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8:00 PM
do you mean to ask what an invariant subspace is?
yup
$W\le V$ is an invariant subspace with respect to $A\subseteq\mathrm{End}(V)$ if $AW=\{aw:a\in A,w\in W\}\le W$.
In other words, what happens (via A) in W, stays in W.
hmm
rotation about an axis in (real) 3-space preserves the plane through the origin that is orthogonal to the axis, for example.
could we use $$
\Gamma(z)=\frac{\Gamma(z+n)}{z(z+1)\cdots(z+n-1)}, $$?
if $\Gamma(z + n)$ is close to $n! n^z$ I think it works
$$ \Gamma(z+1)\sim\sqrt{2\pi z}\left(\frac{z}{e}\right)^{z}, $$
user19161
8:11 PM
Hi people of the math.
@WillHunting Hi Will!
@WillHunting Hi there
user19161
@Melvin Your presence sends out strong waves to me, I don't know why.
Help.
@WillHunting Really? Fascinating!
8:12 PM
this is really nice
$$ \ln \Gamma(z+1)= -\gamma z +\sum_{k=2}^\infty \frac{\zeta(k)}{k} \, (-z)^{k} \qquad \forall\; |z| < 1 $$
Points Matt in the direction of anon, robjohn, ...
I need grief counseling.
Ah - I thought you wanted maths help
Points Matt in the direction of Old John, Will, ...
what has happened?
user19161
8:13 PM
Points everyone to his heart.
@OldJohn I lost my teddy bear, some months ago.
user19161
Geezis.
But I can't seem to get over it.
@MattN. Oh dear..that's awful
I feel so much loss :,(
8:14 PM
@MattN. so you need to find a new one ...
user19161
Well, since you mention it, why is he so special to you?
You never replace a teddy!
@OldJohn I'm not sure this one is replace-able.
@MattN. darn :(
@WillHunting Can't explain.
user19161
8:15 PM
@Melvin Hehe, I think you don't know what he is referring to!
user19161
@MattN. Do you want to marry him?
@WillHunting now that you said that...i'm confused...
@WillHunting I already have someone else.
user19161
@Melvin Yes, you need to be in this room for a few months to understand certain things we say here...
I don't like using log-convex and estimation and stuff to get the limit definition
user19161
8:17 PM
@MattN. Ah, so it is not that kind of feelings.
Now how do I get rid of the feeling of loss?
Tequila and painkillers
user19161
@MattN. So do you see him as a big brother or father or something like that?
@WillHunting I don't see how that follows but this is going off topic... : )
@WillHunting I see him as my teddy bear. On a more serious note: I haven't thought about how I see him. I'm too busy missing him.
user19161
@MattN. Oh, it is clearly on topic. You said you lost him and you are trying to feel better by talking to us, so we need to know a thing or two.
8:19 PM
Maybe I should talk to a pint of lager.
user19161
@MattN. Well, in whatever way you miss him, you need to find a replacement then or just go without it.
@MattN. I would "take" a pint of lager - rather talking to it :)
@Melvin I doubt this works. Have actually experimentally verified your advice?
user19161
@MattN. Don't get rid of it, it will rid itself in time to come.
@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.
@OldJohn Good idea. At it right now.
user19161
Taking intoxicants is only a temporary relief that doesn't deal with the underlying problem.
@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.
8:23 PM
Someone once said to me:"no one is irreplaceble"
@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".
@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.
I have not decided.
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.
@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.
@WillHunting okay, okay.
8:28 PM
@OldJohn Going to refill that pint.
@MattN. that was quick - I am still on my first glass of Rioja
@WillHunting what about you real name?
user19161
@Melvin Ah, you will find out next week.
@OldJohn I'm thirsty.
@WillHunting i'm anxious
user19161
8:29 PM
@Melvin Why are you so anxious? =)
@WillHunting why wouldn't i be?
user19161
@Melvin I am just a random person on the internet! I am only a banana.
@OldJohn To stackexchange!
@WillHunting why people think like that?
@MattN. ?
8:30 PM
@OldJohn toast..
ah! - silly me!
@OldJohn I thought we're drinking together, so a toast seemed appropriate. Do you have a better one?
: )
you're a real person somewhere, with feelings, @WillHunting. people need love
I'm on my first mug of coffee. Can I toast too. ??
@MattN. not off-hand - that sounds good to me :)
8:30 PM
@JayeshBadwaik Hi jayesh! how are you?
@JayeshBadwaik Sure : ) Cheers!
user19161
@Melvin Well said, now I feel some connection with you.
@MattN. Cheers. :D
@WillHunting All we need is love, love is all we need.
@Melvin Hi, I am holding up nice enough.
8:31 PM
@JayeshBadwaik Good, good!
Na Zdorovie!
@Melvin You?
@JayeshBadwaik mmmmeh
user19161
I think I shall have some tea now.
@WillHunting excellent!
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.
@JayeshBadwaik Studying linalg...
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!
@OldJohn Heh. The Russian explaining it to me had it all wrong.
@Melvin Ahh, nice.
8:34 PM
@JayeshBadwaik yeah..i think..... how's life, jay?
@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!
@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.
@JayeshBadwaik same thing...could be better.
8:35 PM
@WillHunting yep - althoough I am not in a rush for that
@WillHunting uuuu jayesh also has XXX?
Good old alcohol. It always works.
@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.
@JayeshBadwaik is XXX the one you mentioned couple of days ago?
8:37 PM
@Melvin yup.
@WillHunting maybe XXX finds you
user19161
@Melvin XXX can stand for anything, just a dummy variable.
@Melvin In Soviet Russia?
2
@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.
8:38 PM
@MattN. hahaha. :D Alcohol hasn't dimmed your quick wit yet. ;-)
@WillHunting yes, of course! someone to shar your problems..maybe heal them...
@MattN. ;D
@JayeshBadwaik Good!;D
@WillHunting I need a miracle, too.
Be a miracle!
user19161
@MattN. There can be miracles when you believe.
The problem with that is that I don't believe.
8:40 PM
If you just believe..if you just believe!
@MattN. I might have mis-remembered - maybe the in-laws actually said "za vashe zdarovye" (means nearly the same, I think)
@OldJohn : )
@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. =)
@OldJohn I can imagine. That's me stereotype of Russia.
@WillHunting I'm not a regular and I'm normal. Hence contradiction?
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..."
@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...
@WillHunting Thanks will.It will be a pleasure
I will open a new branch of psycology
@MattN. not sure anyone would call me wise - and not sure I have any easy answers to coping with loss, I'm afraid
"mathematical psycology"
user19161
8:43 PM
Do you guys here say "I have fever" or "I have a fever"? Just a survey.
a specila psycologist to deal with mathematicians
@WillHunting The latter.
@WillHunting the former...
user19161
@Melvin OK, may I ask which continent you hail from?
@MattN. apart from finding someone you can talk to about your loss - and probably not in a public forum like here, unfortunately
8:44 PM
@WillHunting america
@WillHunting definitely the latter
@OldJohn My friend! : )
@MattN. :)))
user19161
@MattN. Yes, don't you have close friends in real life?
good night people.
user19161
8:45 PM
@JayeshBadwaik See you in your dreams.
@JayeshBadwaik Good night, Jayjay
@JayeshBadwaik g'night
@Melvin :-)
@JayeshBadwaik sleep tight! dream about your XXX ;)
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.
@OldJohn good night.
@JayeshBadwaik Didn't you just drink coffee? Good night.
user19161
@MattN. Some people drink coffee to sleep!
@WillHunting Bizarre.
@WillHunting wtf???
after dinner i don't drink anything with caffeine.
nor anyhitn with estimulatings
8:50 PM
There are several ways. One is like this:$$
\begin{align}
f(z)
&=\frac{z^2 - 2 i z + 3}{(z-2)(z^2+1)}\\
&=\frac{(z-2)^2+(4-2i)(z-2)+(7-8i)}{(z-2)((z-2)^2+4(z-2)+5)}\\
&=\frac1{z-2}\frac{(7-8i)+(4-2i)(z-2)+(z-2)^2}{5+4(z-2)+(z-2)^2}
\end{align}
$$
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)}$
@cassandra0 cause true beauty comes from simple things
@N3buchadnezzar Then you do a power series division.
where you least expect
Hi @aDangerousIdea
8:52 PM
@WillHunting did you give a list of translations recently of the previous names of people in the chatroom?
@aDangerousIdea wassup?
@Melvin Chillin' ... you?
user19161
@OldJohn Yes, I did.
@cassandra0 I think they are both equally beautiful
user19161
@OldJohn I can give it again now.
8:53 PM
@WillHunting could you re-post it?
user19161
cassandra0=jdoe=sperners lemma
@aDangerousIdea cannot complain
user19161
charlie=me and math
user19161
skullpatrol=a dangerous idea=john junior
user19161
old john=john senior
8:54 PM
WillHunting=...
user19161
I am a banana.
...matt damon?
WillHunting = 1/0
Or was it di caprio?
They all look a bit the same.
@WillHunting thanks!!
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!
it could be derived from some estimates and log-convexivity, I didn't like that
@aDangerousIdea hahahahahahaha
@cassandra0 I just think the limit is just as nice as the infinite product - no other views
@WillHunting I like him too
8:56 PM
:(
user19161
@Melvin Hehe, OK. But I am not gay.
@cassandra0 It is a very long time since I looked at things like beta and gamma functions
WillHunting = 1/(1/0)
user19161
@OldJohn Is there an alpha function? I wonder...
@WillHunting never heard of one
8:58 PM
@WillHunting do you think i am?
I aways thought gamma was stupid because who cares about extending functions to non integers
user19161
@Melvin I don't know.
@WillHunting wanna find out?
but it's actually really good
user19161
@Melvin OK, you can tell us if you like.
8:59 PM
@Melvin Want to meet and have coffee?
@MattN. why not?
user19161
Hehe...
I'm not gay. I just like to be kind with everyone.
@Melvin Touché. : ) As I pointed out earlier, I am with someone.
@Melvin How kind, exactly?
...
9:00 PM
@MattN. let's have a coffee three of us
user19161
@Melvin You're not? For a moment I thought you were.
@MattN. kind. Nice. polite.
@WillHunting why?
are you homophobic?
user19161
@Melvin Just from the way you talk above.
user19161
@Melvin Of course not.
@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.
@WillHunting i like tea
user19161
@Melvin I think tea is better than coffee.
@WillHunting Me too
user19161
Also, I prefer wine to beer, but some people here like whisky!
wine...
wine is nice
but i don't use to drink
9:06 PM
O.o
Me neither, alcohol is evil.
user19161
@n3b Your exams are in Dec right?
If you drink don't drive. or as people say:if you drive, don't drink. your drink may fall.
@WillHunting 01, 05 an 12
user19161
@Melvin I think I drink less than a bottle a year.
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.
@WillHunting i don't use to drink bottles...
@Melvin I don't drink and drive - I can't afford both beer and petrol
user19161
@MattN. Just drink and integrate!
@OldJohn GReat!
9:08 PM
@MattN. Drink and derive works exellen, done that a plethora of times.
user19161
@OldJohn HAHAHAHAHA
@WillHunting Not differentiate -- derive!
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.
@Melvin Not when you wake up
user19161
9:10 PM
Hey @amwhy Congrats on getting 9k! =)))
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?
Absinth is good though =)
@N3buchadnezzar Van gogh liked it. his painting was influenced by it
@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.
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!
@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.
@WillHunting he was killed
@WillHunting i really like him
mainly starry night
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.
What happened to Johannes?
geez
@aDangerousIdea Kepler?
user19161
@aDangerousIdea Who is that?
user19161
@N3buchadnezzar Good, now the girl can go home with me.
@aDangerousIdea Bhrams?
9:16 PM
@WillHunting Your "Bro"
user19161
@aDangerousIdea He is Jonas right?
@WillHunting Proves that the ureto get home, sometimes is stronger than the sex urge
user19161
Well, probably halfway through RH now.
@WillHunting I see.
9:17 PM
^^
@WillHunting RH?
user19161
@aDangerousIdea Riemann Hypothesis, just a joke.
@WillHunting So, no idea?
@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.
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.
@N3buchadnezzar what's your real name, N3b?
He is a cool dude...
@N3buchadnezzar is what?
@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...
Jonas?
But we don't the pleasure of their company :(
@WillHunting What about liquid nitrogen, that is pretty cool.
user19161
@N3buchadnezzar I prefer the company of XXX.
@Melvin Yes.
9:24 PM
hmm
@N3buchadnezzar and oxygen, and radium, and talium...
0
Q: Fouriercoefficient of the sawtooth wave help to find that the bessel equation gives $\sum \frac{1}{k^2}=\frac{\pi^2}{6}$

bakabakabakaWhat 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?
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?
9:29 PM
@N3buchadnezzar By the way - I was right about $1/(z-2)$ being its own Laurent series :)
@OldJohn Its own laurent series about z=2?
But $f(z) = 1/(z-1)(z-2)$ ;)
@N3buchadnezzar what is $f(z)$? - you asked for the Laurent series for $1/(z-2)$
hello, does anybody have a second to help me out with a terrible easy question?
9:33 PM
@OldJohn Ops, my bad...
@JustDanyul what is the question?
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.
@N3buchadnezzar no worries :) - I was just beginning to doubt my understanding :)
@JustDanyul yes - but what is the question?
@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
@JustDanyul yep - that would be true
9:37 PM
What properties does the $L^2$ space have?
@N3buchadnezzar what sort of properties are you looking for?
Continous and bounded
@N3buchadnezzar how can a space be continuous?
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.
Hmm - from what I remember, functions in $L^2$ need not be continuous or bounded
9:41 PM
Wikipedia says, that it is both a hilbert space, and complete so?
Yep - it is a Hilbert space
and complete
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.
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
@N3buchadnezzar Haha
Bye everyone.
9:53 PM
@OldJohn Yeah, that is what i did
@MattN. Bye matt, take care!
Oh fuck!I don't know what's wrong with it!
What is the rational irrational function called again?
@N3buchadnezzar I can never remember its name - only what it looks like :)
$$f(x) = \left\{ \begin{array}{cccl} x & \text{if} & x & \text{is irrational} \\
0 & \text{if} & x & \text{is rational} \end{array} \right.$$
@OldJohn I was trying to look it up on wiki, but could not find it.

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