Mathematics - 2012-09-15 (page 1 of 2)

robjohn

00:32

@wj32 like as a paperweight, or doorstop. How did you want to use it?

Or did you want to read it?

Gustavo Bandeira

►

Peter Tamaroff

@robjohn ...lol....

Don't laugh. I'm drowning, actually.

robjohn

@PeterTamaroff Drowning?

Peter Tamaroff

@robjohn $$\Huge\text{.....lol......}$$

Doesn't it look like a guy drowning?

robjohn

@PeterTamaroff Ah! I see... yes it does.

Peter Tamaroff

00:45

Anyways, I'm off to eat.

See you.

robjohn

@PeterTamaroff Good food!

anon

Useful fact: When people drown they don't put their hands up in the air or yell. They use all of their energy bobbing up and down for air.

3

Peter Tamaroff

01:39

@anon Hhehee. Dude.

@anon Could you peer review this?

@robjohn Maybe you?

Qual Fighter

02:17

Does anyone know what "sous-tore" means in French? Literally I think it's subtorus. Not sure if that's a thing

Peter Tamaroff

@QualFighter Some google revelas "sous" is also used as in "sub group".

Whatever "subtorus" means (IRW torus) might be relevant.

Qual Fighter

maybe i haven't been exposed to this kind of a torus before

i guess it's an algebraic torus or something

Peter Tamaroff

Note that sometimes langauges don't share literal translations

for example

Qual Fighter

peter, aren't you agreeing with my translation?

as a sub torus?

i know that sous-groupe or something like that is subgroup. so i got the meaning. maybe i'm just in need of math translation :)

Peter Tamaroff

In English, we call them "Fields" but in Spanish, we usually call them "Cuerpos" literally, "Bodies", and "Campos" (Literally "Fields") is not much used.

Qual Fighter

02:22

corps = fields in french. i think corps means body

Peter Tamaroff

@QualFighter Yes.

@QualFighter But "corpse" is another thing, hehehe.

@anon

wj32

@robjohn Do you think it would be a good book for someone who has done some real analysis and algebra but no multivariable calculus?

Or will I end up not being able to compute the volume of simple objects?

Peter Tamaroff

@wj32 What is "it"?

wj32

@PeterTamaroff Calculus on Manifolds by Spivak

Peter Tamaroff

@wj32 They say that one is as though as Adamantium.

wj32

02:29

Have you used it?

Peter Tamaroff

@wj32 Nope.

Peter Tamaroff

02:53

@GustavoBandeira Bro.

Gustavo Bandeira

@PeterTamaroff Yo

What's up?

Peter Tamaroff

@GustavoBandeira Check this out

Gustavo Bandeira

@PeterTamaroff Soothsayer. =)

Maybe this is going to answer a question I had today.

Peter Tamaroff

@GustavoBandeira What does that mean?

Gustavo Bandeira

@PeterTamaroff Someone who predicts the future.

I'm reading the first pages of Limits today, until now, he gave me the definition of limit

Peter Tamaroff

03:05

@GustavoBandeira You're reading what book?

Gustavo Bandeira

But I'm still with a naive definiton for it.

Paul's Notes and Stewart's Calculus essentials

Peter Tamaroff

@GustavoBandeira Hmmmm. Paul's Notes?

Gustavo Bandeira

tutorial.math.lamar.edu

Look: $$\lim_{x\rightarrow 2}(x^2)=4$$

And:

$$\lim_{x\rightarrow 2}(x^3)=8$$

I thought them similar to function evaluations.

Peter Tamaroff

@GustavoBandeira ?¿?¿?¿?

Gustavo Bandeira

$x^2=4$

and

$x^3=8$

It seems like "solve for 2"

BUT, as I said, still on the first pages.

First - actually.

brb

Peter Tamaroff

03:14

gotta go

byes

robjohn

04:25

@wj32 It is a good book. I don't remember the problem sets, but the exposition is good.

user19161

08:17

It's quiet in here. The kids are still partying.

user19161

@PeterTamaroff Yes, I recommended him and Mohamed because I thought they would be helpful. But they are too simple for you!

Gustavo Bandeira

08:38

@WillHunting I'm at home.

Chris's sister

09:03

Hi. How may I find who downvotes me almost every day?

(downvotes on my questions)

user19161

@Chris'ssister I looked at your rep history. You don't have that many downvotes, except on a day when the serial downvotes were reversed. If you still feel this is a problem, you can raise a question on meta. But I suggest you wait a few more days to see how things go. Usually these people with nothing better to do will stop after a while.

Chris's sister

@WillHunting: I don't understand why is good to punish a good question. I don't see any logic in this.

meg_1997

Hey will anyone help me to solve this math.stackexchange.com/questions/196078/…

user19161

@meg_1997 I was just reading it. From the context of a mountain I can't imagine how it is done as described either yet.

user19161

@Chris'ssister Well, some people may genuinely feel it is not a good question. But we do not know what they think in their hearts. Anyway, don't worry too much about it!

meg_1997

09:16

@WillHunting i did not understand the question itself:(

user19161

@meg_1997 Are those the exact words of the question?

meg_1997

@WillHunting ithink there might be some correction in the sentence formation

user19161

@meg_1997 Get the exact words first then. If those are the words then I think it is a bad question.

meg_1997

@will huntinghey i am so sorry i made an edit its 60 degrees

user19161

@meg_1997 I will post an answer shortly.

user19161

09:27

@meg_1997 Oh, someone posted a pic already...

wj32

Question about sequences: If I define a sequence by $a_1=1$ and $a_{n+1}=\sqrt{1+a_n}$, it is easy to see that $a_n \rightarrow a$ for some $1<a<2$.

My question is: why must $a$ satisfy $a=\sqrt{1+a}$?

user19161

@wj32 If you know that the sequence converges, take limits on both sides of the equation. QED.

wj32

@WillHunting Ah! Thanks

user19161

@wj32 Great minds get stumbled by the most trivial things at times...

wj32

@WillHunting :(

user19161

09:34

@wj32 Hey did you check my proof of the V or inverted V thing? I hope you know where I posted it in chat.

wj32

Yes, I did.

I'm pretty sure it works, but I'm reluctant to "accept" it, if you know what I mean...

user19161

Well, it's ugly in a way.

user19161

But I am not sure if there is a neat way to prove that lemma.

wj32

I guess the ugliness is just a consequence of the ordering of the real numbers - we have to check 2 cases all the time.

user19161

There might be some really nice combinatorial proof, I don't know.

wj32

09:37

Yes, I wonder if that kind of thing is studied in combinatorics

user19161

In fact, I haven't really checked enough to make sure that the lemma and proof are indeed correct.

wj32

Given $x_1,\dots,x_n$ and a set of conditions, how many "completely specified orderings" of those numbers are there?

But this seems to be too general to attack for now

wj32

10:23

What do you guys think about the following notation:

$f : (\mathbb{R} \rightarrow \mathbb{R}) \rightarrow \mathbb{R}$

$f(x \mapsto x^2) = \cdots$

peoplepower

10:46

It is well-defined as long as you know the type of f.

And, of course, the formula must describe a valid $\Bbb{R}\to\Bbb{R}$ function.

unNaturhal

14:24

Good evening!

There's someone that want to help me with some exercises (and theory) about series?

robjohn

16:14

closin' time

@unNaturhal sure

unNaturhal

@robjohn There are some things that I haven't understood...

The first: when I'm handling with series, I HAVE TO know how to obtain it's $s_n$ (sequence of partial sums)?

robjohn

@unNaturhal That is what determines its convergence. You don't need to know the actual values, but you need to be able to show they converge.

If you're just trying to show convergence.

unNaturhal

Mmmmh.. taking this for example:
$$\sum_{n=1}^\infty{(-1)^n \sin\frac1n}$$

To study this we have to refer to the Leibniz's test, right?

robjohn

@unNaturhal Dirichlet test would work well there.

unNaturhal

@robjohn Dirichlet? I know just 4 tests.. Leibniz's test, Comparision test, Square Test and something that is italian is called Criterio degli infinitesimi and uses the limit $\displaystyle\lim_{n\to+\infty}{n^pa_n} = l$

robjohn

16:26

@unNaturhal Okay, Leibniz's test should work here, too.

It's the only one that you've mentioned that works with alternating series

unNaturhal

@robjohn I know :)

My question now is: Which is the first thing that I should do to start to study/solve this series?

robjohn

@unNaturhal However, so does the Dirichlet test.

@unNaturhal are you just trying to show the convergence/divergence, or do you want to find a value for the series?

unNaturhal

@robjohn Just the "nature" of the serie

robjohn

what do you mean by nature?

unNaturhal

@robjohn Convergence/divergence :P

robjohn

16:36

@unNaturhal If it's alternating, then check Leibniz

@unNaturhal You have a list of tests, see which apply and check each of those to see if they give you an answer.

unNaturhal

@robjohn Mh mh.. So to apply Leibniz we have to do the limit $\displaystyle\lim_{n\to+\infty}{a_n}$ and check if it is $= 0$ right?

robjohn

@unNaturhal Yep. I believe the convergence has to ultimately be monotone

unNaturhal

@robjohn $$\displaystyle\lim_{n\to+\infty}{\sin\frac1n} = \sin\frac1\infty = 0$$

robjohn

@unNaturhal well... $\sin\left(\frac1\infty\right)$ is not a number, but that is the idea.

unNaturhal

But now there is a problem... The second condition of Leibniz's test is that $a_n$ has to be divergent (or decreasing).. how I can check this?

@robjohn What do you mean?

robjohn

16:42

You know that $\lim\limits_{n\to\infty}\frac1n=0$ and $\sin(x)$ is continuous at $0$, so...

$\lim\limits_{n\to\infty}\sin\left(\frac1n\right)=0$

unNaturhal

Yeah, I know :p

My "representation" was wrong?

robjohn

No, I just wanted to make sure that you knew that $\frac1\infty$ is not a number and some instructors might mark down for that.

unNaturhal

@robjohn Yeah, it gives $0$ only when you consider it as a limit for something that tends to $\infty$, right?

robjohn

@unNaturhal Yes. when you write $\frac1\infty=0$ what you (should) mean is that $\lim\limits_{n\to\infty}\frac1n=0$.

I am simply being pedantic.

unNaturhal

@robjohn Don't worry :)

And now?

robjohn

16:54

@unNaturhal now what?

unNaturhal

Which is the next step?

robjohn

if the list of tests don't give you an answer?

unNaturhal

No wait, there is another condition in the Leibniz's Test..

The serie has to be decreasing (or divergent).. how I can check this?

robjohn

Never mind, before you just said it tends to $0$ (but it needs to be monotonic :-)

unNaturhal

It needs to be monotonic?

robjohn

16:58

Can you show that $\sin\left(\frac1n\right)$ is monotonically decreasing to $0$?

unNaturhal

@robjohn I don't know how...

robjohn

@unNaturhal Yes, consider the series $a_n=2^{-n}$ when $n$ is even and $a_n=\frac1n$ when $n$ is odd.

@unNaturhal $a_n\to0$ but $\sum\limits_{n=1}^\infty (-1)^na_n$ diverges

unNaturhal

Mmmmh

robjohn

As for $\sin\left(\frac1n\right)$, you know that $\sin(x)$ is monotonically increasing on $[0,\pi/2]$

and you know that $\frac1n$ is monotonically decreasing and takes its values in $[0,1]$

unNaturhal

@robjohn Oh yeah! This is right! But there isn't a condition that says that the serie is defined in a given interval

robjohn

17:05

@unNaturhal but $\frac1n$ takes its values in $[0,1]\subset[0,\pi/2]$

unNaturhal

@robjohn This is right too

robjohn

So $\sin\left(\frac1n\right)$ is monotonically decreasing to $0$.

unNaturhal

Perfect! So, since that the series satisfies the Liebniz's Test conditions, we can say that $$\sum_{n=1}^\infty{(-1)^n\sin\left(\frac1n\right)}$$ converges, right?

robjohn

yes

unNaturhal

And at this point we finished?

robjohn

17:10

@unNaturhal yes

unNaturhal

@robjohn Cool! xD

Do you want to do another serie?

robjohn

@unNaturhal I will help you with another series, if that is what you are asking :-)

unNaturhal

@robjohn lol, yes xD

Do you have any to reccomend? Something that could be didattically helpful?

Link

uh, hi i had a question, how do you tell speed from a velcotiy vs time graph?

robjohn

@unNaturhal well since I wrote it up there, do you see why the series I gave above diverges?

Link

17:14

uh, what?

i have no idea what it means.

unNaturhal

@Link I think @robjohn was asking it to me xD

robjohn

@Link Is that better :-)

Link

oh okay

thanks

robjohn

@unNaturhal Unfortunately, I have to go now. I will be back later.

unNaturhal

@robjohn Okok :) Thanks for the help :)

user1561559

17:32

hi guys

i just want to know, in calculating limits, when I do direct substitution, and it gives 3/0, does it mean for sure that the limit does not exist?

Parth Kohli

18:33

Not necessarily.

I always tend to use Mathematica for checking if a limit exista or not. How? Plots!

Exists*

Qual Fighter

19:10

Hi Peter

@PeterTamaroff

Peter Tamaroff

Qual Fighter

There seem to be technical glitches on the site

the front page isn't updating

Peter Tamaroff

@QualFighter Maybe people aren't making questions.

Qual Fighter

i made a question and it isn't appearing

math.stackexchange.com/questions/197236/…

and if you look under UNANSWERED QUESTIONS there have been quite a few

Jonas Teuwen

20:14

Hi guys.

John Junior

Hi.

What were you doing in here alone ?

Jonas Teuwen

What?

John Junior

This is the first time I've seen this room with only one person in it.

It looks spooky :O

Jonas Teuwen

That's because we are here.

John Junior

I'm not really "here" because of the appearance of my gravatar.

I'm just a logo.

Jonas Teuwen

20:26

Okay.

Logos don't speak so shut up.

5

Parth Kohli

Hello

John Junior

hi

Welcome to the party :)

Parth Kohli

Is there any way to teach myself mathematics till level m.se starting from calculus? Any resource?

Heh, thanks John!

Gustavo Bandeira

@ParthKohli Level m.se?

Parth Kohli

Yes, Gustavo. The type of problems people here at math.se do :)

I really feel tiny here because you all have reputation in thousands!

Gustavo Bandeira

20:36

@ParthKohli Relax.

@ParthKohli What you already know?

@MeAndMath Olá. Eu tinha algo pra te falar, esqueci o que é.

Meu pai dizia que sempre que tal fenômeno ocorre, era mentira - o que tinha a ser dito.

MeAndMath

HIII!It's peanut butter jelly Time!

@GustavoBandeira fala aí!

Parth Kohli

I have already started Calculus.

Gustavo Bandeira

@ParthKohli Keep on doing it. There are also some transitions to advanced mathematics that I guess may be useful.

Parth Kohli

Are there any good websites to do so?

John Junior

12 years old is usually thought of as the "Pre-Algebra/Algebra" stage.

Parth Kohli

20:43

Hehe, well. I guess I went too fast. :)

MeAndMath

His name is @JonasTeuwen

Jonas Teuwen

Who's name?

Parth Kohli

Has anyone heard of Arturo Margidin?

Gustavo Bandeira

@ParthKohli Arturo Digidin - MeAndMath is going to understand.

MeAndMath

@JonasTeuwen Did you know this song?

Jonas Teuwen

20:45

@MeAndMath Unfortunately yes.

One Jonas is enough for this world.

MeAndMath

@JonasTeuwen Funny!

hey,You made curious yesterday...

Jonas Teuwen

Yes?

MeAndMath

@JonasTeuwen you did not want to tell me...

Gustavo Bandeira

@ParthKohli Relax with reputation - just keep studying.

Jonas Teuwen

:-). E-mail me, I will tell you.

MeAndMath

20:47

@JonasTeuwen what's your email?

Parth Kohli

Haha, okay!

Jonas Teuwen

@MeAndMath it is in my profile.

MeAndMath

@JonasTeuwen did it

John Junior

@ParthKohli In my opinion, it is probably best to concentrate more on "Pre-Algebra/Algebra" for now...

And try to relate it to what you did in Arithmetic.

In Mathematics you can build a lot on a strong foundation :)

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$Mathematics$ Mathematics