Mathematics - 2012-05-07 (page 3 of 9)

Gigili

9:00 AM

@DavidWallace: Umm, really?

Ilya

the reason I don't like notation $\mathrm d\mu(y)$ is that how do you write then $\int f(y)K(x,\mathrm dy)$

still reading the same paper

Zhen Lin

I haven't given much thought to notation for Lebesgue integrals, but I don't deal with them anymore...

t.b.

@Ilya well, the lesson to learn here is that it is rarely a good idea to treat variables that mean completely different things on the same notational level. There's a reason for using subscripts, for example!

Zhen Lin

I think I liked the notation $\mu (\mathrm{d} y)$.

Ilya

@tb for example saves you, because one doesn't want to see $x'-\rho(x)$ in the subscript

t.b.

9:07 AM

well, but as the rôle of $y$ is purely dummy-esque you could simply drop it altogether.

Zhen Lin

@tb: That must be the operator-algebraist in you talking!

Ilya

I thought of dropping any summation/integration indices but I rarely seen good examples. Of course you can write $\int f(\cdot)K(x,\cdot)$ but what if you want to show that $K(x,\cdot)$ is a Haar measure for each $x$? I mean smth like
$$
\int f(zy)K(x,\mathrm dy) = \int f(y)K(x,\mathrm dy)
$$

render it

t.b.

Now back up a little: what is $K$ after all? It's a map from $X$ to measures on $Y$, no?

Ilya

as any map of two variables, it can be considered as a map from a product space to reals or a map from states to measures. If we want to stress out its measurability I would go for the map from a product

Brian M. Scott

@tb Me, for one, when I see it; I don't use it.

t.b.

9:17 AM

Thanks for the addendum :)

I'm relieved.

Ilya

hi @Brian

Brian M. Scott

Hullo!

@tb Was it you who made the comment about reputation gaps?

t.b.

@BrianMScott I don't think so, but I'm not sure what you mean.

Brian M. Scott

Someone commented earlier on the large reputation gaps on the first page of the User list, even ignoring Arturo.

anon

That was JM.

t.b.

9:22 AM

@BrianMScott JM

Brian M. Scott

@tb Ah, okay. Had I been around, I'd have pointed out that gaps will widen, if people's work-rates remain roughly constant. (When I started teaching, our annual pay raises were usually percentage-based.)

2

Hi @Brian and t.b

Hullo, Rajesh.

Hi, Rajesh

howdy

I hope you aren't from Texas!

Benjamin Lim

9:31 AM

@tb My god

my lecturer is sneaky as hell

t.b.

what are you talking about?

Benjamin Lim

@tb I had to show some integral operator was a contraction map

and then in the integral you do this trick of multiplying everything inside by $e^{-Ls}e^{Ls}$

bloody hell

t.b.

:)

Benjamin Lim

@tb My god that was sooo sneaky

@tb Hey

@tb What are you doing atm, any teaching duties?

t.b.

no, not right now. I'm working on my own stuff at the moment.

Benjamin Lim

9:35 AM

research

t.b.

that's a big word to use for the trivialities I generate, but okay.

Benjamin Lim

@tb Why trivialities, common man

@tb When I study, sometimes I like to put Hartshorne

t.b.

I am a common man, not a genius :)

Rajesh D

I have a question

Benjamin Lim

or eisenbud's book geometry of schemes next to me

@tb It's like a common to me so that one day I can understand this stuff

t.b.

9:39 AM

If it motivates you that's good, but maybe you'd like to do a little less advanced things first?

Benjamin Lim

@tb It's there for motivation :D

I don't actually understand anything in there

Zhen Lin

Eisenbud/Harris is actually very easy. You don't need much commutative algebra.

Benjamin Lim

@ZhenLin geometry of schemes?

Zhen Lin

In fact, since you have it, I highly recommend reading Geometry of schemes first before Hartshorne.

Benjamin Lim

@ZhenLin ok

@tb In my university I only get to take a measure theory course next year

t.b.

9:42 AM

then be patient, for heaven's sake! Or read a book. There's plenty of stuff out there

Benjamin Lim

@tb I am doing analysis, galois theory and commutative algebra now

@tb I plan next semester to do some geometry perhaps

I don't know what a manifold is :D

Zhen Lin

Oh, that's easy. A manifold is a paracompact locally ringed space locally isomorphic to some $\mathbb{R}^n$ equipped with the sheaf of smooth functions. :p

t.b.

beat me to it :)

Rajesh D

Consider a linear function space which is complete under the $L^2$ norm, where a sequence of functions $\{f_n\}$ converges, does the sequence has to convergence to a unique function ? Especially considering that there could be several functions which are not pointwise equal, but are at the same distance from each other under this norm ?

Benjamin Lim

It'll probably be from lee's book smooth manifolds

Zhen Lin

9:44 AM

There's a more elementary definition but it won't fit in this message box.

@BenjaminLim: That seems... ambitious. That's the textbook for the master's-level Differential Geometry course here.

Wouldn't do Carmo or something like that be more suitable?

Benjamin Lim

@ZhenLin That is what a lot of people have recommended me

t.b.

@RajeshD if you're working in $L^2$ you're not working with functions, but rather equivalence classes of functions modulo null-sets.

Benjamin Lim

wait I'm talking about john lee's introduction to smooth manifolds

Zhen Lin

Yes, and that's the textbook we use.

t.b.

@BenjaminLim people recommended AM, too, didn't they?

Rajesh D

9:45 AM

ok

Zhen Lin

"we" meaning "the lecturer", I haven't read it.

Or, indeed, any differential geometry book...

t.b.

Lee's smooth manifolds is an excellent book. The entire trilogy in fact.

Benjamin Lim

@tb Well yeah :D

t.b.

But I second Zhen's opinion: do some curves and surfaces first.

Benjamin Lim

@tb what about loring tu?

Rajesh D

9:46 AM

thanks @tb : I think i understood what you have said, but what do you mean by 'modulo null set' ?

Do you intend to separate it out

t.b.

@BenjaminLim that's far too advanced as well. Go for do Carmo's curves and surfaces or Kühnel's book on the same topic, for example.

Rajesh D

Ah do Carmo : good one, t.b.'s favourite i guess

Benjamin Lim

@tb Ah I may not be able to do a reading course on that in my uni

they already have a DG course for third year

based on lee's book

t.b.

@RajeshD You identify two functions if they agree outside of a null set.

Zhen Lin

Well, you may as well prepare yourself for it by looking at easy cases first.

My experience of differential geometry here was more-or-less Wilson [Curved spaces], then do Carmo, then Lee.

Benjamin Lim

9:49 AM

@tb The DG course is very frustrating for a lot of people. In the space of 10 minutes they are told what a dual space is, then the tensor product of V and V dual.

Rajesh D

ok, new teminology and a cool one, looks like number theorists infiltrated the analysis world !

Zhen Lin

@BenjaminLim: All the more reason to learn a decent amount of multilinear algebra and multivariable analysis first.

t.b.

@Ben: the advice you'll get from me will always be the same one in the near future: stick to the basics, learn some examples before you learn theory. You can't understand what a manifold is before understanding curves and surfaces.

Benjamin Lim

@ZhenLin I admit my multivariable calculus is not that strong

Rajesh D

@t.b. What is the null set in this context ?

anon

9:52 AM

@Rajesh: We quotient the space of functions with bounded L^p seminorm by the kernel of said seminorm; two functions are in the same equivalence class if the seminorm of their difference is zero.

Benjamin Lim

@tb They may not even allow me to do a reading course on de carmo's book, basically next semester I have no courses to take....

Rajesh D

set with zero measure ?

kahen

@anon: s/norm/seminorm/

t.b.

@BenjaminLim why do you need a reading course in order to read a book?

Benjamin Lim

@tb I don't need to. But what I would like to say is that I don't have any courses to take next semester :(

apart from the next algebra course in the sequel to my current galois theory one

Rajesh D

9:54 AM

@tb In order that you don't substitute it for a sleeping pill

t.b.

And there's no way around basic analysis, multivariable calculus, multilinear algebra. Commutative algebra is no substitute for that.

Benjamin Lim

@tb I know.

Zhen Lin

@RajeshD: A null set is a set with zero measure, or a subset thereof.

t.b.

I understand that the theory is much more exciting and so on, but as Mariano said: the theory is built to solve problems. If you don't understand the problems it is supposed to solve you won't get much out of it, except a strange attitude.

Benjamin Lim

@tb Yeah I suppose. Commutative algebra to me seems so much more appealing than analysis. But I know that things like inverse and implicit function theorems, etc are really important for DG

t.b.

9:56 AM

You can't do DG without them. It's at their very foundation.

Benjamin Lim

a good several variable analysis book? @tb

Rajesh D

thanks @Zhen

Zhen Lin

Though, I am embarrassed to admit that I only know the statement of the inverse function theorem and have forgotten the proof.

t.b.

Banach fixed point theorem.

Rajesh D

@t.b : What is multilinear algebra ? how is it different from LA. any good books, is it easy to know once you are good at LA ?

Zhen Lin

9:58 AM

I'm afraid even that hint isn't enough to remind me...

t.b.

You use the inverse of the derivative to build a contraction on the appropriate space of functions, which will have the local inverse as a fixed point.

Benjamin Lim

@tb You know what

you have given an idea

t.b.

@RajeshD The theory of multilinear maps as opposed to the theory of linear maps. I don't know a good book to recommend, as I never read a book on linear algebra proper.

Benjamin Lim

next semester if I am out of maths subjects to take I will just take literature or something

@tb I wish there was someone at my uni to advise me on things like that...

t.b.

why not? But keep doing some maths in your spare time, and serious math with exercises and all. You'd be awfully surprised how quickly you can become rusty otherwise.

Benjamin Lim

10:03 AM

@tb That's the way I learn.

No exercises, no learning

t.b.

exactly.

Benjamin Lim

@tb Before my analysis exam, we have a selection of problems to solve

I solved as many of them as I could

Zhen Lin

By a quick count, I think I've taken 46 maths courses in the last 4 years... :p

Benjamin Lim

@ZhenLin that is 12 maths courses a year

t.b.

Oh, boy...

Benjamin Lim

10:05 AM

@ZhenLin my uni does not even have a quarter of that

Zhen Lin

Mind you, here, a "course" is either 16 or 24 lectures. Much shorter than elsewhere.

Benjamin Lim

ah ok

where can I find a good several variables book?

Rajesh D

@tb : In case of a sequence of point-wise convergence of a function sequence, the limit function is always a unique function. right ?

t.b.

yes that's the point of pointwise convergence :)

Rajesh D

hurray!

Benjamin Lim

10:09 AM

@tb I heard several variables in Rudin is not so good

Rajesh D

Now i understand the huge difference between pointwise convergence and convergence under a $L^2$ norm !

Ilya

@RajeshD the difference is that the former is a convergence in topology and the second - in metric. If you think that having a unique function as a limit is better, then it doesn't seem you've understood the huge difference. I think, it's much easier to work with metric convergence and equivalence classes of functions.

Rajesh D

@Benjamin : Its pathetic in rudin

Benjamin Lim

@RajeshD where to look then?

t.b.

@BenjaminLim sorry, I can't recommend English literature on those first and second year topics because I had good courses and only read the German books that were around.

Ilya

10:12 AM

@tb when we say that the space is completely metrizable, we mean that there is at least one metric which makes the space complete?

t.b.

yes.

Ilya

thanks

Benjamin Lim

@tb Ok. Second year courses: wwwmaths.anu.edu.au/education/maths-handbook/2nd-year-courses

Rajesh D

i don't know...but look at the intro on vector spaces in Rudin, the simple proof of dimension of a space and the cardinality of basis is a huge mess, a two line proof was done in a full page in a completely turn around way

Benjamin Lim

yes

t.b.

10:13 AM

@Ilya it's a bit of an abuse of language but a pretty common one.

Ilya

@tb ah?

Zhen Lin

@BenjaminLim: Here is the course list at my faculty. There's a book list for each course.

Brian M. Scott

@tb I don't see how it's an abuse of language.

t.b.

@BrianMScott I parse this as "more metrizable" than others.

Brian M. Scott

I just see completely metrizable as a single term, comparable to paracompact, or first countable, etc.

Zhen Lin

10:16 AM

It would be nice if we could bracket words in natural language, but alas, "[complete metric]isable" is silly.

Brian M. Scott

Fun, though!

t.b.

@BrianMScott Yes, that's the way out. But for some reason people tend to be more confused about "completely metrizable" than about other terms, at least in my experience.

Gigili

@ZhenLin That's great.

t.b.

There also were questions here whether it meant that all metrics are complete.

Zhen Lin

What is it about compactness which makes that true, though?

t.b.

10:20 AM

that it is equivalent to sequential compactness for metrizable spaces?

Zhen Lin

Well, the fact that a compact metric space is complete and totally bounded means that a compact metrisable space is "completely metrisable" in the sense that every metric on it is complete, no?

Rajesh D

@Ilya : I don't get you about what i didn't understand, in $L^1$ the elements are not functions but equivalence classes, but in pointwise convergence the objects we are dealing with are actual functions. Am I right ? or there is anything more to it?

t.b.

@ZhenLin that's right, yes. I prefer the pedestrian way of thinking about it: a Cauchy sequence has at most one limit point and a limit point of a subsequence is a limit point of the entire sequence.

Ilya

@RajeshD: you're right, I just said that dealing with equivalence classes and metric for me is better than dealing with actual functions without any metric

Benjamin Lim

@tb Hey, how do you get motivation to do something when there is none?

Ilya

10:24 AM

@BenjaminLim kick yourself

Zhen Lin

@tb: Hmmm... yes, that seems intuitive enough. Thanks.

Rajesh D

@Ilya : I am in total opposite to you in this, I am interested in pointwise convergence ! I just wanted to make sure there are things that this can do but not the $L^2$ convergence. Hence this conversation!

Ilya

@RajeshD in fact I work within $L^\infty$ where you have both the metric and you deal with actual functions

Zhen Lin

$L^\infty$ is a weird space.

Rajesh D

@Ilya : how come you have to deal with actual functions?

Ilya

10:27 AM

sorry?

@ZhenLin in fact, I call it $\mathrm b\mathscr E$ and it is nice! :)

Rajesh D

I mean what is the speciality of $L^{\infty}$ ?

Ilya

@RajeshD that you don't need a measure to define it

Zhen Lin

@Ilya: I am totally unfamiliar with that notation!

Rajesh D

Oh : some light on this please, How are the equivalence classes defined here?

and What is a null set ?

t.b.

Stochastic people like to conflate functions and $\sigma$-algebras.

Ilya

10:29 AM

@ZhenLin if $\mathscr E$ is $\sigma$-algebra, the same symbol is also used for real-value measurable functions; $\mathscr E_{+}$ stays for a cone of non-negative functions and $\mathrm b\mathscr E$ for bounded

@tb *classes of functions and $\sigma$-algebras

Zhen Lin

@RajeshD: The point is, a function has vanishing sup-norm if and only if it is honestly and truly the zero function.

This is not true for the other $p$-norms.

Ilya

@ZhenLin depends on the space :) or a measure (say, a counting one - I don't know if in $L^p(\mu)$ you have to have $\sigma$-finite $\mu$)

Zhen Lin

Oops, should have clarified that I mean the sup norm rather than the a.e. sup seminorm...

Rajesh D

@Zhen : cool to know, but anyway...Just want the long story short, $L^{\infty}$ is in no competition with pointwise converge no ?

t.b.

@ZhenLin Not really. But contrary to the other $L^p$-spaces only the null-ideal enters the definition, nothing else.

Ilya

10:32 AM

@ZhenLin not familiar with the latter. Is it sort of esssup?

Zhen Lin

Isn't that the normal "sup" that's used in measure theory? Or at least that's what I remember.

@RajeshD: It's the norm of uniform convergence. The limit of continuous functions is continuous!

Rajesh D

@Zhen : you mean $L^{\infty}$ is equivalent to the limit supremum norm of uniform convergence ?

Ilya

@ZhenLin no, because even in measure theory you do not necessary have a measure :)

@RajeshD that's at least how I used to think about that space, but @tb has brought some doubts

t.b.

The point is that in $L^\infty$ you identify functions modulo null-functions, that's why you use the essential supremum norm, not the supremum norm.

Zhen Lin

All these modes of convergence confuse me. Even the ones to do with spectral sequences.

Rajesh D

10:46 AM

@Ilya : I am interested in pointwise convergence and I am not too scared about it is because I tread only in the garden of Riemann integrable functions. I am sure I never have to tread in the jungle of Lebesgue integrable functions!

Ilya

I'm a jungle man, hah

Rajesh D

Oops I didn't think about it when i said that!

Ilya

@tb so you don't need to define the measure, but you need at least null sets? I saw that sometimes $(X,\mathscr B,\mathscr N)$ is called a measurable space and $(X,\mathscr B)$ a Borel space. That's quite confuses me because I thought that $(X,\mathscr B)$ is a measurable space

t.b.

@Ilya yes, exactly.

The usual definition of the essential supremum (semi)norm reads something like $\|f\|_\infty = \inf{\{M \geq 0\,:\,\mu(\{|f| \gt M\}) = 0\}}$

robjohn

@RajeshD what a boring garden :-)

Rajesh D

10:50 AM

Hi @rob : its good for juveniles like me

kahen

Indeed, @robjohn. No Carlesson's theorem or other nice results on pointwise convergence to be found there.

t.b.

Now if you write $\mathscr{N}$ for the collection of null-sets, you can replace $\mu(A) = 0$ by $A \in \mathscr{N}$.

Ilya

render

t.b.

What you need $\mathscr{N}$ to satisfy is that it is closed under passing to (measurable) subsets and under taking countable unions. It's a so-called $\sigma$-ideal.

robjohn

@Ilya ?

Ilya

10:52 AM

@robjohn making ChatJax work

t.b.

If you have that, you get a space $L^\infty(X,\mathscr{B},\mathscr{N})$ which coincides with $L^\infty(X,\mathscr{B},\mu)$ if $\mathscr{N}$ is the collection of $\mu$-null sets.

kahen

It really really needs to be converted into a userscript for Greasemonkey and friends

robjohn

@Ilya I press a button in my menu bar frequently

Ilya

@tb I see and even used it a bit - but didn't know that it is how $L^\infty$ defined. Moreover, have you heard about this Borel/measurable stuff?

@robjohn I don't like that bar

kahen

having to press a button to do that is just silly. the script should do it for you automatically

Ilya

10:53 AM

@kahen not a good idea to say that someone does silly things, is it?

robjohn

@Ilya I was going to tell a joke about a priest, a rabbi, and a minister walking into that bar...

Ilya

@robjohn :)

robjohn

@kahen that is what it used to do, but they did something to the chat windows that killed it.

t.b.

@Ilya there are both uses of "measurable", but I'd say $(X,\mathscr{B})$ is far more common than $(X,\mathscr{B},\mathscr{N})$.

Ilya

@tb: another confusion is that "Borel space" also refers to a Borel subset of a Polish space, and not to a usual measurable space

t.b.

10:57 AM

That's why sensible people call them standard Borel spaces.

Ilya

oh

robjohn

@Jonas: have you ever computed the Fourier Transform of $\frac{1}{|x|^2+1}$ in $\mathbb{R}^3$?

t.b.

@Ilya You can axiomatize them by saying that you have a set $X$ together with a $\sigma$-algebra having a countable set of generators that also separates points of $X$.

Gigili

@robjohn Wouldn't it help if we post a question on MSO?

robjohn

@Gigili No, I answered this question, I was just wondering if Jonas has ever computed it to see if there is a simpler way.

t.b.

11:00 AM

Separating points means that for each pair of points $x,y$ you find a generating set $C$ such that only one of $x$ and $y$ belongs to $C$.

Given this definition, you can show that there exists a complete metric on $X$ such that $\mathscr{B}$ is the Borel $\sigma$-algebra of the induced topology.

(that's due to Hausdorff)

robjohn

@tb The separating points I am familiar with says that a family of functions has the property that for every $x\not=y$, there is an $f_k$ so that $f_k(x)\not=f_k(y)$

t.b.

@robjohn take the family of characteristic functions of the generating set.

Rajesh D

@Gigili : What is meant by MSO ?

t.b.

robjohn

The one I am talking about relates to Stone-Weierstrass

Rajesh D

11:04 AM

then why would you want to post a question related to math on MSO?

t.b.

@robjohn sure, but it's the same condition.

You can tell points apart by evaluating a bunch of functions on them.

robjohn

@tb Oh. okay :-)

Gigili

@robjohn You answered which question? When no one here can solve the issue, that might help.

robjohn

@Gigili which issue are you talking about?

you mean the chatjax bug?

Rajesh D

See what I've done!

robjohn

11:08 AM

I have posted a question on meta about it.

t.b.

And that's actually the idea of the proof: you enumerate your generating set as $\{C_n\}_{n \in \mathbb{N}}$ and embed $X$ into $\{0,1\}^\mathbb{N}$ by sending $x$ to the sequence of values of $[C_n](x)$.

But @Ilya seems to be gone, so </monologue>

robjohn

@RajeshD what have you done?

Rajesh D

solved a misunderstanding!

Gigili

@robjohn The chatjax log, yes. I didn't know you posted a question, on MSO or MSE?

Rajesh D

:)

robjohn

11:14 AM

@Gigili here

Rajesh D

@Kahen : seems like you are interested in Real analysis more often. Did you see this class of functions Let me know if you find it interesting!

Gigili

@robjohn Thank you. Seems Willie agrees with me. SE should fix it, in that case we should inform them about it.

Ilya

@tb it was about complete metrizbility, right? I didn't find a way to relate it to $L^\infty$

Manishearth

Take some millimeter graph paper and some colored pens (I like blue and red). Color it in as Pascal's triangle with each color representing parity. You get something AWESOME!

(work in progress, and it really looks nice--my camera quality is bad)

t.b.

@Ilya huh?

Can you say more precisely what you're asking?

Ilya

11:30 AM

@tb This comment was about standard Borel spaces, wasn't it?

t.b.

@Manishearth It's great, yes. Take a look here

anon

Hmm, I wonder what happens if you color Pascal's triangle with modular residues of p-adic orders...

Manishearth

@anon Me too

Seirpinski's gearbox?

t.b.

@Ilya yes, but what's it got to do with $L^\infty$?

Ilya

@tb: we had two lines of the discussion and I just wondered which one you pursued while I had a lunch

Manishearth

11:32 AM

@tb Aaah so...many...triangles!

t.b.

@Ilya I said that you can axiomatize standard Borel spaces without mentioning complete metrizability, just with a condition on the $\sigma$-algebra.

Manishearth

@anon I think I'll program that--coloring takes too long. But I'm still going to continue coloring the 2-residues

t.b.

With the conditions spelled out appropriately, you can embed such a space into the Cantor cube $\{0,1\}^\mathbb{N}$

and show that you get an isomorphism onto a $G_\delta$ in the Cantor cube. Now use the fact that a subspace of a complete metric space is completely metrizable if and only if it is a $G_{\delta}$.

Manishearth

Does not understand anything that's going on, leaves

;-)

t.b.

So, the Borel subsets of Polish spaces is just a convenient way of phrasing it and emphasizing the generality. You could take the unit interval as well (many probability books do that). "Nice" probability spaces are Borel subsets of the unit interval.

Basically it boils down to: there's only one uncountable standard Borel space up to isomorphism.

Ilya

11:38 AM

@tb which kind of isomorphism? measurable or continuous?

measurable, and that is $[0,1]$

t.b.

@Ilya Borel measurable (with Borel measurable inverse).

Ilya

just realized it :)

ok, thanks @tb

t.b.

@Ilya I thought the $L^\infty$-bit was already cleared up before you mentioned (standard) Borel spaces.

And you're welcome of course.

Ilya

just wanted to be sure

Matt N.

Wot? 0_o

Manishearth

11:49 AM

@anon Actually, check the second-last page of the pdf that t.b. linked to wisdom.weizmann.ac.il/~fraenkel/Papers/sierpinski.pdf . They show the 3-gasket. Gives you an idea of how it goes on higher residues.

anon

Yes I saw that. You've slightly misinterpreted my suggestion though.

The $p$-adic order of $n$ is defined to be the $r$ such that $p^r$ is the highest power of $p$ dividing $n$. It's these values I'm considering the residues of, modulo some $m$.

Manishearth

@anon Oh, I see :/ Dunno what p-adic orders are

aah

anon

The distribution of orders of p-adic residues is somewhat connected to a recent area of research in number theory called "supercongruences." Somewhat.

Manishearth

Hmm. I might program something that displays it on the basis of an arbit number-returning function

anon

Actually that's too much of a stretch.

x4d33746153706c306974

12:41 PM

Well I had a question asked last night but had to go suddenly , my apologies

Speed of A = u and Speed of B = v , both moving in same direction , then their relative speed is u-v , how?

anon

In time $t$, A has gone $ut$ units, B has gone $vt$ units, and the distance between them has changed by $(u-v)t$ units. Assuming constant speed.

x4d33746153706c306974

@anon Thanks but I'm unable to understand the relative speed is in what reference?

anon

Meaning object B's position is considered the origin at all times.

x4d33746153706c306974

@anon you mean u-v speed is with respect to object B , right?

anon

The speed of A wrt B, yes.

x4d33746153706c306974

12:50 PM

@anon Thanks a lot :)

@anon So how knowing relative speed is useful?

anon

Useful to whom?

x4d33746153706c306974

@anon I meant can you give me some motivation example?

anon

I don't really know how to respond to that. It seems obvious to me that measuring relative velocity would be somewhat ubiquitous in a world with satellites, cell phones, and vehicles all capable of measuring speed with respect to themselves and in need of synchronizing their measurements to track positions, etc.

x4d33746153706c306974

@anon cool, That is very practical example , Thanks

N3buchadnezzar

I still preffer the wild carchase example from yesterdays discussion on the topic.

John Smith

1:06 PM

hi

Gigili

So you haven't solved your problem yet, @JohnSmith ... Right?

'Ello.

user19161

So @anon how did you make your avatar?

anon

@JasperLoy Your question has earned you one free game of I Spy.

user19161

@anon Ah who would have thought it is related to abstract harmonic analysis.

John Smith

@Gigili Nope

Even with the raw data nobody in here seems to know what's going on

t.b.

1:17 PM

bizarre and mildly amusing exchange on MO

John Smith

Given either pastebin.com/raw.php?i=CUuZkKFy or pastebin.com/raw.php?i=PyLn2xM5 is there ANY relationship that sticks out that I can look into here?

Gigili

@tb So would you call it "cross-posting"?

John Smith

there's got to be some recursive property going on here

t.b.

@Gigili well, yes, why?

Gigili

@tb Just wanted to know your opinion about what they call "cross-posting". And what is a moderator supposed to do in this case?

t.b.

1:27 PM

@Gigili I don't like it too much. It seems like an obvious matter of politeness to me that you should mention that you asked the same question elsewhere and link to it to make it easy on others to take a look. I'd also say that you should wait a little bit (a week, say) before doing so. Moderator intervention is not required in my opinion unless someone does it repeatedly.

Gigili

@tb Great explanation, thank you.

John Smith

Anyone willing to take a look?

t.b.

@Gigili there's been this discussion on meta.MO. There's also a link by Zev to the SO rules on crossposting in the SE-network.

anon

Does the term "cross-posting" connote the absence of mentioning a question was submitted to both sites?

N3buchadnezzar

Cross-posting >> Cross-dressing

anon

1:33 PM

wat

t.b.

@anon I believe so, but I'm not sure.

Gigili

@JohnSmith I did but I don't think I can be much of help there. I saw a bunch of numbers and set.

John Smith

They are counts of valid sets satisfying the condition at the top of the page

with a list of what those sets are

N3buchadnezzar

How do I figre out approximately how many electrons my body contains?

J. M.

@anon Not necessarily. Some people have the decency to append "cross-posted to forum Y" to their posts sometimes...

@N3buchadnezzar You'll want to start with a percentage tally of the elements in your body.

N3buchadnezzar

1:48 PM

Oh, I was thinking a very rough estimate.

anon

I asked because I submitted a question to both MSE and MO (I was unaware of the delay rule), but I linked each post to the other from the get-go.

t.b.

@anon I think it depends very much on the attitude displayed by the OP. If it's linked you can safely assume that it was done in good faith, so: no problem.

J. M.

Hmm, it seems Eric became an eleventh-hour candidate...

anon

According to mixed, this isn't the first time :) Perhaps it's a game-theoretic strategy.

Gigili

Is it? I should have used a political trick or something then.

I'm not a political animal anyway.

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$Mathematics$ Mathematics