Mathematics - 2012-09-14 (page 2 of 2)

S.D.

15:01

I have a short question, if possible

Peter Tamaroff

@unNaturhal Yes.

S.D.

is it true, that
$$
\max_i|a_i - b_i|\geq|\max_i a_i - \max_j b_j|
$$

unNaturhal

@PeterTamaroff :D

S.D.

where, say $\max$ is taken over some finite set, and $a_i,b_i$ are reals

anon

yes

S.D.

15:03

@anon how to show that?

Peter Tamaroff

@S.D. But the max of one number is just that number, right?

anon

well wait, that's only one index on the LHS

:crawlsaway:

Peter Tamaroff

@S.D. You mean $\max |a_i-b_i|\geq |a_i-b_j|$ for each $i,j$?

S.D.

@anon: to avoid confusion, I used $i,j$ in the RHS

@Peter: I've fixed it already there - is it clear now?

Peter Tamaroff

@S.D. Note that $\max a_i=a_l$ and $\max b_i=b_m$ for some indices $l,m$.

S.D.

15:06

@Peter yeap, but in LHS we have only distances between $a_i,b_i$ with the same index

@anon: are you gone now?

anon

well, I still have the tab open..

S.D.

@anon: sorry for pinging then. so that's not necessarily true?

anon

not sure

robjohn

@JohnJunior I have been in LA (County) for the past 53 years (if you discount my time in Princeton, where I still considered myself an Angeleno).

@S.D. yes

@S.D. consider the $i$ for which $|a_i-b_i|$ is maximal...

unNaturhal

Ok, we can say that I've understood (a bit of) the Leibniz's test.. It says something like: "If we have an alternative serie $a_n \geq 0$ and it verifies these conditions: 1. is decreasing 2. $\displaystyle\lim_{n\to\infty}{a_n} = 0$ than we can say that the serie converges." It's correct?

robjohn

15:20

@S.D. if $\max_ia_i\ge\max_jb_j$ then $a_i-b_i\le\max_i|a_i-b_i|$ and there may evem be bigger $b_j$s

@S.D. Similarly for $\max_jb_j\ge\max_ia_i$

S.D.

@robjohn got it, thanks. let me try to write it formally on a paper - to be sure that it indeed the result I needed

robjohn

@anon: if I am wrong, please correct me :-)

$\max_jb_j\ge\max_ia_i-\max_i|a_i-b_i|$

$\max_ia_i\ge\max_jb_j-\max_i|a_i-b_i|$

and that pretty clearly shows it to be true.

Gotta go proctor an exam. bbl

Zhen Lin

15:38

Words fail me.

anon

15:49

lol group theory

Ed Gorcenski

Hey guys plz 2 do my homeworx plz

Frank Science

Yesterday I've proved a property.

Ed Gorcenski

Sometimes, I wish I could open up the brains of people that post things like that just to figure out what's going on inside.

Frank Science

$\{\sum_{k=0}^n\log k\mod 1\}$ is density on $[0\mathinner{..}1)$.

@anon I found that the font of mathjax is ugly now.

John Senior

16:07

@EdGorcenski scary stuff - better not to know :)

Jonas Teuwen

16:19

Hello Sirs.

Frank Science

Hi, folks!

Michael Greinecker

Hello!

John Senior

@JonasTeuwen Yo

Jonas Teuwen

Yo.

John Senior

@JonasTeuwen going on holiday tomorrow, and trying to decide on just one maths book to take ...

Ed Gorcenski

16:30

I have yet to determine whether the heterogeneous nature of a burrito is a flaw or a feature.

Some bites you just get rice and beans and long for a hint of salsa. Some bites you get a mouthful of delicious guacamole.

Jonas Teuwen

@JohnSenior Something soft :-).

John Senior

@JonasTeuwen a paperback, then :)

John Junior

@EdGorcenski I would guess it's a feature.

But again it does depend on how you bite into it.

Ed Gorcenski

With my mouth. How else?

John Junior

I meant where you bite into it.

Frank Science

16:40

Can anybody help me?

John Junior

Askaway

Frank Science

imagebin.org/228427

Too ugly.

Peter Tamaroff

@FrankScience Cauchy Schwarz?

Frank Science

@PeterTamaroff I meant the font.

Peter Tamaroff

@FrankScience The "cyc" part?

Frank Science

16:43

@PeterTamaroff The sigma.

Peter Tamaroff

@FrankScience Don't know.

Frank Science

Thanks.

I'll logout.

John Junior

hi @MarianoSuárez-Alvarez

Frank Science

@PeterTamaroff Do you think it's too ugly?

Peter Tamaroff

@FrankScience Looks fine.

Frank Science

16:48

@PeterTamaroff I found the font is from STIX.

@PeterTamaroff It's not like the one in $\LaTeX$

Peter Tamaroff

@FrankScience Yes, true. That font looks like the old ones.

I posted an answer and it said "Trivial answer converted into a comment". What on Earth?

Frank Science

@PeterTamaroff It might be the critical difference between iceweasel and firefox. Maybe iceweasel forbids that prettier font.

Peter Tamaroff

Perhaps.

John Junior

@PeterTamaroff You should post: "This is a non-trival comment that needs to be converted back to an answer." :)

Peter Tamaroff

@JohnJunior Hehehe I fixed it.

Frank Science

17:05

@PeterTamaroff btw, $\sum_{\textrm{cyc}}$ is commonplace in Mathematical Olympiad.

John Junior

@JohnSenior How about "From Zero to Infinity"?

In my opinion, it would make good holiday reading.

Squid

17:32

Hi all.

0

Q: math.SE policy on inequalities

I have been noticing quite a few posts like this: Double Inequality. $ab+bc+ca \leq \frac{1}{8}\sum{\sqrt{(1-ab)(1-bc)}} \leq a^2+b^2+c^2$ and other questions as these: http://math.stackexchange.com/users/33954/iuli?tab=questions. I do not hold any grudge against an user or any area of mathemati...

support

could someone here please comment

@JohnSenior, what do you think?

Ed Gorcenski

@HenningMakholm, myself and many others have blitzed through review of Low Quality posts... now there are 1.4k first posts to go through O_O

Squid

ah let it go.I deleted my question

Ed Gorcenski

@Squid I think perhaps they can seem too localized, but really it's hard to say. Inequalities could have general applications, as their truth applies across the entire real/compelx field.

I think a "too localized" question is one in which the specifics are unlikely to have broad applicability, like "should I use a 4th or 6th order polynomial to fit this exact data set?", where the author isn't seeking more generalized advice (ie, criteria for acceptance of a fit, etc.)

David K.

17:57

I'm trying to identify a symbol from Hatcher's Algebraic Topology. I've already tried detexify and I can't identify it that way. Can I post an image of it here?

Ed Gorcenski

Sure

David K.

How do I do that? With [img] tags?

Ed Gorcenski

I don't actually know. Paging @PeterTamaroff

David K.

[img] i.imgur.com/whzSA.jpg [/img]

Well there's a link.

Ed Gorcenski

That kind of looks like a phi. Is it used as a variable or an operator?

David K.

18:04

An operator. It's defined on page 35 as a map "...$\symbol:X\to X$ is a map..."

Ed Gorcenski

Try $\textqplig$

in tipx package

David K.

@EdGorcenski That just seems to give me an equal sign.

@EdGorcenski But that is pretty close looking at the tex symbols list.

Ed Gorcenski

Yeah

It looks a lot like a third variant of Phi, though

David K.

The author, Allen Hatcher explains that he wrote the text using Lucida Bright family of fonts. So I'm guessing it's something from there. However, he also says that that font family must be purchased and that it is rather expensive.

John Junior

18:42

``It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment'' - Carl Friedrich Gauss

Getting there isn't half the fun; it's all of the fun -skullpatrol

user19161

@johnjunior What have you done to your pic this time?

John Senior

@JohnJunior That is a good suggestion - but unfortunately, I don't have it :(

John Junior

@JohnSenior Can't you borrow it from the library?
@WillHunting Don't you recognize it?

@FrankScience It probably means to sum the given quantity once each as you permute the variables cyclically, e.g. $\sum_{cyc} a^3b^2c = a^3b^2c + b^3c^2a + c^3a^2b$, and $\sum_{cyc} abc = abc + bca + cab = 3abc$.

John Senior

@JohnJunior no library here that has sensible maths books - and I leave in a little over 12 hours - so it has to be a book I already own, I guess

(but I have a couple of hundred to choose from)

John Junior

@JohnSenior Have you read "From Zero to Infinity"?

Or even heard about it being used in the UK?

John Senior

18:55

@JohnJunior I have heard of it - but never read it - it looks good

John Junior

@JohnSenior Are you going to keep in touch with this web site while on vacation?

John Senior

@JohnJunior your new gravatar reminds me too much of the organisation I used to work for

@JohnJunior I very much doubt it - don't think there is much Internet access there - but a week off might be good

user19161

Have any of you read the book A Beautiful Mind?

user19161

@JohnSenior You should not come here while on vacation!

user19161

@JohnJunior Is that about Cantor?

user19161

19:10

Hello @hoo! Is that what you look like?

John Senior

@WillHunting too far - I hate really long flights - Greek islands are far enough

user19161

@JohnSenior Ah Greece! You will meet Pythagoras there!

John Junior

@WillHunting No.

John Senior

Found the book! - sitting on my shelf, it is light, short and looks interesting

user19161

@JohnSenior Never heard of!

John Senior

19:12

@WillHunting bought it 3-4 years ago and never read it, but it looks like a light overview of AT

Hooman

@will yes. I took that with the web cam, while on MSE

user19161

@JohnSenior Yes, anything with "intuitive approach" sounds like "hand waving" to me.

Hooman

I look a bit plastified here

John Senior

@WillHunting this one looks like 99% hand-waving :)

user19161

@JohnSenior If you are interested in topology, the best single book is Bredon's Topology and Geometry which covers general, differential and algebraic all in one.

John Junior

19:15

@JohnSenior Would you agree with what I read in the book's description: "The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject."

John Senior

@WillHunting I am sure it is excellent, but probably more detail than I want - I am only after a brief overview, really

user19161

@JohnJunior Yes, I agree.

John Senior

@JohnJunior agreed

John Junior

How about "The single most difficult thing one faces when one begins to learn mathematics is to get a feel for the sense of the subject."?

user19161

@JohnJunior Makes sense in a suitable context.

John Junior

19:18

That is does it generalize to the entire subject?

The structure of the subject and its methods.

user19161

For example, that can be said to first year undergrad math majors.

user19161

But to speak to a general audience, those who only know 1+1=2, does not make much sense.

John Junior

@WillHunting @JohnSenior In the context of the original quote, how is "mathematical sense" related to "common sense"?

John Senior

@JohnJunior Hmm - not sure at all - but need to go book a flight to Poland - back in a while ...

John Junior

later

user19161

19:25

@JohnJunior Mathematical sense is perhaps not too common. I don't think the author means with it anything too specific.

John Junior

@WillHunting Just a "sense" of the subject?

user19161

@JohnJunior A sense with some mathematical maturity.

John Junior

@WillHunting They are not "maturing" you and assume you have it before you start, right?

@WillHunting This assumption of maturity seems to be at every level of learning math.

Jim_CS

So...metric spaces...that's some crazy sh*t!

user19161

@JohnJunior Well, for lack of a better word, you know what I mean...

Jim_CS

19:33

Anyone here study anything in the area of metric spaces?

user19161

@Jim_CS Rather intuitive I think.

user19161

@Jim_CS What's up? Got a question?

Jim_CS

@WillHunting oh don't worry I will have LOTS of questions on this area. Started it last week and I see that it is going to take up much more of my time than the other math modules

Im not gonna let it mess up my grades lol

user19161

@Jim_CS The best way to learn math is to keep thinking about it yourself. Ask only when you have thought long enough.

user19161

@Jim_CS Come on, just say shit.

Jim_CS

19:38

Yea I agree. I always give it a go before asking. Really enjoy the math this year but this metric spaces stuff has me unnerved...more abstract than anything ive done yet.

user19161

@Jim_CS Then you ain't seen nothin' yet!

John Senior

Back :)

John Junior

@JohnSenior Wow, that was fast!

John Senior

@JohnJunior Yep - it was surprisingly easy

John Junior

@JohnSenior Will answered my question surprisingly easily also.

John Senior

19:49

@JohnJunior excellent - I thought he would give a better answer than I would :)

John Junior

22 mins ago, by John Junior

@WillHunting They are not "maturing" you and assume you have it before you start, right?

@JohnSenior This is the heart of the argument.

John Senior

@JohnJunior OK

user19161

@johnjunior I wonder what's next on your list of usernames and avatars!

John Junior

I'm workin' on it ;-)

user19161

I will stick to steelblue and change back to JL soon.

user19161

20:16

So few people in the room. The kids are partying on Fri night. I party every day.

John Senior

@WillHunting i'm still here :)

user19161

@JohnSenior Hehe, you will be a kid again one day, if you believe in rebirth!

John Senior

@WillHunting I like the sound of that :)

user19161

Ha, the ELU room is having a timeout now because of a fight.

John Senior

20:34

@WillHunting why don't we have fights here?

user19161

@JohnSenior Because we are bros!

Gustavo Bandeira

http://tutorial.math.lamar.edu/Classes/CalcI/Tangents_Rates.aspx

I can't understand the relation of the $M_{pq}=\frac{f(2)-f(1)}{2-1}=\frac{7-13}{1}=-6$ with the rest of the stuff.

I thought the idea was to build the tangent line in the middle of $f(1)$ and $f(2)$

But according to this picture:

The second point aproaches the first.

user19161

@GustavoBandeira That is just the slope of the secant line. As the point Q approaches P, the secant line becomes the tangent line.

John Senior

@GustavoBandeira That is usually what happens when looking at the idea of the gradient - keep one point fixed, and let the other one get nearer to it

user19161

The derivative is the limit of the slope of the secant line.

user19161

20:38

Read it a few times through first.

Gustavo Bandeira

Oh, I got it.

The slope of the secant line is an aproximation to the slope of the tangent line

John Senior

@GustavoBandeira yep

Gustavo Bandeira

got it.

user19161

@GustavoBandeira You done with the algebra notes already? You should read that first before calculus.

Gustavo Bandeira

@WillHunting Yep, I got my Algebra refreshed with some readings.

bbl

MJD

21:07

So I just got the gold medal for voting on 600 posts, which I would not mention, except that it happened to be my 1729th vote.

I thought that was a happy coincidence.

MeAndMath

Hello!@WillHunting, @GustavoBandeira, @MJD, @JohnSenior, @JonasTeuwen, @DavidK. @Anon!!!

@Limitless

@GustavoBandeira Oláa!!!

Gustavo Bandeira

21:26

Yo!

I'm back.

Deixa eu te mostrar uma coisa.

MeAndMath

@GustavoBandeira what's up?what r u doing?

show me

@GustavoBandeira show me

Gustavo Bandeira

Achei

MeAndMath

@GustavoBandeira what???

Gustavo Bandeira

@MeAndMath Tu na minha barriga.

MeAndMath

@GustavoBandeira Que massa!!Adorei!!!

Gustavo Bandeira

21:35

=)

I was studying calculus - but I had to go to the market.

MeAndMath

@GustavoBandeira how uncovenient...

Gustavo Bandeira

Yep. I wish I didn't need to eat/sleep. =D

MeAndMath

@GustavoBandeira yep...

Gustavo Bandeira

I'm watching a documentary: To infinity and beyond.

MeAndMath

@GustavoBandeira what is it about?

Gustavo Bandeira

21:39

I have one on Fermat's last theorem and another on Paul Erdos life.

MeAndMath

@GustavoBandeira hmmm

Gustavo Bandeira

I guess it's on the concept of infinity and some implications.

MeAndMath

@GustavoBandeira interesting

where are you watching it?

Gustavo Bandeira

Computer. I downloaded it.

MeAndMath

@GustavoBandeira oh

Gustavo Bandeira

21:42

Dia desses entrou um guri de 15 anos aqui, de Belém. Sabia função gama, zeta, limite, equação diferencial, etc.

Morri de inveja.

MeAndMath

@GustavoBandeira sabia de saber, resolver provar ou só conhecia?

Gustavo Bandeira

Ó:

Ian Mateus, Brazil

865 3 12

algebra-precalculus complex-numbers proof-strategy real-analysis regression sequences-and-series trigonometric-identities

MeAndMath

@GustavoBandeira não vi nada de demais...

Gustavo Bandeira

@MeAndMath É que quando eu tinha 15, eu era um inútil.

Eu queria já saber de tudo isso hoje.

Graham Number, já ouviu falar?

Eles "traduzem" a idéia de uma forma simples, né? Esse bagulho deve ser complexo pra caralho.

É igual o barato da conjectura do ABC Paulista.

MeAndMath

@GustavoBandeira faz parte...

@GustavoBandeira não

Gustavo Bandeira

21:50

@MeAndMath Eu sempre fui curioso e relativamente produtivo - se eu tivesse me interessado antes, eu já saberia bastante.

Eu fui fazer música nos 15, de lá pra cá eu fiz quase uns 5 mil fragmentos de música.

MeAndMath

@GustavoBandeira todos nós...

Gustavo Bandeira

@MeAndMath Não, tu não. Tu é vida lôka

MeAndMath

@GustavoBandeira como ?Por quê?

Gustavo Bandeira

Tô brincando.

MeAndMath

@GustavoBandeira ah tá.

Gustavo Bandeira

21:55

O maior número que existe:

$$\infty^{\infty^\infty^{...}}$$

.

MeAndMath

@GustavoBandeira bota $$

Hooman

111111=3*7*11*13*37. good night

MeAndMath

@Hooman Night"

Jonas Teuwen

@MeAndMath Hi.

@JohnSenior Hi.

MeAndMath

@JonasTeuwen Hi!!How are you?

Gustavo Bandeira

22:02

Não foi.

Jonas Teuwen

Mmm.

MeAndMath

@JonasTeuwen what does mean "mmm"?good,bad,so so?

@GustavoBandeira é também tentei...

Jonas Teuwen

@MeAndMath So so :-).

MeAndMath

@JonasTeuwen why?why not good?

Jonas Teuwen

I could reverse the question: why good?

MeAndMath

22:09

@JonasTeuwen good question.

but why bad?

Jonas Teuwen

I said so so, not bad! :-).

MeAndMath

@JonasTeuwen Ok,Ok.

@JonasTeuwen did not get:my or yours?

Jonas Teuwen

@MeAndMath Mine.

No, not really.

It is much wider :-). (please delete)

MeAndMath

@JonasTeuwen we all do sometimes...

Jonas Teuwen

I don't think it is like this.

MeAndMath

22:16

@JonasTeuwen elucidate me.

OK!

Bye!!!Need to eat!

Jonas Teuwen

@MeAndMath Enjoy! :-)).

wj32

23:59

has anyone here used Calculus on Manifolds (Spivak)?

Transcript for

$Mathematics$ Mathematics