Mathematics - 2012-12-05 (page 1 of 6)

@csss they are the values $\lambda$ for which $\lambda\,\mathrm{Id}-A$ is not bijective (note this applies to linear operators in general, with no condition on finite dimensionality).

Wait, I think I'm confusing these with something else.

Nevermind, you are right, I am thinking of the spectrum of an operator.

robjohn

@Khromonkey yes?

@anon spectra are pretty :-)

user19161

@robjohn As pretty as anon's picture. =)

robjohn

@JasperLoy He is spectral

user19161

@robjohn Yes, I know, in at least two ways...

user19161

Gee, we have a user called broccoli.

robjohn

12:45 AM

@JasperLoy anon's parents had to enroll him in a spectral needs class.

user19161

@robjohn I was about to correct your Anon to anon!

user19161

By the way I saw my undergrad supervisor answer a question here yesterday as an unregistered user...

robjohn

@JasperLoy How did you know it was them?

user19161

@robjohn Well, assuming the name matches.

robjohn

@JasperLoy ah, I thought perhaps you talked to them.

user19161

12:50 AM

@robjohn Not them, him.

robjohn

@JasperLoy It is a singular them (often used as genderless).

user19161

@robjohn Yes, but I avoid it myself, sounds too weird! You are a GN!

user19161

I am wondering what he is doing on this site, hmm...

robjohn

@JasperLoy I was not making assumptions :-p

user19161

This guy never accepts my answer. If I write too detailed, not good. If I write not detailed, also not good. Geezis!

robjohn

1:14 AM

@JasperLoy It is possible, especially if you keep going as you have been. Capping each day will get you at least 1400 per week.

user19161

@robjohn Well, now I just need 100 points on each of 18 more days. =)

robjohn

@JasperLoy That should get you there. You seem to have no problem getting that many points a day.

user19161

@robjohn Thanks to my fans! =)))

robjohn

@JasperLoy I used to have some regular voters. They seem to have left, however.

user19161

@robjohn Hmm I see...

Old John

1:23 AM

fascinating question

user19161

@OldJohn HAHAHAHAHAHA

user19161

Not joking, but that guy might just solve the Navier-Stokes.

Old John

and a great choice of tags for it

user19161

Oh I think he is a troll now...

Old John

reminds me of the maths "paper" that was generated by some randomising software - and then got accepted for an online Journal :)

Khromonkey

1:28 AM

Hi guys

is there a media player in linux mint that can play effing .ape?

Old John

@Khromonkey I wrote a script that converts effing ape into effing flac ...

Khromonkey

does it keep the effing quality?

@OldJohn

Oh and what program do you use?

Old John

@Khromonkey absolutely, flac is effing lossless :)

shntool

user19161

@Khromonkey What ape?

Khromonkey

can I have it please?

@JasperLoy Koko the gorilla

Old John

1:34 AM

ah! - it is one of the shortest ever scripts - if you have shntools installed, just run this command on the command line:
shntool conv -o flac *.ape

Khromonkey

@jasperloy .ape is a lossless music format.

@oldjohn thanks. By the way: do you use banshee?

Old John

it will convert all the ape files in a directory

mostly I use Rhythmbox - just stuck to it since Ubuntu days

Khromonkey

wait: I have to run it from the terminal?

Limitless

Hola!

user19161

@Khromonkey You only need the first three characters like @khr.

Limitless

1:37 AM

@JasperLoy, WILL

user19161

Hey @lim!!!

robjohn

@JasperLoy Thanks (I assume) but that wasn't a call for votes :-)

Limitless

@JasperLoy, CAFFEINE = BAD IDEA

Old John

@Khromonkey yes

Khromonkey

@OldJohn SO I run the program in the terminal?

Limitless

1:37 AM

@JasperLoy Cannot type full sentences

@JasperLoy without interruption

user19161

@Limitless Why?

Khromonkey

how do i tell it what directory to use?

Limitless

@JasperLoy because brain too fast.

@JasperLoy Girl issues

Old John

@Khromonkey I made it into a simple executable file called "ape2flac" - it converts all the files in CWD

Limitless

@JasperLoy awesome mathematics too

user19161

1:38 AM

@Limitless Oh then just slow down then.

Limitless

@JasperLoy BUT I SEE SO MUCH

user19161

@Limitless Better than none. I never had one.

Khromonkey

what is cwd?

Limitless

@JasperLoy It's so lovely. Seeing.

Old John

CWD = current working directory - the bit you see at the left of the terminal - before the prompt

user19161

1:39 AM

@Limitless Seeing what? Proofs?

Limitless

LOVE MODULES AND VECTOR SPACES BTW

@JasperLoy Parallel realities and dimensions of possibilities

I think in 3-dimensional timelines

user19161

@Limitless Well, my life has gone so wrong that I really want to reverse time and change things.

Limitless

n-dimensional really

@JasperLoy I LOVED YOUR VECTOR SPACES ANSWER

I read it at school.

user19161

@Limitless It's trivial dude. I think you are just feeling high now! =)

Limitless

@JasperLoy dude

user19161

1:41 AM

All my answers here are TRIVIAL!

Limitless

The trivial is delish sometimes.

Dude, like, I totally started researching modules due to your answer

AND IT WAS BEAUTIFUL!

user19161

@Limitless I think you should go easy you know.

user19161

Topic by topic.

Khromonkey

how do i go to another directory? @OldJohn

Limitless

@JasperLoy I'm hyperactive both in mentality and activity.

Old John

1:42 AM

@Khromonkey cd

user19161

@Khromonkey cd XXX where XXX is the new dir

user19161

@Khromonkey Typing cd alone brings you to the home directory.

Old John

like "cd .." to move to a higher directory

Limitless

@JasperLoy I have a "I can handle reading this" familiarity with the concepts associated with modules, and it was easy to pick up an understanding of a vector space. It helped me elucidate my thought process. Did you know apparently no one else thinks in n-dimensional time lines and weighs the multiple possible realities that could form in an attempt to predict the potential futures and account for them?

user19161

Assuming you are not root.

Khromonkey

1:43 AM

what is root?

user19161

@Limitless Haha, whoa you are thinking too much!

Old John

@Khromonkey superuser

Limitless

@Khromonkey Root is the user that has all authority.

user-mode

Old John

@Khromonkey If you ask the question "what is root" - you need to be sure you never login as root :)

Limitless

@JasperLoy I was talking to my class and I was like, "YO DAWGS, WE SHOULD TOTALLY DO A CUBE TIMELINE AND HAVE THE POTENTIAL REALITY ON LIKE ONE OF THE FACES OF THE CUBE VERSUS THE OTHER STUFF." And they were like . . . mindblown.

anon

1:45 AM

don't go all timecubey on us

Limitless

@anon!!!! Hi!

user19161

Is anon joining in this time cube talk as well?

user19161

If anyone can let me go back to the year I was in high school, I would give you all my rep.

Limitless

@JasperLoy We all love you.

user19161

@Limitless Thanks for the love, John! =)))

Limitless

1:47 AM

Well . . . At least I do. You're a friend to me, and I love my friends.

user19161

But I also think you took too much coffee!

Khromonkey

@OldJohn ok. So i get to the cwd that has the files I want to convert. I need to get to the folder in which they are in right? SO if I where to type ls I could see the sdahd.ape Then what do I do?

Limitless

@JasperLoy It was just one Rockstar.

And I'm not even done drinking it.

Approximately 4 fl oz left.

Old John

@Khromonkey what is sdahd.ape??

Khromonkey

the name of the file I have in ape

Old John

1:48 AM

ah ok

user19161

Let me ask @old. Have you heard of "distinguished elements" in algebra???

Old John

then just type the command I gave earlier

Khromonkey

I type ape2flac?

Old John

@JasperLoy Hmm - I have heard it in some context, but many many years ago

@Khromonkey have you created a command "ape2flac" containing the command I typed earlier (involviong shntool)?

Khromonkey

no

How do i do that?

I Installed mint yesterday

Old John

1:50 AM

if not, then just type "shntool conv -o flac *.ape"

Khromonkey

I dont need to type the name of the files right?

Is there a simple way to get to the cwd I want?

Old John

no - the *.ape tells it to convert all the ape files in the directory

Khromonkey

or do I need to use cd a hundred times?

Limitless

@JasperLoy I think I'm going to legit hardcore focus on Abstract Algebra next year.

I think I'll be ready for it

Old John

you could probably change the command to work recursively so that it converts all the ape files in a directory and all its subdirectories

Khromonkey

1:52 AM

oh

that would be so cool

I guess life is better when you know stuff

Old John

yes - but I can't remember how to do it, offhand :(

Khromonkey

@oldjohn do you know what boxset.ru is?

Old John

@Khromonkey no - sorry

Khromonkey

But you like music right?

Old John

@Khromonkey yep - but only classical

Khromonkey

1:55 AM

Where do you get your music?

Old John

CDs, friends, some legal sites, ... (mostly)

Khromonkey

oh

in case you like sharing boxset.ru is a really good site

but they mostly have ape

Old John

I also have a friend who seems to get loads of stuff from Usenet

he gave me some stuff in ape format - that's when I created that little script

Khromonkey

nice

Old John

I did a whole bunch of them for things like splitting audio files into tracks by ".cue" files

Limitless

2:00 AM

@JasperLoy, my answer is still more stylish, Homedawg.

user19161

@Limitless Yes I saw...

Limitless

@JasperLoy For kicks and grins, I'm going to write the Combing-Like-Terms Lemma

Old John

@Limitless combing?

Limitless

@OldJohn . . . ;D?

Old John

as in ... combing one's hair?

user19161

2:04 AM

Wow @amwhy I see you got over 200 already!!!

Old John

Must go - later all

user19161

@OldJohn Good night!

Old John

@JasperLoy bye!

user19161

I have gotten over 100 today as well, over and out!

Limitless

@OldJohn bai!

Nighty night

Link

2:09 AM

Hmm, anyone know something about subtext in descriptive writing?

Peter Tamaroff

@Limitless And now the OP feels retarded. Peter Griffin retarded.

Limitless

@PeterTamaroff lolwat, why

Limitless

2:31 AM

@PeterTamaroff ! Why you no respond, buddeh. </3

Walkerneo

2:51 AM

Hello

My calculus homework says: "Use tangent line approximation to derive an estimate for (1+x)^n, when x is near 0, and n is any real number

I see that it's going to be 1, but I don't understand how I could use the TLA to figure that out?
We've been taught that f(x) = f(a) + f'(a)*(x-a), but for the equation, I don't know f(a) or f'(a) or a....

Limitless

@Walkerneo, do you care to post that as a question? I will answer you now, I just prefer LaTeXing on a bigger canvas.

Walkerneo

How can that problem be solved with Tangent Line Approximation if I don't know f(a), f'(a), or even a

Limitless

What exactly is the tangent line approximation? I'm aware of what a tangent line is; I am just not familiar with this specific title.

You have that $a$ is $0$, I believe.

Walkerneo

math.hmc.edu/calculus/tutorials/tangent_line/tangent_line.pdf

Limitless

Wait.

Okay.

I think I get it.

Your function is $f(x)=x^n$, yes?

Or is it $f(x)=(1+x)^n$?

Walkerneo

2:54 AM

the latter

Limitless

hm

You want to get close to $0$, right?

Walkerneo

I mean it's 1, obviously, but I don't get what it's saying about using TLA

yeah

Limitless

Mmk. Try this:

$f(x)=f(0)+f'(0)(x-0)$

How does that look?

Walkerneo

What would x be though?

Limitless

I don't think it is going to have a particular value.

user19161

2:57 AM

Ran out of votes for today...

Limitless

@JasperLoy, what do you think?

Walkerneo

@Limitless, mmm, thanks, I'll see how that turns out. You're right, that might be what they mean

Limitless

Let's see what Jasper thinks, @Walkerneo.

user19161

@Limitless Yes, correct that is how you approximate.

Limitless

He is far more qualified than me.

user19161

2:58 AM

Of course it is an approx sign there, not equal.

Limitless

Oopsies

@Walkerneo $f(x) \approx f(0)+f'(0)(x-0).$

@JasperLoy Does both of that sum converge to 0, as I noted in my comment?

user19161

@Limitless deleted

user19161

There is no question there actually. It's just a what do you think of this.

Limitless

@JasperLoy ?

user19161

@Limitless Question deleted by author.

Limitless

3:01 AM

I'm aware, but it's interesting.

@JasperLoy $$\sum_{n=0}^\infty\frac{3^n(3^{3^n}+2)}{9^{3^n}+3^{3^n}+1}=\frac{1}{2}$$

user19161

I am pretty bad at computing things. It is impt to know both theory and computation actually.

Limitless

I argue that $$\sum_n \frac{2\cdot 3^n}{9^{3^n}+3^{3^n}+1}=0$$ since the denominator is clearly bigger than the numerator.

$$9^{3^n}+3^{3^n}+1>2\cdot 3^{n}$$ via $$9^{3^n}+3^{3^n}+1-2\cdot 3^n>0$$?

Could be shown via induction, but it seems obvious.

Peter Tamaroff

3:30 AM

@Limitless Whu?

Limitless

@PeterTamaroff Why did OP feel "retarded"?

Peter Tamaroff

@Limitless All the Elmo stuff.

Limitless

@PeterTamaroff I like Elmo . . . :(

@PeterTamaroff Am I misunderstanding the thrust of this question?

@PeterTamaroff Nevermind, I see my mistake.

smackcrane

4:10 AM

quick question, if anyone's around

what does the notation $R[[x]]$ mean? I've encountered it in the context of modules over rings (apparently $R[[x]]$ is an R-module)

Tyler Langan

Hey guys, I'm not really familiar with math. If you wanted to make a social impact on the world, how could you do that with a math ph.D?

Say you were trying to solve the wicked problems of poverty or education.

Peter Sheldrick

do a phd in economics or education?

maybe a phd isn't the right thing for you...

user19161

@TylerLangan You can't. Change the world one small act at a time. The world is too big to handle.

Peter Sheldrick

@TylerLangan, did you see this? math.stackexchange.com/questions/71874/…

user19161

4:26 AM

@Limitless Are you going to sleep soon?

Limitless

@JasperLoy, no. I have the math virus.

@JasperLoy, do you care to correct me? I have made a fatal error somewhere in a proof.

Peter Sheldrick

on the whole mathematicians are unfriendly and not concerned much about the welfare of others...

user19161

@Limitless Hmm, too tired now...

user19161

@PeterSheldrick I disagree. I think they are just like any other people...

Peter Sheldrick

fair enough

that's kinda gloomy

Limitless

4:30 AM

@PeterSheldrick You can't generalize mathematicians! They are generalizers. :P

@JasperLoy A shame. :(

user19161

4:40 AM

@Limitless What will you be learning from?

Limitless

@JasperLoy I am currently stuck on a problem

user19161

@Limitless OK, won't disturb you...

Limitless

@JasperLoy, no. I meant that is what I am learning from. :-) You did not disturb me.

user19161

@amwhy Are you trying to cap before going to sleep?

Gustavo Bandeira

@limit I am disturbing.

Peter Sheldrick

4:42 AM

@Limitless. what are you doing? What part of math?

lemme guess: complex analysis

Limitless

@PeterSheldrick Trying to figure out whether a complex infinite product converges or diverges and why.

Gustavo Bandeira

Perhaps counting sheep

Limitless

3

Q: Showing that infinite product $\prod{(1+\frac{i}{k})}$ diverges

In Bak and Newman's Complex Analysis they ask to show that the infinite product $\prod_{k \ge 1}{(1+\frac{i}{k})}$ diverges (with $i$ being the imaginary unit). My intuition is that it does not diverge to $0$, but rather just kind of oscillates randomly around the origin for large partial product...

Sanchez

it does diverge, what's your proof?

Peter Sheldrick

mmh if |z|<1?

oh that product

Limitless

4:44 AM

@Sanchez, I don't have one yet . . . Fumbling around with the basic $\sum \log a_k$ diverges if and only if $\prod a_k$ diverges.

At the moment I'm applying an integral test in one section of the problem

Sanchez

@Limitless, I see. I saw in the comments that you think it may converge. Let me reassure you that it diverges ;)

Limitless

So far I am at

user19161

It's pretty easy to ignore a user in chat accidentally by clicking.

Limitless

Prove $\sum_k \sqrt{1+\frac{1}{k^2}}$ diverges.

user19161

I think they should shift the "ignore" to another position.

Limitless

4:47 AM

I think integral test works, @Sanchez.

Khromonkey

Hi guys

user19161

@limit Testing do you get this ping?

Khromonkey

Tower (mathematics)

In category theory, a branch of abstract mathematics, a tower is defined as follows. Let \mathcal I be the poset :\cdots\rightarrow 2\rightarrow 1\rightarrow 0 of whole numbers in reverse order, regarded as a category. A (countable) tower of objects in a category \mathcal A is a functor from \mathcal I to \mathcal A. In other words, a tower (of \mathcal A) is a family of objects \{A_i\}_{i\geq 0} in \mathcal A where there exists a map :A_i\rightarrow A_j iff i>j and the composition :A_i\rightarrow A_j\rightarrow A_k is the map A_i\rightarrow A_k Example Let M_i=M for some R-module M...

Limitless

@JasperLoy, yep

Peter Sheldrick

@Khromonkey, hello

Khromonkey

4:48 AM

Why isnt there an article of what a tower is in the encyclopedia of mathematics?

Gustavo Bandeira

Tower? WTF?

Khromonkey

encyclopediaofmath.org/…

Peter Sheldrick