Mathematics - 2012-12-21 (page 1 of 7)

user19161

12:05 AM

@PeterTamaroff I have 250 answers now Pedro.

Ethan

jasper

can i get in a private chat with u

fora sec

Bitrex

math.stackexchange.com/questions/262845/…

Doesn't it suffice to show that $|\int f(x)\delta(x) - f(0)| = 0$ as $t \rightarrow x$ over the support of f(x)?

for the definition of $\delta(x)$ given?

Jonas Teuwen

The definition does not make sense.

It is like I would define a green elephant and use that to deduce there are pink ones. Bullshit in bullshit out.

Potato

@JonasTeuwen Could you do me a favor at take a look at my question (in the bounty statement) here: math.stackexchange.com/questions/15248/… ? I'm calling in the big guns for this -- it's driving me nuts.

Jonas Teuwen

12:22 AM

What are your big guns? The open mapping theorem? :-).

Potato

@JonasTeuwen Someone who understands how to use the OMT to prove that statement (unfortunately not me....)

But hopefully you.

Bitrex

@JonasTeuwen isn't it analogous to how you can 'define' the delta function as the limit of a sequence, like $\delta(x)$ = $\frac{n}{\pi(1 + n^2 x^2}$ as $n \rightarrow \infty$

user19161

@Ethan There are no private chats, the transcript is publicly available. You can email me for really private talk.

Jonas Teuwen

The integral $\int f'/f$ counts the number of zeros right?

And then you can modify the path continuously - through the holomorphy.

@Bitrex Nope.

That's not the definition.

Potato

@JonasTeuwen It does count the number of zeros, but the argument principle.

*through the

Jonas Teuwen

12:25 AM

That's the argument principle.

Then you shake the curve a bit and you get your statement.

Potato

How does that work?

This shaking?

Jonas Teuwen

By holomorphic 'contractions'

That is usually not in standard (undergraduate) complex analysis.

Potato

Could you elaborate? How does this relate to the OMT?

Any reference would be great.

Bitrex

@JonasTeuwen Yes, sorry, you're right.

anon

homotopy?

Jonas Teuwen

12:27 AM

The statement is about the continuous dependence on number of zeros.

Err, homotopy.

And you can modify your curve continuously.

If you get over one +1

Potato

Indeed.

I don't see how the theorem follows though. I also don't get the bit about f(z) being forced to wind around the unit circle.

Jonas Teuwen

I'm a pretty hungry asshole right now, so I'll make a sandwich! Wish I had a servant.

2

user19161

Well, the people were not happy that I provided the complete solution so I have deleted my two previous answers, sad panda.

Potato

Don't delete answers. :(

Especially if they're complete and correct.

Jonas Teuwen

@JasperLoy Let them assholes bitch.

user19161

12:29 AM

But to be fair, I did not provide all the steps. I could fill in even more steps.

user19161

Let me explain why I decided to give more steps.

user19161

Yes, I like rep, but in this case, it is not really for the rep that I did that.

Jonas Teuwen

I've got a really neat density proof. I like it better than Schmuland's (and Nate's) 8-).

user19161

If someone asks such a basic question, chances are, even with very few hints, he cannot solve the problem himself.

Jonas Teuwen

@JasperLoy I would not explain, if they don't like it they should just bugger off.

user19161

12:30 AM

And also, what is complete or not complete is very much a matter of judgment.

user19161

If there is too little info given, the site degenerates into a site with many basic questions that lack fairly meaty answers, and loses its value as a reference.

Potato

@JonasTeuwen I'm afraid I still don't see the solution.

Jonas Teuwen

I am afraid I didn't explain it well.

But I have seven days.

I need to read about Burkholder now.

And make a sandwich.

Potato

@JonasTeuwen :(. This nagging detail is destroying me. Please, relieve me from my torture.

Jonas Teuwen

That's what mathematics is young man (I guess...? 8-)): suffering.

Pain, agony, despair, suffering, torment.

Potato

12:33 AM

We are masochists.

Jonas Teuwen

Looking for our fix: a proof.

user19161

@JonasTeuwen Anyway, it is not an asshole but amwhy. =)

Jonas Teuwen

It is like some drug craving.

@JasperLoy Does not matter, even if you do it people will still think you are an asshole.

You help some people and they think you are an asshole.

Potato

@JonasTeuwen And I'm having serious withdrawal right now!

Jonas Teuwen

As soon as you gain some visibility, there will be people that wouldn't grant you the light in your eyes and think you are an asshole!

user19161

12:35 AM

@JonasTeuwen No, they think I am not helping them because to help them I should only provide the hints! =)

Jonas Teuwen

Hence, asshole.

A little star.

@Potato Find some other fix!

user19161

But to show every step, I can even show for example that 2+3=3+2 since we need to invoke commutativity.

Jonas Teuwen

Also check my second starred remark.

@JasperLoy I would think the guy explaining me that way is an asshole.

user19161

Hence strictly speaking I did not show every step.

user19161

Hence I am not an asshole. QED.

Jonas Teuwen

12:37 AM

You always are an asshole, as soon as you are helping.

So do it your way.

Ah! Good idea, I'll play Sinatra.

user19161

@JonasTeuwen QED bro.

user19161

@ethan Are you here?

user19161

@JonasTeuwen I like that song bro.

Jonas Teuwen

@JasperLoy It has some good lyrics.

user19161

So hints to elementary problems and complete solutions to difficult problems? What is elementary? What is difficult? Maybe millennium problems are elementary!

user19161

12:44 AM

Also, the most difficult things lie in the most elementary things. For example, what is pi?

user19161

So I get downvoted for providing complete solutions when X thinks I should provide hints. And later I get downvoted for providing hints when Y thinks I should provide complete solutions.

user19161

FACEPALMHEADDESKRAGEQUIT

Jonas Teuwen

@JasperLoy Yes, so you are always an asshole as I've said. So do it your way and the ones that disagree should f...bugger off.

user19161

Now the asker will not get the correct solution because he only knows the hints, sad panda.

user19161

He will maybe know that this is a solution to the trigonometric equation, but he won't know that there are infinitely many solutions and what they are...

user19161

12:56 AM

@JonasTeuwen I thought you would say "More beer!"

Jonas Teuwen

Well, basically yes. If you do not spend time on people finding you less an asshole (and failing to do so), you better have a beer.

user19161

WTF, did is using QED in his answers too!

user19161

Ah, comments on deleted posts don't expand!

user19161

Why do you keep spitting out full-fledged solutions? – amWhy 54 mins ago

@amwhy In a way, not all the steps are provided. The asker also has to fill in some gaps himself. =) – Jasper Loy 51 mins ago

You know what I'm getting mean, Jasper. – amWhy 50 mins ago

user19161

Well, it's OK, I will recover... =)

user19161

1:09 AM

@JonasTeuwen I will be your servant bro!

user19161

Hey @mechanical, I see you are here too.

user19161

Wow BMS got 11 stars for that line.

Mechanical snail

@JasperLoy What line?

user19161

@Mechanicalsnail -------------------------------------------------------------------------> Look to the right!

Mechanical snail

@JasperLoy I see nothing by BMS or with 11 stars.

Oh. Had to expand it.

user19161

1:15 AM

@Mechanicalsnail Are you on a small screen?

user19161

So you see, two people can see the same thing but see different things. Very deep...

Mechanical snail

@JasperLoy 1280x800

With tiny fonts.

user19161

Also, two people can see different things but see the same thing, also very deep...

user19161

That ethan guy keeps appearing when I disappear and disappear when I appear.

Jonas Teuwen

Good night guys.

user19161

1:20 AM

@JonasTeuwen Night bro, see you in your dreams...

user19161

1:33 AM

Hey @iseth I see you are here too!

iSeth

@JasperLoy I'm running tracerout on you

user19161

1:50 AM

Hey @ethan.

Bitrex

Type full answer, javascript crashes on page, browser quits, answer all gone.

:(

user19161

@Bitrex Browser?

Bitrex

Guess I should be typing up my answers in an external editor.

user19161

@ethan What is it you wanna tell me?

Bitrex

Yes, some script on the page crashes, and the web browser locks up.

user19161

1:55 AM

@Bitrex I mean what browser are you using?

Bitrex

@JasperLoy Chrome.

user19161

2:14 AM

Ethan's gone again, over and out!

Peter Tamaroff

I need @BrianMScott

user19161

@PeterTamaroff Haha, you even commented on that post to get him here, pretty desperate.

Peter Tamaroff

@JasperLoy Yes! Of course.

Ethan

hello

Peter Tamaroff

@Ethan Is your surname Hawke?

Ethan

2:28 AM

lol

user19161

@Ethan What is it that you want to tell me?

Ethan

can i go into a seperate chat with you?

user19161

@Ethan Did you get my message? I said there are no truly private chats here.

Ethan

nvm

il figure it out later

lol

look at this

lolololololol

at 2nd series

MSEoris

wow what a nightmare

Ethan

2:34 AM

double exponential convergence

:f

lolololol

user19161

@Ethan Would you like to accept the answer I gave to your question? =)

Ethan

which one

jasper

user19161

@Ethan The one on infinity!

user19161

@Ethan Hey I got the invitation, but I prefer to talk here. Even if we talk there, everyone can read.

Ethan

oh

wana answer my bounty

and then I can try to answer one of yours

user19161

2:36 AM

@Ethan So if you want to say some secret, email me.

user19161

@Ethan I have no questions for you now I am afraid.

Ethan

you can make one up

nvm

user19161

Well, I don't like to give bounties...

Ethan

do you know of any partially additive functions, that are also periodic

that arn't the composition of additive functions with periodic multiplictive functions

user19161

Nah, I don't know these things. I only know very little like I said.

Ethan

2:39 AM

o

If I want to look up articles on a particular subject

user19161

Try posting your question on the site.

Ethan

do you know any archives

user19161

@Ethan There is arxiv.org

Ethan

I don't have a question, and even if I did lol, I cant post more then 30 questions in 50 days

or somthing

or vice versa

user19161

@Ethan Well, if you are asking that many that is not a good sign.

user19161

2:41 AM

anon is here, you can ask him.

Ethan

i dnt have a question

though

anon

wana see a relation between the barnes G function and chebyshev function

BenjaLim

@Ethan you have a lot of questions

Ethan

isn't that what the sites for?

user19161

2:56 AM

@Ethan Yup, but if there are too many questions then maybe one should consider changing the learning habits...

user19161

I think the upper cap on questions is reasonable.

Ethan

never

lolol

are there any additive periodic functions?

are there any additive periodic integer functions

other then 0

or some other

retarded example

anon

f(n)=f(1+1+...+1)=f(1)+f(1)+...+f(1)=nf(1).

Ethan

I don't understand

f(1)=0

if its additive

anon

what makes you say that?

f(0)=0, sure.

Ethan

3:03 AM

a(1)=a(1)+a(1)

subtract a(1) from both sides

lol

anon

additive means f(x+y)=f(x)+f(y).

peoplepower

f(0)=2f(0) :)

Ethan

no

f(ab)=f(a)+f(b), when gcd(a,b)=1

well atleast

anon

if you wish

Ethan

thats my

definition

are there any additive functions, that are periodic?

anon

3:04 AM

define f(-1) and f(p) arbitrarily for primes p; everything else follows.

user19161

@Ethan You can save space by typing more things on the same line.

user19161

Today is a sad day, I got two downvotes...

Ethan

were dirichlet characters only created because there multiplictive and there dirichlet series admits an euler product

BenjaLim

@Ethan If you study representation theory

Ethan

what?

BenjaLim

3:06 AM

You will know the reason for the use of the word "character"

For if $\rho : G \to \textrm{GL}(V)$

Ethan

Benjalim

BenjaLim

is a representation

Ethan

do you know about analytic number theory

user19161

I better not say anything about character. Otherwise Benja will say "Don't use terms you don't understand".

BenjaLim

@Ethan Algebraic number theory yes :D

anon

3:07 AM

@JasperLoy do downvotes not show up in your public profile to others?

Ethan

Have you seen any of these before

BenjaLim

@Ethan Analytic no.

Ethan

wait

do you know about the vonmangoldt function

Peter Tamaroff

@BenjaLim Duuuuude. Did the world end yet?

BenjaLim

@Ethan What are my top tags? math.stackexchange.com/users/38268/benjalim

Peter Tamaroff

3:08 AM

@Ethan $\Lambda$

user19161

But I am thinking, how would Benja know if I know about characters or not? =)

BenjaLim

@PeterTamaroff Yes because I am talking to you now.

@JasperLoy I know of your character.

Ethan

look at this identity

Peter Tamaroff

@BenjaLim How is it chillin?

BenjaLim

@PeterTamaroff Quite good.

user19161

3:08 AM

@anon It does, but that's not the point. I am not trying to be perfect. I just got downvoted for trying to provide a more complete solution to help the asker.

BenjaLim

I finished some algebraic number theory problems

Ethan

BenjaLim

@Ethan What are my top tags ?

Ethan

I cant look at your page

have you seen that identity before?

user19161

@BenjaLim Nah, you don't know me well...

BenjaLim

3:09 AM

@Ethan I have not studied analytic number theory: Look at my top tags here

@Nur hey

Nur

Hello, BenjaLim.

Ethan

oh

Peter Tamaroff

@Ethan That is undreadable.

Ethan

benja lim

Nur

I agree. What's up with your handwriting?

Ethan

3:10 AM

BenjaLim

@Nur where you from?

Ethan

lololololol at 2nd one

user19161

@anon I deleted the post dear anon.

anon

oh. peer pressure.

BenjaLim

@Ethan The reason why I like algebra is because I find it more elegant and beautiful

Ethan

3:11 AM

3 terms should give you several hundred digits of accuracy

Nur

@BenjaLim U.K.

BenjaLim

Dealing with that kind of stuff just seems ugly.

Ethan

lmao

Nur

What about you?

Ethan

ok

how

BenjaLim

3:12 AM

@Nur You can see my about me on my profile page.

user19161

@anon I was ranting about it in chat just now if you go back further in the transcript.

Nur

@BenjaLim It says "We're sorry, we couldn't find the page you requested."

Are you sure you got one? :p

No worries, anyway.

user19161

@Nur Haha, that is because his account is bugged.

user19161

You need to search the main site for his searchable account.

Nur

Oh xD

user19161

3:15 AM

BenjaLim, Canberra, Australia

12.4k 2 14 54

user19161

The great Benja.

Ethan

what is algebraic number theory good for?

like what are some main results

anon

if you put analytic and algebraic number theory together you get langlands program

Nur

@JasperLoy Another annoyingly good mathematician then! :]

user19161

If you put algebraic geometry and algebraic number theory together you get arithmetic geometry.

Ethan

3:18 AM

benja

you know about dirichlet L functions

right?

user19161

@Nur Yes, unlike me. I am only a banana.

Peter Tamaroff

@JasperLoy I have a problem,.

$\epsilon$-nets.

user19161

You can ask and we can all take a look at it.

Ethan

why the hell is there so much terminology in abstract math

user19161

@Ethan Well, all the sciences have that I guess.

Ethan

3:20 AM

I know like biology

they need to name everything

wtf

user19161

Why do they have pneumonoultramicroscopicsilicovolcanoconiosis?

Ethan

fake

Peter Tamaroff

The book, says, verbatim:
"We then call a set $B\subset P$ an $\epsilon$-net for the set $M\subset P$ if the distance from every point $x\in M$ to some point $y\in B$ (in general, depending on $x$) does not exceed $\epsilon$"

Ethan

what is all that set crap

Peter Tamaroff

Can we put it has "for each $x\in M$ there exists $y\in B$ such that $\rho(x,y)<\epsilon$"?

anon

3:22 AM

I think that's what they mean, yes.

user19161

@PeterTamaroff Yes, that is right.

peoplepower

Or $B\cap B(x,\epsilon)\ne \varnothing$.

Peter Tamaroff

@peoplepower Indeed.

Gustavo Bandeira

@JonasTeuwen Hat is ready to go.

Nur

@JasperLoy banana mathematician! :]

user19161

3:23 AM

@PeterTamaroff Are you working in a metric space P?

Peter Tamaroff

@JasperLoy Aye.

It is about precompact spaces.

user19161

@PeterTamaroff Then yes. This concept will come up in totally bounded sets.

user19161

A set in a metric space is totally bounded if for every $\epsilon>0$ there is a finite number of $\epsilon$ balls that cover it.

user19161

Of course, totally bounded implies bounded.

user19161

And bounded implies totally bounded in Euclidean space.

Peter Tamaroff

3:27 AM

Is @MarianoSuárez-Alvarez around?

Nur

You wouldn't like that name sticking on you. There's this guy who advocated for creationism by arguing that bananas are perfectly curved for the human hand and he's now known as Banana Man.

►

user19161

@PeterTamaroff You want to ask him the same question?

Peter Tamaroff

@JasperLoy Not really.

user19161

@PeterTamaroff OK, because if you do, I will RAGEQUIT.

Ethan

lol they show him like the first species of banana, it looks like a fucked up squash

user19161

3:34 AM

I am having a terrible headache. I think I am doomed.

user19161

@potato Do you know that there is a book with "argument principle" in its subtitle?

Peter Tamaroff

@JasperLoy Man, I am loving some proofs in this Russian text.

They are delicious.

user19161

3:53 AM

@PeterTamaroff Good for you. You know, I think I will take a break from this site to recover from the shock of getting two downvotes just now... Merry Christmas!

Transcript for

$Mathematics$ Mathematics