Mathematics - 2012-02-01 (page 1 of 3)

Jonas Teuwen

00:21

Kannappan Sampath

You look Smart @JonasTeuwen.

=)

Jonas Teuwen

At least I look smart 8-).

Kannappan Sampath

@Jonas I'm sorry if I hurt you by saying you "look" smart.

Jonas Teuwen

Of course you didn't!

robjohn

@JonasTeuwen I don't see the egg thing, though.

Jonas Teuwen

00:36

Yeah, it just came off my head.

Brian M. Scott

Looks like there’s a bit of a breeze blowing from your right. :-)

Jonas Teuwen

:-).

I'm off to bed. Good night guys!

Brian M. Scott

G’night!

Fortuon Paendrag

Does someone have a link to a well posed question at stackexchange we can show OPs who command us to solve their problems?

It seems to be a large problem here.

Something simple, polite and showing that the OP actually tried to solve the question would be nice. Maybe you, @BrianMScott ?

Brian M. Scott

This one doesn’t ask for a solution, but it’s a nice request for an explanation. I’ll see if I can find one with a request for a solution.

Fortuon Paendrag

00:42

Thank you, Brian! Could we include an example in the FAQ's or something. Not that many people even read them, but it might be worth it!

Brian M. Scott

00:57

@FortuonPaendrag This one looks pretty good.

Fortuon Paendrag

That looks wonderful! Many thanks, @BrianMScott! How has your afternoon been?

Brian M. Scott

Kind of slow, mathematically.

Rajesh D

01:30

hellooowooooooooo

Kannappan Sampath

04:04

Can anyone here tell me how is a map indicated as a homomorphism?

(I know there are none here, but may be a later visitor will give his piece of mind over the issue)

Mariano Suárez-Alvarez

there is no notation for that

anon

If $G$ and $H$ are algebraic structures (group, ring, field, etc) then "$f:G\to H$" is generally understood to be a homomorphism, at least in any particular context, no?

Mariano Suárez-Alvarez

yes

if you are considering a function which may not be an homomorphism, you are usually explicit about it

Kannappan Sampath

$\overset{\thickapprox}{\to}$

Mariano Suárez-Alvarez

one rarely does that, so it is not such a burden

Kannappan Sampath

04:09

Stands for a isomorphism ?

anon

@Kanna: I've seen something like that indicate isomorphism.

Mariano Suárez-Alvarez

to put things on top of arrows, use \xrightarrow{\sim}

the spacing is much better

$\xrightarrow{\sim}$ vs. $\overset{\thickapprox}{\to}$

anon

testing $\xrightarrow{\sim}$ vs $\stackrel{\sim}{\to}$ vs $\stackrel{\sim}{\rightarrow}$

Mariano Suárez-Alvarez

moreover, xrightarrow extends the arrow: \xrightarrow{\text{something long}} gives $\xrightarrow{\text{something long}}$

anon

Nice, I like it. Thanks.

Kannappan Sampath

04:11

$\xrightarrow{\sim}$ and not $\xrightarrow{\thickapprox}$, am I right?

@anon me too!

It's cool! Without much pain, we get things done!

@Mariano

Mariano Suárez-Alvarez

I tend to add extra space, so a\xrightarrow{\;\sim\;}b giving $ a\xrightarrow{\;\sim\;}b$ instead of $ a\xrightarrow{\sim}b$

Kannappan Sampath

Is it $\sim$ or $\thickapprox$ over the arrow? @Mariano

anon

Eh... I'd put more spaces in. Testing $a\;\xrightarrow{\;\sim\;}\;b$

Mariano Suárez-Alvarez

mathjax is not getting the spacing right, though; TeX does it better

anon

@Kanna: Depends on author maybe?

Mariano Suárez-Alvarez

04:13

@KannappanSampath, to denote what?

Kannappan Sampath

Isomorphisms?

Mariano Suárez-Alvarez

I'd use $\xrightarrow{\sim}$ to denote, for example, homotopy equivalence

$\xrightarrow{\cong}$ for isomorphism

Kannappan Sampath

You confused me! no, not that for what?

anon

I believe I saw Pete L Clark use just \sim overhead for isomorphism in his notes before, though he doesn't really do algebraic topology I don't think. And I'd prefer it that way because doing more than one wisp over the arrow seems superfluous to me.

Mariano Suárez-Alvarez

there is no universal notation for that

if he does use that, then somewhere he explains the meaning

well, that is because you are only denoting one thing

if youwant to talk about homotopy equivalences and homeomorphisms, for example

you need two different things

I prefer a $\cong$ on the arrow because it makes it obvious that I mean isomorphism :)

Srivatsan

04:17

How about $f: A \cong B$? :-)

anon

I suppose it depends on the area one is working on which notations one would feel are best.

Mariano Suárez-Alvarez

I've seen that in old papers

I don't like it

Kannappan Sampath

OK, Rule 1: Explain your notation, atleast once however intuitive they are! Right?

anon

I don't like it either. Morphisms should be arrows, dammit!

Mariano Suárez-Alvarez

@KannappanSampath, indeed

anon

04:18

@Kanna: Whenever notation isn't standard, absolutely.

Srivatsan

Ah, I was just facetious.

Kannappan Sampath

OK, good!

A lesson well learnt!

Mariano Suárez-Alvarez

there are certain areas where a lot of notation is needed, and they've had the good sense of more or less standarising it

Srivatsan

@anon "morphisms should be arrows" is probably only a half-century old idea, isn't it? (At least I read so in some post in MSE/MO.)

Mariano Suárez-Alvarez

a talk on Lie theory could need a good 20 minutes of explaining notation otherwise, for example: let $G$ be a semisimple Lie group, $\mathfrak g$ its Lie algebra, $\mathfrak h$ a cartan subalgebra, $\Delta$ the root system, $\Delta^+$ the set of positive roots, and on and on and on... they have lots of notation and they cannot say anything without involving two thirds of it! :D

the first arrows used to denote maps were used in the 50s

anon

04:19

Hell if I know. I'm a notationally impressionable mathematical youth.

Kannappan Sampath

ok folks Thank you for shedding light!

Mariano Suárez-Alvarez

1940s, rather

Mac Lane attributes the idea to Hurewicz

Srivatsan

@Mariano: If you are free for a bit, can you take a look at the tag situation in a question? See this: math.stackexchange.com/questions/38517/…. Also see this chat conversation.

(I don't have much idea, so I am asking everyone else. =))

anon

one more vote and that gets a guru. (sorry Asaf but it's already had my upvote ;) )

Srivatsan

@anon "Accepted answer and score of 40 or more." Questions don't get Guru badges.

anon

04:31

Whoops nevermind. Does a question get something for 40 votes?

Srivatsan

Just checked. Nothing.

Mariano Suárez-Alvarez

@Srivatsan, «category-theory» seems the obvious thing.

«definition» is 110% uninformative :D

Srivatsan

:)

anon

What is it -10% of?

Srivatsan

intuition is a slightly better replacement, in fact.

anon

04:34

Yes, that's a good idea.

perhaps at least one algebra tag for good measure

Kannappan Sampath

Nothing was here!

Rajesh D

hhi folks

Kannappan Sampath

@RajeshD Hi

Rajesh D

@anon : Is it 3 Am there ?

Srivatsan

hi Rajesh

@RajeshD Quite off. It's 11.35.

anon

04:36

No, it's about 11pm @Rajesh :)

Rajesh D

ok

anon

(actually 10:35 here, dunno where you are sri)

Rajesh D

its 10 in the morning here !

Srivatsan

@MarianoSuárezAlvarez Thanks, Mariano. (BTW does your keyboard have guillemet symbols in it? Or did you remap some keys to produce this output?)

Kannappan Sampath

@Srivatsan Thanks for asking!

Srivatsan

04:38

@anon Pittsburgh.

Rajesh D

@Mariano : Are you from Argentina ??

Mariano Suárez-Alvarez

@Srivatsan, under X there is a magical Compose Key which allows you to make all sorts of funny characters

@RajeshD, yes

Srivatsan

Ok. thanks.

Mariano Suárez-Alvarez

See, for example, hermit.org/Linux/ComposeKeys.html

Kannappan Sampath

@MarianoSuárezAlvarez what key is that?

Rajesh D

04:47

Argentina is my favourate FootBall team....and not to mention Maradona and Messi

Mariano Suárez-Alvarez

(Most distros ship with the key disabled; you then have to activate it)

Rajesh D

@Mariano

Mariano Suárez-Alvarez

Sadly, you are stuck at the moment with the one argentinian who could not care less about football :P

Rajesh D

You do not like....no problem !

Kannappan Sampath

@Dylan why does the automorphism group show irregularities at n=6? I know it is because of outer automorphism but that is a bit unnatural and why does the genral procedure fail?

anon

04:50

By football do we mean what Americans call "soccer"?

Kannappan Sampath

@anon I think!

Srivatsan

@anon that's right.

Rajesh D

the which actually sounds like its name...the one you play with feet and not hands !

anon

I always thought soccer / football was more fun than American football.

Rajesh D

sadly American foot ball is played with hands but they call it football

and the actual football they call it soccer ! ridiculous

anon

04:52

Agreed.

Srivatsan

what's in a name?

Rajesh D

This shows that American's can do anything to make themselves feel superior ?

Kannappan Sampath

A rose by any other name smells as sweet, (to complete)!

Srivatsan

@RajeshD And everything they do somehow points to them feeling superior?

I'm playing devil's advocate here.

anon

No, this shows Americans don't care about making sense. There are many other things that point to America making a show of being superior.

Kannappan Sampath

04:55

May be we can start discussing about sth which is abstractly nonsense! (leaving this concrete non-sense aside)

Srivatsan

@anon That's somehow not the impression I get/got. Maybe I was just looking at the wrong places.

On second thought, maybe I agree with you. =)

Rajesh D

@Sri : and am I playing the "Troll" ? just kidding

Srivatsan

I suggest that you read the first paragraph of this wiki article.

"There are confilicting explanations of the origin of the word "football". It is widely assumed that the word "football" (or "foot ball") references the action of the foot kicking a ball. There is a alternative explanation, which is that football originally referred to a variety of games in medieval Europe, which were played on foot. There is no conclusive evidence for either explanation."

See this for a more detailed explanation: en.wikipedia.org/wiki/Football_(word)#Etymology.

Somehow I don't buy that the Americans wanted to display their superiority -- in this case, at least.

anon

the what?

Dylan Moreland

@KannappanSampath Hm?

Srivatsan

05:04

@anon rewrote it now. :)

anon

Oh, right. That's what I was saying.

Srivatsan

@anon Yes, I just realised that myself. In any case, I was addressing Rajesh implicitly. =)

Kannappan Sampath

We look at Automorphisms as a permutation of generating transpositions, don't we?

@Dylan

anon

Yes, I know.

Kannappan Sampath

Since there are $n$ of them, we must have $S_n=\operatorname{Aut} (S_n)$

Dylan Moreland

05:06

Automorphisms of what?

anon

@Kanna: I don't follow what you just said. automorphisms of what?

Kannappan Sampath

Automorphisms of $S_n$, I thought I asked clearly in my question!

anon

Automorphisms of the symmetric and alternating groups

In group theory, a branch of mathematics, the automorphisms and outer automorphisms of the symmetric groups and alternating groups are both standard examples of these automorphisms, and objects of study in their own right, particularly the exceptional outer automorphism of S6, the symmetric group on 6 elements. Summary {| align="right" cellspacing="2" |----- bgcolor="#A0E0A0" | n | \mbox{Aut}(S_n) | \mbox{Out}(S_n) |----- | n\neq 2,6 | S_n | 1 |----- | n=2 | 1 | 1 |----- | n=6 | S_6 \rtimes C_2 | C_2 |} {| align="right" cellspacing="2" |----- bgcolor="#A0E0A0" | n | \mbox{Aut}(A_n) | \m...

Dylan Moreland

Ooh.

Kannappan Sampath

I read that, that is least organised, discrete collection of facts chosen from a world by coin tossing ! =)

@anon

Dylan Moreland

05:09

The blog posts at the bottom at SBSeminar are probably good.

Kannappan Sampath

They don't explain my question.

Dylan Moreland

The "why"?

Kannappan Sampath

I am wondering what is the reasonable way to think about $\operatorname{Aut}(S_n)$ that will naturally lead us to concluse $S_6$ is different from other $S_n$ for $n \ge 3$.

Dylan Moreland

I wouldn't know. This is the first I've heard of it. It does seem interesting.

anon

Dima says "a group-theoretic answer to why n=6 is so special is that a nontrivial outer automorphism has to map the conjugacy class of transpositions to some other conjugacy class of involutions. But this is only possible when n=6, as easy counting of class sizes tells you."

comment on SBS

Kannappan Sampath

05:13

@anon Oh, looks like this is born from the class equation of $S_n$.

Dylan Moreland

@anon Ah, good find!

Kannappan Sampath

May be I should think a little more! But, still wondering how something about automorphisms come from something that can tell us about normal subgroups, except for the tiny link that normal subgroups are invariant under inner automorphisms.

(And the case of $S_6$ concerns the outer automorphism which is an involution)

anon

I love abstract algebra even though I don't have any special talent for it. Doing it feels like alchemy.

Dylan Moreland

I try to suppress this feeling, but I feel the same way about analysis.

Kannappan Sampath

I think you won't feel the same way about all analysis @Dylan

Dylan Moreland

05:21

That's one thing I hope my time here improves: I read these neat arguments by robjohn, J.M., etc and maybe get a little bit better at it.

Srivatsan

executioner needed: math.stackexchange.com/questions/104458.

Kannappan Sampath

For instance, those with set theoretic flavour might interest you, no?

@dylan

Dylan Moreland

@Srivatsan Already voted. But with some hesitation because answer merging does not work or is not ever done.

Srivatsan

Well, that is true. But the two posts still exist; only future answers are affected.

Rajesh D

@anon : are you a student ?

anon

05:24

I'm not enrolled in any courses, but you could still call me a "student of math" figuratively.

Rajesh D

i mean your occupation ?

anon

I think you can only say your occupation is "student" on paperwork if you're enrolled somewhere, even if it's just a diploma mill. Maybe I'm wrong about that. I certainly read and learn math in my free time every once in awhile.

Dylan Moreland

I could really spend all day fixing crummy titles/tags. That's dangerous.

@KannappanSampath I enjoy functional analysis every once and a while.

Rajesh D

@anon : I mean where do you work ?..software engineer, ..etc., ?

Kannappan Sampath

@DylanMoreland Even I get that feeling sometimes.

GTG, bye people!

Rajesh D

05:30

bye Sampath

anon

I do phone surveys for my paycheck. (As in I call people and they take surveys with me.) The results get on news channels sometimes, which is interesting.

Dylan Moreland

G'night.

Rajesh D

its morning here anyway

@anon : sounds cool

anon

I read a definition of the nth symmetric product of V as "the subspace of $V^{\otimes n}$ which consists of the tensors that are symmetric under permutation of components." Is this really the same as saying the quotient space of $V^{\otimes n}$ obtained by equating component permutations of tensors?

anon

05:52

Don't mind me $\color{Red}{\text{just }}\color{Blue}{\text{testing }}\color{Green}{\text{colors}}$.

Mariano Suárez-Alvarez

@anon, only when the characteristic of the field does not divide n!

consider what happens for $n=2$, to get a feeling of what happens.

Srivatsan

@MarianoSuárezAlvarez Is that an exclamation point? Or a factorial? :) // This question partly for clarification, partly rhetorical.

Mariano Suárez-Alvarez

a factorial :D

Srivatsan

Thanks.

anon

Let me clear up one confusion I have first. In the latter definition one can just write $a\otimes b$ and understand it to be identified with $b\otimes a$. Of course in the space $V^{\otimes n}$, the expression $a\otimes b$ isn't necessarily a "tensor that is symmetric under permutation of components" so what does the $a\otimes b$ then correspond to in the first definition? $a\otimes b + b\otimes a$?

Mariano Suárez-Alvarez

06:02

it is better to use another notation for elements in the quotient

denote $a\odot b$ for the image of $a\otimes b$ in the quotient.

anon

image under projection? isn't that the same as what I said ("understand [$a\otimes b$] to be identified with $b\otimes a$"?)

Mariano Suárez-Alvarez

that might work in another context

but you are in the process of talking simultaneaously about elements of the quotients and of $V^{\otimes 2}$.

the notation is then ambiguous if you do what you want

(no one writes symmetric tensors with $\otimes$, in any case :) )

Anyhow, there is indeed an isomorphism from the quotient to the subspace of symmetric elements of $V^{\otimes 2}$ mapping $a\odot b$ to $a\otimes b+b\otimes a$

anon

You could have just said so... :O

Mariano Suárez-Alvarez

In characteristic 2, this breaks down, as $a\odot a$ is not zero

Dylan Moreland

Let's try to organize things: call the quotient $S^n(V)$. You've got a projection $p\colon V^{\otimes n} \to S^n(V)$. Write the image of $v_1 \otimes \cdots \otimes v_n$ as $v_1 \cdot \cdots \cdot v_n$. You have a map $i$ going the other way that sends $v_1 \cdot \cdots \cdot v_n$ to something like $\sum_{\sigma \in S_n} v_{\sigma(1)} \otimes \cdots \otimes v_{\sigma(n)}$.

anon

06:07

Yes, I saw it break down in V=F2 and k=F2, n=2.

Dylan Moreland

And then, horribly, you have another map $q = \frac{1}{n!} i \circ p$.

Mariano Suárez-Alvarez

Both spaces are useful, and the subspace is sometimes written $\Gamma^n(V)$.

anon

Okay, thanks Dylan. That's what I was trying to see - I was already familiar with the quotient definition, and the notes I'm reading used the other one, so I was having trouble seeing explicitly how they're equivalent.

Mariano Suárez-Alvarez

they are different in many aspects—in particular, when one is doing representation theory over positive characteristic, the two variants are important

Dylan Moreland

So your tensor in $V^{\otimes n}$ can correspond to something symmetric-looking in either the quotient or something in $V^{\otimes}$ if you shove it through $q$.

I never really had this straight until I read an appendix in Fulton and Harris.

[The reason you have the $1/n!$ is so that the image of $i$ is fixed by $q$, so you can call it a projection.]

anon

06:14

Aha.

Dylan Moreland

Algebra books will always quotient, and differential geometry books will always do the projection thing (which I never liked, since it seems like you have to put $1/(n!k!)$s everywhere whenever you multiply anything).

But there must be some good reason...?

anon

Think it would make a good MSE question? ;)

Mariano Suárez-Alvarez

diff. geometers work in characteristic zero

and the correct definition of symmetric powers is the one with the quotient: this is the one which satisfies the universal property.

Dylan Moreland

I guess they also write $V \otimes V$ where an algebraist would write $V^\vee \otimes V^\vee \approx (V \otimes V)^\vee$, because they want to evaluate. All sorts of fun to be had.

Mariano Suárez-Alvarez

They don't do that

they ;ll write things like $T^n(V)$ or something

Dylan Moreland

06:24

Maybe I am misrepresenting.

These are vague recollections of Spivak and Lee's books.

Gigili

Hello there, my question has got a response and I understood it but I want to know what was wrong with my interpretation. Anyone can help me out?

anon

I'm seeing $S^n V$ and $\Lambda^n V$. Are these what you two are talking about?

Mariano Suárez-Alvarez

Nope, those are the symmetric power (constructed as a quotient) and the exterior power

anon

What is T^nV and what is V^\vee?

Mariano Suárez-Alvarez

the "other" symmetric thing, constructed as a subspace of $V^{\otimes n}$ is usually denoted $\Gamma^n(V)$—but it only appears in contexts where the characteristic is positive, for otherwise it is canonically isomorphic, for all purposes, with $S^n(V)$.

anon

06:28

@Gigili: I don't think the domain in the answer is right.

Dylan Moreland

You're right, Lee does write $T^n(V)$ and even talks about $V^* \otimes W^*$ and such as alternatives. I knew I liked this book for a reason. I remember more clearly that Spivak does something funny at some point.

Gigili

@anon That's what I said, but the answer is right somehow, I guess the poster missed a part of his/her own explanation.

But I'm saying, isn't it a normal integral? and it'd be a normal polynomial with the domain of all real numbers?

Dylan Moreland

But it isn't a polynomial.

anon

@Gigili The issue is that the answerer took the continuation of the power series inside the integrand, which automatically extends it outside its valid region of convergence, and then integrated. The question is difficult to make sense of where you have a series inside of an indefinite integration.

Dylan Moreland

It's a power series. Look at $1 + x + x^2 + \cdots$. You can't just evaluate that wherever you like.

anon

06:31

No, a polynomial has finite degree, these are infinite power series. You can't sum 1+2+4+8+16+... for example in the reals. But you can write 1/(1-x)=1+x+x^2+... and then plug in x=2. There are a number of MSE questions on this sort of thing, it's tricky.

Gigili

I cannot integrate $\int (x+x^2+x^3+\dots) dx$?

anon

Given the answer choices, what they probably intend for you to do is integrate term-wise and then investigate the region of convergence of the resulting power series.

Gigili

Aha, then the function is defined where the series converges?

anon

I assume that's how they want the problem to be interpreted.

Gigili

Got it, thank you @anon.

Thank you @DylanMoreland too.

Daniil

06:55

What's up

anon

The lightest of all quarks.

Daniil

Indeed; how are you doing, @anon?

anon

Pretty good.

Rajesh D

07:13

@Daniil : Hi

Zeeshan Mahmud

The feeling you get when you see your reputation points go up. :)

@10 k users, I deleted a question which had 0 votes. If anyone gets a chance can you please take a look at it and help me out. :)

anon

07:28

I don't see you on the Users listing and we can't look at deleted questions without somehow knowing their url (and they are likewise unlisted as far as I can tell).

Zeeshan Mahmud

I go by "Mahmud"

anon

Okay. The deleted question is not shown on your questions list to me so you're going to have to find a url I think...

Or just ask your question here.

Zeeshan Mahmud

@anon, it's kind of cumbersome and has no urgency... actually I am too lazy to type that whole thing in. Thanks for the help anyway

Matt N.

@Srivatsan Why is this called "matrix space"? I think it should be "metric space".

anon

clearly a typo

Mariano Suárez-Alvarez

07:43

can someone tell me if my answer at math.stackexchange.com/questions/12192/… is comprehensible?

anon

I didn't realize geometry was used in factoring polynomials! Or at least checking their shape. I'd have to be familiar with the underlying methods to make sense of your answer, but I don't find the concept surprising.

Mariano Suárez-Alvarez

The keyword is *Newton polytope*—they are very useful.

The geometry of the polygons reflects the arithmetic of the exponents in the monomials of the polynomials.

math.stackexchange.com/questions/104530/… is pretty amazing :)

In particular, Henry's answer is weird

anon

08:01

Editing one more question and then bedtime.

MaX

Hey guys

Rajesh D

hi Max

MaX

I have this problem,

ABC is a triangle with sides AB = 6m, BC =8m, and AC = 10m. A line k in the plane of the triangle ABC moves along the segment AC at the rate of 1cm per sec. The line starts at A and ends at C and is always perpendicular to AC.

1. How long does it take the line to reach the point B?

I think the answer should be 500 secs, as the distance needs to be traveled is 5m, am I right?

anon

HELP. I'm halfway through editing a question and my browser froze? How do I keep my work? :O

Asaf Karagila

Top of the hangover to you, and whatnot.

anon

08:12

wat

Jonas Teuwen

08:23

@Asaf Hi.

anon

Alright, for future reference: what can I do to prevent Google Chrome from freezing while I'm editing answers/questions? I've had to retype things so many times. I would try Firefox but when I do that the preview takes too much time to reload after every character I time and it constrains me.

Srivatsan

@anon hm, I guess copy-paste into a text file is not an option?

anon

@Sri: When the page freezes I am unable to highlight the text. (Also view source and save page as do not work properly.)

Srivatsan

For the future reference question: Why not first compose an answer in a TeX file first, and then paste it?

I do this sometimes for the longer answers.

anon

Because I like looking at previews every sentence or two :P But I suppose writing an answer in notepad, or pasting one into notepad and editing it, is eminently doable.

Srivatsan

08:25

Notepad? You don't use LaTeX environments?

anon

I do but what's the point?

Srivatsan

Ok, I was just surprised. (I am not sure about this, but there should be editors which give you online preview as you type.)

anon

Well, codecogs does it for single equations, which isn't terribly helpful unless you need help getting used to latex for math in particular.

Asaf Karagila

I really don't get how this got 2 upvotes... :|

Srivatsan

@anon Another thing I do is this: if I have a 2-3 part answer, I write it in a few passes, saving it each time.

But I don't think I have ever "lost an answer" -- or a significant portion of any answer.

Oh my god.

anon

08:33

Maybe Il y a doesn't know what E[n] means?

Srivatsan

Yes, Ilya's comment is fine. But Henry has confused a random variable with the dummy index for summing.

anon

Oh, yes, true. Not sure why I didn't see that.

Anyway, I have to be going to sleep as I have to be somewhere in 7 hours. Don't remember where but I'll worry about that tomorrow :P

Srivatsan

=)

robjohn

08:57

@Jonas I hope my comment is taken with the humor with which it was intended

this comment :-)

Srivatsan

@robjohn Who does that anyway? Using different notation for the integration variable and the limits. =)

robjohn

@Srivatsan :-p

@anon at least saying what $n$ is would be useful in a discussion of $\operatorname{E}[n]$ is :-)

Srivatsan

@robjohn context: math.stackexchange.com/q/103927/13425

robjohn

@Srivatsan yes, I was referring to that post :-)

Srivatsan

@robjohn In the last comment, I describe what n is.

Asaf Karagila

09:08

@Srivatsan "Your mother"?

Srivatsan

Close; it's a mother-valued random variable.

robjohn

@Srivatsan Indeed, but it should be incorporated into the question.

Srivatsan

@robjohn True.

I assumed you were "blaming" anon for not mentioning what $n$ is.

robjohn

Oh, no... I was complaining about the question, not anon

Srivatsan

And the first line of the post says "calculating the estimated number of jobs $n$ in the queue is given by:"

Admittedly the language could be clearer..

robjohn

09:11

Hmm... it does. I missed that reference to $n$

okay, I retract my comment :-)

Asaf Karagila

My cat is running like crazy around the house.

robjohn

@AsafKaragila our kitten does the same.

right now she is napping.

Srivatsan

How come cats don't get to go for a walk in the park?

robjohn

@Srivatsan some people put cats on leashes, but I don't think that they are very happy when on leash.

@Srivatsan you're not married are you :-)

Rajesh D

Managing with people itself is a big big headache....why would anyone want to deal with cats and dogs ???

Asaf Karagila

09:17

Dealing with a cat is fine.

The lack of meaningful verbal communication makes things easier.

Rajesh D

No it isn't

I am scared of such things

robjohn

@AsafKaragila Rajesh doesn't seem to be a dog or cat person.

Rajesh D

when there isn't any verbal communication how could you be sure they won't hurt You ????

robjohn

@RajeshD with verbal communication, how do you know you won't get hurt?

Rajesh D

I would know when i am goin to get hurt...atleast i could run away....

anyway its my problem....not any with you

Asaf Karagila

09:20

What about cows, or elephants?

Srivatsan

@robjohn I don't think so, no. =)

Asaf Karagila

@Srivatsan But you're not sure that you're unmarried...

robjohn

@AsafKaragila He has choice and doesn't like being leashed.

That is almost a proof :-)

Asaf Karagila

Almost a proof? That's what they have in all those non-mathematics sciences.

Jonas Teuwen

@robjohn I have changed the variable 8-).

robjohn

09:25

@JonasTeuwen That will make for a better answer :-)

Srivatsan

@robjohn Unless he changed all the occurrences to $y$. :)

No, he didn't. :/

Jonas Teuwen

Haha, then I would be trolling robjohn.

robjohn

@JonasTeuwen I will remove my comment :-)

Jonas Teuwen

Okay.

Rajesh D

This bounty is going waste in another few hours

Srivatsan

09:27

@JonasTeuwen I even made up a new name. How do you like Trollas Teuwen? =)

Jonas Teuwen

Nice one.

Asaf Karagila

@RajeshD That's life.

Rajesh D

yeah i know it sucks

!

Jonas Teuwen

If you increase the bounty, will it be renewed for another 7 days? 8-).

Rajesh D

I have already solved the problem...my answer is there.....so no point in extending @Jonas

Asaf Karagila

09:32

I'm gonna take a shower and head out to the university now. See you all later.

Srivatsan

bye Asaf

Any ideas how to make this effect? meta.math.stackexchange.com/questions/975/…

Rajesh D

09:50

@Matt : hi

Benjamin Lim

Hey guys :D

There is a meta thread I started and it is turning into a wrestling match between two users. Shoukdvi just delete thevthread or something?

Benjamin Lim

10:24

@Srivatsan What do you think I should do now?

Srivatsan

@BenjaminLim I briefly replied: "why did you post it in meta?" and removed the message. Do you want to answer that question?

Benjamin Lim

I wanted to know if the moderators could do something.

Maybe I should not do anything the thread will die off eventually.

Srivatsan

@BenjaminLim Sure you didn't like it, but I don't think it is offensive enough to require moderator intervention.

@BenjaminLim That might be the best thing to do.

Benjamin Lim

Yeah. I just found the behaviour of that user to be incredibly childish.

Thanks anyway :D

Srivatsan

BTW, just so that you know, I downvoted your meta question not because I don't sympathise with you, but because I disagreed with whether it should be discussed in meta.

But I don't understand your downvote either. In the sense that I haven't downvoted it, and I wouldn't downvote it.

But of course you should feel free to vote down posts that you consider harmful, wrong, or unhelpful.

Rajesh D

10:44

link please @Ben

Rajesh D

10:58

@Ben : IMHO the question doesn't deserve 7 upvotes and the answer by Myself does not deserve 23 upvotes.....truly.....i sense something wrong happening there !

robjohn

11:54

@RajeshD I agree that for some reason the votes on that have been inflated.

@Srivatsan which effect?

Srivatsan

12:14

@robjohn the "lighting effect" in the picture?

robjohn

@Srivatsan probably layers in Photoshop.

Srivatsan

ok. Thanks.

Jonas Teuwen

I have to teach analysis 2 for mechanical engineering, I have asked their professor mechanics if he has a book for me where I can get example from that I can relate to the material 8-).

Srivatsan

analysis course for engineering makes sense. What's special about mechanical engg.?

Jonas Teuwen

Well, it is not really "analysis" as we would call it.

Srivatsan

12:20

oh

Jonas Teuwen

It's just studying derivatives, limits, Riemann integrals, differential equations, you know.

I'm not sure if you can call it calculus either.

Srivatsan

Calculus with differential equations...

Jonas Teuwen

But people at mechanical eng. usually get very bad grades because they don't see why they need it.

@Srivatsan Yes, but in calculus they don't usually give $\epsilon$-$\delta$-definitions do they?

Srivatsan

It depends. I had to take a calculus course (again I wouldn't call it analysis) where they did rigorous epsilonic proofs.

robjohn

@Srivatsan like that?

Srivatsan

12:25

@robjohn Yes, I guess it looks like that. Thanks.

Jonas Teuwen

@Srivatsan Okay, then let's call it calculus 2 for mechanical engineering 8-). (By the way they can also do "real" analysis as an elective).

Srivatsan

@robjohn Can you post another pic with a much bigger lighted region? I am looking for something...

I'm off for now. Bye!

robjohn

13:25

@Srivatsan What are you looking for?

Transcript for

$Mathematics$ Mathematics