Mathematics - 2012-11-28 (page 3 of 4)

@MattN. hmm..another pain to replace another... no it doesn't work... i still feel some pain...it gets less painful with time... but will hurt forever....

user19161

8:21 PM

When unpleasant thoughts enter your mind, do not suppress them, let them enter and leave your mindstream naturally, maintaining equanimity throughout.

user19161

Also, try to focus on other things and derive solace and joy from other sources.

Matt N.

@OldJohn Good idea. At it right now.

user19161

Taking intoxicants is only a temporary relief that doesn't deal with the underlying problem.

Old John

@MattN. most of my better ideas are non-mathematical these days :)

user19161

Finally, you can talk to the rest of us here if you miss him, though we can't be his substitute in your eyes.

Melvin

8:23 PM

Someone once said to me:"no one is irreplaceble"

Matt N.

@WillHunting I know. But the loss comes in waves and today is a particularly bad day.

user19161

@MattN. If he is just a "teddy bear" I cannot understand, unless "teddy bear" stands for something that is more than a "teddy bear".

Matt N.

@Melvin I thought that before but now I'm not sure about it anymore.

@WillHunting But... you know who we're talking about.

user19161

Also, I guess you won't be emailing me @matt, but that is alright.

Matt N.

I have not decided.

Melvin

8:25 PM

I don't know who we're talking about but i feel your pain

user19161

@MattN. Yes, but I don't understand why he is so special! Because you haven't explained to us, which you don't need to.

user19161

@Melvin Do you feel mine? I have been in pain my whole life, but that is my secret.

Melvin

@WillHunting I feel your pain will, deep in my heart.

user19161

@Melvin My name Will Hunting is chosen for a reason, I have similar experiences as Will Hunting.

Melvin

@WillHunting okay, okay.

Matt N.

8:28 PM

@OldJohn Going to refill that pint.

Old John

@MattN. that was quick - I am still on my first glass of Rioja

Melvin

@WillHunting what about you real name?

user19161

@Melvin Ah, you will find out next week.

Matt N.

@OldJohn I'm thirsty.

Melvin

@WillHunting i'm anxious

user19161

8:29 PM

@Melvin Why are you so anxious? =)

Melvin

@WillHunting why wouldn't i be?

user19161

@Melvin I am just a random person on the internet! I am only a banana.

Matt N.

@OldJohn To stackexchange!

Melvin

@WillHunting why people think like that?

Old John

@MattN. ?

Jayesh Badwaik

8:30 PM

@OldJohn toast..

Old John

ah! - silly me!

Matt N.

@OldJohn I thought we're drinking together, so a toast seemed appropriate. Do you have a better one?

: )

Melvin

you're a real person somewhere, with feelings, @WillHunting. people need love

Jayesh Badwaik

I'm on my first mug of coffee. Can I toast too. ??

Old John

@MattN. not off-hand - that sounds good to me :)

Melvin

8:30 PM

@JayeshBadwaik Hi jayesh! how are you?

Matt N.

@JayeshBadwaik Sure : ) Cheers!

user19161

@Melvin Well said, now I feel some connection with you.

Jayesh Badwaik

@MattN. Cheers. :D

Melvin

@WillHunting All we need is love, love is all we need.

Jayesh Badwaik

@Melvin Hi, I am holding up nice enough.

Melvin

8:31 PM

@JayeshBadwaik Good, good!

Old John

Na Zdorovie!

Jayesh Badwaik

@Melvin You?

Melvin

@JayeshBadwaik mmmmeh

user19161

I think I shall have some tea now.

Melvin

@WillHunting excellent!

Matt N.

8:32 PM

@OldJohn That is Russian and means "you're welcome". They don't use it to mean "cheers". In fact, they don't have a word for cheers, they always say toasts.

Or so I'm told.

Melvin

@JayeshBadwaik Studying linalg...

Old John

Literally it means "to your health" - it is what my in-laws say when they knock back a vodka or three :)

user19161

@old Did I tell you I finally reached 25k on Eng? Now I can retire from Eng!

Matt N.

@OldJohn Heh. The Russian explaining it to me had it all wrong.

Jayesh Badwaik

@Melvin Ahh, nice.

Melvin

8:34 PM

@JayeshBadwaik yeah..i think..... how's life, jay?

Old John

@MattN. not necessarily - Russia is an emormous country, and they have different customs in different places, I think

@WillHunting Congratulations!!

user19161

@OldJohn Let's both aim for 10k on math now that we have 5k!

Jayesh Badwaik

@Melvin Life is nice enough. Not terribly good, but chugging along. Howz yours?

user19161

@JayeshBadwaik Hehe, yes, especially when you have an XXX, unlike me.

Melvin

@JayeshBadwaik same thing...could be better.

Old John

8:35 PM

@WillHunting yep - althoough I am not in a rush for that

Melvin

@WillHunting uuuu jayesh also has XXX?

Matt N.

Good old alcohol. It always works.

Jayesh Badwaik

@WillHunting Once I find a way to make a living from mathematics, I will retire from life. :D

@WillHunting ;-)

user19161

@Melvin Well, he has an XXX, I want an XXX but have none, but at the same time I am also not in a position to have an XXX now, but I also lookout for potential XXX.

Melvin

@JayeshBadwaik is XXX the one you mentioned couple of days ago?

Jayesh Badwaik

8:37 PM

@Melvin yup.

Melvin

@WillHunting maybe XXX finds you

user19161

@Melvin XXX can stand for anything, just a dummy variable.

Matt N.

@Melvin In Soviet Russia?

2

Jayesh Badwaik

@WillHunting dude, it is the schrodinger's cat all over again. you can't know yes or no, unless you open the box.

user19161

@Melvin That would be a miracle, but then sometimes miracles do happen.

Jayesh Badwaik

8:38 PM

@MattN. hahaha. :D Alcohol hasn't dimmed your quick wit yet. ;-)

Melvin

@WillHunting yes, of course! someone to shar your problems..maybe heal them...

@MattN. ;D

@JayeshBadwaik Good!;D

Matt N.

@WillHunting I need a miracle, too.

Melvin

Be a miracle!

user19161

@MattN. There can be miracles when you believe.

Matt N.

The problem with that is that I don't believe.

Melvin

8:40 PM

If you just believe..if you just believe!

Old John

@MattN. I might have mis-remembered - maybe the in-laws actually said "za vashe zdarovye" (means nearly the same, I think)

Matt N.

@OldJohn : )

Old John

@MattN. My memories of Moscow were heavily clouded by masses of vodka

user19161

You know, now I have a feeling that every regular in this room is a nutcase. =)

Matt N.

@OldJohn I can imagine. That's me stereotype of Russia.

@WillHunting I'm not a regular and I'm normal. Hence contradiction?

Melvin

8:42 PM

"I ain't happy, felling glad, gotta sunshine in a bag feel useless, but not for long the future is coming on..."

Matt N.

@OldJohn Seeing as you call yourself old you are probably also wise. Do you have any advice on coping with loss?

user19161

Well @melvin I might share some secrets with you when I get to know you more...

Melvin

@WillHunting Thanks will.It will be a pleasure

I will open a new branch of psycology

Old John

@MattN. not sure anyone would call me wise - and not sure I have any easy answers to coping with loss, I'm afraid

Melvin

"mathematical psycology"

user19161

8:43 PM

Do you guys here say "I have fever" or "I have a fever"? Just a survey.

Melvin

a specila psycologist to deal with mathematicians

Matt N.

@WillHunting The latter.

Melvin

@WillHunting the former...

user19161

@Melvin OK, may I ask which continent you hail from?

Old John

@MattN. apart from finding someone you can talk to about your loss - and probably not in a public forum like here, unfortunately

Melvin

8:44 PM

@WillHunting america

Old John

@WillHunting definitely the latter

Matt N.

@OldJohn My friend! : )

Old John

@MattN. :)))

user19161

@MattN. Yes, don't you have close friends in real life?

Jayesh Badwaik

good night people.

user19161

8:45 PM

@JayeshBadwaik See you in your dreams.

Melvin

@JayeshBadwaik Good night, Jayjay

Jayesh Badwaik

yup

Old John

@JayeshBadwaik g'night

Jayesh Badwaik

@Melvin :-)

Melvin

@JayeshBadwaik sleep tight! dream about your XXX ;)

Matt N.

8:46 PM

@WillHunting I have a few and a few more who very much would like to be my friends but I don't like people. Why? Talkin' won't bring him back.

Jayesh Badwaik

@OldJohn good night.

Matt N.

@JayeshBadwaik Didn't you just drink coffee? Good night.

user19161

@MattN. Some people drink coffee to sleep!

Matt N.

@WillHunting Bizarre.

Melvin

@WillHunting wtf???

after dinner i don't drink anything with caffeine.

nor anyhitn with estimulatings

robjohn

8:50 PM

There are several ways. One is like this:$$
\begin{align}
f(z)
&=\frac{z^2 - 2 i z + 3}{(z-2)(z^2+1)}\\
&=\frac{(z-2)^2+(4-2i)(z-2)+(7-8i)}{(z-2)((z-2)^2+4(z-2)+5)}\\
&=\frac1{z-2}\frac{(7-8i)+(4-2i)(z-2)+(z-2)^2}{5+4(z-2)+(z-2)^2}
\end{align}
$$

cassandra0

why such a beautiful formula
$ \frac{e^{-\gamma z}}{z} \prod_{k=1}^\infty \left(1 + \frac{z}{k}\right)^{-1} e^{z/k}\,, $ comes from something so ugly $ \lim_{n \to \infty} \frac{n! \; n^z}{z \; (z+1)\cdots(z+n)}$

Melvin

@cassandra0 cause true beauty comes from simple things

robjohn

@N3buchadnezzar Then you do a power series division.

Melvin

where you least expect

Hi @aDangerousIdea

a Dangerous Idea

@Melvin hi

Old John

8:52 PM

@WillHunting did you give a list of translations recently of the previous names of people in the chatroom?

Melvin

@aDangerousIdea wassup?

a Dangerous Idea

@Melvin Chillin' ... you?

user19161

@OldJohn Yes, I did.

Old John

@cassandra0 I think they are both equally beautiful

user19161

@OldJohn I can give it again now.

Old John

8:53 PM

@WillHunting could you re-post it?

user19161

cassandra0=jdoe=sperners lemma

Melvin

@aDangerousIdea cannot complain

user19161

charlie=me and math

user19161

skullpatrol=a dangerous idea=john junior

user19161

old john=john senior

Melvin

8:54 PM

WillHunting=...

user19161

I am a banana.

Matt N.

...matt damon?

a Dangerous Idea

WillHunting = 1/0

Matt N.

Or was it di caprio?

They all look a bit the same.

Old John

@WillHunting thanks!!

cassandra0

8:55 PM

@OldJohn, I don't get the limit one, do you haveany views on it?

user19161

@MattN. I prefer to be Taylor Lautner, ooh!

cassandra0

it could be derived from some estimates and log-convexivity, I didn't like that

Melvin

@aDangerousIdea hahahahahahaha

Old John

@cassandra0 I just think the limit is just as nice as the infinite product - no other views

Melvin

@WillHunting I like him too

cassandra0

8:56 PM

:(

user19161

@Melvin Hehe, OK. But I am not gay.

Old John

@cassandra0 It is a very long time since I looked at things like beta and gamma functions

a Dangerous Idea

WillHunting = 1/(1/0)

user19161

@OldJohn Is there an alpha function? I wonder...

Old John

@WillHunting never heard of one

Melvin

8:58 PM

@WillHunting do you think i am?

cassandra0

I aways thought gamma was stupid because who cares about extending functions to non integers

user19161

@Melvin I don't know.

Melvin

@WillHunting wanna find out?

cassandra0

but it's actually really good

user19161

@Melvin OK, you can tell us if you like.

Matt N.

8:59 PM

@Melvin Want to meet and have coffee?

Melvin

@MattN. why not?

user19161

Hehe...

a Dangerous Idea

Hoho...

Melvin

I'm not gay. I just like to be kind with everyone.

Matt N.

@Melvin Touché. : ) As I pointed out earlier, I am with someone.

@Melvin How kind, exactly?

...

Melvin

9:00 PM

@MattN. let's have a coffee three of us

user19161

@Melvin You're not? For a moment I thought you were.

Melvin

@MattN. kind. Nice. polite.

@WillHunting why?

are you homophobic?

user19161

@Melvin Just from the way you talk above.

user19161

@Melvin Of course not.

Melvin

@WillHunting you said you suffered you whole life, wanted to make you feel better

user19161

9:03 PM

Anyway, I am going to make some tea now.

Melvin

@WillHunting i like tea

user19161

@Melvin I think tea is better than coffee.

Melvin

@WillHunting Me too

user19161

Also, I prefer wine to beer, but some people here like whisky!

Melvin

wine...

wine is nice

but i don't use to drink

N3buchadnezzar

9:06 PM

O.o

Me neither, alcohol is evil.

user19161

@n3b Your exams are in Dec right?

N3buchadnezzar

Indeed

Melvin

If you drink don't drive. or as people say:if you drive, don't drink. your drink may fall.

N3buchadnezzar

@WillHunting 01, 05 an 12

user19161

@Melvin I think I drink less than a bottle a year.

Matt N.

9:07 PM

@Melvin I thought it was "Don't drink and derive."

user19161

@N3buchadnezzar They should just make it 1,2,3 and be done with it.

Melvin

@WillHunting i don't use to drink bottles...

Old John

@Melvin I don't drink and drive - I can't afford both beer and petrol

user19161

@MattN. Just drink and integrate!

Melvin

@OldJohn GReat!

N3buchadnezzar

9:08 PM

@MattN. Drink and derive works exellen, done that a plethora of times.

user19161

@OldJohn HAHAHAHAHA

Matt N.

@WillHunting Not differentiate -- derive!

Melvin

if you wanna drink, stay home, drink as much as you want. at least you're home

user19161

@MattN. Yes, I know the pun, and I created another too, integrate (with someone), hehe.

N3buchadnezzar

@Melvin Not when you wake up

user19161

9:10 PM

Hey @amwhy Congrats on getting 9k! =)))

Melvin

i always been afraid of living alone beacause of that. what if something happens to me? i will die alone? and people only will miss me days later and my dead body startsto stinks?

N3buchadnezzar

Absinth is good though =)

Melvin

@N3buchadnezzar Van gogh liked it. his painting was influenced by it

N3buchadnezzar

@Melvin No matter how much you drink, you will always wake up at home. Seriously. The human ability to find its way home, is stronger than any other human urge ^^

user19161

@Melvin It is van Gogh, not Van gogh.

user19161

9:12 PM

@N3buchadnezzar Except sex.

N3buchadnezzar

Oh, I have to walk 2 miles, over a field, then through some sticky bushes and crawl through a bog to get home? No problem! I am drunk!

Melvin

@WillHunting you understood.

i'm afraid to lose my way home when i'm normal... imagine drunk...

user19161

@Melvin He is also a poor soul, suffered like shit and then died.

user19161

I read quite a bit about his life and works.

Melvin

@WillHunting he was killed

@WillHunting i really like him

mainly starry night

N3buchadnezzar

9:15 PM

@WillHunting A friend of mine drank a lot, and a chick wanted to go home with him. Then we asked if he wanted some water. He then suddenly seemed to realize he was intoxicated, and replied "No, I am drunk and need to go home". Then he promptly walked home, alone.

a Dangerous Idea

What happened to Johannes?

Melvin

geez

@aDangerousIdea Kepler?

user19161

@aDangerousIdea Who is that?

user19161

@N3buchadnezzar Good, now the girl can go home with me.

Melvin

@aDangerousIdea Bhrams?

a Dangerous Idea

9:16 PM

@WillHunting Your "Bro"

user19161

@aDangerousIdea He is Jonas right?

a Dangerous Idea

yup

N3buchadnezzar

@WillHunting Proves that the ureto get home, sometimes is stronger than the sex urge

user19161

Well, probably halfway through RH now.

Matt N.

@WillHunting I see.

N3buchadnezzar

9:17 PM

^^

a Dangerous Idea

@WillHunting RH?

user19161

@aDangerousIdea Riemann Hypothesis, just a joke.

a Dangerous Idea

@WillHunting So, no idea?

N3buchadnezzar

@WillHunting More likely a bottle of Glenfiddich

user19161

@aDangerousIdea Well, I haven't talked to him, but it's not like people need to be here all the time.

N3buchadnezzar

9:20 PM

@aDangerousIdea I see he on fb from time to time, so possibly not dead.

Most likely just figured he had to work, instead of procastinate in chat.

Melvin

@N3buchadnezzar what's your real name, N3b?

a Dangerous Idea

He is a cool dude...

N3buchadnezzar

*is

Melvin

@N3buchadnezzar is what?

N3buchadnezzar

@Melvin He is a cool guy. It is not like people suddenly loese their cool satus, just because do not wish hang around in chat.

tb <3

user19161

9:23 PM

Bananas are the most cool...

Melvin

Jonas?

a Dangerous Idea

But we don't the pleasure of their company :(

N3buchadnezzar

@WillHunting What about liquid nitrogen, that is pretty cool.

user19161

@N3buchadnezzar I prefer the company of XXX.

a Dangerous Idea

@Melvin Yes.

Melvin

9:24 PM

hmm

@N3buchadnezzar and oxygen, and radium, and talium...

argon too

lol

0

Q: Fouriercoefficient of the sawtooth wave help to find that the bessel equation gives $\sum \frac{1}{k^2}=\frac{\pi^2}{6}$

What are the complex fourier coefficients of the function $f:\mathbb{R}\rightarrow \mathbb{R}$ defined by the $2\pi-periodic$ continuation of $f(x)=\pi-x$ , for x $0\le x < 2\pi$ ? And how can one use that fact together with the Bessel equation to show that $$\sum \frac{1}{k^2} = \frac{\pi^2...

what is the bessel equation?

N3buchadnezzar

Any quick counter example to

$$ \lim_{x \to a} f(x) \cdot g(x) \neq \lim_{x \to a} f(x) \cdot \lim_{x \to a} g(x) $$

When we are not looking at the $L_2$ space?

Old John

9:29 PM

@N3buchadnezzar By the way - I was right about $1/(z-2)$ being its own Laurent series :)

N3buchadnezzar

@OldJohn Its own laurent series about z=2?

Old John

yep

N3buchadnezzar

But $f(z) = 1/(z-1)(z-2)$ ;)

Old John

@N3buchadnezzar what is $f(z)$? - you asked for the Laurent series for $1/(z-2)$

JustDanyul

hello, does anybody have a second to help me out with a terrible easy question?

N3buchadnezzar

9:33 PM

@OldJohn Ops, my bad...

Old John

@JustDanyul what is the question?

JustDanyul

basically, I been revisiting my old course notes, the idea was to try and convert them to english and have some fun revisiting my days of studying. Apparently, I gotten quite thick in the 15years time since I wrote them.

Old John

@N3buchadnezzar no worries :) - I was just beginning to doubt my understanding :)

@JustDanyul yes - but what is the question?

JustDanyul

@OldJohn well, I only just gotten up to inverse functions. And I'm struggling to understand my notes about checking if a function is symmetric around y=x

@OldJohn, my notes claim that if I can swap the x and y in the function, and end up with the same equation, its symmetric around y=x

Old John

@JustDanyul yep - that would be true

N3buchadnezzar

9:37 PM

What properties does the $L^2$ space have?

Old John

@N3buchadnezzar what sort of properties are you looking for?

N3buchadnezzar

Continous and bounded

Old John

@N3buchadnezzar how can a space be continuous?

N3buchadnezzar

I meant all functions living in the $L^2$ space. Sorry

I thought capital L was reserved for functions, and little l was reserved for refering to sequences.

Old John

Hmm - from what I remember, functions in $L^2$ need not be continuous or bounded

N3buchadnezzar

9:41 PM

Wikipedia says, that it is both a hilbert space, and complete so?

Old John

Yep - it is a Hilbert space

and complete

N3buchadnezzar

Okay, let me give you my question in full ^^

I am looking at when it is allowed to do the following

$$ \lim_{x \to a} f(x) g(x) = \lim_{x \to a} f(x) \cdot \lim_{x \to a} g(x) $$

I am wondering what sort of restrictions need to lie upon $f$ and $g$, and possibly what space these functions must lie in.

Old John

hmm - tricky

that would certainly be true for continuous functions - but I can't see why it should be true for $L^2$ functions

@N3buchadnezzar you could take $f$ and $g$ so that $f(x)$ goes to infinity as $x$ approaches $a$, while $g$ approaches 0 as $x$ approaches $a$, while $fg$ is constant