Mathematics - 2013-02-16 (page 4 of 4)

user58512

18:06

I finally cracked it

it's one of those things that dont make sense right up until the end, then it magically gives you just what you need

Dominic Michaelis

heyo

user58512

hi

user19161

@gar One can read $a+b$ as "$a$ plus $b$" and $a\times b$ as "$a$ times $b$".

user19161

@JonasTeuwen Well, first you must know all the chess rules!

Garbage Collector

@JacobBlack OK. Thanks.

user19161

18:18

Although many know about castling, they have not heard of en passant.

user19161

It is really hard to mate with two bishops, two knights or bishop and knight.

Andrew Salmon

@JacobBlack You can't force checkmate with 2 knights.

user19161

@AndrewSalmon Hi! Welcome to this chat!

Andrew Salmon

Hi

user19161

Ladies and gentlemen, I have capped for today, thank you for your support.

user58512

18:22

Overfull \hbox

thanks for telling me latex.... but what am I supposed to do

Dominic Michaelis

what exactly ?

how many points to wide?

user19161

@rob OMG I capped on two days consecutively just for answering -1 times -1 = 1, HAHAHAHA

user19161

And I didn't even bump the post today.

Andrew Salmon

I don't quite understand why a question like that gets so many upvotes...

Dominic Michaelis

same here :D

user19161

18:26

Well, it is rather interesting actually, to the general public.

Orange Harvester

@JacobBlack well love triangles are never comfortable anyway.

Andrew Salmon

The thought to upvotes ratio should be more or less the same across various areas of math.

user19161

I have tried to figure out voting patterns on this site. My conclusion is that there are none.

Dominic Michaelis

@jacob they vote for my answers when i capped :D

user19161

@DominicMichaelis Yeah, don't answer too many a day then.

anon

18:30

ℝⁿ

Dominic Michaelis

anyone here knowing the poincare cartan invarianz ?

user19161

@anon What about him?

user19161

@DominicMichaelis Never even heard of that term despite seeing 9000 books.

Dominic Michaelis

even the english wikipedia doesn't seem familar to it

user19161

I am very tempted to answer all the reference request questions.

user19161

18:33

But it seems that every topic asked for already has 9000 duplicates.

user19161

The questions just have some variation here and there, like this or that requirement.

user58512

why

user19161

Why what?

user58512

I want to study some theorems and work out some examples and do my writing up

but I can't do all that because I don't have time

user19161

@gar Somehow I think you are xport. You both like pstricks. You both are writing books. You both give many bounties.

Garbage Collector

18:45

@JacobBlack By accident!

user19161

@GarbageCollector I still don't know what you look like...

Garbage Collector

@JacobBlack I look so ugly. :-)

user19161

@GarbageCollector Oh my ghost!

Garbage Collector

@JacobBlack You were so adorable when you were a baby.

user19161

@GarbageCollector Haha, that is NOT me...

Garbage Collector

18:49

@JacobBlack I will go to Munchen soon.

user19161

@GarbageCollector OK, very good. I will go to Germany in my next life.

Garbage Collector

@JacobBlack Why? You can go without Schangen visa.

Dominic Michaelis

@garbage you mean münchen (munich in english isn't it?)

Garbage Collector

@DominicMichaelis Yes. Munich is equal to Munchen. QED.

user19161

I always feel a deep connection to Germany. Maybe I was there in my previous life...

Garbage Collector

18:51

@JacobBlack So it implies you are a buddhist?

Khromonkey

What are some libraries that have a lo of math books?

user19161

@GarbageCollector Sort of.

user19161

@Khromonkey Depends on where you are.

user19161

@Khromonkey If you are in a university, just use your school library.

Garbage Collector

@JacobBlack I see. I have no faith anymore. I lost it.

Peter Tamaroff

18:52

I need peer reviews!

user19161

@PeterTamaroff So what are you trying to prove there?

Peter Tamaroff

@JacobBlack Am I not clear in my writing?

"Then Γ is infinite, and dense over [a,b]."

user19161

@PeterTamaroff But does that answer the question?

Peter Tamaroff

@JacobBlack The OP asked me to add that...

Dominic Michaelis

what is OP ?

user19161

18:56

@PeterTamaroff Well, the Lebesgue criterion is the real criterion there.

Peter Tamaroff

@DominicMichaelis The original poster.

@JacobBlack But this is tangential to that.

user19161

So although your proof may be right, it does not lead to important information I think.

Peter Tamaroff

"Thanks! Will you elaborate on the interesting last sentence and/or post your comment as an answer? – Ryan"

@JacobBlack I think it is interesting, at least.

user19161

Then you should say Ryan, this result is not important, hence I shall leave the lesser mortals to prove to you the important result.

Charlie

¡Hola, @peter!

Peter Tamaroff

19:00

@Charlie Hola.

Charlie

@PeterTamaroff everything good?

Peter Tamaroff

I guess. I finished S2 of Game of THrones yesterdat.

I hear S3 premieres next month.

user19161

@peter Guess what? We are now adjacent in rep, that makes us bros.

Charlie

@PeterTamaroff cool!

Peter Tamaroff

@JacobBlack I thought this moment would never come.

Khromonkey

19:02

@JacobBlack How does it depend? does the number of books in a library change depending on the part in the world i'm in?

user19161

@Khromonkey Of course, in fact every library is so different, even if they are on opposite streets!

Khromonkey

ok, but what are some of the biggest libraries (in number of math books) in the world?

user19161

I don't know. Although I know about books, I know not about libraries.

user19161

And there is no use knowing too.

Garbage Collector

@JacobBlack: I presented this for you tex.stackexchange.com/a/98502/19356.

user19161

19:06

@GarbageCollector Thanks. I hope you tell me your real identity one day...

Garbage Collector

@JacobBlack Oh my ghost!

Charlie

@GarbageCollector I'm curious too

user19161

@GarbageCollector I still don't get why so many like pgf when pstricks is so powerful...

user19161

@Charlie Are you still upset with me?

Dominic Michaelis

i am just able to use includegraphics :D

(and a lil bit of tikz-cd

Garbage Collector

19:09

@Charlie No need to be curious. I am just a single point in the complex plane. I have an ugly face. :-)

Charlie

Yes,.and I don't know if it will gi away soon...@jacob

user19161

@DominicMichaelis Yeah that is specially for commutative diagrams.

user19161

@Charlie I don't know why you are upset, you may email me if you like...

user19161

@GarbageCollector Was the picture you showed before your real one?

Charlie

@GarbageCollector I bet you are not :)

user19161

19:11

@GarbageCollector Maybe you are the point at infinity on the Riemann sphere!

Garbage Collector

@JacobBlack I cannot answer.

user19161

@GarbageCollector Well, if that was you, then you look rather adorable.

Garbage Collector

@JacobBlack I have a tuberculosis.

user19161

@GarbageCollector Really? You have TB?

Garbage Collector

@JacobBlack TBC

Charlie

19:12

@GarbageCollector you shouldn't play with it...

user19161

@GarbageCollector You really have tuberculosis? You should not joke about it...

Garbage Collector

@JacobBlack I will die like Riemann.

Charlie

@JacobBlack i don't think out would work

user58512

we all die like Riemann: without proving Riemann hypothesis

user19161

@Charlie OK, feel free to tell me anything.

user19161

19:14

@user58512 I might try to work on it in future, lol.

user58512

Good!

Garbage Collector

@JacobBlack Yes. Recently, I have a severe cough.

Charlie

@JacobBlack I feel free to tell you anything, the problem is that you never understand

user58512

@JacobBlack, by the way, no one has proved the zeros are all simple

Dominic Michaelis

mh in german there is a LaTeX no-go list is there something like that in english ?

Charlie

19:16

@GarbageCollector oh my God!

user19161

@DominicMichaelis l2tabu?

Dominic Michaelis

yeah like that

user19161

Yeah isn't that in English?

user19161

It's in a full TL install.

Garbage Collector

Is $f'(x)=0$ the condition to find the critical points? How about the point in which $f'(x)$ does not exist?

Dominic Michaelis

19:17

i only find the german one (which is great cause i am german) what's teh date of yours ?

user19161

@DominicMichaelis I have a TL2012 full install.

Dominic Michaelis

i mean of l2tabu

robjohn

@JacobBlack :-p

Dominic Michaelis

mine is from 2011 can't believe there is no newer

Charlie

@GarbageCollector yes and there's no derivative

user19161

19:19

@DominicMichaelis 17062007 l2tabuen

Garbage Collector

@Charlie So it mean the point in which the first derivative does not exist can be called as a critical point as well?

@JacobBlack Is it a pirated edition? :-)

user19161

@GarbageCollector No way! TL is free software!

Charlie

@GarbageCollector if it doesn't exist , it don't exist. Criticals are derivative ewual zero

user19161

Guys I have no pirated books now, all my books are real paper books OK?

Charlie

All my books are pdf books

user58512

19:22

prove it

user19161

I do look at online copies to decide if I want to buy it though.

user19161

@Charlie I think I understand now...

Dominic Michaelis

i guess if it is on ctan its the most actual one

user19161

@DominicMichaelis I don't update my TL after doing a DVD install.

user19161

Supposedly the DVD version is more stable than a continual update.

Charlie

19:25

@JacobBlack what you understand?

user19161

@Charlie Why you are upset.

Dominic Michaelis

but some packages are improved with just the dvd version there is no need of maintenance

user19161

We just need to do a DVD install once a year.

user19161

I burn my own DVD.

Dominic Michaelis

i update mine installation about 3 times a week

Garbage Collector

19:26

You can make a local mirror as explained in my answer: tex.stackexchange.com/a/63263/19356

user19161

@DominicMichaelis Haha, that is crazy! Not necessary...

Charlie

@JacobBlack I don't think you do

user19161

@Charlie Then you must tell me. Is it because I don't say hi to you?

Charlie

@JacobBlack it goes beyond this

user19161

...

Dominic Michaelis

19:28

argh 160 reputation points -.-

user58512

hi

I posted a quesstion

Dominic Michaelis

which one ? ^^

Charlie

@user58512 hello

user58512

@DominicMichaelis, here

I don't really know what is so important about the error terms yet

Dominic Michaelis

me neither

user58512

19:36

I like when i get work done

@DominicMichaelis ask me anything you like about category theory

Dominic Michaelis

mh at the moment i don't have a question in category theory

still thinking about this one math.stackexchange.com/questions/305316/…

user58512

im just bored

Charlie

@user58512 why, you have nothing to do?

user58512

@DominicMichaelis, this is trivially equivalent to irrationality of a nontrivial root of sin (i.e. pi)

Dominic Michaelis

mh why is the equivalence trivial ?

user58512

19:44

ill tell you when I figure out how to prove it

Dominic Michaelis

maybe i hit today the 200 to much reputation -.-

btw how is the hotness of a question calculated ?

user58512

@DominicMichaelis, this is nasty because we can only say that cos(x) is a quadratic irrational

Dominic Michaelis

yeah and i don't see how that helps

and i wish a more easy way :D

user58512

if we know cos(x) was rational we could use pythagorean triples

there's no trig identity that will give us let us create a rational x' such that sin(x') and cos(x') are rational from x :[

duplication rationalizes cos but turns sin into a quadratic irrational

tripling leaves sin ok, but also leaves cos quadratic irrational

I can't reduce it to irrationality of pi

Dominic Michaelis

20:06

and i think even the irrationality of pi isn'T trivial

seems like i will set a bounty when it times come

user58512

it's a really good question

but you have to be a bit smarter than me to see that right away

Suppose $\sin(x) = y$ for rationals $x,y$ then by $\sin(x)^2 + \cos(x)^2 = 1$ we deduce that $\cos(x)$ and hence $e^{ix}$ are quadratic irrationals. Let $e^{ix} = \frac{A+\sqrt{B}}{C}$ then $$C^2e^{2ix}-2ACe^{ix}+A^2 = B$$ taking imaginary part implies $$\sin(x) = \tfrac{C}{2A} \sin(2x) = \tfrac{C}{A} \sin(x) \cos(x)$$ which forces $\cos(x)$ to be rational (unless $\sin(x)$ is zero).

but I even with pythagorean triples I can't conclude

Dominic Michaelis

is it impolite to ask someone to accept a question ?

accept an answer

user19161

@DominicMichaelis It's OK to ask nicely.

amWhy

20:24

@user58512 I thought your question earlier today was great!

user58512

@amWhy, thanks amy your answer is very helpful to me

amWhy

@user58512 I wish more mathematicians had that kind of sensitivity!

Dominic Michaelis

ah now he accepted great :)

user58512

@DominicMichaelis, i think I got it now

@DominicMichaelis, also I think this gives the majority of a proof that pi is irrational: math.stackexchange.com/questions/287637/… but you need some facts about generalized continued fractions

Victor

Hi, Is anyone here familiar with probability

Peter Tamaroff

20:35

@Victor Probably someone is!

Victor

@PeterTamaroff - Are you familar with stochstic process?

Dominic Michaelis

@user58512 i am still thinking about your solution how do i have e^(ia/b)=A+IB with A,B rationals ?

sry with integers

Peter Tamaroff

@Victor Nay.

user58512

@DominicMichaelis, yeah I'm wrong, this breaks the proof

Victor

@PeterTamaroff - Are you a math major?

Peter Tamaroff

20:38

@Victor What would that imply?

Victor

@PeterTamaroff - That may imply you might know how to intepret the solution in my recent problem: math.stackexchange.com/questions/305739/…

Dominic Michaelis

tomorrow i can place a bounty on that question

Peter Tamaroff

@Victor I am not a major, whatever that means,

user58512

we only have e^{ia} = (A+iB)/C for integers a,A,B,C

Dominic Michaelis

@peter maybe a general ?

Peter Tamaroff

20:40

@DominicMichaelis Ah?

Theorem

Define $\pi : G \to G/N$ where $N$ is a normal subgroup . if $G'$ is a commutator of $G$ then why is $\pi (G')= G'N/N$ ?

user58512

@DominicMichaelis, at least this reduces the problem to saying that e^{iN} is Gaussian-irrational

Peter Tamaroff

@Theorem What does it mean that $G'$ is a commutator of $G$?

Victor

@JacobBlack - Are you familiar with stochastic process?

user58512

that might actually be easier to prove than pi irrational, haven't tried

Dominic Michaelis

20:42

@peter General is a military rank isn't it ?

Peter Tamaroff

@DominicMichaelis I think so, yes.

Dominic Michaelis

same as major

Theorem

@PeterTamaroff : that means $G'$ is a derived subgroup of $G$

Peter Tamaroff

@Theorem And what oes it mean for $G'$ to be a derived subgroup?

Stress on derived.

Dominic Michaelis

@user don't we assume pi to be irrational anyway?

Theorem

20:44

@PeterTamaroff : en.wikipedia.org/wiki/Commutator_subgroup

there you go :)

Dominic Michaelis

oh i see

Peter Tamaroff

@Theorem Hehe. No clue on that.

I mean, I understand what is there, but I have never studied it.

Theorem

@PeterTamaroff : what do u do ? are u in university yet ?

Peter Tamaroff

@Theorem I'll start my first year next month, hopefully.

Theorem

cool .

:)

where are u doing ur undergrad ?

@PeterTamaroff

Peter Tamaroff

20:50

@Theorem I live in Argentina, in Buenos Aires.

Theorem

Oh nice @PeterTamaroff

i like argentina

how is the university ?

Peter Tamaroff

@Theorem It is the UBA.

University of Buenos Aires

The University of Buenos Aires (, UBA) is the largest university in Argentina and the largest university by enrollment in Latin America. Founded on August 12, 1821 in the city of Buenos Aires, it consists of 13 departments, 6 hospitals, 10 museums and is linked to 4 high schools: Colegio Nacional de Buenos Aires, Escuela Superior de Comercio Carlos Pellegrini, Instituto Libre de Segunda Enseñanza and Escuela de Educación Técnica Profesional en Producción Agropecuaria y Agroalimentaria. Entry to any of the available programmes of study in the university is open to anyone with a secondary ...

Theorem

@PeterTamaroff : is there some kind of entrance exam or something ?

what is the enrollment procedure ?

Peter Tamaroff

Entry to any of the available programmes of study in the university is open to anyone with a secondary school degree; in most cases, students who have successfully completed high school must pass a first year called CBC, which stands for Ciclo Básico Común (Common Basic Cycle). Only upon completion of this first year may the student enter the chosen school;

until then, they must attend courses in different buildings, and have up to 3 years to finish the 6 or 7 subjects (which vary depending on the programme of study chosen) assigned in two groups of 3 or 4. Each subject is of one semester duration (March–July or August–November). If someone passes all 6 subjects in their respective semester, the CBC will take only one year.

user58512

21:04

@DominicMichaelis, oh I got an idea

@DominicMichaelis, en.wikipedia.org/wiki/… Lambert showed tan(x) is irrational if x is rational (except 0)

Peter Tamaroff

@Theorem So, I finished the CBC in one year, and now I am starting 1st year.

user58512

@DominicMichaelis, maybe you can repeat his proof using math.stackexchange.com/questions/298029/…

Dominic Michaelis

oh that should help a lot

user58512

i am not sure if the irrationality critera works on that CF though

Theorem

how many years undergrad prog do u have @PeterTamaroff

user58512

21:06

it hopefully will...

ah yes it does

Peter Tamaroff

@Theorem 5 years.

Theorem

5 years undergrad ??? @PeterTamaroff

then i guess u can directly go for Phd ?

Peter Tamaroff

@Theorem I think so.

Dominic Michaelis

@amWhy you have g(f(x)) in the last post it should be g(f(3))#

Peter Tamaroff

@Theorem 4 years of courses, then a year of optional courses and Thesis.

user58512

21:17

what is goingon?

skullpatrol

prayers=meditation=memorize

user58512

21:47

hello

Dominic Michaelis

zhi

user58512

omg deaf cat: i.imgur.com/GbtmTRQ.jpg

Khromonkey

22:10

I know where I want to study math finally!

I still need to know if they will accept me though

user58512

what subjects do you want to study in math

Khromonkey

I like all of it, However I seem to suck at visual stuff (like stuff from euclids book) and at inequalities (GM-AM tchebychev, moebious). I like all of it however.

I also love books

Michael Corleone

I'm having difficulty showing that $D=\{(x,y,z)\in\mathbb R^3\mid zx+z^3 y>xy+zy+z^4\}$ is open and that $f(x,y,z)=\frac{1}{x-y-z^3}$ is continuous on $D$. Can anyone give me hints?

user58512

22:37

does a polynomial has the same number of roots mod a prime power as it does mod that prime?

anon

@user58512 not necessarily. consider x^2-1 mod 2^n. look up Hensel's lemma, which gives conditions for roots to lift (uniquely)

user58512

thanks

can we at least ensure degree d one has at most d solutions mod a prime power?

anon

for the polynomial x^2-1, the roots are: mod 2: just 1; mod 4: 1 and 3, mod 8; 1,3, 5 and 7; mod 16: 1,7,9,15. in general, +/-1 and 2^(n-1)+/-1 are precisely the square roots of 1 modulo 2^n, for n>2.

user58512

ahh :(

anon

if p does not divide the degree you should be okay, otherwise there can be issues

@MichaelCorleone can you write D as the inverse image of an open set (like ... (0,inf)?) A rational function is continuous at every point it is defined at; plugging in x=y+z^3 into the inequality, is it true? (I haven't actually checked, that's just my first thought.)

Michael Corleone

22:44

@anon Thanks, I will check if the inequality is true at $x=y+z^3$, I'm not really sure what you mean about the first thing though

user19161

@Khromonkey So where are you applying?

Khromonkey

TU berlin

anon

@MichaelCorleone one definition of continuous is that the preimage of any open set is open. there is a polynomial in that inequality, and polynomials are continuous.

user19161

@Khromonkey Euclid's Elements? Nobody reads that now.

Michael Corleone

@anon oh plugging the inequality worked immediately, assuming $x=y+z^3$ led to $y^2<0$, which is a contradiction so $x\neq y+z^3$ and $x-y-z^3\neq 0$ on $D$. I was thinking I might need to use that definition of continuity (in our course it's a theorem) for the first part. I will check it out tomorrow it's a bit late now

Charlie

22:48

@Khromonkey nice!

Khromonkey

@JacobBlack I didn't mean euclids elements exactly, but I meant geometry. Like the geometry problems in the imo

user19161

@Khromonkey Ah, don't worry, I can't do IMO problems either.

user19161

The IMO contestants go through much training.

Khromonkey

Really?

user19161

They see many questions of that sort and learn various techniques to solve them.

Khromonkey

22:51

So then it's not that useful later on?

user19161

Whether you take part in IMO or not has little relation to whether you can excel in your undergrad course.

user19161

@Khromonkey Not really related to your university studies I would say.

Khromonkey

thats awesome news

Charlie

you guys have a bad time thinking which uni should you apply...

Khromonkey

cause i'm allready too old to go to the imo anyways. (well, i would still have one chance, but geting it right on the first try is really hard)

user19161

22:54

@Khromonkey I see no point in competing in these competitions at all.

Khromonkey

besides, I really hate competitions

user19161

These competitions are like sprints. Mathematical research is like a marathon.

Khromonkey

I agree, also these competitions use very specific tools and reasoning

user58512

you will learn lots of good maths and get a lot of strong practice at problem solving and develop your skills by competeing

Charlie

Doesn't that make you a machine of solving problems?

Khromonkey

22:58

@user58512 in my experience it is really demanding and it isn't really very enjoyable

I prefer doing maths without having to be part of a continuous elimination program, where 99% of the people get eliminated at some point while their friends are still in there

Michael Corleone

@anon Oh I decided to do it now anyway and that worked as well. If $f(x,y,z)=zx+z^3y-xy-zy-z^4$ then $D=f^{-1}((0,\infty))$. $(0,\infty)$ is open and $f$ is continuous on $\mathbb R^3$ so $D$ is open. Thanks for the help

user19161

If I really wanted to work on more problems, I would just do all the exercises in the book. That is hard enough.

anon

@MichaelCorleone yup

user19161

There are also enough problem books out there for one to work on without competing with others.

Charlie

@JacobBlack I solved my stats book

user19161

23:00

@Charlie I hate stats, lol.

Charlie

@JacobBlack stats is funny, not a big fan, but it can be nice

Khromonkey

yes, The only thing cool about it is that you get to meet other people who are good at math, however the atmosphere is really competitive in the training camps.

user19161

@Charlie Of course, it is a respectable branch of math itself that can be very hard, but I just hate it.

Charlie

@JacobBlack ok

ablmf

Is there any difference between $a_n < \infty$ for all $n$ and $\sup a_n < \infty$?

user19161

23:02

@ablmf Yes.

user19161

1, 2, 3, 4, ...

user19161

That satisfies the first but not the second.

ablmf

@JacobBlack, I see, thx

Peter Tamaroff

23:24

@anon Duude.

anon

yes, high peter?

Peter Tamaroff

@JacobBlack So, it has come to this.

@anon Will you never see I'm saying hello?

anon

never

Peter Tamaroff

@anon I'm sad.

@anon Any news to share?

anon

not really

skullpatrol

23:28

no news is good news

an application of the above

Transcript for

$Mathematics$ Mathematics