Then Aldi said 'we sell quality products for a low price, nothing like that train.'.

cheap as hell where poor people like me go to buy vegetables that are really cheap

Which is a low price, but falls apart - aha.

I agree the quality of the produce at ALDi is

Alrighty, I'm going. Talk to you later.

@JonasTeuwen they make cheap spinoffs of expensive brands that taste like hell

not ok

@OldJohn yoyoyoyoyoyoyoyoyoyoyoyoyoyo

@OldJohn localisation is very powerful

@BenjaLim Hi there

@OldJohn How would you prove in a Dedekind domain that $a \cap (b + c) = a \cap b + a \cap c$ without localisation?

@BenjaLim I am sure it is - for those that have time to study it :)

hahahahahahahah

@BenjaLim No idea!

@OldJohn I can't believe will jagy reposted what I posted on facebook here

Hello, Previously Young John. :)

@BenjaLim Ah ... Will is an interesting guy

as in?

@BenjaLim ...you're friends with Will Jagy on FB? :D

yes.

@BenjaLim Somewhat, yes. Have a look at his posts on meta.MO, for instance...

@J.M. Me too - I have been discussing some number theory questions with him

@OldJohn I saw your number theory question the other day on MO

@J.M. and not seen you around for some time - welcome back :)

@OldJohn Well, nothing better than getting things straight from the mathematician's keyboard. :)

@J.M. Indeed

@BenjaLim ah yes - my first tentative steps in MO-land :)

@OldJohn somehow meta.mathoverflow is not really well linked to the main site.

@OldJohn Don't unfurl the welcome banner just yet; I'll be away for a long time once more after this. (I'm exploiting a short amount of free time I managed to get. :))

@BenjaLim Well, the architecture of an SE 1.0 site is quite different...

@J.M. what are you doing if not maths?

@J.M. OK - I will keep it handy, though, for when you do make a real comeback :)

@BenjaLim What I'd euphemistically refer to as "sticky personal stuff"... :)

@J.M. Right

@BenjaLim I spent 2 days convincing myself that I really hadn't overlooked a "simple argument" before I posted to MO - didn't want to get chided for not looking at it properly first!

hahahahahahahahhahahaha

As an aside, I haven't touched a computer from when I left in November up until today...

@OldJohn I upvoted your question on MO :D

@BenjaLim I love it when Erdos says things like " ... by a simple argument ..." - and I can't see what on earth he is thinking of :/

@BenjaLim Thank you!

haha

@OldJohn Of course he probably wrote that while high on meth

@OldJohn I suppose that's one good thing about MO's painfully high standards: you're forced to think things through before posting a question, lest you be shamed enough to trigger spontaneous combustion... ;)

@OldJohn Simple is such a relative word.

@OldJohn Link please?

@J.M. absolutely

@BenjaLim ...maybe not "high"... "enlightened"? :)

@skullpatrol here

@OldJohn Thank you :)

@J.M. nirvana

Apparently it's a good thing I was away during the "Great Mod Kerfuffle of 2012"...

I was just recently introduced to the class of functions like the following: a(b) = c(b)/d(b) where lim b->e of c(b)= lim b->e of d(b) = 0. (perhaps that's clear?)

@J.M. Indeed - not an enlightening spectacle

@LimitedAtonement Indeterminate forms, yes?

lim_{b->e} c(b)= lim_{b->e} d(b) = 0

@j.

latex please

@J.M. Why is it called indeterminate?

@BenjaLim Is that about right?

?

@LimitedAtonement Example 1: Consider $c(b)=2b^2$ and $d(b)=b$.

@J.M. Considering :)

@LimitedAtonement Example 2: Consider $c(b)=b^2$ and $d(b)=b^2$.

@J.M. this one in particular I dealt with this morning.

@J.M. (Although I don't see anything particularly indeterminate about it...)

@LimitedAtonement Consider what happens as b approaches 0 in both those examples.

@J.M. also $c(b)=b^3-8$ $d(b)=b-2$ for intsance.

@LimitedAtonement That's another fine example, yes.

@J.M. So, in the case $c(b) = d(b) = b$

@LimitedAtonement Both the numerator and denominator approach 0, but their ratio doesn't, yes?

I thought, "the denominator gets close to zero, so the function should be very large"

then, "but wait! the numerator gets very small... so... I guess it stays straight."

"No problem. Now then, what about this $c(b)=b^3-8$ ... ? The numerator changes size at a different rate than the denominator..."

And when I plotted, my mind exploded.

In the math texts, they always draw functions like this (polynomials with one point missing), and I always thought they would need to be represented in a case-wise way! Oh how I have been sheltered.

I will forever thank the man who recommended Michael Spivak's Calculus text to me! (Not the Calculus on Manifolds)

(And likewise with $c(b) = b^2-9$ $d(b)=b-3$)

Yo @Charlie - wassup?

(tries to speak "the lingo")

@J.M.: Hey there!! Long time, no see.

Right, so, $c(b) = b^3-8$ approaches $0$ very slowly, but $d(b)=b-2$ approaches zero relatively quickly.

@robjohn Hello rob! I had a bit of free time, so I decided to drop by. Unfortunately I'll be away again in a few...

Or... $c(b) = b-2$ , $d(b)=b^3-8$ so, the denominator becomes very close to zero when the numerator is relatively far from it...so I would expect something of a spike? Oh well.

@LimitedAtonement You could put it that way, yes.

@J.M. Aww... that's too bad. I had noticed that you were absent here and on Mma for a while. The old gang has been thinning.

@LimitedAtonement The cubic polynomial is a bit "flatter" around the point of interest...

Exactly.

@robjohn I noticed. The crowd has changed quite a lot, I see.

@J.M.: I first noted your return by your comment on one of my answers :-)

(But I'm glad you're here at the same time I dropped by.)

I'm old and thick

@J.M. there are still a lot of people here, and some good math going on.

That's good to hear. On another note, I hope there won't be anything like the "Mod Kerfuffle of 2012" ever again...

@LimitedAtonement hi.

@OldJohn @J.M. Bye I should go it's late!

@BenjaLim OK - bye for now!

@BenjaLim It's been nice to hear from you!

@BenjaLim: I notice that your chat account seems to be disjoint from any site. Is that on purpose?

for when he returns

@rob, apart from December's kerfuffle, did anything else happen to math.SE while I was away?

@J.M. The kerfuffle was about it. Zev has come back, and MathGems started posting again.

There was a "December Bash"...

From which we were "opted-out"

...to match the "kerfuffle."

@robjohn Oh, cool that Zev's back. MathGems OTOH is a most peculiar fellow... :)

@J.M. I see now what's indeterminate about it. Thanks for telling me that.

@LimitedAtonement Glad to hear that you got the hint. :)

@skullpatrol We needed some seasonal decor

@J.M.: how have things been with you?

@robjohn Lots of "sticky personal affairs" keeping me busy. In between today and when I left in November, I haven't even touched a computer! :)

@J.M. How the hell did you survive?

(I need computer to do routine stuff like paying power/water bills, taxes, booking travel tickets etc etc.)

@JayeshBadwaik Well, it's certainly possible to live without a computer where I went. :) Not a very pleasant way of living, tho.

Did you have any symptoms of withdrawal?

@J.M. Ahh.

...and I'll be going back to that after I leave this public computer.

Best luck. :-)

Thanks for the nice thoughts. :)

@J.M. I'm sorry to hear that. It sounds unpleasant. I hope things turn around soon.

@robjohn I hope so. :) Thanks. I'm still in one piece, so things aren't too bad.

Well, my time's up. :( It was quite nice to talk to you guys again. See you all, hopefully soon...

later

@J.M. Come back soon!

Hi @WillJagy

@OldJohn, hi there. There is a post from seven hours ago, WillJagy When will you make one about what you do? - 7h ago by Jonas Teuwen....which must mean something. A documentary movie?

@WillJagy Yeah - that post had me wondering what on earth they were talking about ... but I often get that feeling in this chatroom ...

@OldJohn, I guess it was from my previous line about posting a youtube song . Plus, I did not repeat the material from MO here about Kap and quadratic forms.

Well, give me a few minutes, errands and more tea.

@WillJagy OK - later

@OldJohn Re: Erdos and "simple arguments". I once needed the details of a two-line argument in a paper of Erdos. It took me two pages to fill everything in.

@MikeSpivey So I am not the only one - that is good :)

@OldJohn And I'm glad to hear I'm not the only one. :)

I don't even know what that is about. :) Hope that will make everyone else feel better.

@Tim: Thanks for the affirmation. :)

@robjohn: I noticed that there's now an "Informed" badge that you get for reading the entire "About" page. However, I can't find the link to the "About" page on the main site. It seems like that should be prominently displayed. Do you know anything about that?

@JasonBourne Thanks. I did find it, and I think it's a really good page, but if new users are going to get anything out of it then it needs to be obvious on the main site.

@MikeSpivey Hmm... I have this link in my bookmarks, but I haven't looked for a link on the usual pages...

@MikeSpivey I remember being able to read it without typing the address directly. I will have to track to remember what I did.

well, there is a link, on the top of the home page.

@JayeshBadwaik Where, exactly? I'm not seeing it.

Did anyone read this?

@JasonBourne See the top line.

@JasonBourne Are you kidding me?

@JayeshBadwaik Interesting. Mine just has "Review Chat Meta Faq" across the top. No "About."

@JasonBourne You see an about in my screenshot right?

@JasonBourne ohh. okay. I thought you did not see it in my screenshot.

@MikeSpivey Ohh.

@JayeshBadwaik O.K., I see "About" when I use Firefox. But not with Chrome or Internet Explorer.

@MikeSpivey Even more interesting.

@MikeSpivey I see it in chromium without even being logged in. So, it is not a rendering engine issue.

I also see it in rekonq.

The infamous set theorist from Augsburg is back.

Wolfgang Mückenheim

@JayeshBadwaik I see it on Stack Overflow, even in Chrome.

I use chrome - "about" is not there when I logout, but is there when I login

Sheesh!!

@MichaelGreinecker why is he infamous?

@JayeshBadwaik I see it on several other SE sites, too (also in Chrome) - just not on math.SE. Weird.

@OldJohn Google spits up this.

@OldJohn He is professor in Augsburg (for physics, but he also teaches math) where he fights against the evil ideas of Cantor and his followers. He once prooved that the continuum is countable.

@MikeSpivey Seems something cranky is going on.

@skullpatrol That caused quite a stir around here.

@EdGorcenski Indeed it should.

@MichaelGreinecker Ah! - I think I read something about him some time ago ... and dismissed him as a nut :)

@OldJohn That would be a natural reaction. I think he had a long suspension here and on MO.

@skullpatrol That incident ended up with two moderators having their privileges temporarily revoked, and one of them leaving the site.

@MichaelGreinecker I guess he is also quite outspoken, then :)

@EdGorcenski Hmm... thanks for the information :)

@OldJohn He actually has a trolling-diary (it's in german though): hs-augsburg.de/~mueckenh/KB

@MichaelGreinecker darn - its been 40 years sine I studied German ...

@skullpatrol Here is a meta summary of events: meta.math.stackexchange.com/questions/6837/…

Help me out here, how can so widely discredited person be still a prof?

Tenure.

@OldJohn This is the last thing that should prompt you to learn it.

@JayeshBadwaik Following Old John's comment, I logged out, and there it was. I logged back in, and it was gone.

@MichaelGreinecker probably - but it irks me that I once used to write things in German that I really can't read anymore!

@MikeSpivey yep - I wasn't seeing things then - hope for me yet :)

@MikeSpivey This is getting stranger and stranger post by post!!

@OldJohn LOL.

@OldJohn When was that, roughly? I thought German was done as a science language after ww2.

@CBenni Have you tried standard numerical integration techniques?

@OldJohn Either that, or we're both seeing things. :)

I assume they use some sort of include-file system - and haven't uodated the logged-in include properly yet? - probably just an oversight

@MikeSpivey Of course - we might both have the same delusions ...

@MichaelGreinecker I studied German in high school in the 1960s

@EdGorcenski Just a normal box-fitting algorithm or riemann sum is not really preformant. This function is continuous and just the Quotient of two algebraic functions, I bet there is some optimization to be found

Unusually, I did 3 languages: French, German and Latin

@OldJohn So it wasn't academic publishing in German?

@OldJohn, new discovery. If there is a (dead) ant floating in ones tea, one may take one of those flat staple prybar things and just lift out the ant. Progress!

@MichaelGreinecker No - I have read a few papers in german, and a few more in Russian and French - but not much

@EdGorcenski Optimally, the resulting algorithm would be executable hundreds of thousands of times per second on an ordinary GPU

I see.

If you're doing GPU computing, that's a whole different class of algorithms.

@WillJagy excellent!

@EdGorcenski This would require a closed form of some sort.

You're unlikely to find an elementary closed form.

Just because something is the quotient of continuous functions doesn't mean it will have a nice integral, or even one that is easy to integrate numerically.

You wont. But I hoped there is like a standard approach to functions like this.

Not really.

damn :/

You might try some Pade approximants, that could give you something to integrate.

Another approach is a radial basis function series approximation, then you can compute the integrals with Gaussian quadrature very easily.

Can anyone explain to me what this is about: "Ein Dingsbums ist offensichtlich nicht eine Menge von Dingsbumsen"

@CBenni If you want closed forms, you should probably include tags other than numerical methods.

@OldJohn "A something is obviously not a set f somethings"

@WillJagy I don't like the sound of them at all ...

@MichaelGreinecker Ah - makes sense - thanks

Is Dingbums actually a word?

@OldJohn, I think in England they are called rent boys

Dingsbums is my new favorite word.

@Tobias I'm not sure it's in the dictionary, but it is a well known term in informal spee ch.

@JayeshBadwaik There is no closed form to this Integral. A closed form of a numerical approximation would be good enough. No tag I could think of was (more) fitting...

@WillJagy Only just stopped laughing :)))))

@CBenni Closed form for a numerical approximation? Hmm, interesting, how much accuracy do you want?

well, probably 3-4 digits would be enough

I'm not even sure what you mean by a "closed form of a numerical approximation"

A finite series

for example

A finite series that is exact?

@EdGorcenski Something which can approximately represent the answer with a say a linear accuracy.

However, if I calculate 10000 terms to approximate it to 4 decimals, I would not call that real-time.

This is something that needs to be computed real time?

I think I see now what you're looking for.

Yes. Optimally, It should be calculated in a pixelshader

Mm, you're going to want to look for approximations to the integrand that have closed form integrals.

there is a (not so beautiful) way around, but I was searching for a prettyer method

@EdGorcenski Yes.

Really?

Yeah

Or is the expression for $\boldsymbol{l}(t)$ more convoluted?

You say you have not written the expression in full.

Is that better than finding a formula to approximate the integral?

I wonder what that means

well

Yes, if you can approximate the integrand with reasonable accuracy (eg a Talyor series), then you can integrate over each term in the series.

the entire expression is ~100 lines long

@CBenni But its linear?

l(t) is

okay. good.

Would be good if it wouldnt necessarily have to be

but for a start, yes it is

I agree with Ed. You probably should substitute a taylor series around $t$ to the required accuracy and compute the integral, the number of terms you want to have can be worked backwords by the error introduced by your numerical integration and the error introduced by your taylor series.

Actually, removing the assumptions got me a closed form.

(In mathematica)

Which assumption?

"In his explanation why $\pi$ does not exist, he denies the existence of ideal circles because a physical circle deforms Euclidean space and because the wave character of matter prevents a sharp boundary." - Franz Lemmermeyer reading Mückenheim, zentralblatt-math.org/zbmath/search/?q=an%3A1195.00004

In mathematica, I had assumptions such as $t_0>0$ etc

pastebin.com/qA1gbB0z

use mathjax to see the Latex output

that's a crazy expression!! Are you sure you are doing it right?

Well I hope mathematica is ;)

No, I mean, isn't having such a long expression a sign of not having done the analysis properly? Or it is a normal thing in pixel shader business?

No its not

but this is a very advanced and unusual approach

Okay.

@JayeshBadwaik How did you like my classic?

@skullpatrol I listened to it. (I generally take time to like music, except for a very very few songs.)

@JayeshBadwaik Basically the idea is to calculate lighting by a shining tube. We Integrate over the part of the tube that is infront of the triangle, use standard n-dot-l lighting to calculate the values and then add the attenuation

@CBenni triangle?

problem is: usually (If there is no integral) This can be calculated explicitely, but in this case, not.

@JayeshBadwaik polygon graphics. You approximate any 3d surface by triangulation

@JayeshBadwaik very good policy :)

@CBenni Ohh, okay got it. Yes, I know triangulation.

That is the standard approach that graphics work since mid 1980s

@CBenni Hmm, I did not understand what you said by in front of. Now, I know its the area being lighted and covered by that particular triangle.

@WillJagy Just been perusing zakuski and stumbled upon Baker's obituary - did you know him?

@OldJohn which Baker?

@JayeshBadwaik Noel Baker - complex analysis and iterations

@WillJagy I see - I only ask because Noel Baker was a collaborator of my supervisor

@JasonBourne haha

I'm half baked.

@WillJagy That is quite an awful title on that question

@Tobias, yes. As I answered, there are some functions which can be "iterated i times" but that is quite special.

I meant more in terms of being rather uninformative

@WillJagy That is extremely interesting (and tough reading!) - but FA replay is about to start, so I think maths will have to take a back-seat for the next 90 minutes :)

Titles should by definition tell you more about the contents...

Most good authors spend a lot of time thinking of an informative title.

Smells tell you about a person's reproductive capacities. Well, it works for dogs.

@OldJohn, enjoy FA

@WillJagy later!

@WillJagy Don't you agree that chapter, section and lesson titles are worth remembering?

@OldJohn Me too. :-)

later.

neat, a proof that first works in positive characteristic and then deduces the result in characteristic 0 as a trivial consequence (and where the positive characteristic is needed to even make sense of the method used)

(The proof of Kempfs vanishing in the book by Jantzen)

@Tobias Do you agree that young students should be taught to memorize chapter, section and lesson titles?

@skullpatrol why on earth should they do that?

@Tobias To add structure to their learning, in the same way that remembering the objective of a lesson does.

lessons have objectives?

They should.

I guess

but I don't see why they should memorize that other stuff

To help remember the objective ie it gives the objective context.

Before the content is presented.

at what point do you want them to memorize those things?

As they read and learn them.

I am not sure I am completely following what you want them to memorize. So you mean that if they later want to invoke the mean value theorem, they should be able to quote the name of the chapter and section of the book where that is?

(without looking it up)

hmmm, weird ..

@Chris'ssister right

except I think points for editing does not count there, and bounties certainly don't

Correct, there is a daily "cap"

Got it.

@Tobias Well, the lesson on invoking the mean value theorem should have a clearly stated objective, such as, "To apply the mean value theorem." and they should remember in what context the theorem was presented.

That context is best summarized in the various titles.

@skullpatrol what do you mean the lesson on invoking the mean value theorem?

invoking that theorem is something they will usually be asked to do in exercises

there will not be a lesson devoted to invoking a specific theorem (most of the time)

@skullpatrol God No!!

@skullpatrol I have seen such kinds of books in Physics, (Sears Zemranksky, Halliday Resnick), but I would never think even they wanted such sort of memorization. Names and structure presented by an author are the names and structure of the "exposition" which can be quite different from the personal structure developed by the student themselves, and often the personal images are very unique, with the formal exposition just a way to express them in an understandable manner.

OK, thanks.

Anyone willing to share some insight on construction of a Brownian motion?

No.

@tim hi timmy!

@Charlie Hi, Char! Do you plan to call Old John "Johnny", Will Jagy "Willy" and Jonas Teuwen "Jonasy"?

@Tim I call john john, jonas jonas , jasper jas, Aaron Aary, jayesh jay....

My advisor gave me an 'open' problem today. Now I feel a bit more like @HenningM.

what is the integral of $\cos^{4}(x)$

??

??

@Charlie hi

any idea about this integral