Mathematics - 2012-01-31 (page 1 of 3)

Henning Makholm

00:00

@JonasTeuwen TeX's parser eats spaces after control sequences.

Norbert

@JonasTeuwen So why we must waste time writing words and making abbreviations. Let's write math texts in first order langauge? :)

Jonas Teuwen

Argh.

robjohn

@JonasTeuwen Is that hyperbolic-arg?

Brian M. Scott

@Norbert And you’re allowed only the existential quantifier and the Sheffer stroke.

Henning Makholm

(bam! 183 yesterday. Whaddawaist.)

Jonas Teuwen

00:03

@robjohn Yup 8-).

@BrianMScott That would be torture.

Brian M. Scott

It sure would.

Henning Makholm

It's like Intercal for mathematics.

Let's do it in reverse polish, too. The Sheffer stroke is notated $\phi\psi S$ and existential quantification is $x\phi E$.

Brian M. Scott

I thought about suggesting that.

robjohn

@HenningMakholm I am playing the world's smallest violin... :-p

Srivatsan

I just made up a notation here. Has anyone seen any other notation for this?

Asaf Karagila

00:09

Hmpf.

robjohn

@HenningMakholm and 15 of that was not counted for capping.

Henning Makholm

@robjohn There used to be a piccolo member of the violin familiy. It turned out to be so difficult to play that it was easier to play high notes on standard-sized violins.

@robjohn If I understand it correctly, the badges don't count caps but merely "reached 200".

Jonas Teuwen

@Asaf ?

Asaf Karagila

What?

Norbert

Good bye, have a nice chatting

robjohn

00:12

@HenningMakholm Oh, I was only considering capping. What badge were you going for?

@Norbert visit again :-)

Henning Makholm

@robjohn Epic.

Jonas Teuwen

@AsafKaragila "Hmpf.".

Asaf Karagila

What about it?

Brian M. Scott

@Srivatsan Not that I can recall. (Leapfrog, anyone?)

Srivatsan

@BrianMScott Thanks.

anon

00:14

Does the Epic badge require consecutive caps, or just total caps?

Henning Makholm

Total, I very much hope :-)

Asaf Karagila

Total.

Jonas Teuwen

I've ran out of Glendronach.

I must go to bed.

Asaf Karagila

Bed is always a good thing.

Someone please give me the right spelling of Godel.

Jonas Teuwen

Bed is certainly a good thing when there is not enough whisky.

Asaf Karagila

00:18

There is never enough whisky.

Jonas Teuwen

True that.

anon

Certain dead persons might retrospectively disagree.

Asaf Karagila

And both me and Jonas disagree with them.

Jonas Teuwen

Good night.

robjohn

@AsafKaragila Gödel

Henning Makholm

00:25

Goodnight Jonas. Off to bed myself, too. SYANW.

robjohn

@HenningMakholm ttfn

Asaf Karagila

Thanks!

Can you tell me if my ramble about the Banach-Tarski makes sense?

robjohn

@AsafKaragila Like I would know :-)

Asaf Karagila

@robjohn It's not very set theoretical...

It's a pro-choice ramble.

robjohn

@AsafKaragila where is it?

Asaf Karagila

00:31

@robjohn Right here.

@Srivatsan: Did you think of a good retag?

Srivatsan

@AsafKaragila No: In fact, I wasn't sure of how to retag, is why I wrote that comment in the first place. =) (I.e., If I had an idea, I would've retagged it myself.)

Asaf Karagila

I'm not sure either!

Srivatsan

"If you forget it, it goes away, and you can't be sure what it was.". Huh??

Asaf Karagila

Dylan or Zhen Lin would know, methinks.

Srivatsan

Yes, that seems likely.

Asaf Karagila

00:37

Well, I think I'll go to sleep.

Srivatsan

Later, Asaf.

Asaf Karagila

@Srivatsan: Read my answer about Banach-Tarski linked above, let me know what you think. I tried to write for non-set theorists.

Brian M. Scott

@Asaf: Did you really mean no non-free uf’s?

Srivatsan

@AsafKaragila Pretty neat. I guess even an undergrad can understand it..

Fortuon Paendrag

Indeed, this undergrad certainly found it understandable.

robjohn

00:48

@AsafKaragila It makes as much sense as any. :-) All of the arguments make reference to mathematical oddities (Banach-Tarski, Incompleteness, etc.) but most are simply impassioned points of view.

In my imperfect opinion :-)

Brian M. Scott

Your opinion has isolated points? :-)

robjohn

@BrianMScott well, it certainly isn't the sum of its divisors. :-)

Brian M. Scott

And it’s not closed with compact fibres? :-)

Still, I don’t think that perfect offers quite so many opportunities as normal.

robjohn

@BrianMScott This is starting to sound like a bad medical problem...

Brian M. Scott

Or at least an unusual one.

Fortuon Paendrag

01:13

@Bri

an

If you're not busy, could you please look at math.stackexchange.com/questions/104116/… and tell me if this OP is asking to prove that distinct points map to distinct points?

Brian M. Scott

Hang on a minute.

Fortuon Paendrag

or that distinct group elements map the same thing to disjoint images?

Kannappan Sampath

Yes the last version is correct! @FortuonPaendrag

Fortuon Paendrag

Ah, many thanks, @Kannappan.

Kannappan Sampath

No problem. I am working on an assignment and I won't post an answer. So, It's good it gets answered by someone!

@FortuonPaendrag

Brian M. Scott

01:21

I agree with Kannappan’s reading: if $g\ne h$, then $(g\cdot V)\cap (h\cdot V)=\varnothing$.

Fortuon Paendrag

@BrianMScott Thank you! I hope I did not disturb you.

Brian M. Scott

No, I was just in the middle of answering a question in a comment to an answer that I’d just made, and I wanted to finish that first.

Bartek

01:42

Hello.

anon

02:09

X^Y means the set of functions Y to X, right?

robjohn

@Mariano you've returned :-)

@anon yes

anon

@rob, wanna try your hand at a bijective approach here?

robjohn

@anon I will have to think about it while walking my dog...

@anon however, your answer looks good in any case :-)

anon

Nevermind, the bijection is just one $k!$ removed from Brian's answer.

Srivatsan

@Kannappan: Where did you get your gravatar from? I noticed it today in a poster on the road...

Kannappan Sampath

02:23

@Srivatsan That is a QR code I generated using some message!

Srivatsan

For an image generated by you, the coincidence is uncanny.

What is QR code?

Kannappan Sampath

@Srivatsan Here is one place where you can generate such codes!

And QR code is one way of sending across secret messages to people.

Srivatsan

Oh, it seems that all the messages have 3 of their corners decorated with the same box-shaped pattern. Which explains the coincidence. I just saw the prominent part of the picture.

Kannappan Sampath

Much like the bar codes, but only more efficient in terms of the amount of info they can store.

@Srivatsan Yes, true.

The interior is rarified for more information and more packed for less information.

QR code

A QR code (abbreviated from Quick Response code) is a type of matrix barcode (or two-dimensional code) first designed for the automotive industry. More recently, the system has become popular outside of the industry due to its fast readability and large storage capacity compared to traditional UPC barcodes. The code consists of black modules arranged in a square pattern on a white background. The information encoded can be made up of four standardized kinds ("modes") of data (numeric, alphanumeric, byte/binary, Kanji), or by supported extensions virtually any kind of data. Created by Toy...

robjohn

@anon I will think more on my walk, but I think the generating function approach is going to be the simplest one.

Srivatsan

02:30

Wow!

Example of a QR code with artistic embellishment that will still scan correctly thanks to error correction. Content: "M.WIKIPEDIA.ORG"

Kannappan Sampath

My goodness, I thought we cannot read the message because of this Wikipedia hanging around there.

robjohn

@anon: The author of this question heard the question, but doesn't seem to have gotten the idea of using residues.

@Srivatsan: see you in a bit. Out with Lilly.

Srivatsan

That's the QR code for: Mathematics Chatroom.

Kannappan Sampath

Haha!! True Veteran!

Srivatsan

Veteran?

anon

02:35

of barcoding, or something

Kannappan Sampath

Forgetting helps!! @Srivatsan

@Srivatsan Where should I learn general topology from?

Srivatsan

One second

Kannappan Sampath

Is anyone facing this persistence problem?

Srivatsan

@KannappanSampath Why not wait until they introduce it in a course?

Kannappan Sampath

@Srivatsan Yes, that's always good. But, it is a kind of interesting.

And, here they introduce it very late!

Srivatsan

02:46

how late?

Kannappan Sampath

(In the third year!)

leo

hello all

Kannappan Sampath

@leo hello!

Srivatsan

@KannappanSampath I guess you could ask the resident topologist.

Kannappan Sampath

@Srivatsan Isn't that Brian we are talking about?

Srivatsan

02:48

Yes.

Is your question: what book to use for topology?

Kannappan Sampath

ASIDE: Are you facing the persistence-of-orange-shade problem when you click on a link to an answer?

@Srivatsan Yes.

Srivatsan

@KannappanSampath how long does it persist?

See math.stackexchange.com/q/7520/13425 and math.stackexchange.com/questions/903/choosing-a-topology-text.

And math.stackexchange.com/questions/59805/…

Kannappan Sampath

For ever, I posted that image like 5 minutes back and even now, it is still there(the orange shade).

And, thanks for the link.

I need to go through them

Srivatsan

I am not sure anyone mentioned Bourbaki. It might be one of the choices (not sure if you want to consider it though)

Kannappan Sampath

Bourbaki is a good place to learn from if you have time.

Srivatsan

02:56

are you speaking out of experience? =)

Kannappan Sampath

If you believe in rushing through and seeing nice results immediately, it is not a good place.

Yes, Having read the Abstract Algebra of theirs, I gave up!

Srivatsan

ah, well.

Kannappan Sampath

They talk about those structures in general, magma, and blahblah and later group, rings are all special structures from there!!

@Srivatsan The persistence problem? Is it happening to you?

Srivatsan

No, I checked. It is slightly slow, but not so slow.

Kannappan Sampath

It is still there for me!

Exact Duplicates! (the new question on the site, I mean!)

anon

03:18

eleven plus two... rearrange the letters --> twelve plus one

Srivatsan

Ha, are they anagrams? I'm lazy to check =)

anon

yes

Mariano Suárez-Alvarez

«I wish some mathematician of the highest level could see this question.»
*Sigh*

Srivatsan

Ah, Vassilli

I deleted my first guess now =)

Mariano Suárez-Alvarez

«*The Count* from sesame street is more of a vampire than eduardo will ever be.»

anon

03:33

«[... then] maybe some of us could understand you (and maybe you'd even understand some of it yourself)» Sha-zing.

Brian M. Scott

@anon Yours is a nice approach to the problem of proving the equality, but I will point out that it doesn’t actually answer the OP’s question!

anon

Yes, I know that. :)

I attempted something along the lines of your answer until I realized what I was shooting for was (essentially) your answer.

Rajesh D

hi all

leo

hi

Brian M. Scott

@anon It took me a while to see just what was going on; I’d not seen that identity before.

anon

03:39

I knew ahead of time that $$k! S(n,k)=\#\{f\in[k]^{[n]}\text{ onto}\}$$ but I had trouble translating the $1^\circ 2^\circ\cdots k^\circ$'s into counts of surjections associated to the compositions.

Rajesh D

I finally got the proof, in my mind i am convinced that the proof holds, but it is very far far away from correct mathematical language, and its just an raw idea, I scratched my head to put it in correct math language, but i am not good with these notations and notions and give up. Although the answer looks lengthy it is very simple and hope someone wll put it in a concise form. Please criticize freely.

@Brian : I am eager for your comments

Brian M. Scott

@anon I wrote out the $\left\{\matrix{5\\3}\right\}$ case in its entirety and figured out which partitions had to be counted by each term of the sum, and then it fell into place.

@RajeshD I may not manage it tonight: my brain seems to be turning off, since I’m starting to make silly mistakes.

Rajesh D

ok @Brian : have a great night !

Brian M. Scott

Thanks!

Rajesh D

@anon @leo : whats up with you guys

anon

03:52

just being lazy and surfing

Rajesh D

@anon : in that case, plz check my answer if you are really free

anon

I don't even understand your question. Also see: lazy.

Rajesh D

ok cool

i didn't think it meant mentally lazy too

@anon

Rajesh D

04:38

hi @Sri

anon

Heh heh. @J.M. put the Weierstrass-on-torus image as his GV, and added suggested enhancements.

Rajesh D

04:56

@anon : I am not able to find J.M. on users list ??

anon

He's on page 2 of the monthly list, and front page of the all-time list.

Rajesh D

got him

anon

05:13

Hmm, I remember seeing something like $$\frac{\partial u}{\partial v}\frac{\partial v}{\partial w}\frac{\partial w}{\partial u}=-1$$ somewhere on Wikipedia or MathWorld. Can someone jog my memory?

Srivatsan

06:06

@RajeshD hi Rajesh

Kannappan Sampath

How is it that I don't see your gravatar and you still talk, @Sri?

Or so you left in jiffy!

Srivatsan

@KannappanSampath Do you see now?

Kannappan Sampath

@Srivatsan Yeah I do! puzzled

Srivatsan

actually i am gonna sleep now. bye!

anon

(triple product rule)

Kannappan Sampath

06:12

bye!

@anon They are called the Euler Identities, @anon if that helps you!

anon

Also called triple product rule, as I just said :)

ht: efnet's #math's Polytope

Kannappan Sampath

Oh I see!

@anon ???

anon

ht means "hat tip" (in other words, the source for something). EFNET is a server for IRC (internet relay chat), and #math is the math channel. Polytope is a frequenter there.

Kannappan Sampath

That explains all that I never knew about that line =)

Thank You anon.

anon

07:02

@MarianoSuarezAlvarez: When there are less than 5 close votes on a question, can moderators see who it is that put the votes in?

Mariano Suárez-Alvarez

no

likewise for delete votes

anon

Interesting. I ask because I saw you edited the question I downvoted, but it was someone else who closevoted.

Mariano Suárez-Alvarez

I cannot stand badly indented code :)

Asaf Karagila

07:49

By golly I am tired.

Jonas Teuwen

08:03

By golly, so am I.

Asaf Karagila

Isn't he a physicist?

Asaf Karagila

08:40

Holy cow! There is an answer on SO that has 2000+ upvotes. And it's not CW!

anon

Link?

Asaf Karagila

Unholy.

Rajesh D

@Mariano : please see my proof here

if you really have some time

Looks like one cannot award bounty for one's own answer of one's own question, I am not getting that option. Is there any such rule ??

Rajesh D

09:18

hi @nine

Ninefingers

09:30

@RajeshD Morning

Or afternoon/evening/night/whatever it is where you are!

Rajesh D

afternoon

howz the day

u from Europe ?? @nine

Ninefingers

09:47

@RajeshD Yep, UK

Matt N.

@BenjaminLim Hi! Am I being confused here?

Ninefingers

@RajeshD Much better now, was struggling to write an answer on crypto and now feel I've got it covered off ok.

Rajesh D

10:02

@Matt : please check my answer

Matt N.

@RajeshD I don't understand it.

Rajesh D

@Matt : I've deleted it ! doesn't matter now

Jonas Teuwen

10:33

Cool, my office mate has two silver medals @ IMO.

Benjamin Lim

Hi guys

@MattN Brian M. Scott has replied and what he said was what I meant to say.

unNaturhal

Good morning

Kannappan Sampath

10:51

@JonasTeuwen May I know who does the term office mate refer to?

Dumb question, but I think I don't know what that means!

Rajesh D

hi @kannappan :

Kannappan Sampath

hi @rajesh!

Rajesh D

@kannappan : check this....I know its not in mathematically correct and precise language....(couldn't scratch my head more)........but now i am fully convinced that the set is closed under convolution

I am pretty excited !

Kannappan Sampath

@rajesh: I am reading you answer, but at first sight I spotted this: When you say a function is $n$ times differentiable, it does not make sense, if $n \in \mathbb Q \backslash \mathbb N$.

That is, you need not specify that $n \in \mathbb N$.

Jonas Teuwen

@KannappanSampath The other guy in my office.

Rajesh D

11:06

yes ofcourse....apart from silly things it is still not fully in math language

Kannappan Sampath

@JonasTeuwen That clears up my head. But, can your office mate be from an entirely different university?

Jonas Teuwen

Well, it is in the office in the same university.

So usually they will be from the same.

Kannappan Sampath

Minor typo: D1 and D2 should have been $D_1$ and $D_2$ respectively.

@rajesh

Rajesh D

ok

Kannappan Sampath

@JonasTeuwen That's clear! Thank You!

Rajesh D

11:10

no its not clear as to what @Jonas actually means ! am I right ?

Kannappan Sampath

In convolution we flip $f_1$ about the y−axis and shift it by $\tau$ and place it on the function $f_2$ and multiply pointwise and take a summation to get $f_3(\tau)$.

@RajeshD Why, Jonas means the office mate will be from the same university!

Rajesh D

This is where it is not in appropriate language ! @kannappan

Kannappan Sampath

@RajeshD That's what I'd like to point out!

Let me think how I'll fix it!

Rajesh D

my comment is related to the convolution thing u just typed

ok cool

first go through the entire thing before thinking of fixing it...will be much neat then

I'd liked to know at first whether you are fully convinced with the proof ! @kannappan

Kannappan Sampath

Yeah, I will go through it fully now!

I am not quite convinced about the number of times a function is differentiable at a point.

@rajesh

Rajesh D

11:18

@kannappan : when you have fixed things post it as a separate answer, useful for the bounty.

??

you mean ?

Kannappan Sampath

Your claim that "The minimum value of n = sum of, the number of times f1 is differentiable at τ−x and the number of times f2 id differentiable at x, ∀x∈(0,1)."

needs proof, I think.

Rajesh D

Yes....I should state this....but it follows from a standard theorem...do not remember its name

wait a bit

See this @kannappan

Kannappan Sampath

@RajeshD Then it is fine. But, I cannot comprehend these things as I have not formally learnt them.

Rajesh D

check some of my early questions, might find them interesting and good exposition

Kannappan Sampath

But, your proof is unmathematical, only at the point I pointed out. And, it looks unused in the rest of the proof.

And, please consider fixing the typos. There are quite a few of them.

Rajesh D

11:29

Its used here $n = \min\limits_{(x_1,x_2) \in C} ck_1(x_1) + ck_2(x_2)$....the whole thing rests on it.....I need to go a few rounds at it to fix things and typos.

@kannappan

Kannappan Sampath

@RajeshD I mean that thing about reflecting, translating and so on...

Rajesh D

yes....may be....i thought its good to give some intuitive feel about convolution......it helps in the second part of the proof i guess

and The statement you have mentioned about differentiability definitely needs proof, I will consider asking a separate question on its truth......i guess

Kannappan Sampath

That might be good and will improve the answer a bit.

Rajesh D

@kanna : were you the one who upvoted it

Kannappan Sampath

No.

Rajesh D

11:37

i am asking because it happened just while our conversation is taking place.

Kannappan Sampath

@RajeshD That's no problem.

You can try and answer questions on the site. That will improve the way you write.

Rajesh D

yes

Kannappan Sampath

And, @Rajesh, you are a CS major right?

Rajesh D

nope

Kannappan Sampath

then,?

Rajesh D

11:39

ECE

Kannappan Sampath

Alright!

Rajesh D

engineering.....never had a go at pure math.....not much at applied math either

Kannappan Sampath

@RajeshD Oh, I see.

Rajesh D

Yesterday someone told me that you could award a bounty to your own answer in theory....but this statement seems false

i do not even find such a option or button at my answer

@kannappan

Kannappan Sampath

It was @anon who told you that. May be we need to understand what "in theory" means

Rajesh D

11:43

hahha....i guess

robjohn

11:54

I have one answer for every degree in a circle :-)

just sort of seemed neat in a Monk-ish sort of way.

Jonas Teuwen

Is there a possibility to remove the hard line breaks at 70 characters in emacs that it has already done on a file?

Without messing up the other newlines.

robjohn

@JonasTeuwen I am not an emacs person.

Jonas Teuwen

What kind of person are you then, @robjohn? 8-).

I can only think of something that removes all the hard newlines and then adds them again where they are needed (or exclude that in the first place). I was hoping that was some C-magic C-magic.

robjohn

@JonasTeuwen I use BBEdit

Jonas Teuwen

@robjohn Oh :-). Why? There are so much free editors. What makes BBEdit so good?

robjohn

11:59

Before that, I used a text editor that I had written in assembly.

Jonas Teuwen

With syntax highlighting? 8-).

robjohn

@JonasTeuwen No syntax highlighting :-(

@JonasTeuwen BBEdit will preview webpages, and using MathJax I can preview LaTeX.

Jonas Teuwen

Right, preview-latex in emacs can also preview latex.

robjohn

Cool. I had no idea, not being an emacs person :-)

Jonas Teuwen

But it runs it through latex... So might be slower.

If you want to parse the whole document, that is.

Rajesh D

12:02

hi @rob @jona

robjohn

@JonasTeuwen Well, MathJax is not real LaTeX, so it works well for previewing stuff before I type in in chat or a comment, where there is no preview (as with answers)

Rajesh D

texmaker has a good GUI....

robjohn

Hey @Rajesh :-)

Kannappan Sampath

Going to take a nap, bbl!

Jonas Teuwen

@robjohn Yes, but you only want to check if the syntax is correct no?

Rajesh D

12:03

@kannappan : devils sleep at this time !

robjohn

@RajeshD I should look at other TeX-editors. I use CMacTeX which does not live-preview.

Jonas Teuwen

TeXShop?

Vim(-latex)?

Emacs with AucTeX?

robjohn

@JonasTeuwen and that it looks right, yeah

@JonasTeuwen do these run on PC or Mac?

Rajesh D

sorry..texmaker does not do live preview....but does it at the press of a button with a popup window centered at where the changes are made

robjohn

I know Vim is on Unix/Linux

Jonas Teuwen

12:05

You have OS X, so Vim will work perfectly fine :-).

Plus there is probably a Windows cygwin-port...

You do have MacVim and Aquamacs (emacs) for OS X.

(But don't forget that emacs has a vim-mode 8-))

robjohn

@JonasTeuwen I will take a look, but I already have BBEdit and I am used to its interface. However, I am not adverse to change.

Thanks!

Rajesh D

someone star my last comment pinging kannappan....plz :-)

Jonas Teuwen

Emacs has quite a steep learning curve...

Rajesh D

thanks.

Jonas Teuwen

@robjohn For what it's worth, I can recommend Aquamacs for OS X. It works nicely together with the OS X interface.

robjohn

12:13

@JonasTeuwen I will look it up right now :-)

Downloading 2.4 now :-)

Jonas Teuwen

It detects for example already if your file is in a repository :-).

Rajesh D

@rob @jonas : do you know any specialist in real analysis who could be of some help......i need to communicate with someone with expertise in this field

?

Jonas Teuwen

Of help for what?

Rajesh D

I am studying things like this.....i need some general insights and tips

robjohn

Ack! Saeed is downvoting all the answers to this question because he is assuming it is an untagged homework.

Jonas Teuwen

12:23

@RajeshD I don't think they are so hard, why would you need an expert?

Rajesh D

not any great expert....but to give some general tips (not solutions to problems)....whether to study, what could be the uses....some big picture ideas or pitfalls....

@Jonas

Jonas Teuwen

You should either be patient and wait for people to answer or go talk to somebody from the math department at your university. I can't give you names because I think I'm right if I assume that they will not like that I send other people to them with questions many other people are very qualified as well to answer.

Rajesh D

ok. its complicated i guess.

Jonas Teuwen

12:49

@RajeshD If you could add some motivation I will take a shot at it.

Rajesh D

ok

@Jonas : Its not about the answer to that question, I want to discuss some general ideas not necessarily in mathematical language but intuitively...i just happen to see your profile and you might be just whoom i was looking for

I'd like to ask my queries through e-mail (not on this site)....

Jonas Teuwen

Why not on this site?

Plus, there are so many problems to solve that I prefer to take a look at the problems that actually have some motivation.

Rajesh D

its not about problem solving that i need help....i can ask for help on SE for problem solving....but to think of creating a theory and problem solving would be a part of it

Jonas Teuwen

What kind of theory?

Before you can mail me interest me 8-).

Rajesh D

I guess you were there on that day when i was discussing with t.b. and J.M., i remember you and rob being there....if you couldn't recollect i'll type a few lines on the motivation

Transcript for

$Mathematics$ Mathematics