@tb Oh, I see. I get it. I have seen this word used in Math texts--top-down/bottom-up approaches to a problem-- and all that. Now I understand it better.

Thank you.

I think it might be good to add the two points we discussed here.

:)

Sorry, you were right!

Hmph, why would I get "Aw! Snap!" every time I write an answer!

"In recognition of your contributions to Stack Overflow, we’d like to invite you to create a professional profile on Stack Overflow Careers 2.0." What a hilarious thing to write.

huh? is this the kind of spam you get if you give them your actual email address?

Hmm, I fail to appreciate the fun?

@tb Apparently. The first time I get spammed by SO though. I'm almost offended by it. But also slightly amused.

@KannappanSampath They just want me to join as many of their sites as possible. So they try to suck up.

I see.

Hi @DavideGiraudo

Hi guys

hey.

I'm in lazy and sleepy mode. I should read the proof of the identity theorem.

Probably you are in a wrong frame to do that, no?

Yes.

I am confused now. Then, why would you do that?

Because I shouldn't sit around all day and do nothing.

Well, I have nothing but this smiley to reply with: :-!

Not sure what it means : D

I don't smoke.

That is not that!

I neither understand what that means and I use it interchangeably for what I said before! :)

Hi @Matt : you are not alone ! I've been doing exactly the same and thinking exactly the same

not about Identity theorem though

That's bad.

I think I'll be back later.

bye

What "kind" of math?

That indeed makes a difference, IMO.

I haven't taken back my statement...just that i don't want to make it public

:4135077 Well, teaching them group theory would be immediately useful, if immediate is defined as 6 months, say, for a 12th grade student. Teaching the routine stuff will be immediately useful too.

@Kannappan : like the basic stuff....limit sequesnces, co-ordinate geometry, derivatives, probability, combinatorics geometry etc.,

Hmm, we are soon heading to off topic discussions. ^

@RajeshD Looks fine to me. : )

BTW, Will, why is that so black? To tell SkullRobtroll that dark can be real dark?

@Kannappan : a lot students are stuggling while trying to get through the entrance exams...I just like to make their experience with it not only successful but also a good learning experience and probably make them interested in the subject

@RajeshD Hey, are you going to help with Entrance exam things?

@Kannappan : its not the way as it looks

there are a lot of people already doing that....and thats not my goal

Exactly. But, then you may want to pick and choose your audience whenever you get to. :)

I should rest now to get well soon. Bye.

k bye

@WillHunting Hi

yes , i have some idea....trying ways to get an opportunity

@WillHunting You too!

hello all

hi

Hi

Whats up @Robjohn : How is the Easter?

@RajeshD It is just early Good Friday here. How is it for you? the weekend that is

it is ok

about 4:17 in the afternoon?

exactly

Does the 30 minute differential mean you don't go on Daylight Time?

been sitting in front of the comp the whole day so far

no

I don't even know what is daylight time means

I've been scratching at a piece of pulverized wood with a bit of cylindrical clay.

oops no clue what it is

using pencil and paper

making a statue ?

Oh

Proving $\displaystyle\sum_{k=1}^\infty\frac{\Gamma(k)^2}{\Gamma(2k+1)}(2x)^{2k}=[\sin^{-1}(x)]^2$

times are hard, there is no denying that.

@WillHunting thanks. It seems so archaic these days.

hi

huh?

sheesh

@MattN In your recent answer, the set bracket for the first polynomial example is missing.

@KannappanSampath Thanks. Only just woke up. : )

And we have a major crisis here: we've run out of coffee and the shops are closed.

Not sure how to deal with the situation.

Seems to be crisis weekend : D

Holy.... That's bad. But I wish some cafe is open at this time?

Sure. But we don't want to go out. : )

Then, you may want to look up to the heavens. :)

And yesterday apparently I had left the door open when I left in the morning and when I came home in the evening the girlfriend had left it open (didn't notice) and one of the cats was missing. (Only two of them go out, the one that doesn't was missing)

I wonder what happens next.

Huh, strange!

Yeah, not so. I was in a right hurry yesterday morning.

So I had to run. But I forgot something so I had to run back... you get the idea.

Yes, I get it. But, the last message is strange in many aspects, but OK. I am going back to take some rest.

@KannappanSampath Rest well!

(I think it's perfectly normal : ))

@Rajesh: Here is the proof I was mentioning eariler.

Darn! he left :-(

people tend to leave quickly these days :)

@tb It probably has to do with the crappy management here these days ;-)

@robjohn You should increase your nonsense posting, but it's gonna be hard to match Asaf :)

@tb I need to start commenting on female parental units.

@robjohn please don't!

@tb They probably leave when they see this.

:)

@MattN Is that worse than my gravatar?

@robjohn Yes.

Much worse.

I have to make mine grumpier then...

hum. I just answered a question on Grothendieck spaces to a guy who can't prove that $\ell^1$ is dense in $c_0$... :/

@robjohn In fact, it's un-bear-able.

A picture is probably not worth a thousand words...

(Couldn't resist. Now I'll stop.)

A Picture is probably not worth a thousand words. ^

@MattN Please Don't! Stop! :-)

@KannappanSampath Do you use Omnigraffle?

Hmm, no. Why?

@robjohn, Not my post. And, I don't use Mac. Omnigraffle looks like it's Mac-Exclusive.

@KannappanSampath oh, okay. I wasn't sure why you posted the image.

@robjohn You got it finally, no?

Thousand words $\neq$ 118 characters....:) @robjohn

@KannappanSampath I don't have Omnigraffle

@KannappanSampath facepalm doh!

Hmph, :/

Is this far fetched?

@robjohn Working on another tab?

Anyway, I'll head to the hospital and be back.

@KannappanSampath Is what far-fetched?

@KannappanSampath Yes. I was in another window.

Off to the park with Lilly. BBL

(Doh : ) Just prevented myself from asking a stupid question)

In the proof of the lemma here, why do they write $ z \in B(z_0, r)$? I think that should be on all of $\Omega$.

@MattN of course not! For example, $1/(1-z)$ is defined on $\mathbb{C} \smallsetminus \{1\}$ but if you develop it into $\sum z^n$ around zero this will converge on the ball of radius $1$ but not anywhere else.

(analyticity gives you local representation as a power series, but not a global one). It turns out that you can always develop up to the nearest pole, but that requires some thinking.

Hm. I wonder how I got around knowing what an analytic function is until now. Thank you.

But it's a trivial proof. Just have the right out the definitions. Must. Resist. Temptation. To. Comment.

My favorite kind of edit

@TheChaz a remarkable improvement

I need to register for that site and earn commenting privileges so I can ridicule him.

@TheChaz nothing to earn, if you register you have 101 points for free :)

Oh, right! Well... I'm already a black sheep in most of the SE communities that I frequent.

So many elitists unilaterally deleting my comments!

hm... showered in badges again. This is getting suspicious.

Why, isn't it nice?

@t.b. I noticed something similar with the "... visited by ______ unique IP addresses" badges.

Well, similar in that they are awarded all at once.

I wish I was showered in badges :(.

@tb I think most of the proof is in this answer

@JonasTeuwen Well, it is nice, but it's the second time in a very short time that I get 5 or 6 badges in a row (the votes were cast within 4 minutes or so and some of the answers are long)

Have you had rep taken away for serial upvoting?

@TheChaz nice answers are awarded immediately and shortly afterwards you're enlightened if you were quick in answering.

@TheChaz not yet, but let's see.

@tb It wasn't me, but I often take the opportunity to scan the posts of people whom I have found to give interesting answers. So sometimes I will end up voting for a bunch of one person's answers in a relatively short time.

Hmm... I guess when you have sufficiently many answers on the network, it's possible that a serial upvoter could bring a few answers from (+9) to (+10). I still wonder about the timing of, e.g. the booster badge awards

@robjohn you should tell Matt :) this is also a nice thread

@TheChaz well, some badges are awarded once in a day. I think stuff that needs bigger calculations like generalist is awarded after they cleaned up the data base around UTC midnight.

I see

Poor Rory first question and (almost) closed in no time.

Almost.

Is GEdgar parroting me?

@tb Technically he would only be if he read your comment.

right.

i'm trying to show that given a sumbersion from $M$ to $N$, that you can always lift a smooth vector field on $N$ up to a smooth vector field on $M$. I think this is obvious now, since we can just take the sums of the preimage of the coordinate function derivatives. Can someone tell me if this is right?

@tb why is it being closed?

@robjohn Would it be possible to link me the continued fractions pdf ago? :-). Then I can get it on my iPad.

That is, if $Y$ is a vector field on $N$, we can write $Y$ as $\sum a_i \partial_i$, and then lift back via the local coordinate maps

@JonasTeuwen whim.org/nebula/math/pdf/contfrac.pdf

i would be eternally grateful if someone could just tell me if i'm being stupid or sound smart here

@EricGregor well, it looks like you're using the local normal form of a submersion. But how do you patch those locally given vector fields together?

@JonasTeuwen I started writing that paper when I was in high school (before 1977) and continued adding to it until about 6 of years ago.

@robjohn yeah, it's my fault... :/

@robjohn Cool :-).

@tb But don't worry, your comment is way better 8-).

@tb thanks. maybe i could make a partition of unity argument?

@tb i guess i was trying to use the Rank theorem

@robjohn Thank you, mean square.

@tb that is a smooth map $F$ of constant rank (as submersions are) has local smooth coordinates centered at every point $p\in M$, and smooth coordinates centered at $F(p)$ in $N$. So that $F(x^1,x^2,\dots,x^m)=(x^1,\cdots,x^k,0,\dots,0)).$ This is what I meant when I wanted to lift the partials

am i being dense? if i'm bothering you let me know, i am just frustrated by what should be a straightforward problem

oh, and then i guess we could cover $M$ with such charts, and then use a partition of unity

@MattN since it is closed being a set of accumulation points?

@tb can you just say whether i'm on the right track? then i'll leave you alone

He might just be away.

He is probably working in another tab or window :-)

ok

@robjohn if $f: \mathbf C^d \to \mathbf C^d$ is a polynomial, and $f$ is injective, then some algebraic arguments can show that it is surjective, do you know an analytic proof? :-).

@EricGregor as long as the derivative of the map $M\mapsto N$ has a non-singular derivative, does the inverse function theorem help?

yes, but i think that's subsumed by the Rank theorem

@robjohn

you still have local functions, so you have to use a partition of unity argument

i'm pretty sure that i'm on the right track

@EricGregor It sounds like it.

i have to run, but i will leave chat open and check later if tb sees this

@JonasTeuwen hmm... lemme think

thanks for your help, too, @robjohn

@EricGregor no sweat :-)

@JonasTeuwen an injective polynomial. That is pretty restrictive is it not?

@robjohn I also have these kinds of files like your continued fractions. I call them Jonas's random ramblings.

@robjohn Yes.

For $d = 1$ we can just use Louiville, right?

If you are interested in Spherical Trig, I also have a similar paper on that.

I like these kinds of random ramblings.

I should make changelogs for these things.

@EricGregor sorry I was on the phone. You are on the right track, but you need to be a bit more explicit on how exactly you stitch those lifts together.

@JonasTeuwen doesn't each variable appear to degree at most 1?

@robjohn What does that mean?

So the power of each variable is at most $1$?

the partial of the polynomial with respect to a particular variable would be a constant that is a function independent of that variable

Oh! Let's see about that.

Also, it's harmonic :-)

@MattN Maybe they should have said "is nonempty", but note that "has an accumulation point in $\Omega$" is part of the hypothesis. You want the result to be as strong as possible, so you want the hypotheses to be minimal.

@robjohn Well that's pretty obvious from the previous statement right? 8-).

yes :-)

@robjohn here?

@KannappanSampath yes?

I was asking if the joke was far fetched.

@robjohn Hmm, is that supposed to be obvious about degree at most $1$?

(joke or observation or whatever you want to call it)

@JonasTeuwen no, I was just ascertaining that I understood the functions we were talking about.

Can you hint me how I could see that?

@JonasTeuwen see what?

@robjohn This!

@robjohn short English question: is it possible to say rephrasing instead of reformulation?

@JonasTeuwen Hmm... I'm not sure that it is right... I was missing something. Back to square 0

@tb example? I think it is, but I may be missing something.

@robjohn well, in the last paragraph of my answer here I was first thinking about saying "... but maybe someone more familiar with such rephrasings will be able to contradict me." (I'm talking about recasting the problem in the language of operator algebras which I'm always happy to avoid because I don't understand it)

I am sorry to interrupt you guys, How to find Square Root of X - Lets say x can be any natural number / positive integer

@Medex do you want to do it by hand?

@tb rephrasing is usually just a rewording of the same ideas. reformulation usually means a deeper change.

@robjohn So I should definitely use rephrasing :)

Thanks

@t.b

any quicker to break for example : 288

calc is not allowed, so i have to break it manually ..

So, you do know that there's a square nearby, right?

@tb a reformulation necessitates a rephrasing, but not vice-versa :-)

144 * 2

12 sqrt 2

@Medex that's just two gross ;-)

Well, this looks good. What do you want more?

so, breaking a number as least as possible is the best way to find the square root of x

@tb Just checking. Thank you, mean bear.

okay, i am leaving the chat room - Thanks

@Medex The most efficient way to simplify a square root by hand is to try dividing the number by squares of primes.

@MattN mean fluffy bear :-D

@The, can you please provide an example

@robjohn You forgot about grumpy

just confusing ..

@robjohn Yeah well, dunno 'bout that.

Are we enough 3k+ers to kill and resurrect this question?

@Jonas: are you there?

@tb Yes.

Too late :-).

resurrection time

@tb killed it! :)

@MattN How about touchy or temperamental bear?

one more vote needed

Well, I am all wrong today, sorry about that @tb

@tb good for Easter weekend ;-)

@robjohn I think he's not anymore.

@robjohn Is there no kind of Louiville theorem for multivariate complex analysis that we could use? :-).

I forgot testy bear :-D

Thanks everyone!

@JonasTeuwen I am not that versed in many complex variables

@tb But why did we have to do that closing and resurrection?

@robjohn (not for that :))

@tb sorry, I never got there :(

@robjohn Too busy coming up with names.

@robjohn Okay, no problem :-).

@MattN indeed :-)

@tb, thanks for your response. i am trying to do it formally and think i will be able to finish. maybe i can share it in a bit. i also want to answer the question whether this lift is unique. my answer is that it is not, since you can find two constant vector fields on $\mathbb{R}^2$ that project to the same vector field on $\mathbb{R}$, namely any two that have the same $x$-component, but differing $y$-components. Do you agree that this shows that such liftings are not unique?

@KannappanSampath because it had four votes to close and it is easier to take care of this dangling sword when enough people are around. It definitely was no longer a duplicate of the linked question.

@tb understood. :)

@tb You're back to happy bear, aren't you?

@JonasTeuwen and most of what I've seen is $\mathbb{C}^n\mapsto\mathbb{C}$

@EricGregor They most definitely aren't. Typically the differential of a submersion has a kernel, so you can always perturb with a vector field belonging to that kernel.

(your example shows well).

great, that's what i thought. just wanted to make sure i wasn't being obtuse

@tb May be I was playing a part by asking annoyinq questions?

I sincerely hope not.

@KannappanSampath oh, no. That's nothing to do with it.

^ Missed that.

@KannappanSampath Hey you. Weren't you going to rest hours ago to help you be cured of typhus? You know it can be lethal in some cases.

@MattN Yes, I had to go to the hospital. I just returned and I am thoroughly bored!

I just posted an exact copy of what I had written there.

:)

^nitpicker (one line before)

@robjohn you can use this for inspiration.

@WillHunting They poked me where they contended they saw a vein, but alas, they were wrong like every other time. Poked me a second time--thank Erdos--they were right!

Where does Erdos come in? : )

@MattN ganja bear?

@MattN That is THC Bear.

@robjohn T = testy and what do H and C stand for?

Well, I believe in Erdos' notebook and his Fascist! :)

@WillHunting perhaps Kannappan holds Erdös as a deity?

@robjohn that's the way I understood it, too :)

who is fascist?

Mariano's way is to write $DEITY

erdos?

@MattN THC

@robjohn You're right.You as well @tb

@robjohn LOL. You're funny! : D

@EricGregor see here look for Supreme Fascist

@MattN Well, that's what the bear is smoking...

@tb thanks, i remember now

@robjohn Your grandmother already knows how to suck eggs. : D

@MattN my precioussss...

@robjohn But seeing as you kept coming up with adjectives I thought might as well find 3 suitable ones for t,h and c.

@MattN are you channeling Asaf?

what happened to Asaf?

@WillHunting Right. So, you know of what I'm talking about.

@EricGregor He left.

@tb left in what sense? even his website is basically removed

@robjohn No, I'm just being my usual self. Now that people know me in here I can gradually come out of the closet...

has he quit mathematics?

@WillHunting He left the chat room.

@EricGregor not at all.

@WillHunting Yeah, he has not left MSE, just chat

he's been gone for 11 days

and he left a cryptic message: "See you in another world."

@robjohn But for educational purposes: In case you've not heard it before. : )

sounded suicidal, but maybe i'm paranoid

oh, lol

@EricGregor He's still alive.

he was here 18 minutes ago

long live Asaf

@EricGregor which one you mean?

His univ's?

@MattN I looked up the idiom after coming across it in The Hobbit.

That explains your previous comment : )

@MattN that's where it came from.

@robjohn The Wikipedia I linked to disagrees with you.

@MattN what do you mean. Wikipedia knows where my comments come from?

Wow :-)

I thought you were telling me that the idiom came from the hobbit. Never mind!

@EricGregor That's how it looked for long!

@Kannappan i didn't know. i just got scared for our friend

@EricGregor :)

mathematics is a dark art, it can lead people astray

:)

@robjohn Didn't you know that you are a celebrity at the latest since you're the room's owner?

No, it leads people into good ways!

@EricGregor They're not really your friends. You don't know them. And sometimes one of them decides to disappear, like that. I'm sure Asaf doesn't care what you think of that.

Atleast math grads know how to do things better!

@EricGregor How is that? dark arts require studying of arcane tomes for hours, sequestered from sunlight and human contact... oh, wait.

@MattN, i use the word friend loosely

@robjohn lol