@anon Hi

hello

sup?

@anon: hey there! I messed up and wrote up a couple of answers, one of which got 6 upvotes, but after I capped :-)

not much

@anon that can be good.

I could have swore I've seen that proof without words diagram, and not just the one you linked, before, even on MSE.

@anon hmm. It is pretty simple, so I wouldn't doubt it.

Proofs without words are hard to remember because there are no words to remember :D

@anon you weren't thinking of this one, were you?

or this one?

nah

@anon Let me know if you find it. I am off to the park for a while. bbl

I'm not going to bother looking for it!

If Mariano drops by, can you tell him I'm looking for him?

@PeterTamaroff You can leave him that message in his "inbox."

@skullpatrol How?

@PeterTamaroff Put @his-name "message" here.

@skullpatrol I thought one could only tag if the user was in the room.

@Mariano-Suárez-Alvarez Let me know when you drop by.

Bleh, it is already 3:30 AM and I have so much work to do and I am doing quite well :-).

@skullpatrol OK.

Pings do end up in a user's inbox on the main. However I have a sense that Mariano is avoiding chat so as not to be attacked by questions...

lol @skull you realize moderators (which Bill is now) can see removed posts in chat?

@anon I'm just expecting a mail from him from a long time, like 2 months I think.

But he's been busy, which I understand.

@anon No, I didn't realize that thanks for the info ;-)

pretty epic fight going on in MO

@PeterTamaroff You can find out his activity here.

@Eugene TL; DR

@anon then you won't be letting me know :-p

@robjohn Back so soon?

@anon questions?

@skullpatrol back from the park

@anon one could always invite him to chat. the überping

4 AM seems like a good time to take a shower 8-)).

@JonasTeuwen a lot of good math is done in the shower.

@robjohn Hmm, usually I'm like: This is too shitty, I'm not going to publish that. Even about stuff I have done in the shower! Maybe I should stop that or I will publish nothing 8-).

While "writing" on the steamed glass...

@robjohn this is the truth

so is $O(x) \cdot O(x) = O(x)$?

@Eugene I think that being forced to think without writing things down allows one to use a different part of the brain.

@robjohn yes. it's been well documented i believe

@Eugene I think it is $O(x) \cdot O(x) = O(x^2)$

@robjohn how about $O(1/x) \cdot O(1/x)$? this should be $O(1/x)$ right?

@robjohn So I should stop "writing" on the steamed glass...???

@Eugene as $x\to\infty$, yes, but you can also say it's $O(1/x^2)$, which is stronger

@Eugene $O(1/x^2)$ which, depending on whether $x\to0$ or $x\to\infty$ is worse or better

@anon so in general $O(g)O(f) = O(gf)$?

yes

sigh. i'm off by a factor then...

@robjohn here we go

now i have to go search for the factor i lost...

"A man was washing windows on a high-rise building when he fell from the 40-foot ladder to the concrete path below. Amazingly, he was unhurt. Why?"

@skullpatrol If the path was smooth, didn't he slide?

@PeterTamaroff How would that help explain why he was unhurt?

@skullpatrol He just slided down.

The concrete path.

@PeterTamaroff That is a possibility ...

@skullpatrol Then maybe he wasn't that high up the ladder.

How many meters if 40 feet?

hint: skim the article Eugene linked

@PeterTamaroff "He slipped from the bottom rung!" Aha...

Hhahaha that'd be, he wasn't that high.

You got it :D

Anyone watches True Blood here?

@PeterTamaroff 40 inches is about a meter, so 40 feet is about 12 meters.

@robjohn Ok, that's pretty high.

He could have slipped from any of the lower rungs onto a sloping concrete smooth wet path and slid down unhurt ;-)

@robjohn I think I just found a "bug" in the chat room.

I typed "[" Answer "]" and got an automatic link to a MSE page How to Answer

math.stackexchange.com/questions/how-to-answer

bug = feature

@anon bug = feature = useless

@skullpatrol Nice comeback!

@PeterTamaroff thx :D

is there a name for the smallest n such that a group G is isomorphic to a quotient of a rank n free group?

I wish there were a feature to save a draft of a question or an answer and come back later to finish it.

@anon: Is that the same as the size of the smallest set of elements that generate $G$?

@MarkDominus that is a feature isn't it?

@MarkDominus oh, duh

Oh duh what?

@MarkDominus Mozilla seems to save them.

Huh. It didn't occur to me to trust the browser to do it, but maybe that will be enough.

$$ E_S(n) = N^{-|S|} ({1 + E_S(n-|S|+v)} + (N^{|S|}-1)E_S(n-1))$$

Now what do I do with that?

If I'm writing a question or answer and close a tab and come back to it, it's still there. And while I'm writing a post, there sometimes appear the words "Draft saved" at the end of the text box.

Hey, you're right!

I think it might only save one answer draft and one question draft at a time though..

Also it won't remind you that you have a draft, or where it is.

But it's good enough. Thanks!

Just a thought

looks like the chat rules bookmark got pushed of the star feed

@anon It does that if you wait past one of the auto-save times. Get rid of the cached post with the "discard" link

Please Read: Chat Rules

@Eugene Thanks :-)

@robjohn Updated?

@PeterTamaroff No, it got timed out of the starred list. I needed to refresh it.

@robjohn no thank you.

@Eugene heh, punctuation is a marvelous thing :-) one comma changes that whole sentence.

@robjohn hahaha! well i shall correct that then. no, thank you!

@Eugene you do know how to edit old lines?

@robjohn yes i do. unfortunately i can only do it in a limited amount of time.

@Eugene I thought it was less than two minutes. okay :-)

$70$ more points to $13^4$ :-)

Enjoy guys

@robjohn 40 more i think

@Eugene why, thank you :-) I have to watch closely...

@robjohn good luck

@Eugene I had a scare earlier, I was downvoted! luckily, they retractted when I made my answer a bit more explicit.

That sets the score mod 5 off!

@robjohn hahahaha. 13^4 is a really nice coincidence!

@robjohn however you could ask a really quick question and accept the answer.

or

@Eugene Eugene, I'm finding the book you reccommended a little tiresome.

get 4 more downvotes

@PeterTamaroff messer?

@Eugene Yeah.

@robjohn Is there anyway to find out if there are anymore hidden "bugs/features" like the one I found in the chat room?

@Eugene I could, but that is not easy to do ether :-)

@PeterTamaroff what's wrong with it?

@skullpatrol "["Reveal all bug/features"]"

Nope. Nothing there.

@skullpatrol experimentation?

@robjohn that is also true. you don't usually get downvoted.

whoa. t.b is back...

@Eugene All the "crossroad" "strategy sessions" and stuff makes the reading cumbersome

I like more straightforwards texts.

@Eugene on the main site?

@PeterTamaroff it's meant as a intro to proofs.

Like Landau's (hehehehehe)

@Eugene Yes, I see.

@robjohn indeed! he edited a question

@Eugene Heh, I don't think he has left the main site altogether

You can find his activity here.

@robjohn you are indeed right. apparently he was here two days ago as well

@Eugene I see a comment by him a day ago...

@robjohn i guess he can't kick the habit completely eh

Who can?

@skullpatrol people who don't like math?

@Eugene I can quit anytime I want...

@robjohn Prove it.

@robjohn that's what every addict says

@Eugene Hahahaha.

Hello, my name is Peter. I've been hooked to MSE for 3 months now.

we should have MSEA

@Eugene precisely!

@robjohn i figured.

@Eugene People who don't like math won't be here in the first place.

@skullpatrol i beg to differ

@Eugene MSEA I didn't see yours :-)

@skullpatrol [coughs] Jordan [coughs]

@Eugene don't beg; it's demeaning :-)

@robjohn i don't know anything else that would suite this idiom though

MSE-Anon

@robjohn the problem with MSEA is we wouldn't be able to meet off MSE which raises a paradox.

@Eugene it would involve a $2^2\cdot3$ step program :-)

We could go to one of the many empty rooms...

@robjohn in our case that is the second sign of addiction =)

I'm a MSE junkie :)

wait. is being addicted to chat.SE counted as an MSEA problem?

YES

then we're doomed

that's why I'm leaving

@Eugene chat-addiction and math-addiction are both addictions...

@skullpatrol if you could leave you wouldn't need MSEA

@Eugene But never again is what I swore the time before

@robjohn we couldn't really have a support group without the chatroom though. i know nobody in the flesh who is as absorbed with MSE as i am.

@Eugene I don't know anyone in IRL who knows what MSE is. I have met Terry Tao, but I am sure he doesn't remember me, and he may feel that MSE is more like an amoeba.

@robjohn he probably knows about mathunderflow though.

@Eugene He posts there, doesn't he?

@robjohn on mathoverflow? yes he does. i was calling MSE by its nickname on MO though.

@Eugene MathUnderflow?

@PeterTamaroff yup

@Eugene Oh, yeah. I thought you were refering to another site, not MSE

@robjohn this is my favorite comment of his

@Eugene Ah, I thought you said "over"

@Eugene Yeah, that is quite awesome.

@Eugene "Neither can I."?

@robjohn yes.

Gowers has an account there too.

several fields medalists do

I think that is where the "fan club" mentality comes from.

with regards to fields medalists, i think it's reasonable to be "fans" of their research.

This also leads to "fans" of their answers on MathOverFlow.

For example 268 up votes?

and 171 Answers...

@skullpatrol I admire the activity of MO.

♫♪♪►♪♫♪

@PeterTamaroff Who's been makin' those scratches?

@skullpatrol Cool, song, ay?

@PeterTamaroff Smoooth...

@skullpatrol Yeah.

True Blood Soundtrack

@skullpatrol What do you do in Oxford?

This is interesting statistics BTW: Reputation to Post Ratio.

t.b. is ranked 4th among 5k+ users

@MartinSleziak that means he has more rep than he posts right?

@MartinSleziak How can I calculate my rate?

Rep/(Answers+Questions)?

Peter go to the link I gave you.

Oh, you mean yours.

@PeterTamaroff Nothing.

@PeterTamaroff Peter Tamaroff 376 Post 8830 rep 23.484042553191 ratio

That's what I get after I put 8000 threshold at that query I linked to.

The data at data.SE are slightly older than the current status than the main sites.

Could you please elaborate a bit on " I think that being forced to think without writing things down allows one to use a different part of the brain." as it relates to studying math? @robjohn

@DylanMoreland @FrankScience Hi.

@skullpatrol eh?

@FrankScience sup?

@Eugene @ZhenLin Hi.

@skullpatrol What? $\sup$?

@FrankScience "What is up?" = sup?

@anon i was working on the question you gave a hint on. do you mind if i post an answer?

Alright.

@Eugene it's lhf, you have to be competitive if you want to nab those. asking me if I mind isn't very competitive :)

$\limsup_{n\to\infty}$

@anon well it's polite though.

@anon i did what you suggested and bumped one of my unanswered questions when mattE was active. no response.

lol

oh, I remember the question you were talking about, En's generating the space of modular forms or whatnot

yup

you never know, ME's still active and might see it

i'm curious why people always ask about computing intersection numbers

Well, my 400 point bounty has been awarded and I'm ready to join MSEA.

there's a really easy procedure in fulton. is it because people haven't really heard of it?

I think a lot of books make it seem hard.

well good luck with that @skullpatrol

@DylanMoreland yes. this poor fella looks like he had a hard time with it.

I will be known as the founding member of MSE Anonymous ...

Which one is more conventional? $O\left(\log^3n\right)$ or $O(\log n)^3$?

or $\mathcal O\left(\log^3 n\right)$ or $\mathcal O(\log n)^3$?

probably the first, imo

I've seen that somebody uses $\mathcal O$ instead of $O$, well.

@FrankScience i haven't seen that before. mathcal is nonstandard for big o

big o is actually omicron. omicron looks nothing like $\mathcal{O}$.

And CMath points out that $\log^3 n$ is ambiguous, for $\log\log\log n$ or something like $\dfrac{d^3}{dx^3}$.

hmm, I often use $\mathcal{O}$ in answers...

$\log^3 n \neq \log \log \log n$ is pretty clear IMO

@anon for the ring of integers i do.

I mean that, upper indices sometimes mean the iteration.

@FrankScience I've never seen superscript notation for functional iteration used for $\log$, and I'm pretty sure parentheses go around the 3 for the triple derivative..

How do you write the functional iteration used for $\log$?

For example, $\log\log\cdots\log$ (100 times)

i use underbrace

In practice, something like a 100-iterated logarithm function would rarely turn up (I'm used to asymptotics in the context of number theory), so no standard conventions are necessary for such.

$\log^*n$ is sometimes useful.

You mean that $\displaystyle\underbrace{\log\cdots\log}_{\textrm{100}}$?

@robjohn The weather here is insane.

@DylanMoreland seriously? it's so nice and cool there now...

@FrankScience yes

@Eugene That's what I mean. It's pleasant and looking at the past month on weather.com it never even threatens to be anything else.

@DylanMoreland sigh. i want to live in california. it's freaking hot in waterloo these days.

@Eugene : Are you there?

heh heh

Why he he?

@DylanMoreland 80° and raining in the middle of the night?

sup?

@N3buchadnezzar not much really, just checking what is going on.

I sometimes hate latex, it is impossible to fill a quarter of a circle!

50% is fine, 100% is fine, even 75% is fine. But if I dare to try to fill 25% of a circle, It seems I recieve the wrath of the lord himself.

Some people have too little to do

I would love to see the tikz solution being used in an mathematical journal.

@N3buchadnezzar Does a package need to be used for tikz? I have never used it.

@robjohn Yes, you basically have tikz, pgfplots, and pstricks. Where the former and latter are for graphical images and the pgfplots is as the name suggests used for plots.

@robjohn Here is a MWE of the image I am recreating

@N3buchadnezzar MWE?

Minimal working example =)

@N3buchadnezzar Ah :)

Yesterday was an insane day: I got 260 rep and had 70 lost to the cap.

then today has been pretty dry.

@robjohn Sometimes one wishes for "This person has already capped for today; do you still want to vote his/her post?"

@robjohn @JM Hi! 8-).

I have never capped. What's this obsession with capping? That said, please make me cap!

Hey Jonas. :)

I didn't realize you're a cap-virgin...

wooo jm's here

That being said, it's not that fun to see multiple upvotes not getting you rep due to the cap...

hey anon.

@JM 8-).

"Stop voting for me already!! Can't it wait until tomorrow?!" :)

"You're hurting my feelings!"

@JM Do you know anything about how bad Carleson can be?

@JonasTeuwen Bad how?

(Heh, I wanted to say it this way. What I mean is how bad can the null sets in Carleson's theorem be)

So, given a null set $E$ does there exist an $L^2$ function $f$ such that the Fourier series of $f$ diverges precisely on $E$?

Or does not converge to the function, that might be a small relaxation.

8-).

And here is a short wikipedia article explaining how bad Karlsson can be

...is that a rotor stabbed on his back? :o

Not only that, he can fly with it!

How to define strong zero rigorously?

@FrankScience Is this in the context of Iverson brackets?

@J.M Not only.

Oh? Where else did you see this?

Wait for a moment

For example, while proving general Leibniz rule $(uv)^{(n)}=\sum_{k=0}^nu^{n-k}v^k$

Sorry

I do believe there should be a binomial coefficient somewhere in there...

Yes

and the index indices are wrong

We don't use Lagrange's notation. Instead, we use Cauchy's notation: $D^n(uv)=\sum_{k=0}^n\binom nkD^{n-k}uD^kv$.

Any particular reason ?

We can prove it by induction on $n$

So, what do you look to do with the derivative of a product?

And how does "strong zero" enter into this?

We rewrite it as $\sum_k\binom nkD^{n-k}uD^kv$, sum up over all integer $k$ where $\binom nk$ is strong zero for $k<0$ or $k>n$.

@FrankScience That would be because the definition for the binomial coefficient is that it is zero at those argument ranges...

@N3b, reminds me: since you once expressed a fondness for belly-dancers... have a look.

@JM $\binom nk$ should be strong zeroes, otherwise, $D^kv$ would be illegal, say, $k=n+1$.

@FrankScience Why "illegal"?

@JM just like Iverson bracket $[x>0]1/x$.

@JM That was awkward.

@JM or $k=n+2$? we cannot suppose that $v$ is infinity differentable.

Take a look at this instead

recent observation: typos are occasionally like exercises within mathematical solutions

@FrankScience That I would say is zero if $x=0$...

@N3buchadnezzar :D

@anon Sometimes you wonder if they're deliberate...

@JM Yes, for example, $f(x)=[x>0]/x$, we have $f(0)=0$.

@JM I want the same effect, for example $\binom n{-1}D^{-1}v=0$

@FrankScience Okay, so that issue you bring up shows why you need to interpret the binomial coefficients as "strong zeroes" off the range...

@JM This help me to keep away from boundary condition.

@FrankScience Yes, that's a fine interpretation.

Too bad they butchered the movie in that short clip. It is actually a fairly long Norwegian animated movie. The most viewed at cinemas too. They speak a very distinct Norwegian dialect in the original, which is impossible to recreate in English. A fun note, Swedes and Danes have a hard time understanding this dialect, and therefore it is dubbed to both Danish and Swedish.

@JM For example, proving general leibniz rule.

Then I don't really see the trouble with "strong zeroes" here; it is convenient for the purposes of that topic to use "strong zero", and thus one does so.

Really, the only time you worry is if the "strong zero" turns up as a denominator of something...

@JM

Okay, and due to the strong zeroes, you reindex the sums appropriately to get rid of them...

@JM Yes. otherwise, the manipulation should be very careful. This example is not too hard, but when we treat something like $2k<n$, it should be very weird to treat $\sum_{0\le k<n/2}$.

Sorry, my equation is too long.

So, I still don't understand your issue with strong zeroes; you treat the entity as zero, singular multipliers be damned.

Notice that $D^ku$ and $D^kv$ is defined only when $0\le k\le n$, not over all integers.

Hi blue guys; I'm here. No need to panic.

But I want $\binom nkD^{n-k}uD^kv$ defines for all integer $k$, which $=0$ when $k<0$ and $k>n$.

Just like $1/x$ is not defined when $x=0$.

But we restrict $[x>0]/x=0$ when $x=0$.

Is it clear?

@FrankScience Restrict? Not the word I'd use...

@JM eh?

@JM blue?

@robjohn Yes, two blue guys showed up in response to some flags raised here...

@JM Incidentally, where have you learnt Iverson bracket?

@FrankScience It's not what I'd call a "restriction", see. A convention, maybe.

@FrankScience I was using something like it for quite a while before seeing what Don Knuth wrote about it...

(BTW, hi rob!)

@JM Cmath?

@JM CMath?

@JM Or taocp?

@FrankScience That was the second place where I read about Iverson's bracket.

@JM Where first?

This nice article.

@JM ah, mods?

@robjohn Yes, mods (apart from me).

@JM is that why you showed up?

@robjohn No, I was already talking with Frank here when these flags suddenly popped and BOOM, mods.

@JM Has he defined rigorously?

@FrankScience and done so rigorously?

@FrankScience Defined what rigorously, the "strong zero"?

@JM yes

I don't think I've seen a rigorous notion of it, but it doesn't bother me...

@JM Thanks.

@JM Because I have read Concrete Mathematics, it bothers me to think boundary conditions.

@FrankScience I understand. Effectively, you're implicitly using the "strong zero" bit when you reindex sums, so...