Mathematics - 2011-12-13 (page 2 of 3)

Dylan Moreland

05:00

It's interesting to see Peter May of all people telling folks to come back down to earth.

Everything's relative, I guess.

J. M.

05:17

Hey @Dylan, look who's here...

Dylan Moreland

Well that's exciting.

I've been forced to look in Bourbaki recently for certain things. I had always assumed that the books would be very organized but it turns out that's not true.

J. M.

What did you see?

Dylan Moreland

Harry always raved about these things so it's a little disappointing.

t.b.

@DylanMoreland Really? It probably depends on how much you got used to them.

Srivatsan

who's Harry?

t.b.

05:26

fpqc, I guess

Dylan Moreland

I forget his handle on here. It was a bunch of numbers.

t.b.

So I guessed right. His account is deleted.

J. M.

@DylanMoreland 97832123

Dylan Moreland

Do those numbers have any meaning?

J. M.

No idea why Harry chose those.

t.b.

05:29

Type them on the numerical keypad.

J. M.

@tb His meta account went first. His main account was nuked about a week later.

Rajesh D

hi @tb @jm @Dylan

t.b.

Hi, Rajesh

J. M.

Hey Raj.

Dylan Moreland

Hey there.

Ah, he's gone. I think he just clicks on here accidentally and then it leaves him up for a while.

Rajesh D

05:30

I have a question and would like to know if its worth asking on M.SE after your suggestions

Dylan Moreland

But for the record I'm working super hard always.

t.b.

@DylanMoreland What book by Bourbaki did you look at?

@RajeshD shoot

Dylan Moreland

@tb I've needed stuff out of a few of them today. Topological vector spaces, commutative algebra, some of the algebra books that aren't translated...

Just thinking aloud, really. Nothing serious.

t.b.

Ah, okay. I think you need a while to immerse yourself into the style. But after that, things become quite easy to locate. There are also searchable versions lying around on the 'Net, those are pretty useful sometimes.

Dylan Moreland

I was going to answer this class field theory question today and then Matt answered it with almost exactly what I would have said. I sometimes wonder if I have any thoughts or opinions of my own in these matters.

@tb Ah I was just looking up references and some of this stuff isn't really written down elsewhere, as far as I can tell. I don't think I want to become immersed just yet.

Rajesh D

05:35

I need a list of examples for a type of set of functions which is closed under addition, multiplication and convolution . One example of a set is the set of $\mathcal{L}^p$ functions. I want to know all other examples of such sets .

BTW is it some ground hog day today ?

i can see an icon here

Dylan Moreland

It's a snowman, I think.

t.b.

Or a ground hog with a cylinder

Rajesh D

it can be seen only when pinged !

t.b.

@RajeshD here we go

Rajesh D

thanks tb

Srivatsan

05:38

@Srivatsan Wonder if I can see the snowman now.

t.b.

@Srivatsan can you?

Rajesh D

i just wanted to know if this question is non trivial before asking on the main site

@Rajesh

nope

Srivatsan

@tb Yes, thanks. I was wondering if I can ping myself.

Rajesh D

sorry

it doesnot work that way

pinging is a binary operation

Dylan Moreland

Trivial stuff is asked on the main site all the time.

:)

Your question sounds kind of... broad? But it doesn't sound silly or trivial or anything.

t.b.

05:40

@RajeshD It is somewhat non-trivial. The standard answers would involve $L^1$, $C^k$, $\mathscr{D}$, $\mathscr{S}$. The $L^p$-spaces aren't closed under convolution, by the way (unless you're working on the unit circle/tori).

Rajesh D

okay i thought whether it is trivially trivial ?

t.b.

For me the question is more "What do you want to do with it?"

Rajesh D

okay.........may be $L^2$ are

t.b.

No they aren't

... In other words: I'd prefer a more focused question.

Asaf Karagila

Good morning.

t.b.

05:46

Morning, Asaf

Srivatsan

Hi Asaf

Rajesh D

What a relief ! the Set theorist is here !

hi @Asaf

Asaf Karagila

What's up?

t.b.

You didn't say "Top of the morrow and whatnot"

J. M.

Indubitably so, t.b.

Rajesh D

05:47

it from the movie Angels and Demons....with symboligist replaces by set theorist

Asaf Karagila

Yes. I did not say that because I didn't say that.

There is something somewhat sad that Gerry Myerson and Robert Israel always write one liners and end up on the "low quality posts" list.

J. M.

@AsafKaragila Well the software doesn't believe in the "brevity is the soul of wit" bit.

Asaf Karagila

@tb >:-]

J. M.

Then again, it's apparently pretty common in SO to post oneliners, which as it turns out are mostly crap.

Asaf Karagila

Man, that past few days seem active on set-theory, I might actually hit 20k before getting that Generalist badge.

J. M.

05:53

Speaking of "Generalist"... we've a pretty nice clique.

David Speyer and Phira are particularly impressive.

Asaf Karagila

Indeed.

Srivatsan

@JM how so?

J. M.

@Srivatsan Compare their rep to the 38 other people... ;)

Asaf Karagila

Oh shoo, [set-theory] is being pushed down from the top 40 tags. My journey towards a Generalist is getting longer by the day! :-P

Srivatsan

@JM Oh, I thought of that, but dismissed that possibility because I assumed Chandrasekhar was still is less than 10k =)

J. M.

05:57

anon was impressive himself; IIRC he got Generalist before hitting 10k.

Asaf Karagila

Yeah.

Arturo would have got it before 10k if there was a Generalist badge before he got to 10k ;-)

Srivatsan

@JM Likely, considering he is 10k+1 right now :)

t.b.

J. M.

Bah, what's one point? :D

Asaf Karagila

Mod Tools.

J. M.

06:00

Besides, he's got quite a lot more questions floating around that got disassociated from him...

Asaf Karagila

@JM I don't like his questions, and many times his answers too. Also, he got that same thing like TG where he keeps calling everyone "sir" and whatnot.

J. M.

@AsafKaragila At least he got better after about two or so suspensions...

Okay, "slightly".

Asaf Karagila

@JM So you say there's still hope? Perhaps the improvement is $1/n$ so after an infinite number of suspensions he'll be alright?

Srivatsan

J. M.

I don't have good asymptotic estimates of this "improvement", sadly. ;)

t.b.

06:06

@Srivatsan well, I just had to temporarily shift that down to 9999 for taking that screen shot

Benjamin Lim

Hi

t.b.

Hi Ben

Benjamin Lim

the master is around :)

Asaf Karagila

Yes, I am.

J. M.

@AsafKaragila =))

Benjamin Lim

06:08

@AsafKaragila I did not mention explicitly who the master was

J. M.

@BenjaminLim He'll assume it was him anyway.

Asaf Karagila

@BenjaminLim No, but I did.

t.b.

Why does this have a vote for deletion?

OP I guess

Asaf Karagila

@tb My bad, sorry.

I was quick on the draw ;-)

Benjamin Lim

I am doing some problems in Rudin and he asks if there exists a non-empty perfect set of R that contains no rational points

Asaf Karagila

06:09

I am going to wash the dishes, so I may find a clean cup for something to drink.

Benjamin Lim

I think this is not possible because the rationals are dense in R

t.b.

@BenjaminLim yes, there is.

Benjamin Lim

I know, the example given uses measure theory which I don't know

t.b.

Seen this thread?

Benjamin Lim

ah thanks

J. M.

06:14

I'm off to the supermarket. See you guys in a bit.

t.b.

See you later

Benjamin Lim

@JM to buy balut?

I have to go now, goodbye

teatime :)

see you @tb

t.b.

See you @Ben

t.b.

06:28

Do we really need elementary-proof?

What's supposed to be tagged that way?

Srivatsan

I don't like that tag. I vote to delete it. =)

t.b.

I vote to close as subjective and argumentative

Ramana Venkata

Can somebody explain this statement
"A metric and its corresponding standard bounded metric induce the same topology because the collections of e-balls with e<1 under these two metrics are the same collection."

t.b.

Well, a set is open if it contains a ball around each of its points. Show that every ball in the original metric contains is open with respect to the standard bounded metric and vice versa.

If you think what you need to do in order to prove that, you'll see that this boils down exactly to the statement you posted.

Ramana Venkata

Yeah Understood thanks...

t.b.

06:41

@Srivatsan could you please change the tag of the post you just edited to (real-analysis) and (analysis). I wouldn't count that as (functional-analysis).

Asaf Karagila

@Srivatsan @tb I hate that now even moderators cannot delete tags. That's a bad thing.

t.b.

But empty tags get eliminated once a day, so it's not that bad. I'm not a fan of how the tagging system is organized anyway, but I'm repeating myself.

Srivatsan

@RamanaVenkata Another way of thinking about this is: in any metric space, the collection $\mathcal B = \{ B(x, \frac1n) \mid x \in X, n \in \mathbb Z_{\gt 0} \}$ is a basis. Notice that a metric and its standard bounded metric have the same basis, which means that they are equivalent topologically.

I hope you have installed the MathJax bookmarklet, so that the TeX will be rendered nicely.

Asaf Karagila

@Srivatsan $\mathbb Z_{>0}$?? I thought you had your notational nightmare of $\mathbb N$ and $\mathbf N$ and $\mathscr N$ and whatnot...

Srivatsan

@AsafKaragila Come on, you seriously thought I would use $\mathbb N$ and $\mathbf N$ to mean different things?

Ramana Venkata

06:45

No I haven't installed Can you tell how install it??

Srivatsan

@RamanaVenkata Check this answer: meta.math.stackexchange.com/a/3297/13425

Asaf Karagila

@Srivatsan Well, now that I think about it you are a computer theorist... :-)

@RamanaVenkata There is a pinned message on the top of the starred list with 15 stars by its side.

You may want to check the link there :-)

Srivatsan

@AsafKaragila I would've used $\mathbb N$ here (although usually it includes $0$), but I didn't -- just to avoid comments on me being a computer scientist and all... =)

Asaf Karagila

Sure ;-)

So, are we killing [elementary-proof]?

Rajesh D

@tb : Is it ok to go ahead and post the question or are you very particular about it ?

Asaf Karagila

06:54

There. It's done.

I killed him.

Now to go groceries shopping, ciao.

Srivatsan

ciao, Asaf

t.b.

@RajeshD As I said, I'm not particularly thrilled, because I don't see the point, but please, go ahead, I'm not standing in your way.

Bye, Asaf.

N3buchadnezzar

07:18

Exam in 45 minutes

Rajesh D

@tb : may be i should be able to tell why am I asking this question, to sound better, but i do not have anything interesting even to myself, but curious to gather some examples, and i have one example in mind......and want to know if i have found some rare diamond....i do not know if its a good manners but considering me a non professional it is ok

Srivatsan

@RajeshD - I don't understand this comment at all... =)

Rajesh D

there is a context if you could look it up an hour back or so

i had asked a question as to whether its worth asking it on main site

Srivatsan

@RajeshD Well, I think I do know the context (may be I don't know it completely, but I know what you're talking about).

Rajesh D

wait a bit @Sri

Srivatsan

07:22

er, sorry!

t.b.

@N3buchadnezzar good luck, then!

Rajesh D

it is

I need a list of examples for a type of set of functions which is closed under addition, multiplication and convolution . One example of a set is the set of $\mathcal{L}^p$ functions. I want to know all other examples of such sets .

@Sri

Srivatsan

And I told you I know that you were talking about this =)

@N3buchadnezzar All the best. Do well.

t.b.

@RajeshD there's no chance to know them all! And as I said, $L^p$ is not closed under convolutions.

Rajesh D

ok

@tb : could you express $\mathscr{D}$, $\mathscr{S}$ in words so that i could look it jup on wiki ?

t.b.

07:25

smooth functions with compact support, Schwartz functions

Rajesh D

ok

bumps

why my earlier post is not visible to me

but @tb was able to reply it

could you express $\mathscr{D}$, $\mathscr{S}$ in words so that i could look it jup on wiki ?

@tb ok got it

Srivatsan

[We both can see your comment -- both the times.]

Rajesh D

got it...there could have been an interruption in my connection

i had to try several times

t.b.

@RajeshD $\mathscr{D}$ : smooth functions with compact support, $\mathscr{S}$: Schwartz functions

Rajesh D

i am not able to get what is quote ?

what is it ?

t.b.

07:30

I edited my comment

Rajesh D

got it...thanks tb

ok

i wonder if there are any weird and not particularly famous examples ? (to put it in a non mathematical way)

would this line be a good question for m.se ?

@tb

t.b.

Well, you can take any collection of, say, $L^1$-functions and look at the space generated by them under addition and convolution. Most of the time you won't get anything famous.

very funny... TheoBromine and Giggle :/

Srivatsan

07:48

@tb I'll pass on that one. =)

I find it ridiculous when the contents page is omitted from the book preview. =/

t.b.

@Srivatsan they're working hard on making books.google less and less useful from day to day...

4

Srivatsan

I couldn't see the pages 248-251 either.

t.b.

Try changing .com to .ch or .ca for example. Sometimes they can still be fooled.

Srivatsan

@tb They did get fooled =)

Btw, what does the banner say for you? This one: math.stackexchange.com/questions/80649

t.b.

@Srivatsan you mean the bounty? ended 25 mins ago, grace period ends in 23 hours

Srivatsan

07:53

@tb Oh, ok fine. Thanks.

t.b.

I'm really not a fan of all these petty edits Zev's making recently. Come on, changing a V into $V$ is worth bumping such a silly question?

Srivatsan

=)

@tb Well, if the OP already knows that the answer is $V$ itself, then it's even sillier.

I guess the comment look better with that edit =)

t.b.

I left a comment at Zev's answer on meta.

Srivatsan

Wow, the Hilbert Cohn-Vossen book looks quite interesting to me.

@tb Thanks for that. Let's see what happens now

t.b.

It's a great book.

Rajesh D

08:03

@t.b. : well I am stumped !

t.b.

stumped?

Rajesh D

my question was no big deal

its a form of dismissal in cricket

Srivatsan

@RajeshD Yes, I too think tb will make a good wicketkeeper.

=)

Rajesh D

Stump (cricket)

Stump is a term used in the sport of cricket where it has three different meanings: # part of the wicket # a manner of dismissing a batsman # the end of the day's play ("stumps"). Part of the wicket The stumps are three vertical posts which support two bails. The stumps and bails are usually made of wood, and together form a wicket at each end of the pitch. The overall width of each wicket is 9 inches (22.9 cm). Each stump is 28 inches (71.1 cm) tall with maximum and minimum diameters of 1 inches (3.81 cm) and 1 inches (3.49 cm). They have a spike at o...

i mean the second one

t.b.

Okay, got it. I'm not really into watching any kind of sports (and non-commonwealthers don't even know the first thing about cricket), so it's not a particularly good idea to talk to me in specialized language :) By the way, when I hear "I'm stumped" I interpret this as "I'm completely lost".

Srivatsan

08:09

@tb I thought one could be stumped by the beauty of some X. Is that correct usage or no? I thought it was correct, but several dictionaries seem to think otherwise.

I find these meanings:
- to nonplus, embarrass, or render completely at a loss: _This riddle stumps me_.
- to challenge or dare to do something.

t.b.

@Srivatsan You're asking me about English usage? Oh, well... I never heard that, I always had this negative connotation of total bewilderment. I'm baffled, I'm perplexed, completely out of my depth.

Zev's already replied

Srivatsan

@tb Well, from what I understand, you speak English as well as -- if not better -- than me. So I don't see why not ask you... =)

t.b.

Here's the first meaning of the verb *stump* from my Oxford Dictionary of American English: (usu. be stumped) (of a question or problem) be too hard for; baffle : education chiefs were stumped by some of the exam questions.
• ( be stumped) be at a loss; be unable to work out what to do or say : detectives are stumped for a reason for the attack.

@Srivatsan Thanks for the compliment :)

Srivatsan

@tb Yes, and that matches the entries I posted as well (see my comment 4-5 posts before this)

@tb Well, although I don't know how you speak =)

t.b.

@Srivatsan I saw it. Then there's also:

2 [ intrans. ] walk stiffly and noisily : he stumped away on short thick legs.
3 travel around (a district) making political speeches : there is no chance that he will be well enough to stump the country | [ intrans. ] the two men had come to the city to stump for the presidential candidate.
4 use a stump on (a drawing, line, etc.).

Rajesh D

08:19

math people prefer texting over voice chat I wonder

t.b.

@Srivatsan By the way, don't you have OS X? You should have the dictionary app containing all this info. It's got a handy dashboard widget (in fact the only reason I use the dashboard at all)

@RajeshD I honestly don't know. I tend to use the phone or Skype with my friends and co-workers.

Srivatsan

@tb well, I almost never use the dashboard these days.

t.b.

@Srivatsan as I said, the only reason I use it is for the dictionary/thesaurus. There's a word trainer I use from time to time, but I prefer the full app for that.

Apparently someone found the Klein 4 group question interesting...

Srivatsan

@tb Why? One more vote?

t.b.

one more vote for both question and answer.

I wonder why I'm getting so many upvotes for my no continuous bijection from (0,1) to [0,1] answer these days.

Rajesh D

08:36

link ?

Srivatsan

@tb Do you want to make it a nice 50?

Rajesh D

please

t.b.

@RajeshD here

Srivatsan

there's a minor edit suggestion... Wonder whether to reject it.

The question is too old and it's a dup.

t.b.

I rejected it

Jonas Teuwen

08:45

Good morning.

Srivatsan

@JonasTeuwen Stalk the devil in the main site and he doth appear.

Hi Jonas

t.b.

Morning, @Jonas

@Srivatsan your turn

I think we could safely close this one

Srivatsan

@tb Perhaps @Jonas can execute the question?

t.b.

@ZhenLin speaking of which

@Srivatsan I think he was already vote number 3.

Srivatsan

Oh, a'right.

t.b.

08:59

Whoever programmed those snowflakes for that blog I just linked to deserves to be spanked for a whole day. The darn thing eats up 40% of one of my CPUs...

Srivatsan

That's hilarious. =)

Why isn't this a dup?

t.b.

@Srivatsan No idea. It seems to be one in my book. Maybe J.M. didn't want to have the question closed immediately for a newbie.

@Srivatsan Could you capitalize the names in the title of the post you just edited, please?

Srivatsan

Done. Thanks.

robjohn

Hey all.

t.b.

Hey robjohn

Srivatsan

09:11

Hi newguy. =)

robjohn

@Srivatsan :-)

@Srivatsan I see there is a grace period for bounties. I guess I missed that fact.

Srivatsan

Glad to be of help =)

robjohn

@Srivatsan Is it late night for you or early morning?

that is, are you still up or just up?

Rajesh D

hi @rob

GM

Srivatsan

@robjohn Yes, figured that. Let's say that the night is still young. =)

[I don't know from whom I picked up that phrase; I find it fascinating for some reason.]

robjohn

09:16

@RajeshD Hello, anything interesting today so far?

Matt

Good morning everyone.

Rajesh D

hmm......i wish i'd know what you mean.....but nothin interesting as yet

robjohn

@Matt Good morning.

Srivatsan

@Matt hi Matt.

t.b.

Morning, Matt

Rajesh D

09:17

hi @Matt

robjohn

@RajeshD sometimes interesting things come up and sometimes things are mundane...

Srivatsan

@robjohn I'm up, doing quite a bit of nothing. I just finished watching a movie... =)

robjohn

@Srivatsan which movie? if you don't mind :-)

Srivatsan

@robjohn One second, let me check the title.

Rajesh D

the man from nowhere ?

or a Tamil one ?

Matt

09:20

@RajeshD That was quite good!

Srivatsan

@robjohn Sunday Bloody Sunday.

Rajesh D

@Matt they are making a local version of it here in telugu named Businessman

eager to watch it

robjohn

@Srivatsan Ah, I think I've seen that. About a Super Bowl (or some football game)?

Srivatsan

@RajeshD I'm yet to watch this one. Netflix keeps recommending it. I was skeptical of it. If it's good, I can watch it some day.

@robjohn Far from it =)

robjohn

Perhaps I am thinking of another.

@Srivatsan I'll have to find what I am thinking of...

Rajesh D

09:22

@Sri : are you aware that netflix uses a bloody algorithm to recommend movies ?

Matt

@RajeshD I'd like to watch A peck on the cheek again, I thought it was really good at the time but now I can't even remember what it was about.

t.b.

@robjohn Any given sunday

Srivatsan

@RajeshD How many died during the run of the algorithm? :=)

@RajeshD On a serious note, what do you mean?

robjohn

@Srivatsan I was thinking of Black Sunday

Rajesh D

it grabs user ratings and what they had rated other movies before giving it

Srivatsan

09:25

@robjohn Israeli anti-terrorist agency and Super bowl in a single movie? No, thanks. =)

Rajesh D

i am off for a while.....c u guys....bye

Matt

Bye Rajesh!

Asaf Karagila

Top of the noon to you. Cheers too!

robjohn

@RajeshD See you when you get back!

t.b.

@AsafKaragila ...and whatnot

bye Rajesh

Asaf Karagila

09:27

@tb No, no whatnots today ;-)

t.b.

Glad to hear that!

Srivatsan

Bye Rajesh.

Asaf Karagila

Also, a quick beer before the class.

Srivatsan

Afternoon, Asaf.

Asaf Karagila

After? It's just 11:30 :-)

Yay. I regained a point after a flagged downvote was deleted. I am going to wait until I have 19,999 and then recalc :-D

Srivatsan

09:30

@AsafKaragila I hope there are no surprises in store for you. "Asaf, your new rep is 19994."

Asaf Karagila

@Srivatsan Don't worry. We'll take care of that when we get there ;-)

Dammit, I wanted to try and prove something about vector spaces but I forgot what it was.

t.b.

Well, prove it, then you'll remember the statement when you get to the end...

Asaf Karagila

It was something about endomorphisms with a nontrivial kernel... or something like that maybe?

Something to do with totally indecomposable spaces...

It has to do with the proof I gave to the Lauchli generalization, only in a general context independent of the model construction.

It's amusing, isn't it? My M.Sc. thesis started from a question on math.SE :-)

@Matt you here?

t.b.

Definitely better than the situation in which it stopped with a question on math.SE :)

Asaf Karagila

@tb Heh, yeah. I agree. I hope to answer my own question from MathOverflow though.

Indecomposable vector spaces and AC

Srivatsan

09:41

Duck. I just approved an edit to a really old post.

Asaf Karagila

s/D/F :-)

Matt

@AsafKaragila Was having a shower. What's up?

Srivatsan

@AsafKaragila I leave that to your imagination.

Asaf Karagila

Oh nothing.

@Srivatsan Sure you do. It is well known that I am "Koenig Obvious" ;-)

Matt

@AsafKaragila Dunno better not find out and delete that. : )

There is already one person too many that know.

Asaf Karagila

09:46

You may want to delete all those messages, by the by.

Matt

:2697032 No, someone I "ignore".

Jonas Teuwen

@AsafKaragila MSc theses suck. You have to pay to be able to write them.

Matt

Every time I read Kowalski's measure theory notes I'm surprised again at just how good they are.

Srivatsan

No points for guessing the plural of Jonas though.

Asaf Karagila

I have to go to class now, see you in a couple of hours.

Jonas Teuwen

09:54

@Srivatsan 8-).

@Matt Is that a short course?

Matt

@JonasTeuwen Yes and then you get zero supervision because the PhD student supervising you just defended their thesis and went on to making their own company and no longer gives a crap.

@JonasTeuwen One semester. Is that short?

Jonas Teuwen

@Matt Hmm, depends on how deep it goes. I think it is okay.

@Matt Here we get supervision by professors 8-).

Wow it is 13/12/11 today!

Matt

Lucky you.

robjohn

@AsafKaragila König Oblivious?

Matt

In my non-existent, ideal world there are no lectures and Kowalski writes all the notes.

Srivatsan

09:58

@JonasTeuwen Sad: here they write it 12/13/11.

Transcript for

$Mathematics$ Mathematics