Mathematics - 2012-05-16 (page 3 of 9)

t.b.

07:00

Self-guided boomerang missiles?

Matt N.

: )

Rajesh D

This and comments above it

Hi

I think i stumbled across a disappointing problem

t.b.

Apply a self-guided boomerang missile. That solves (almost) all problems you might have.

Rajesh D

These things don't work the way i was fantasizing

Lesson learned : never fantasize and simultaneously take it serious

Matt N.

Here's one for @BrianMScott.

t.b.

07:05

Actually Ben solved that problem about an hour ago.

Matt N.

I didn't know that.

Brian M. Scott

@MattN I’m writing right now.

Matt N.

@BrianMScott Good : )

robjohn

@Mariano when an answer is auto-marked as "low quality", and we disagree, are we supposed to mark it as an invalid flag? does that flag it to the mods anyway?

Rajesh D

@tb : did you see my comments link?

Matt N.

07:06

No surprise. Last time I answered a topology question I really had to run to beat you to clicking the post button. I know you're fast.

robjohn

@Bill I could have asked you, but I don't know if you've gotten any of these yet :-)

Matt N.

@tb These elections here are like elections IRL: I voted for robjohn and he didn't get elected.

Nimza

Hello everybody!

robjohn

@MattN So that's why I didn't get elected! :-D

Matt N.

@robjohn : D

Rajesh D

07:10

@robjoh : You can count me too with Matt

robjohn

@RajeshD Argh! anti-votes!! :-D

Matt N.

No comment.

Nimza

Can you advise me some literature on Riemannian manifolds please?

t.b.

@MattN doesn't necessarily imply intent.

@Nimza Lee

robjohn

@MattN can you roll that back?

Nimza

07:13

@tb and which book?

Matt N.

@robjohn Nah, he's added a paragraph at the bottom.

robjohn

@MattN at least correct the misspellings that were introduced.

Matt N.

@tb What?

t.b.

@Nimza that one

Nimza

@tb thank you very much!

robjohn

07:14

@tb Good pick!

Matt N.

@robjohn No, he can keep his typos that make him look stupid, I don't care. But feel free to correct it if it disturbs you : )

t.b.

@MattN if gargoyle thought about adding that paragraph and started editing before you made your edits he isn't necessarily notified of the changes, so he didn't necessarily undo them on purpose.

Rajesh D

after reading the book by sylvian nasar, just roughly half way through, I came to the conclusion that I cant do Mathematics, I am not insane...gee am i right on this one?

robjohn

@MattN I fixed it for the good of the site :-)

Matt N.

@robjohn Thanks : ) Problem solved.

@tb I see, I didn't know that.

robjohn

07:18

@RajeshD the book was able to make a psychological evaluation as well? that is some book! :-D

Matt N.

@tb But... I thought you didn't like Lee's books because they're too wordy and boring? Am I misremembering? : )

Rajesh D

@robjohn This one

t.b.

@RajeshD Nazar means the evil eye in Turkish.

@MattN says the person who recommended a Carrey movie...

robjohn

@RajeshD I wouldn't use that as a guide as to whether you can do math.

Rajesh D

@tb In Hindi : "bure nazar" bad glance

David Wheeler

07:26

although the archtype of the "mad genius" is a common one, the truth is: much of the progress made over the centuries is the result of plodding exploration, with the rare glimmer of inspiration from time to time.

Rajesh D

i am not interested in reading any further into it, I am done.

David Wheeler

it often appears to outsiders that giants cast such a long shadow over a field of knowledge, but closer inspection often reveals a finer web of cross-communication and dissemination of ideas.

t.b.

Unfortunately madness isn't sufficient, fortunately it isn't necessary for being good at math.

David Wallace

@tb How would any of us know?

Matt N.

@tb Ok. Got me. I'm actually still sorry for that.

David Wheeler

07:31

it was not uncommon in the 17th and 18th centuries for profound mathematical discoveries to be made by people who just did it in their spare time.

Benjamin Lim

@BrianMScott

David Wheeler

mental instability can give you an edge in making connections "normal" people might not...but has the drawback of...well, mental instability.

Brian M. Scott

@BenjaminLim Yo.

Benjamin Lim

Is the OP asking to prove that separability implies second countable in a metric space?

That's what I'm getting from him

t.b.

@MattN Hey, I didn't mean to complain... Anyway, yes I don't rate Lee's books as highly as some others here do, but they're fine books and definitely something I'd recommend to anybody who's probably new to the subject. Especially the Riemannian manifolds one.

Brian M. Scott

07:36

@BenjaminLim No. He’s asking whether separability implies that for every base $\mathscr{B}$, countable or not, it’s true that every non-empty open set is the union of just countably many members of $\mathscr{B}$.

Benjamin Lim

ah ok

Brian M. Scott

It’s a nice little problem.

Benjamin Lim

I think I misunderstood his question. Shall I delete my answer?

Brian M. Scott

@BenjaminLim You probably might as well; it really doesn’t answer the question, and several people have now noticed this.

Benjamin Lim

ok

@BrianMScott I think because I was solving that problem this afternoon somehow I assumed the OP was asking the same question :D

Matt N.

07:38

@tb So you... actually read all of the trilogy?

Brian M. Scott

@BenjaminLim Yes, that thought had occurred to me, too. :-)

Matt N.

You're full of surprises : )

t.b.

@MattN I enjoyed the Riemannian manifolds one very much. I was less excited about the smooth manifolds and I only skimmed the topological manifolds.

Benjamin Lim

@BrianMScott hahahaha It's like everytime I solve some maths problem whenever I see another similar problem immediately I try to use methods from the previous problem on the new problem :D

Brian M. Scott

@BenjaminLim That’s a natural tendency; up to a point it’s probably even a good one.

Benjamin Lim

07:40

But I'm interested about this result that if we have a separable space

that is a metric space

the first question then is that is every basis countable

Brian M. Scott

@BenjaminLim No, it can have lots of uncountable bases.

Matt N.

heads out to read Brian's answer

t.b.

@BenjaminLim No, the topology itself is a basis. Rarely countable.

Benjamin Lim

ok

Brian M. Scott

But no matter what base you pick, every non-empty open set can be written as a union of just countably many members of that base.

Benjamin Lim

07:41

yeah

I'm looking at munkres for such a result, can't find it

Brian M. Scott

@MattN It actually took me a little while to work out the second part.

t.b.

@BenjaminLim Lindelöf (and the hereditary cousin) is the magic word.

Benjamin Lim

I heard

Brian M. Scott

@BenjaminLim I doubt that it’s there, unless it’s an exercise.

Matt N.

@BrianMScott Yes, I noticed. I was wondering what was taking you so long!

Benjamin Lim

07:43

It's gettin' hot in here, so take off all your clothes....

Brian M. Scott

@MattN Tried a couple of bad (even silly) approaches first.

@BenjaminLim Most of mine are off! (Bet you didn’t need to know that.)

Benjamin Lim

@BrianMScott It's from this song: youtube.com/watch?v=M-qN6TCY85c

Matt N.

@BenjaminLim Just remembered that you challenged me (topology). Since I'm home sick with flu I might have a go at it today. (didn't have time until now, term's been busy)

Brian M. Scott

I still like the idea of self-guided boomerang missiles.

Benjamin Lim

@MattN Produce an example in a general topological space to show that if we have a countable collection of non-empty compact sets satisfying the finite intersection property, their infinite intersection is empty.

Matt N.

07:45

@BrianMScott To nuke the flu viruses? : D

Brian M. Scott

Not a bad idea, that.

Benjamin Lim

@BrianMScott Actually I think the result you proved about Lindelöfness is very similar to what we discussed earlier today.

I mean if we delete the word lindelof I could probably have proved it.

Brian M. Scott

@BenjaminLim Do you mean an example showing that this is possible? Because it obviously doesn’t always happen.

t.b.

I still don't understand the Sorgenfrey hint...

Brian M. Scott

@MattN Have you tried climbing into the microwave?

Matt N.

07:47

@BrianMScott We don't have one.

I could alternatively try sitting on the bbq...

Brian M. Scott

@MattN Hm. That does make it a bit difficult.

t.b.

@BrianMScott that's only for drying pets...

Brian M. Scott

@tb Not for nuking flu viruses?

Rajesh D

sometimes i wonder i am very incompetent in math, proof is I have asked 95* questions and answered none of other people's questions. My God even teenagers are answering questions very well...darn it sucks, I want to know the reason why?

t.b.

@BrianMScott that might be a slightly longer-term side-effect.

Brian M. Scott

07:50

@RajeshD No, that’s an indication that there are some youngsters here who are exceptionally knowledgeable in some areas of math.

Rajesh D

Yeah and the fact is i am nowhere near to any of you guys here! Is that the interpretation of yours?

Benjamin Lim

@BrianMScott I meant if we don't call lindelof but every open cover having a countable subcover

Brian M. Scott

@RajeshD Honestly? I mostly don’t think about such things, beyond trying to remember who’s good at what, in case I want to ask questions.

user19161

@RajeshD It's Sylvia Nasar, not sylvian nasar by the way. And I read that book twice from start to end.

Brian M. Scott

A lot depends on how early one got really interested in math, and on the resources that were available then.

Benjamin Lim

07:54

@BrianMScott I have to say that topology has a lot of weird monsters lying around......

Brian M. Scott

@BenjaminLim That’s one reason I like it. Some people like the nice mathematical objects; I tend to like the pathological ones.

user19161

@BenjaminLim Hey why delete that message? It was pretty funny!

Benjamin Lim

@BrianMScott I have to say the proof of the result was very very close to what we talked about this afternoon. Perhaps if I had looked closer I could have proved it myself. Sigh.......

@ClarkKent Do you know how old I am?

Brian M. Scott

It does help to realize what’s being asked ...

Benjamin Lim

@BrianMScott Maybe I should go back to ritalin.....

user19161

07:56

@BenjaminLim Did you not say you were a teen?

Benjamin Lim

I meant my exact age

@ClarkKent Deal: I'll tell you mine you tell me yours

@ClarkKent How old are you?

user19161

@BenjaminLim I would like to keep it a secret for now.

Benjamin Lim

ok. Can you delete the comment above about my exact age?

user19161

@BenjaminLim Done.

Brian M. Scott

@BenjaminLim You’re half a Mariano. :-)

Benjamin Lim

07:57

@BrianMScott he is 38?

wow ok.

Brian M. Scott

So he said, earlier today.

Benjamin Lim

@BrianMScott There seems to be so much out there about topology.

Brian M. Scott

Just a kid, he is.

Benjamin Lim

Like a wild jungle out there waiting to be explored

@MattN Did you come up with that example? Hint: Your space has to be weaker than $T_2$.

@MattN On any set you can always put at least two topologies.

Brian M. Scott

But there’s a very nice $T_1$ example.

user19161

07:59

So @ben have you decided on what to read for your analysis?

Matt N.

@BenjaminLim You sit back and relax, young grasshopper. I'm still thinking about Brian's answer. So I haven't even read your previous comment in chat.

Benjamin Lim

@BrianMScott My example is really stupid.

@MattN Why am I a grasshopper????

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$Mathematics$ Mathematics