Mathematics - 2013-01-25 (page 4 of 5)

@JasonBourne Duuuuuuuude.

user19161

@OrangeHarvester Yes, are you Pedro?

@JasonBourne Mwuhahaha. (I won't tell.)

user19161

@OrangeHarvester Are you crazy now?

@JasonBourne Nopes.

user19161

10:06 AM

@OrangeHarvester Did something happen just now? I see mods here from other sites.

@JasonBourne Not now, but something happened while I was sleeping. I guess sometime around 0100 UTC. I am not sure what happened but there were a LOT of flags, many of them simple revenge flags.

Too much headache for moderators I guess.

user19161

@OrangeHarvester Oh well, there are many kids here after all.

@JasonBourne I am Jayesh if you haven't already figured it out.

user19161

@OrangeHarvester I asked you about it yesterday.

@JasonBourne I did not see it I suppose. (I don't rem)

user19161

10:09 AM

@OrangeHarvester I asked why you changed your name.

I am drifting in and out of exercises and questions papers.

Ahh I see. @JasonBourne By the way, in terms of flags, how is math room? Is it more quite as compared to others?

user19161

@OrangeHarvester There aren't that many these days. Not referring to mod flags which I don't see. But gaming has the most, followed by maybe math, LOL.

user19161

There are some people who like to flag while outside the room. They don't want to talk, they just want to spy on us.

@JasonBourne Yeah, last night something similar happened I think.

user19161

To flag while not in the room, you have to log in to chat, and then read the transcript of the room.

user19161

10:12 AM

So you need not be in any room at all.

I don't understand the concept of being able to flag while outside the room.

user19161

I am thinking of deleting my tex and eng accounts. I will decide this month.

Its not like people get mugged in real time online.

I seriously think the concept of flagging from outside the room should be disallowed.

user19161

I just hope TPTB won't ask me too many questions about deletion.

TPTB?

user19161

10:15 AM

The Powers That Be = SE staff

user19161

TPTB > mods > 20k users in terms of powers on the site.

I don't know why you want to delete your accounts. Let them be as they are. What's the problem?

user19161

Well, I am just a minimalist. I like deleting things which I won't have use for anymore.

user19161

Also, to prevent myself from spending time there so that I can focus on math SE alone, yay!

As you wish, @JasonBourne...

user19161

10:20 AM

@Novice Who is banned? You? LOL

@JasonBourne You have been banned.

user19161

@Novice By the way, three dots after the name doesn't ping.

user19161

@Novice Nonsense!

Okay, I'd never put three dots after a username @JasonBourne...

@JasonBourne Really, you have been banned.

user19161

By the way, note that deleting an account doesn't remove the posts of the user, only the votes he has cast.

10:24 AM

@JasonBourne Obviously, that's why we still have a bunch of waste \rms still on the database.

user19161

So really, I don't see any real damage at all to the site.

Wait no.

That is suspension.

You'd then look like userXXXXX.

user19161

@Novice Suspension rep is at 1. Deleted users don't appear anymore on the user list.

user19161

@Novice Yes, your posts look like user1234

@JasonBourne Anyway, I have suspended you

You will not be able to post throughout the network because I have suspended you on all the sites.

10:28 AM

@Novice \rms?

@OrangeHarvester I meant Bill D.

@Novice Hmm. I hope you know who rms is though.

@OrangeHarvester Who is rms again?

@Novice google it.

Richard Stallman?

oooh.

Root mean square.

So robjohn?

10:32 AM

Stallman.

I like Stallman.

@robjohn: are you here?

@Ilya I am...

@robjohn: do we have a kind of FAQ with math questions?

@Ilya Hi.

10:37 AM

@Jonas: hey!

@robjohn I found that people often ask about the representation of random variable and connections to their distributions

just now I've found a nice place in one textbook which discusses it in a cute way

Which one?

and thought that such answer can be posted without having a question

Convoluting my measures?

It can I suppose; many other of the SE sites do this.

@Jonas: "Coupling, Regeneration and Stationarity"

Then you put 'answer your own question'.

Start typing already!

10:39 AM

@JonasTeuwen so first I ask a question, and then answer it?

and make it CW

@Jonas: I watched the Trollhunter yesterday

Kickass.

@Ilya Yes, that is how you do it.

I just write it in a .pdf and link it when needed - also good.

hm

now I only have to find some time to do this

But can do both as it is both .tex 8-)).

You have to do it now. I tell you to and you must listen to the great bunghole.

For I have TP.

Also it might save you time in the future and people will find your post. Blimey eh?

Also, I would just put it on my website as well, so people can link it to you.

@Ilya The FAQ we have that is listed as a FAQ is more a meta FAQ, how to do things and what is appropriate, rather than a list of math questions that are frequently asked.

@robjohn icic

10:43 AM

@Ilya You could ask a question about such books and mention the one you found.

I would just pick the part and recompile it into something more awesome.

@JonasTeuwen heh... did you mean convolving?

@robjohn Err. Yes, I did.

@robjohn Well, actually, convoluting also kinda means the same right? Does not not mean something like curling up such that distinct parts are less distinct? 8-).

convolute
2: practice sophistry; change the meaning of or be vague about
in order to mislead or deceive; "Don't twist my words" [syn:
{twist}, {twist around}, {pervert}, {convolute},
{sophisticate}]

convolution has two meanings and I use convolve when I can :-)

@robjohn Alright, that covers it right?

If I have convolution kernel operator - do you know where I could find conditions (if it exists in such generality) on the spaces such that I can invert it?

And that I get a reasonable expression for, yes.

10:50 AM

@JonasTeuwen I am sure some are covered in SIO by Stein...

I have that somewhere in this office.

But there are like >100 books here.

And I know it is covered I just want to have a good expression for the kernel itself 8-(. Neumann series kinda suck.

@JonasTeuwen what kind of kernels are we talking about?

Related to semigroups of operators.

I will ponder a bit about the precise question.

Perhaps I can answer it myself then 8-).

Damn... my computer just fell out of its socket.

And it was still running... Good boy it is.

11:08 AM

@JonasTeuwen Does it have a name? ;-)

@robjohn Yes! dutiaw59.

@JonasTeuwen fellout? how?

@DanBrumleve It did not occur to me as such.

Frank Science

Is there anybody familiar with philosophy?

Theorem

11:47 AM

@FrankScience : i like philosophy , but i am not that good .

Hi everyone

badp

12:46 PM

This article presents the following as a syllogism, but is it?

∀A: B
¬B
-------------
¬A

("All good things come to an end. Internet arguments never come to an end. You don’t need me to finish the syllogism.")

Yeah, not even that formalization is correct.

You'd need first order logic and that's not what syllogisms are about, IIRC

right?

Frank Science

Are you a logician?

Sandy Lee_user53167

howdy!

Does anyone know how to read a log table?

David Toth

1:18 PM

Let f:A->B, g:C->B be functions in topological spaces. For f and g to be equal is it necessary that dom(f)=A=dom(g)=C or it is sufficient that A would be homeomorphic to C?

user19161

1:32 PM

@DavidToth If two functions are equal, their domains must be equal.

user19161

There are different ways to define a function. I have taken it to mean a set of ordered pairs here.

@SandyLee_user53167 I think I know how to read a log table.

@badp LOL.

not much staff happening here

let's burn some dance!

>-|:

>-\:

>-/:

>-]:

>-[:

>-|:

>-/:

nobody wanna join?

huh, nerds...

2:24 PM

$y=\sum\limits_{n=1}^{\infty } x^n$

$z=\sum\limits_{n=1}^{\infty } y^n$

$w=\sum\limits_{n=1}^{\infty } z^n$

$...$

2:36 PM

►

@MatsGranvik Nice, Mats!

Thanks.

:)

$$\sum\limits_ {n = 1}^{\infty} a_n x^n = x + \sum\limits_ {a = 2}^{\infty} x^{a} + \sum\limits_ {a = 2}^{\infty}\sum\limits_ {b = 2}^{\infty} x^{ab} + \sum\limits_ {a = 2}^{\infty}\sum\limits_ {b = 2}^{\infty}\sum\limits_ {c = 2}^{\infty} x^{abc} + \sum\limits_ {a = 2}^{\infty}\sum\limits_ {b = 2}^{\infty}\sum\limits_ {c = 2}^{\infty}\sum\limits_ {d = 2}^{\infty} x^{abcd} + ...$$

hahahah

badp

2:51 PM

@FrankScience Logics is a large part of my computer science studies, yes.

Frank Science

@badp I cannot even understand logic stuff and CS.

This series of videos is nice: youtu.be/P024Vv2eiQA

@GustavoBandeira Oh!

@Charlie The one with repeated notes is really nice. =)

Congratz trying to to it at half speed without breaking the arm. xD

What is the thing with writing papers addiction?

2:56 PM

It is cool, having your own brain child.

@JonasTeuwen My thing s it seems people just want to write papers, no matter the subject, just to write, like if write a paper gave you super powers. My opinion.

It feels like that if it gets published I suppose.

@Charlie They should write magazines then?

I don't know.... I'm too dumb to understand those things....

@Michael: so, I've found myself non-familiar with the notion of a conditional probability given a value of a random variable. I knew only about the conditioning on the $\sigma$-algebra generated by a random variable

oh, hell - he's not here...

3:04 PM

@Charlie This is the reason.

@Charlie I guess it is really joyful I guess to see your work in a well-organized and presented document. Similarly like people like writing poems, or books.

@OrangeHarvester Or people doing porn movies like me.

Peter Tamaroff

3:34 PM

@Charlie I will write a paper about people who write papers about meaningless baloney!

@Jonas: need your help

@PeterTamaroff that's a nice one

a very basic question: let $X,Y$ be two sets and $Z = X\times Y$ be their Cartesian product. Define $\Delta_X,\Delta_Y$ and $\Delta_Z$ be the correspondent diagonals of $X^2,Y^2$ and $Z^2$. Is it true that $\Delta_Z = \Delta_X\times \Delta_Y$?

@everybody please feel free to comment on this

this is very basic, but I'm not sure I am in a very precise form now

here e.g. $\Delta_X = \{(x_1,x_2)\in X^2: x_1 = x_2\}$

@GustavoBandeira cê num presta

:P

@Charlie Eu sô muleke piranha.

3:44 PM

hahahahah

c'mon, folks...

@mr.FS hello

Tobias

@Ilya no, they are not equal. The first consists of elements of the form (x,y,x,y) and the second of elements of the form (x,x,y,y)

they are not even contained in the same set to begin with

(of course, there is an easy way to get one from the other)

@GustavoBandeira aquela identidade Euler quase me mata de rir....igual à equipolência

@Tobias oh, indeed

kahen

3:49 PM

Please type more MathJax! I need to debug my attempt at getting a greasemonkey script to auto-re-MathJax the chat :)

${\huge\text{Apple}}$

@Tobias what about $(\Delta_X\times Y^2)\cap (X^2\times \Delta_Y) = \Delta_X\times \Delta_Y$?

@jason Hi, Jaspy!

Tobias

@Ilya yes, those are equal

@Ilya This seems correct.

user19161

3:52 PM

@Charlie I changed to brown.

thanks

${}$

@JasonBourne I see!

@Orange: did you have a different username before?

@JasonBourne any specific reason?

3:52 PM

@Ilya Yes. I am Jayesh Badwaik.

kahen

Really weird. Using $(document).ajaxComplete(mathjax_callback) should work, but it isn't :(

user19161

@Charlie No.

@OrangeHarvester oh

@JasonBourne :)

user19161

@OrangeHarvester While Ethan deletes his lines, you edit yours.

3:54 PM

@Charlie XD

@JasonBourne The TeX was not getting rendered in my browser, saying there was a Math Processing Error. It is a perfectly correct TeX, so I did not know what the problem was and did not want to leave a RED mark to annoy people.

@GustavoBandeira vou te contar.... :D

user19161

@OrangeHarvester Yes, but you have done that to cover your tracks before. Note that edited lines have an edit history even in chat.

@JasonBourne Yes. I have done that, and everytime I have different reasons.

user19161

Hello @amwhy, good morning.

3:59 PM

@JasonBourne Good day, Jas!

@Ilya Yo here?

@amWhy Hi!

@Charlie hello!

@Michael: yo!

hello time here :)

@Ilya So wat's with the conditioning?

4:01 PM

good morning, good day, yo, hi, hello...

@MichaelGreinecker I've just learnt that $\Bbb P[X \in \cdot|Y = \cdot]$ can be a formal expression. Before I thought only $\Bbb P[X\in \cdot|Y]$ makes some formal sense

@MichaelGreinecker: btw, I've found a couple of small typos in the pdf you sent me yesterday. Not sure if you are still interested in fixing them

arber

hi

@Ilya I found some too. There is soe law of the universe that you find them quickly after sending some final version off... $\Bbb P[X \in \cdot|Y = \cdot]$ represent some kind of Renyi probability?

@MichaelGreinecker never heard of that. It appeared to be exactly a general version of regular conditional probabilities

so they are not measurable in $\sigma(Y)$ like $\Bbb P[\dots|Y]$ but they are measurable in $\sigma$-algebra of the range of $Y$

@Ilya Renyi came up with some axiomatization of probability in which all probabilities are conditional and probability is a function of two sets.

@Ilya Any source?

4:06 PM

@MichaelGreinecker Thorisson, "Coupling, Regeneration and Stationarity". But he takes it from Ash, "Real Analysis and Probability": Theorem 6.6.5 and Problem 8 in Section 4.4

I guess the latter is very famous, but I've never had it in hand

@argon hi

@Ilya Yes, Ash is famous. But that book is a bit less...uhm..electronically accessible then others of his.

:)

@Charlie Hi Marilia!

@Argon How are you?

4:09 PM

@Charlie Good, and you?

@Argon good!

@Charlie Good

:D

@MichaelGreinecker ok, so you mean that I can never mind them, right?

user19161

Who starred David Toth's question?

user19161

4:14 PM

Is it tradition to star every math question in this chat?

@JasonBourne Nice new avatar!

user19161

@Argon Haha! Just a colour square.

@JasonBourne Ah! But a new coloured square!

user19161

@Argon When do your exams end?

@JasonBourne My last one is Tuesday

4:17 PM

@Ilya It seems Thorisson simply uses this as a different notation for the conditional probablity given a random variable. But I'm not sure I got the numbering system. You mean the things on page 88 I guees?

user19161

@Argon Oh I see. So you will be a free man soon!

@Michael: 87 to be precise. There he has $\Bbb E[X|Y_1]$ and $\Bbb E[X|Y_1 = \cdot]$ which are different objects

@JasonBourne I am looking forward to Tuesday... evening!

@Argon ahem...so what are you doing in Chat? Just teasing...good luck

@amWhy Hehe Jasper has been bugging me about that for a while too :D

4:18 PM

@Michael the first one is a random variable, measurable in $\sigma(Y_1)$ and the other one is a function from $E$ (the range of $Y:\Omega\to E$) which is $\mathscr E$-measurable

@Ilya I see, I see. Give me a moment.

@Michael: sure

user19161

By the way, who were the two people flagging yesterday? I missed the drama!

@Ilya If $X$ and $Y_1$ are real valued, the two notions are basically equivalent, i think. By the Doob-Dynkin Lemma, being $\sigma(Y_1)$.measurable is the same as being a measurable function of $Y_1$.

@MichaelGreinecker sure, the point is that their difference depends on the underlying sample space

4:30 PM

@JasonBourne drama?

user19161

@Charlie Well, yes. If two people keep flagging it is drama.

@JasonBourne hahaha

@Charlie Hello, strange I didn't get notified of your message

@fs oh..you're not Mr. anymore....

user19161

@fs There are many strange things in the world.

4:32 PM

@Charlie yes, is it worse now?

@JasonBourne indeed

@Ilya So $E[X|Y_1=y]\circ Y_1=E[X|Y_1]$. The other direction works for "nice" spaces. Why is he doing that?

@fs no...

good :)

@MichaelGreinecker well, $E[1_B|Y_1]$ does not seem to give directly some kernels from the range of $Y_1$ to $B$ in the domain of $X$

@fs yes, it is worse. Yyou are now just a filesystem. Before you were magically reliable file system.

4:34 PM

@Ilya That makes sense.

@OrangeHarvester haha

@fs and I'm not stranger... we talked before

@Charlie I'm sorry what do you mean?

@Charlie He meant, "Hello! Strange (that) I did not get notified of your message." Eat, shoot and live guys.

ok

4:37 PM

@Michael: aha

o I see haha yes that is what I meant

Can someone translate for me? math.stackexchange.com/questions/286741/sum-integral-l1-mu

@MichaelGreinecker don't overestimate simplicity of some sentences :)

lol "Math Gems" makes no secret of being Bill Dubuque, right down to using the roman font and referring to old posts by Bill Dubuque: math.stackexchange.com/questions/281906/…

@Ilya It seems he thinks I'm worried that others won't help me in doing his homework...

4:43 PM

@MichaelGreinecker really?

at least it doesn't seem to me that was his intention

@Ilya I don't know. He seems to ignore comments or posts very strange things.

@MichaelGreinecker there are such people on MSE

@Ilya "I was thrilled knowing that someone could answer my exercises" (math.stackexchange.com/questions/286746/…)

3

@MichaelGreinecker easy to thrill him, hm

I wonder how does he survive IRL

The excitement?

4:47 PM

pardon

@fs well, he can be a user for a year, and then later, when his suspension is lifted, merge both the accounts. woow.

@OrangeHarvester yes but I think he should be working on his platform which was going to be better than mse :)

@Ilya Whether he survives the excitement IRL.

not only, everything

it seems that even simple things make him nervous

hot blood

@fs ahh, well....

4:49 PM

perhaps, South Mediterranean. Not so far from you, be aware

His self-description: "A student, who for several days don't found the teacher to ask questions, nor whose colleagues until yesterday had no idea how to do the exercises, a student who was from morning until midnight trying everything I could do. This morning I found this site. Be patient with me. I'm glad I found this site."

@OrangeHarvester I remember he came into chat just after his suspension and I naively agreed with everything he said. I'm not sure I do now though

Tobias

@fs I had kinda assumed that BDub was Bill, as that account had been in existence for a few months before it started earning rep, which happened at just about the time Bill was suspended

those people come with a visit unexpectedly

@MichaelGreinecker So glad he could stay forever...

:-)

4:50 PM

@Tobias I'm not sure I know that account but who knows how many accounts he has

I watched the Trollhunter @Michael

@Ilya And? Liked it?

to be honest, it's a nice movie but does not seem to impress

neither it seems it was filmed to impress

@Ilya Yes, opinions seem to be divided on that one.

@Tobias I see BDub now and it would be strange if it wasn't him but if it is him it's also strange that he's not using the distinctive roman math font

4:53 PM

@Michael I also found quite unnatural that one's their camera man was killed, they cryed for a couple of minutes and quickly decided to call for a new one

though I'm not that familiar with the Scandinavian mentality

maybe there it's normal

@Ilya :-)

I shall ask Henning, perhaps

@MichaelGreinecker talking about movies: Mulholland Dr.?

@Ilya Yes, I like the movies by Lynch. Not that I understand them, but still.

@MichaelGreinecker First time I watched this movie I found it strange and interesting. But second and third times (>1 year gaps) the drama there impressed me deeply. Not like in other his movies

I haven't watched the Inland Empire yet, though

@Ilya I like lost highway a lot. Mostly for Patricia Arquette and the soundtrack.

4:57 PM

@MichaelGreinecker oh, I liked "I'm deranged" so much when I watched it!

Manson and Rammstein at that time I was perfectly aware of already

@Ilya Me too. I'm a big fan of Bowie.

@MichaelGreinecker I must confess, I like M.D. mostly for Naomi Watts

@Ilya I can relate.

:)

@MichaelGreinecker didn't get a chance to listen to a lot of his stuff. From old school I mostly love Pink Floyd. The last album of Queen also

@Ilya I don't know thi stuff that systematiclly. I liked "The Wall". Do you like "The Darkness"? They sound a bit like Queen.

5:01 PM

@MichaelGreinecker haven't heard of them. "The Wall" I do like, but mostly prefer "The Dark Side of the Moon" and "High Hopes" from the last album

@MichaelGreinecker: 30stm?

@Ilya Not generally, but they can rock.

their very first album is not famous, but I liked it a lot - reminds of Pink Floyd

taking into account that Jared is not the worst player, neither the worst singer - it's quite a rare coincidence

@Ilya Some of their stuff is too agressive for me. I like calm songs by loud bands. Ballds by Motörhead are perfect..

@MichaelGreinecker that I heard about, but never listened to. Any particular ballad to advise?

@Ilya If you are not religious, "God was never on your side" is great

5:06 PM

@MichaelGreinecker I'll check it, thanks

@Ilya I'm gonna leave. Bye!

sounds nice - though I guess lyrics is important there, and I'm not so perfect in hearing it from songs. Shall check out lyrics

@MichaelGreinecker bye, and have a nice weekend!

You too!

5:19 PM

@JasonBourne YOU TURNED RED ?!!!?????!!!!

user19161

@math101 Yes! It's officially "brown".

It looks maroon to me

user19161

Well I typed "brown" into GIMP and this is what I get.

"Chameleons (family Chamaeleonidae) are a distinctive and highly specialized clade of lizards. The approximately 160 species of chameleon come in a variety of colors, including pink, blue, red, orange, turquoise, yellow, and green. They are distinguished by..."

How doChameleons fit into the picture?

user19161

5:24 PM

@MatsGranvik Haha, are we all chameleons?

user19161

@math101 Maybe it doesn't. Just a random thought of his.

The sequence $\{S_{n+1}\}=\frac{1}{3-n}$ With $S_1=2$ Can we say its bounded above by 2 and below by 0?

I am just wondering what the sequence would converge to?

hmmmmmmm

@robjohn Can you help me?

I am not even bothering to ask @JonasTeuwen cuz he refuses to help those of a lower stature than his

5:42 PM

@math101 Do you mean $\{S_{n+1}\}=\frac{1}{3-S_n}$

Yes I do. Sorry abt the typo.

oh nevermind what i said then

@JasonBourne I miss steel blue, boo-hoo :-(

never mind.

@OrangeHarvester Sort of, why?

$\frac{1+\sqrt 5}{2}$?

5:51 PM

@math101 A quick hack I use is $S_n = \frac{1}{3-S_n}$, which gives $S_n = \frac{3 \pm \sqrt{5}}{2} $

yes assuming convergence right?

and then find which one of the two lies between the bounds

@fs Yes, convergence has to be proved separately then.

@fs sorry, I made two mistakes there, first I wanted to ping math101, and second I silly miscalculated and instead of 3, I got 1, which gave me $S_n = \frac{1\pm \sqrt{5}}{2}$ as the solution.

@OrangeHarvester ok no problem :)

@OrangeHarvester How did you get that quick hack of yours?

@math101 I don't remember.

If you are asking me for a derivation, then I guess I can provide one. (Will have to work it out again.)

5:55 PM

Yes please

@math101 if it converges you can sort of say that the next term will be equal to the previous term (all a bit handwaving but i believe it can be made rigorous)

$S_{n+1}=S_n\implies \frac{1}{3-S_n}=S_n$

and then solve the resulting quadratic equation for $S_n$