tells you that you can do it.

It's strange. The book i'm reading didn't bring this information.

What book are you reading?

amazon.com/Comprehensive-Mathematics-Computer-Scientists-1/dp/…

I see. A friend of mine wrote her thesis with Mazzola. I've never read one of his books, though.

Thanks for the help.

I want to read his topos of music and use the rubato music composer.

factoring stuff is so difficult

I cant get a single problem correct

graphing is so difficult

I need to find a way to cheat with my ti-36x

I am so bad at math for whatever reason I always forget things I have already learned

at the beginning of this class I spent weeks doing problems where I multiply c onjugates and all that sort of algebraic trickery and manipulation but I have already forgotten it all

@tb I'd like to know a good place to learn about convergence concepts in probability. Please tell me where should I look?

Durrett, for example

In the time I have been ill, we have been assigned several things. :/

@tb Where does he define things, like convergence in probability and all that?

@KannappanSampath the pdf is searchable... Convergence in probability is defined on page 47, beginning of section 2.2

@tb The first hit I got while searching was pg.57 :/

Weak convergence (convergence in distribution) is on page 83, beginning of section 3.2

@tb Thank you for helping me with that. I am to assimilate the definitions quickly. 6 problems--due on Monday. : (

I'll get back and ask for help either here or on the main site, I think. I have no clue about this.

What do you need to know?

In other words: on what level. I'm not so acquainted with basic probability texts. I guess Durrett is a bit advanced.

All the modes of convergence of random variables--Convergence in Probability; distribution; almost sure convergence; in moments were covered in class.

Some nice properties and relations between them; and examples why converse is not true was done.

No measure theory; some results assumed.

Durrett has the very basics on measure theory collected in an appendix. I think it's a fine book and it looks like he's eliminated a lot of typos.

All the 6 problems here give me a property of convergence; a real number sequence, some sequence of events on a sample space and connect them. Let me see where I go.

I hope Michael will start a meta thread on downvoting of comments.

I hope he will learn proper formatting besides LaTeX...

: D

I think it would be a useful feature. It wouldn't have to cost any rep.

Then I could downvote all the unhelpful/spiteful/dumb comments I've come across.

That would be great.

downvoting of comments must have been discussed to deaf on meta.SO, no?

I don't know. If that's the case I'd guess they're too lazy to implement it.

I don't think they are needed.

They probably agree

I think it would be a vital feature. : )

here's one discussion. remarkably short, I must say...

Yep. Says it all: 90 upvotes.

Also, the first comment confirms the reason: too lazy.

Because The Masses Are Known For Making Great Decisions!

And hilarious, listen to this:

"If a comment is wrong, respond to it with another comment. That provides a lot more information than a downvote which could mean anything."

That's the answer with 40 upvotes.

If this applies to comments, why not to answers?

Bleh.

well, Jon Skeet gets 40 upvotes for free for being Jon Skeet, then 3 more votes that are to be taken seriously.

Doesn't it make perfect sense?

Someone will respond to it with another comment and people will upvote it.

still no 1+1 = 2 question for you, @Gigili? I start worrying...

@Gigili How is it different from downvoting questions?

But never mind. I just wanted to complain, I can see that it's futile.

@tb Everyone got it just when I can answer a question about it. I'm out of luck. Peh.

@MattN Answers and questions are something more serious, comments are just opinions. That's why people complain when someone answers a question by a comment.

But you can complain as much as you need, of course.

Thank you. : )

If they allow upvoting for comments, as stated in that meta thread, other features are also needed, e.g. edit, blabla. So there'll be no difference between an answer and a comment.

I don't see why comments have to be different.

I give up Matt, keep complaining.

math.stackexchange.com/q/129009/274 is a mess :/

Michael's suggestion to use \ldots is not quite correct, either, by the way: the ideal is to use\dots and let amsmath figure out where to put the dots :)

Don't dare contradict Don Michael in formatting things... He's The Only One Who Can Use LaTeX...

Like using \; in front of the dx

Why does Michael want to down vote your comment? None that appear ther look wrong. @tb

OP tried to mimick the cases environment. I copied his source and forgot to adapt the ... into \dots

mathjax should be smarter about copy and paste

$\int f(x) \mathrm{d}x$ vs. $\int f(x)\, \mathrm{d}x$ vs. $\int f(x) \;\mathrm{d}x$--testing.

I'd go with $(2)$.

@tb Is that guy mad?

I usually write 2, too

but fighting over that here is a bit silly

it is. I'm in a silly mood.

an actual tex file is rendered at 600dpi usually, here, we are looking at it at most at 200 pi

the difference between , and ; on an LCD screen can be compensated by antialiasing

Whatever, but his comment there is an overkill!

(I doubt the new ipad screen makes a different, because I doubt mathjax is precise enough)

On a different note: does MathJaX now support labels and references? I tried to adapt this LaTeX copy-paste thing into proper formatting here and in the last proof there's a linked ?? appearing.

(which is \ref{something} in the source)

you have to write \tag{xxx} and it will add an (xxx) to the equation

then you refer by hand

\ref does not work

(here, at least; maybe is something that can be configured)

Dinner time. Bbl

Then where does this linked ?? come from there? It's \ref{OuterMeasure} in the source, even outside dollar signs.

@MattN Lass es dir schmecken.

@tb Right. I think it supports but may be we need to modify the command a little.

@MarianoSuárezAlvarez on that note: if you want xxx to be a * how do you do that? The only way I found out is to add empty characters on the left and right.

BTW, one assignment problem done.

use \star :)

No, that doesn't work. \ast doesn't work either.

and \tag{$\star$} ?

I don't have magic compose.

hm?

$$E=mc^2 \tag{$\star$}$$

Works!

This didn't work for me last time I tried. But it was before they introduced MathJaX 2.0 here.

amslatex's \tag's argument is set as text

$$\tag{$\star$}$$

bfore 2.0, nested math did not work, iirc --- $\text{$hola$}$ messed the parser

Exactly.

Good to know that it works now.

$$a$b$$

$\text{$\exp$}$

Now it accepts too much, like the above

which was $$a$b$$

«how do you explain X to Y year olds» questions are beyond useless

Didier if IIRC uses(d) $$f(x)=\text{donkey}=(*)$$

useless but as so many useless questions popular beyond belief.

Do I hear Holy Donkey?

@JonasTeuwen No, you heard that any function of $x$ denoted by $f$ is a donkey. :)

Almost the same...

@JonasTeuwen They are the same almost surely, you mean?

Almost everywhere.

I'm not a probabilist.

Me neither, except for this night.

I feel insulted by this insinuation. 8-).

Had to look up "insinuation", after which an attempt to understand the last sentence ended in vain.

Someone please correct me there^

@MarianoSuárezAlvarez BTW, I am sure that guy is an Indian, it is a problem in 8th class NCERT textbook.

NCERT=National Council for Education, Research and training.

hm? What guy?

the log one?

The halving the orange juice one...

ah

Hi

Hi @Srivatsan

hi

I am slightly nervous... Regarding my latest answer. Surely it is going to attract negative comments from someone.

Reading through now, but upvoted it, ;)

ok. Don't have to. Upvote it only if you find it useful. :)

But thanks anyway.

I think I am familiar with this discussion. We have done a similar thing in class.

Sure. The reason I liked Artin's explanation better is it tries to explain why the isomorphism holds. I am surprised -IMO- none of the current answers explain the intuition so well.

Oh my goodness, so late...

IIRC, we solved the OP's same problem in class by looking at explicitly the ideal and all that and this was introduced as an aside.

@Srivatsan I am not well. So, I go to hospital in the morning. Only now do I find time to catch up with school... So no way out in principle. :/

Oh, what happened? Are you feeling better?

Yes, now I am ok.

I still have another cycle of injections to take. :(

I guess I will catch up with you tomorrow. Got to go to bed. (My mom is asking to close the computer right away... :))

Sure, Take care, bye.

@Gigili Thank you : )

Looks as if I just missed Srivatsan...

Wow, this sounds very cool: youtube.com/watch?v=MvSAs2oa2O0

!!! :)

Bourned. One down, two more to go : )

I'm sort of disappointed. I expected more of this.

@KannappanSampath What does f(x) = donkey mean?

@MattN Nothing at all. I just wanted to say that: Didier uses(d) that kind of a construct; I can't recall what $f(x)$ was in his case; so, it better be donkey. ;-)

Hail mean square! : )

@KannappanSampath I see : )

Hi Robjohn.

I am about to complete that assignment. One more problem and I am done..

@leo yes. Let me know if there was a reason to bring that up when you get back.

@KannappanSampath Hello. I had some weird internet problem. It seems to be fixed now.

Good. How are you?

@KannappanSampath I'm fine and yourself?

@robjohn Ok, I guess.

@KannappanSampath how did the last trip to the hospital go?

@robjohn Fine. I still have the IV injection thingy fixed. I'll visit the hospital tommorrow; probably the last trip for this time, I guess.

@JonasTeuwen Yeah, unless you had to hear it at the end of every month. When I lived with my parents, there was a high school right behind the house. They had an air raid siren right in the corner of the field that shared a fence with our back yard. At the end of every month, they tested it. I think ours had a higher pitch, and our dogs went crazy.

@robjohn Why does a high school have an air raid siren? :-).

Oh, right, that is probably a long way back.

@JonasTeuwen where would you place an air raid siren? They were placed wherever they were deemed necessary to alert people.

Oh, right, it was not property of the school :-).

@JonasTeuwen This was in the 60s and 70s

A high pitched one doesn't sound so hellish.

@JonasTeuwen It was quite loud and piercing.

being outside in our yard was a bit painful.

Yes.

Did it make you think of Operation Impending Doom?

I have never had to listen to a siren as yet.

They test the sirens once a month here.

@KannappanSampath How do they warn people for Impending Doom in India?

@JonasTeuwen still?

Do you know how to compute $(x^{-1} + x^0 + x)^n$?

@robjohn Yes.

Mainly for high water, I guess.

Yes.

@JonasTeuwen Not sure; Radios? I don't know at all.

If you don't I might've just written a useless answer.

(still right though : ))

I'm a few meters below sea level.

Sounds dangerous.

Oh well, the worst it can be is like -10m.

@MattN: Something like this?

@tb I looked at that already but it looks too complicated. It should be much simpler once you replace a,b, and c with x^-1, 1 and x...

Yes, there are some simplifications. But it's not complicated.

That thing there looks horrible.

There are quite cool places here, you see a river to the left and to the right, 20m lower houses!

I'd start with applying the binomial theorem to $(1+ (x+x^{-1}))^n$, then it shouldn't be too hard to collect the terms with the same exponents. Too lazy to do that now.

Aces! Why didn't I think of that. : ) Thank you.

I'm too lazy too but I wanted to know how to do it.

For next time.

Or in case the OP notices that it's a pain and asks me to do it.

@JonasTeuwen Doesn't sound safe. : )

Well, it keeps rising, that might be problematic in the future 8-).

Night folks.

night

Time for me to go to bed too. Bye people.

I'm failing to see any significant difference between OP's argument and the argument he complains about...

But probably this just means that it's not me who is able to answer his question :)

@tb I fail to see it too 8-). Maybe it is just not very obvious to see the difference.

@JonasTeuwen there's a minor permutation: the point of contention seems to be that the author concludes that $\partial \psi$ is an automorphism and then computes its determinant and INO wants it the other way around.

but it really doesn't matter. You know that a block triangular matrix is invertible if and only if the two diagonal entries are invertible. No need to compute determinants.

@Jonas: I was thinking about writing out the proof of the $\ell^\infty$ case here do you think that would be a worthwhile thing to do?

@tb I would like it but not many people will read it I'm afraid :-).

that's true. Well, if I wanted points and many readers I'd explain what (w)log means :)

well, if I can't sleep or have nothing better to do tomorrow, I might do it...

(and it is slightly uncanny that a user who's apparently here for 11 days only knows my first name :))

:-).