@JacobBlack He not going to recognize you :P

@JacobBlack Who?

Him?

Why would you say that?

Nice try.

@JacobBlack Is he^ your hero?

Hey guys

hi

Is it possible to obtain 'good' estimates on the error of a fourier series approximation?

Like If I wanted to estimate $$\sum_{k=n}^\infty\frac{\sin(2\pi k x)}{k}$$

@Charlie Scarlet

(removed)

@BenjaLim did you delete your account?

hello all! @Jacob where'd you go?

hi

@Alexander, open mapping theorem?

Semi-obvious question: Did Jason Bourne change his username?

@anorton Yes: Jacob Black, now.

@Charlie This would make a cool gravatar for "skullete," no?

@skullpatrol Hahaha

@Argon Did you see the lightening bolt?

@skullpatrol Classy

Careful with that @ amwhy

Yeah, I know. But I was specifically saying careful with the @.

Yeah, I don't think there are many Jacobs on the site so it's not really an issue.

If I was getting pinged a lot I would just change my username to JSchlather

@Khromonkey math.stackexchange.com/users/38268/benjalim

Yeah, I knew that mainly because of whoever changed their name to R^n.

Samsung Trolling People big Time

Pretty much

@skullpatrol I think you have already seen this.

does anybody here contribute to oeis

I know someone who does every once in awhile

so when you look at a draft sequence it's got a status on it which looks like "proposed +33 −2"

or something like that

i am trying to figure out what those numbers mean. i don't think it's votes or anything.

@JacobBlack well, having a big database of them is pretty useful when you find yourself with a bunch of weird numbers you don't understand.

> Are number sequences so interesting?

That question disqualifies you to speak here for 5 hours!

The OEIS is the closest we've gotten to a god that actually answers your prayers...

I hate when I have a hard sequence that I look up in Sloane only to find that yes, it is indeed a hard sequence and the only characterization known is the one I already had.

At least if there were no hits I could hope for an easy formula that no one cared about before.

What sequences are you dealing with?

Oh, nothing very recently. I can see if I can come up with an example if you want...

Hey@JacobBlack

Why are u still awake?

I have a question for you

I have a dumb meta-chat question. On my screen, my chat name is not the same as my main math.se name (it's my previous one). Is that the same for everyone else? If so, is there a way to change that?

If you have to show that $\lim_{x\to 0}\sin\frac{1}{x^2}$ doesn't exist how would you show that?

Re-write it as $\lim_{x\to\infty}\sin(x)$

and the limit doesn't exist

because $\sin(x+2\pi)=\sin(x)$

it just oscilates

@Ethan, well, that works for the positive sided limit. You probably should do repeat with -$\infty$ for the other side.

Ok I was able to get it to $sin( \infty)$

oh wait, squares

Using the composition law

@MarkS. If you can show limit does not exist from one side, you are done right? (Although that would not be the full use of the information, but enough for the problem I suppose?)

@math101, do you have a definition of limit you're using that you can use to show that sin(x) doesn't have a limit as x tends to infinity?

@Orange, of course; I was being too hasty in at least two ways.

Well you gotta show that the right hand and left hand limit dont equal

@math101, for $\lim_{x\to\infty} \sin(x)$, there isn't a right hand limit. You need some other fact, like a definition of limits at infinity, to handle this cleanly.

ok gonna do some research

Cuz that is what I gotta do :)

Well presumably math101 was asked to show it doesn't exist in a homework problem

Great idea @Ethan

lol

@OrangeHarvester, I did that earlier today, and in fact when I click on my image here, it in fact leads me to a page with the name I wanted. I infer from your previously referring to me as "MarkS." that the name I see on my screen is not displayed to you, in which case I have no issue. Thanks!

Admittedly, there's some "recent names" feature in my profile, but meh.

@MarkS. Ohh. In that case, try a deep refresh Ctrl+Shift+R. Probably that might help.

holy moses, there are no affordable haskell books in whole of India!

@OrangeHarvester ah, that worked!

@MarkS. cool. :-)

hah

i am drunk and latexing a course assingment

perhaps this is a bad idea :(

@Eric its not a long as you know which LaTeX you are using......

@Eric, make sure you spell it "assignment" in you LaTeX file.

$DEITY

oh crap

more (removed)

yeah, assignment

nice

oh no

not another

I was actually just testing how the grey "(removed)" messages work. Typing "(removed)" doesn't cut it; but you can get it by deleting your message.

Can people lose reputation if they're terrible in chat or are they just banned from chat?

no

but they lose respect

for which reputation is but a silly proxy

A star for you @Mariano !

Another star for you!

Respect is the new thing that's going to replace accept rates, right? </joke>

@amWhy Hy.

@OrangeHarvester high!

heh

It just occurred to me that at exactly 500 reputation, I'm better off reputation-wise downvoting some answer (-1) and then retagging something in an acceptable way (+2 if <500) than if I just retag something.

a staggering loophole

@MarianoSuárez-Alvarez Hi.

@Sanchez Hi.

@Khromonkey No.

Say that an overgroup $B\supset G$ is a "homocover" of $G$ if for any $H$, any homomorphism $G\to H$ may be factored as $G\hookrightarrow B\to H$ for some homomorphism $B\to H$. What kinds of homocovers are there besides taking a free product of $G$ against something (or direct summing)?

I imagine other sorts of 'canonical' quotients of the free product route might be available, and that free products might characterize all other homocovers through some or other universal property.

@BenjaLim, hi

@anon, I think your condition already forces $G$ to be a direct summand of $B$

@anon Your question sounds interesting. Free products have to work, but they seem like a bad answer in some sense because they give you so many homomorphisms $B\to H$ that work (although for $G*X$ you can canonically pick the one corresponding to the trivial homomorphism $X\to H$). On the other hand, the smallest homocover is just $G$.

I tried looking for canonical quotients of the free product, and couldn't really find anything, but maybe I just didn't understand enough of the Bass-Serre stuff I skimmed.

@Sanchez Is G a direct summand of G*F_2, where F_2 is the nonabelian free group on two elements and * denotes the free product?

I'm not sure how to make it explicit, but if you start with the lift of the identity $G \to G$, you get a surjection $\pi: B \to G$, and you have an inclusion to start with that splits the sequence $1 \to ker \pi \to B \to G \to 1$, is it not enough to conclude? Maybe splitting doesn't work like what I think @anon

Ah I see, I can only say that $B$ is a semidirect product of $G$ and something else

Right. B will be a semidirect product of G and ker(pi), bot not in general a direct sum.

(What I was getting at with 'canonical quotients,' is that for instance we have $G\oplus X\cong\displaystyle \frac{G*X}{[G,X]}$.)

but I feel like this is already an equivalent description

i.e. you are looking for an alternative description of $B$ being a semidirect product of $G$ and something else

Is there an easy example of a semidirect product that isn't a homocover?

If not, maybe Sanchez is right?

I already showed one direction

Well yes.

and the other direction is just, given $G \to H$, use the projection from semidirect product $B \to G$

and compose it, $B \to G \to H$, this is clearly a lift of $G \to H$.

Right. So it seems these are in fact precisely the semidirect products. Alas, I am off to bed.

Good point, Sanchez

good night @anon, and thanks @MarkS.

Have a question on volumes of solid revolutions if anyone's interested ;)

Trying to formalize when to cut disks out of an area that are perpendicular to my axis of rotation, and when to cut disks that are parallel.

I am for example trying to rotate this (bit.ly/WFxLV3) bounded region across the x-axis.

And I intuitively know to cut vertical cross sections, but I'm wondering if it's possible to cut out disks horizontally, and if not, why?

how do i delete my profile picture :(

Go to Gravatar.

hmm stackexchange ditched gravatar

Really?

yup

pretty recently

i missed my chance to delete the image :(

Let me go check my account...

to be fair gravatar was awkward

but at least it wasn't missing basic features

I liked it because it had a way of storing all the cool images I found :-(

...

...and then using them for my avatar.

hmm

it's funny how every social websites insists on it's own image storing solution

I think animated gif avatars can be cool too...

twitter, facebook etc have their own stuff - and don't use imgur, flickr etc

i go to a custom site with gif avatars and it is pretty jarring

Where, if you don't mind me going there to check it out?

it's private... there are loads of forums and so on with animated avatars...

If n has more then 2 distinct prime factors does $$\sum_{d\mid n} \ln(d)^2\mu(d)=0$$?

True and you can create your own.

But it looks too time consuming for me.

Most of the GIF's are too flashy. I like my sites demure and muted.

@PeterSheldrick You can still edit your avatar..

..through Gravatar.

@PeterSheldrick You can edit your avatar by going to your profile page and clicking on the picture.

i deleted all my gravatar pics...

Upload from computer.

Click on edit then under the image is change picture,

my main motivation was to delete pics i uploaded that maybe are copyrighted - how do i do that if they are not deleteable

@skullpatrol, that only changes it

I do like your current image because it reminds me of Bill D.

@PeterSheldrick Generate a random image from here and replace your current image with this? That is a compromise I think.

@PeterSheldrick Once you have deleted from gravatar. Its done I think.

@JacobBlack Said by some with a black pic. :P

Yay you're^ not even a color

@JacobBlack You can't be serious, Black. Now be gone!

:P :P

@JacobBlack Yes.

You are a colorlesscolor ;-)

translation of "achromatic."

I'll try.

in exactly what sense is "2^57885161-1" the largest known prime number?

Let S be the set of all known prime numbers..... ;-)

maybe "known" means its digits must be known in which case "the first prime larger than a googolplex" is disqualified

um what is unclear about such a statement

to get digits have a look at modular arithmetic

but what about "the first prime larger than 2^5788161-1"? that can maybe be computed in polynomial time if Cramér's conjecture is true

try it

too hard for AKS

polynomial time is nice and all but it still maybe takes really long/uses powerful hardware

mersenne primes are easier to test

It sort of like the statement the last known digit of $\pi$

but what is the standard for "known"?

Calculating any digit of pi is not that big of deal now.

polynomial time is for theoretical computer scientists, then there are guys who look at linear time algorithms, sub-linear and then there are even some who look at the constants

that all that matters is polynomial time or not is nonsense

and some who just look...