Mathematics - 2012-08-13 (page 4 of 6)

To me, it seems like the US does not really have a very exciting culture. But it does seem to have very beautiful nature. Also, very big buildings. Can be impressive.

David Wheeler

yes, very nice, lots of trees, and rivers everywhere you look.

Jonas Teuwen

@BrianM.Scott For first next.

Brian M. Scott

@JonasTeuwen Just next.

David Wheeler

2:24 PM

the US. home of the terrorist targe-....erm, skyscrapers!

Jonas Teuwen

@BrianM.Scott Oh, right. But I want to add the connotation that it will not be the only one!

@DavidWheeler But then again... plenty of beautiful nature in Europe as well (Scandinavia!).

Or even Germany (oh my).

David Wheeler

i might could visit australia first next. sure yes.

Henning Makholm

Why are some people so bent on cleansing MSE of questions that they consider too good for us?

Jonas Teuwen

Sounds like I would not really know what I would want to say if I phrased it that way...

Brian M. Scott

@JonasTeuwen Next carries a bit of that connotation, though it’s compatible with there being only one more.

Jonas Teuwen

2:26 PM

@HenningMakholm Eh?

Brian M. Scott

@HenningMakholm Example?

David Wheeler

@HenningMakholm i have no idea of what you mean....

Jonas Teuwen

@BrianM.Scott It is! But I want to added this connotation as in there will hopefully be plenty more!

Henning Makholm

@JonasTeuwen There's a meta question proposing that questions that are too interesting for MSE should be migrated to MO instead when/if it becomes techincally possible.

Old John

@HenningMakholm talking about moving stuff to MO?

Matt

2:27 PM

@OldJohn = person who pretends to be someone that they are not. Would you prefer "impostor"?

Jonas Teuwen

@HenningMakholm Ah! Downvote! Downvote!

Old John

@Matt I understand the word - Just wondered why you thought he is?

Matt

@OldJohn Because he is not our beloved teddy bear! : )

Old John

@Matt Ah! - OK

Jonas Teuwen

I'm not even sure what I should downvote 8-/.

Brian M. Scott

2:29 PM

@JonasTeuwen You pretty much have to add that information separately.

Jonas Teuwen

When in doubt downvote everything!

@BrianM.Scott Okie!

Brian M. Scott

@JonasTeuwen I guess that I’m never in doubt!

Jonas Teuwen

8-D.

David Wheeler

@HenningMakholm hopefully the number of such questions is "small". the choice of "where to put a question" is an awfully subjective one. taking such a choice out of the hands of the OP, and putting it in the hands of "the community"...i have mixed feelings.

sos440

It's calm here...

Brian M. Scott

2:36 PM

@DavidWheeler My feelings aren’t mixed at all. I’m perfectly willing to suggest that a particular question might stand a better chance of getting a good answer on MO, but I firmly believe that the only person who should be able to make the decision to migrate a question is the OP.

David Wheeler

the strangeness i feel...it's because every time someone suggests a "should" instead of a "could" i feel they are imposing their world-view on me. i have a world-view already, i'm not shopping for another one.

in JDH's answer, he writes: "It is important for us to retain community control over this issue..."

Brian M. Scott

@sos440 Oh, I don’t know: Henning just lit a bit of a fire under me. It’s not often that I look at meta, but I feel pretty strongly about this one.

David Wheeler

I am not sure who the "us" is, nor why "community control" is so important

Brian M. Scott

@DavidWheeler And he’s wrong: it’s important that the questioners maintain control.

David Wheeler

But the way it is written...i don't feel like one of the "us", nor do i feel like i will be "controlling" anything

Such a statement is asking for a lot of "trust" on my part...without giving any substantial reason to do so

In fact, the more i think of it, it sounds like unkindness disguised as kindness: "here, we want your question to get more quality attention...so let us decide where it belongs (you freaking idiot--implied, but unsaid)"

Henning Makholm

2:44 PM

@DavidWheeler What I see when somebody tells an asker to use MO instead of MSE is "I think your question is so interesting that people like Henning should not be allowed to suggest an answer".

No matter whether they say "should" or "could".

sos440

Hmm...

David Wheeler

i don't see anything wrong with someone pointing out that MO exists, as a resource. that's a matter of fact.

Henning Makholm

Well. But that is completely different from saying "because that other resource exists you might consider asking the moderators here to block answers from MSE members".

David Wheeler

indeed.

i think moderators should trim stray hairs, not do hair-styles

Brian M. Scott

@HenningMakholm And the fact of the matter is that at the moment I don’t particularly want to be active on MO; I’ve occasionally found useful questions and answers there, but overall the place has left a slightly bad taste in my mouth.

David Wheeler

2:51 PM

the thing is...my own observation is that there are a few users whose opinions predominate on meta. i think it is unwise to say these vocal users are representative of the MSE community as a whole, but apparently sometimes policy decisions seem to be made on that basis.

why does MSE want to start adopting "exclusionary" policies? who benefits?

Old John

@DavidWheeler people who believe that MSE is too inclusive?

David Wheeler

and that's a bad thing? because...?

Old John

@DavidWheeler Oh, I don't think it is a bad thing

Jonas Teuwen

When do we use hyphens? Initial-value or initial value? Right-hand side or right hand side?

sos440

Umm... maybe when people uses them so frequently?

Jonas Teuwen

3:05 PM

Uh?

Jack Schmidt

@JonasTeuwen They are like parentheses. big, red dog means a dog that is big and red. big-red dog might mean a mascot for the Big Red chewing gum company or something. right-hand side tries to eliminate the possibility of confusion with the right hand-side. Since hand-side isn't sensical, right hand side is also fine.

Jonas Teuwen

I see people using them in differently. I wonder which one is correct. In Dutch there would only be one.

David Wheeler

right-hand as an adjective is usually hyphenated. initial value usually is not.

Jack Schmidt

@JonasTeuwen the rules for hyphens in English are not very strict. Several ways can be correct

Jonas Teuwen

@JackSchmidt I see. But it might be possible that in certain sentences it is ambiguous and in others it is not?

sos440

3:07 PM

@JonasTeuwen Maybe this can be informative... grammarmudge.cityslide.com/articles/article/426348/2805.htm

Jonas Teuwen

Then it would be rather inconsistent to use hyphens in some places and not in others.

@sos440 That is basically a part of a style guide?

Jack Schmidt

@JonasTeuwen Correct. "The initial-value is x0=1" is probably incorrect. "The initial-value problem is given by x0=1" is correct. "The initial value problem is given by x0=1" is a little ambiguous if "value problems" were under discussion.

Jonas Teuwen

@JackSchmidt I see. That is helpful. Thanks!

David Wheeler

the "reason" why right-hand is hyphenated, is that right hand has a different meaning: "right-hand" means on the side of the right hand, "right hand" means the hand on the right: the right-hand hand.

Jack Schmidt

(then "initial value problem" would be the first of the various value problems under discussion)

Jonas Teuwen

3:09 PM

Yes, I see. So basically... I will use hyphens 8-).

sos440

:)

David Wheeler

as far as "initial-value" is concerned, you often see it both ways, interchangeably, a similar situation exists with boundary-value. the hypen emphasizes the "cohesion" of the idea

Matt

@JonasTeuwen I think I will have to have drink first. So: going out. Have not been productive today at all : (

BBL

Jack Schmidt

@DavidWheeler oh that is true. initial-value could also be a compound noun phrase and my "probably incorrect" example would be fine.

At any rate, I like to think of them as parentheses. If they make the expression clearer, then it is good. If you use too many then you get things like (((2)+(3))*(7)).

David Wheeler

another example: "euclidean plane-geometry" means the type of plane geometry that is euclidean, out of many kinds. "euclidean-plane geometry" means we are focusing exclusively on the euclidean plane, and doing geometry. they are "almost" the same thing, a slight difference in emphasis.

Brian M. Scott

3:13 PM

@DavidWheeler However, the default interpretation of Euclidean plane geometry is Euclidean (plane geometry).

Jack Schmidt

This makes my skin crawl: many math.SE questions get "decent" answers here, to use your term, but would get far better answers at MO, which the OP may not appreciate, but which many other users would.

David Wheeler

it's like parentheses in algebraic expresssions, yes

Brian M. Scott

@JackSchmidt Yes, I thought that my response was remarkably restrained.

Jack Schmidt

but it matches my experience on MO. I rarely felt anyone was actually answering me. I was often just an excuse.

Jonas Teuwen

@Matt Good :-). Enjoy!

Peter Tamaroff

3:19 PM

@BrianM.Scott Hello, Prof.

@OldJohn Willard is quite amazing.

Brian M. Scott

@PeterTamaroff Hullo, Peter; I’m afraid that you caught me just as I was about to head for bed. I’m overdue: I meant to be there three hours ago!

Peter Tamaroff

@BrianM.Scott Oh, OK. We have our timelines crossed. It it midday here.

Brian M. Scott

@PeterTamaroff It’s about 11:25 here, so almost midday, but I’ve been up since yesterday afternoon.

Peter Tamaroff

Bye.

@BrianM.Scott Oh, wow. OK.

J. M.

Oi, that "move to MO?" meta question is starting to bubble slightly...

Brian M. Scott

3:24 PM

@PeterTamaroff I admit it: I’m a complete nightowl.

J. M.

@BrianM.Scott Oh dear. Have a good one.

Old John

@PeterTamaroff I certainly liked it - and used it as a reference for years

Peter Tamaroff

@BrianM.Scott Hahaha. I went to bed past 5 am, but I got a `phone call 1 hr ago so I was woken up.

Brian M. Scott

@J.M. Thanks. (It’ll be interesting to see what’s happened to that move to MO question by the time I get back to it!)

Old John

@PeterTamaroff His book certainly has some good exercises in there to keep you busy :)

Peter Tamaroff

3:27 PM

@OldJohn Yes. I was surfing swifly through some stuff but I got stuck.

Old John

@PeterTamaroff Expect that to keep happening - but it is good for the learning experience :)

Peter Tamaroff

@OldJohn I'm just halfaway proving it. But I'm not sure about a hypethesis.

sos440

Hmm... I have known that I'm bad at English, but now I feel keenly that I can't chat... :(

Peter Tamaroff

@sos440 Why?

Old John

@PeterTamaroff proving what exactly?

Peter Tamaroff

3:31 PM

@OldJohn That a certain collection of continuous functions separates points from closed sets iff blahblah....

David Wheeler

@PeterTamaroff specifically, what do you mean by "separates points"

Old John

@PeterTamaroff OK

David Wheeler

also...the blah blah blah is most likely important

sos440

@PeterTamaroff It takes too many time to make a sentence. When I finish writing one line, there are now a bunch of new lines;;

Peter Tamaroff

@sos440 Well, if you don't practice you wont get better at it =)

@DavidWheeler Let me write it out.

sos440

3:34 PM

@PeterTamaroff Yes, that's right :)

Peter Tamaroff

@sos440 BTW, you're quite the boss in integration and related stuff.

David Wheeler

@PeterTamaroff yes, please, if you will. slower is better for me. i'm old, and my mind is not always reliable.

Peter Tamaroff

@DavidWheeler Definition: Let $\{f_\alpha:\alpha \in A\}$ be a collection of maps on $X$ (to say $X_\alpha$). We say that $\{f_\alpha\}$ separates points from closed sets if whenever $x\in X$ and $x\notin B$, $B$ a closed set, it follows $f_\alpha(x)\notin {\rm cl}{f_\alpha(B)}$ for some index $\alpha$.

sos440

@PeterTamaroff That's just I have been doing them for a long time. My actual math ability is not so good... as you can see in my other answers.

Peter Tamaroff

@DavidWheeler Maybe I should say "for at least one".

David Wheeler

3:46 PM

ok, each $f_\alpha$ has a different co-domain?

Peter Tamaroff

@DavidWheeler Yes, say $X_\alpha$.

Not necessarily different though.

David Wheeler

sure, some of them might coincide, or even just overlap.

so f maps points outside of a closed set B to outside some closure of the image of B, for one of the collection.

Peter Tamaroff

@DavidWheeler Right.

Henning Makholm

I seem to have gotten a Mortarboard badge on meta! Even though it is defined as "Earned at least 200 reputation in a single day", and meta doesn't earn reputation at all.

Peter Tamaroff

@DavidWheeler ...at least one.

David Wheeler

3:49 PM

if it does it for one, it does it for at least one, sure ( didn't mean "precisely one")

Peter Tamaroff

@DavidWheeler Sorry, yes.

David Wheeler

so the topologies on X and the $X_\alpha$ are given

Peter Tamaroff

@DavidWheeler Yes.

OK, so the theorem is
**Theorem** . A collection of continuous functions $\{f_\alpha\}$ on $X$ separates points from closed sets *iff* the collection $$\mathscr B=\{f_\alpha^{-1}(O_\alpha):O_\alpha \text{ open in }X_\alpha\}$$ is a basis for the topology on $X$.

David Wheeler

ok, now what's the "blah blah blah" and is it: "if" or "iff"

ok, so you know the drill, start with the the basis part first.

Peter Tamaroff

@DavidWheeler Yes.

Assume that $\mathscr B$ is a basis.

Then every open set in $X$ is a union of basis elements.

Let $x\in X$.

David Wheeler

3:53 PM

and if x is not in B, x is in its complement

which is open

Peter Tamaroff

Let $x\notin B$ a closed set.

Then $x\in X\setminus B$, which is open.

David Wheeler

since the complement of B is open, it lies in "some" basic set.

Peter Tamaroff

Whence for some $\alpha$ we have $x\in f_\alpha^{-1}(O_\alpha)\subset X\setminus B$.

@DavidWheeler You mean it contains a basic set?

David Wheeler

every open set is a neighborhood of its points

Peter Tamaroff

@DavidWheeler Yes.

@DavidWheeler But I'm worried about the basic open sets now.

David Wheeler

3:56 PM

so there is a basic set containing x lying entirely in X\B.

and that basic set, is, as you wrote, a pre-image of some open set $O_\alpha \subset X_\alpha$

Peter Tamaroff

This means that $$x\notin X\setminus f_\alpha^{-1}(O_\alpha)$$, $$x\notin f_\alpha^{-1}(X_\alpha \setminus O_\alpha)$$

David Wheeler

so f(x) is in $O_\alpha$

Peter Tamaroff

@DavidWheeler OK, yes $f_\alpha(x) \in O_\alpha$

David Wheeler

yeah, i forgot the subscript

Peter Tamaroff

Then $f_\alpha(x)\notin X_\alpha\setminus O_\alpha$

But

David Wheeler

4:01 PM

now, ask yourself: is $f_\alpha(x) \in f_\alpha(B)$?

Peter Tamaroff

@DavidWheeler No, it isn't.

David Wheeler

ok, so it lies in an open set in $X_\alpha \setminus f_\alpha(B)$

Peter Tamaroff

@DavidWheeler Just stop there. We have $f_\alpha(B)=f_\alpha({\rm cl_X}B)\subset {\rm cl_{X_\alpha}}{f_\alpha(B)}$ by the continuity of the functions.

David Wheeler

so clearly $f_\alpha(x)$ lies outside of the closure we seek.

Peter Tamaroff

@DavidWheeler So one part is done.

Now suppose it separates points from closed sets:

David Wheeler

4:07 PM

the point isn't just that x is outside of B, its outside of B and "surrounded by an open set" that maps outside of $f_\alpha(B)$

Peter Tamaroff

Then for each $x\in X$ and $x\notin B$, for some $\alpha$ we have

@DavidWheeler OK.

$$f_\alpha(x)\notin {\rm cl}f_\alpha(B)$$

David Wheeler

ok, now let's suppose we have an open set U in the topology on X.

Peter Tamaroff

But by the continuity of the functions $f_\alpha(x)\notin f_\alpha({\rm cl} B)= f_\alpha(B)$

@DavidWheeler OK.

David Wheeler

then X\U is a closed set, right?

Peter Tamaroff

@DavidWheeler Yes, you don't have to ask me that.

=P

David Wheeler

4:10 PM

ok, pick x in U.

Peter Tamaroff

@DavidWheeler Done.

David Wheeler

we know that for some $\alpha$, $f_\alpha(x) \not \in \text{cl}f_\alpha(X\setminus U)$

Peter Tamaroff

@DavidWheeler Yes.

$$f_\alpha(x)\in f_\alpha(X\setminus B)=f_\alpha(O)$$, $O$ is open.

David Wheeler

let's call that closed set $V_\alpha$

Peter Tamaroff

@DavidWheeler OK.

David Wheeler

4:13 PM

then $X_\alpha \setminus V_\alpha$ is open

Peter Tamaroff

@DavidWheeler Yes.

David Wheeler

so its pre-image is open, and contains x.

Peter Tamaroff

@DavidWheeler Yes.

David Wheeler

hmm....that's not very useful

ok, a different approach.

same U, but now, let's take the interior of $f_\alpha(U)$

Peter Tamaroff

@DavidWheeler I was doing it. Could you let me?

David Wheeler

4:19 PM

this is non-empty, $f_\alpha(x)$ is in it.

alrighty...you see where its going, i think.

Peter Tamaroff

13 mins ago, by Peter Tamaroff

Now suppose it separates points from closed sets:

13 mins ago, by Peter Tamaroff

Then for each $x\in X$ and $x\notin B$, for some $\alpha$ we have

12 mins ago, by Peter Tamaroff

$$f_\alpha(x)\notin {\rm cl}f_\alpha(B)$$

12 mins ago, by Peter Tamaroff

But by the continuity of the functions $f_\alpha(x)\notin f_\alpha({\rm cl} B)= f_\alpha(B)$

David Wheeler

yes, but that O is awfully big

i think you need to take the intersection of the interior of $f_\alpha(U)$ with $X_\alpha \setminus \text{cl}(f_\alpha(B))$

Peter Tamaroff

@DavidWheeler We need to prove that given $x\in O$ an open set, $x\in f_\alpha^{-1}(O_\alpha)\subset O$

David Wheeler

then take the pre-image of that intersection, which will be an open set contained in U, that contains x.

which we can then recover U from, by taking the union over all x in U

Kannappan Sampath

4:47 PM

Bye folks. 8/13/'12.

sos440

4:57 PM

Goodbye~ It's 1:57 am here and I believe it's time for bed.

Old John

@sos440 Bye!

Mariano Suárez-Alvarez

I leave for a weekend and caos ensues

Old John

@MarianoSuárez-Alvarez Chaos? where?

Mariano Suárez-Alvarez

Dunno. My inbox, at least :-)

Old John

@MarianoSuárez-Alvarez Ah - you need more filters :)

Mariano Suárez-Alvarez

5:00 PM

Yeah...

I keep rediscovering that from time to time

I used to have the most complex procmailrc in record

until that hard drive died...

Old John

@MarianoSuárez-Alvarez I hate it when they do that :(

Mariano Suárez-Alvarez

indeed

I remember the sound of a washing machine in need of oil that it started making

shivers

I learned how to do backups about that time :-)

Old John

@MarianoSuárez-Alvarez Ah yes - I learned the hard way too, many years ago. Now I keep two backups, 1 in my home and 1 in a friends :)

Mariano Suárez-Alvarez

I wonder if with eeven more age I will get less amazed by the way people can experience things so differently... Jack's comment on the starbar to the point that «[He] rarely felt anyone was actually answering me. I was often just an excuse» is so remote from my personal experience!

Old John

@MarianoSuárez-Alvarez I was curious about that, but I have never posted on MO (yet) as I don't think any of my questions are "significant enough"

Mariano Suárez-Alvarez

5:13 PM

"significance" does not have anything to do with it

:-/

Old John

well - I feel that questions are more likely to get closed there

Mariano Suárez-Alvarez

sure they do

that's sort of natural, though

Old John

by "significant" I guess I mean "research level"

Mariano Suárez-Alvarez

that's very different :-)

Henning Makholm

@MarianoSuárez-Alvarez "significance", "importance", "sophistication", "powerful methods" ... apparently there are all kinds of ways to characterize the questions that are good enough for MO, and they are all wrong. But for all the wrongness there are still apparently some questions that some people want to have excised from MSE because the MO people are somehow uniquely deserving of getting to answer them.

Mariano Suárez-Alvarez

5:15 PM

I hve not read the whole thread, to be honest

but I cannot imagine anyone proposing that MSE users be banned from answering those questions on MO?

Old John

bye for now

Mariano Suárez-Alvarez

or using the verb deserve

Henning Makholm

@MarianoSuárez-Alvarez Closing the questions on MSE implicitly means that we ordinary peons don't get to answer them. The software won't accept answers to closed questions.

Mariano Suárez-Alvarez

no, it doesnot mean that

it has never meant anything remotely similar to that!

we move questions to Stats

or CSTheory

Henning Makholm

Shall we discuss the semantics of "means"? The fact is that the software does not accept answers to be posted after they are closed or migrated.

Mariano Suárez-Alvarez

5:19 PM

more or less 75% of the questions that have been moved to CS I could have answered here

Henning Makholm

@MarianoSuárez-Alvarez You don't expect me to deliver a defense for the closing of CS questions here, do you?

Mariano Suárez-Alvarez

I am not attacking anyone, in particular you

I don't expect you to do anything

I have lots of trouble getting inflamed with such matters, so I will just drop the matter

user19161

5:36 PM

Well, I see the MO and MSE discussion. I think there will always be doubt where one should post. This problem is not unique to this.If I have an Ubuntu question for example, I can post on Ubuntu, Superuser or Unix.

user19161

If I were the owner of the site, I would merge all the sites with the same topic into one. Then there will be no doubt, and people can always just look at the questions they are interested in and ignore the rest.

user19161

It does not take that much effort to manually filter out the questions one is interested in.

Henning Makholm

@JasperLoy Oh yes! It would be so much easier if everything was more integrated -- providing there was a good way to construct personal / subject-specific front pages that listed only things with the tags (plural!) one was interested in. As it is, it seems that the only way to follow more than one tag regularly is to view each tag's newest-question lists separately.

Jack Schmidt

@HenningMakholm ms.uky.edu/~jack/mse.html Recent questions from my tags is a combination of all your tags

(just drag the link to your toolbar, go to the normal front page, click the new button in your toolbar, and then you have a reasonable front page)

Peter Tamaroff

@JackSchmidt Jack, sorry to interrupt.

For each $n$, let $S_n=\{n,n+1,\dots,\}$. Then the basis $\mathscr B=\{B\in 2^{\Bbb N}:S_n\subset B :n\in N\}$ induces the cofinite topology on $\mathbb N$?

Jack Schmidt

5:50 PM

@PeterTamaroff I think so yes. Isn't $\mathscr{B}$ itself closed under unions and finite intersections? $\mathscr{B}$ seems to be the set of cofinite subsets of $\mathbb{N}$.

Peter Tamaroff

@JackSchmidt It is closed under unions and finite intersections, yes.

@JackSchmidt But, for example, Let $\{5,6,\dots\}-\{50\}$. How do we obtain that open set from the basis?

I mean, open set in the cofinite topology.

Jack Schmidt

$S_{51} \subset \{5,6,\ldots\}-\{50\}$, so $\{5,6,\ldots\}-\{50\} \in \mathscr{B}$.

Peter Tamaroff

@JackSchmidt Oh, sorry. I was thinking about the previous basis I wrote.

Jack Schmidt

(The $S_n$ by themselves are very broken; but allowing any subset that contains them fixes all the broken parts.)

Peter Tamaroff

@JackSchmidt Yes. So the open sets will be those containing at least one $S_n$, correct?

Jack Schmidt

5:55 PM

@PeterTamaroff exactly

Peter Tamaroff

@JackSchmidt Great. Now I have a (I think) more complicated question.

Do you happen to have a copy of Willards topology?

Jack Schmidt

At home, but not here

Peter Tamaroff

@JackSchmidt Oh. I have a question on families of functions that separate points, and separate points from closed sets.

@JackSchmidt Here

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$Mathematics$ Mathematics