Mathematics - 2012-09-19 (page 2 of 5)

3:00 PM

Solving for $x^3+2x^2-5x-6=0$

@ParthKohli I'm glad you found it helpful. It is surprising that no one ever noticed that before (perhaps someone did, but I've never heard of it).

Dan the Man

The possible roots are $\pm 1, \pm 2, \pm 3, \pm 6$

I tried $-1$ and it looks like it is a root

Parth Kohli

What is the easiest way to factor a cubic?

Dan the Man

$(-1)^3+2(-1)^2-5(-1)-6=0$

$-1+2+5-6=0$

$+1-1=0$

So -1 is a root

I mean a zero

$(x-1)$ is one of the factors

I divide the original equation, $x^3+2x^2-5x-6=0$, by the first found factor, $(x-1)$

anon

@ParthKohli the easiest way to factor a general cubic is still pretty tedious and hard to remember. the sort of cubics a typical class will get as factoring exercises though will likely need only rely on integer divisibility considerations and experience with the patterns.

Dan the Man

3:12 PM

But the problem is that I get a remainder when dividing.

Sorry, I can't figure out how to write synthetic or long division in latex

anon

writing it in latex would be too tedious anyway

Perhaps you should divide by (x-(-1))=x+1 instead, because it's actually a factor :-)

Dan the Man

What do you mean?

anon

What makes you think x-1 is a factor of your cubic?

You found the root x=-1, so it should be divisible by x-(-1)=x+1. It should only be divisible by x-1 if x=1 is a root, but 1 is not a root so it is not divisible by x-1.

Dan the Man

Doh!

That's what it was...

so $(x+1)$ is the factor

And I should divide by that.

The roots are $+2,-3,-1$

Am I right?

anon

I'm not your calculator man, just plug em in and test

3

user19161

3:23 PM

@ParthKohli Trial and error. Find one root first, and then you get a linear factor and a quadratic factor.

user19161

@anon You are the calculator checker. :-)

user19161

@math101 Strict? Say everything that needs to be said, no more no less.

Dan the Man

@anon Lol ok

anon

On MSE a user may not know precisely how much needs to be said, so I think they should err on the side of full transparency and comprehensive disclosure: write all of the context because if you could reliably tell which details are relevant to others and which aren't you might not be asking the question in the first place.

Also, a user may have narrowed in on an inefficient path towards a conclusion, and readers will lose the chance to explain better paths and better illuminate the whole territory if the user only indicates an interest with the path they're focused on.

Dan the Man

3:38 PM

Well said

$x^2 +x=6$ I can easily see that $x=2$

But how do you solve it?

Or what are the procedures of solving it?

anon

If $x^2+ax+b=0$ and the roots are $r,s$, then $r+s=-a$ and $rs=b$. Thus if $r$ is the root you're looking for, $r+2=-1$ and $2r=-6$.

Parth Kohli

Quadratic formula.

Jayesh Badwaik

@Evan Your question was formulated in a way that I though I should be responded with some more vigor. To put it mildly the three workhorses of computation are Fortran, C, and C++. And except for legacy libraries, no one uses FORTRAN and C.

Dan the Man

@anon @ParthKohli Right. thanks

Parth Kohli

$$x^2 + x - 6 = 0 $$ You can always use factoring, by the way.

Dan the Man

3:44 PM

Oh right.. Why didn't I think of that...

Parth Kohli

$$x^2 + 2x - 3x - 6 = 0 \\ x(x + 2) - 3(x + 2) \\ (x - 3)(x + 2) = 0 \\ \therefore x = 3 \vee x = -2 $$

Is vee($\vee $) okay to use in the above?

Jayesh Badwaik

@robjohn I am on Linux.

Parth Kohli

Sorry, my answer is incorrect

The correct answer is the following:

Jayesh Badwaik

Can you explain a little more of what you mean with the $\sqrt{trace}$ and $\sqrt{norm}$ method? @ParthKohli I am a little curious since I have not heard that terms before.

Parth Kohli

$$x^2 + 3x - 2x - 6 = 0 \\ x(x + 3) - 2(x + 3) = 0\\ (x - 2)(x + 3) = 0 $$

robjohn

3:48 PM

@JayeshBadwaik Okay, that explains somewhat. Firefox on the Mac (and I assume the PC) displays color using HTML-CSS

Parth Kohli

Sure, @Jayesh.

Jayesh Badwaik

@robjohn Ohh, okay.

robjohn

@JayeshBadwaik and, at least on the Mac, has the same problem with SVG.

Parth Kohli

You can find it here.

Dan the Man

Just curious, what does $\vee$ mean?

robjohn

3:51 PM

@ParthKohli as long as you're working in a ring with no zero divisors :-)

Parth Kohli

$\vee$ is mathematical notation for "or".

Similarly, $\wedge $ for "and".

Jayesh Badwaik

@robjohn Okay. It most probably means that its a problem with MathJAX then. Also, I suspect the HTML-CSS thing has to do more with something of my setup, I use ArchLinux, and one of the disadvantages is that the minimal system specifications means you may not know what you are missing if it is not essential. Also, I made some font tweaks to my browser. May be it is because of that. I will have to check then. ;-)

robjohn

@JayeshBadwaik It might be, but it could point to limited SVG support on several platforms.

Dan the Man

@ParthKohli Ah. interesting.

Parth Kohli

@DantheMan I suggest you start with Set Theory. Anyway, this is a helpful link.

Jayesh Badwaik

3:54 PM

@robjohn Okay. My guess was SVG is a image rendering thing, so font support should not really bother stuff, since in the end what I am seeing is an image and MathJAX is generating that image. But I might be wrong, I am largely ignorant about displays, fonts and stuff.

Parth Kohli

May I ask what the difference between $\pm$ and $\mp$ is?

Dan the Man

@ParthKohli yes. thanks

Jayesh Badwaik

$2 \pm 3 \pm 5 = 10 \text { or } -6$
$2 \pm 3 \mp 5 = 0 \text{ or } 4$

2

Dan the Man

@JayeshBadwaik That's insane!

Jayesh Badwaik

@DantheMan Why?

Dan the Man

3:58 PM

@JayeshBadwaik I mean awesome.

Parth Kohli

Oh, I got the difference very well. Thanks @JayeshBadwaik.

Jayesh Badwaik

@DantheMan Hmm. Lot of stuff is. :-)

robjohn

@ParthKohli they represent a dual answer; use either the top or the bottom function

Parth Kohli

Also, are imaginary numbers considered irrational as well?

@robjohn Yes, that is what I understood from Jayesh's example.

robjohn

@ParthKohli yes, rational algebraic integers are integers, so it must be that rationals are only the real rationals.

@ParthKohli and by their definition, they are ratios of integers.

Jayesh Badwaik

4:00 PM

@robjohn I always thought irrationals meant $\mathbb{R} - \mathbb{Q}$

Parth Kohli

According to the definition, $i$ cannot be expressed as a ratio of two integers... wait... of course I can't be expressed as p/q! I'm a human!

anon

Since rationals are Q, anything outside of it, including nonreal numbers, are irrational. though I've seen rationals redefined as Q(i) for some purpose before.

robjohn

@anon There are Gaussian integers, are there Gaussian rationals as well?

anon

that would be Q(i), the fraction field of the gaussian integers

they are of the form (a+bi)/(c+di) or equivalently (p/q)+(r/s)i.

robjohn

@anon but are they ever called Gaussian rationals?

anon

4:02 PM

dunno

robjohn

@anon I don't think I have heard them called that.

John Junior

Imaginary irrationals?

robjohn

@JohnJunior That's just not a rational response, as you can well imagine!

Dan the Man

If I use the quadratic equation on a 2nd order polynomial that doesn't have a term $c$, do I substitute $c$ with 0 in $-4ac$?

Parth Kohli

@DantheMan I don't get your question.

Dan the Man

4:06 PM

I have the equation $x^2-3x=0$

Parth Kohli

For example,$$x^2 + 10x + 25 = 0 \implies a = 1, b = 10, c = 25 $$

John Junior

Yes, the formula still works.

Parth Kohli

Yes, it still works.

In your equation, $c = 0 $.

John Junior

It only doesn't work when a=0.

Dan the Man

$c\stackrel{?}{=} 0$

Ah ok

Thanks guys

John Junior

4:09 PM

For an obvious reason, right?

Dan the Man

@JohnJunior Division by zero ;)

Parth Kohli

In general, if $p(x) = a_1^{n} + a_2^{n - 1} \cdots a_{n + 1}^{0}, a \ne 0$.

John Junior

Division by zero is not irrational, but pathological in the set of real numbers.

Parth Kohli

Never divide by zero, or else...

math101

@robjohn THANKS :)

Parth Kohli

4:11 PM

This is what happens if you divide by zero: i.stack.imgur.com/qY34s.jpg

3

John Junior

^In the set of real numbers.

robjohn

@math101 Does that match what the book asks?

Dan the Man

@ParthKohli Hahaha. favorited.

math101

@robjohn I am work when I get home I'll check it

But it seems correct

Dan the Man

@JohnJunior I hardly understand that.

Parth Kohli

4:14 PM

Yo, Pippa.

robjohn

@JohnJunior That is pretty drastic. On my dad's mechanical calculator, it just kept subtracting $0$. I guess when the lubricant wore out, it might seize up, but nothing so explosive.

John Junior

@robjohn I meant it destroys the world of real numbers :)

user19161

@anon Though "irrationals" typically refers to R-Q.

robjohn

@JohnJunior It maps all the non-zero reals to the non-real $\infty$. It doesn't know what to do with $0$.

user19161

@JohnJunior This chat has had 9000 discussions of division by 0 it seems.

John Junior

4:21 PM

@WillHunting Well this is the 9001st :)

@robjohn Am I not correct if we restrict the discussion only to the set of real numbers?

user19161

@ParthKohli Lovely! You should use that for your pic.

robjohn

@JohnJunior are you correct about what? About destroying the world of real numbers? I guess it depends on how one would destroy a fictional world to begin with.

Parth Kohli

Oh yeah, didn't realize that.

Thanks for the suggestion. :)

John Junior

@robjohn Even the "positive integers" are a fictional world too then right?

robjohn

@JohnJunior are they a world?

Dan the Man

4:29 PM

When I graph this system of equations, two of the points never intercept... would those be irrational or imaginary?

fooplot.com/plot/r436o5fdut

John Junior

@robjohn No they are not, you are correct.

robjohn

@JohnJunior I just don't know what definition of "world" you are using.

John Junior

@robjohn Neither do I, my apologies for not clearly defining that at the beginning.

robjohn

@JohnJunior but you are correct that dividing by $0$ is not allowed in the reals (or even the complex plane).

user19161

Ah, I finally thought of how to move my chatjax bookmark so that it does not take up another row on my browser!

Parth Kohli

4:36 PM

Another confusing question is, what's $0^0 $?

John Junior

undefined

Parth Kohli

$n^0 = 1 $, but $0^n = 0 $... there's a contradiction.

Yes, undefined.

user19161

@ParthKohli Depends on how you want to define it.

Parth Kohli

Still, some mathematicians agree with 1, or some with 0.

user19161

In most cases, one does not have to worry about its definition!

user19161

4:38 PM

So this become a rhetorical question.

Nimza

Good day, mathematicians!

Parth Kohli

Hey, @Nimza! Good day to you too (even though the word "mathematician" doesn't suit me well).

Nimza

I have a question for somebody who has a sense of beauty!)

Parth Kohli

This is beauty: $e^{i\pi} = -1 $

Nimza

No, geometrical beauty)

user19161

4:43 PM

@ParthKohli It is more beautiful if you write it as $e^{\pi i}+1=0$.

Ed Gorcenski

Morning

Nimza

hehehe)

@EdGorcenski hi

Parth Kohli

@WillHunting doesn't make any difference.

Jonas Teuwen

@Matt Yeah! Shocks! Plenty. What food poisoned you? You ate in France?

user19161

@ParthKohli It does, that is because of the physical presence of important constants and operations.

user19161

4:44 PM

@JonasTeuwen Like escargots?

Jonas Teuwen

Yes.

user19161

I have not eaten French snails, only German sausages.

John Junior

@JonasTeuwen How are you feeling?

Nimza

Torus $z_2^2 -z_1^4 = -1$ has 2 points at infinity. How to draw a contour around one of such points but not around another one?

Parth Kohli

So, you imply that $2x = 4 $ seems better written as $x + x = 0 + 1 + 1 + 2 $?

Hey, @Alpha! Good work so far.

user19161

4:46 PM

@ParthKohli No, that is because it is well-known that the most beautiful way to write that formula is so.

Parth Kohli

Usage of the word beautiful is so arbitrary.

Ed Gorcenski

This paper is nearly indecipherable

Nimza

beauty is relative :)

Jonas Teuwen

I am absolutely beautiful. Just like Will!

Parth Kohli

Yes, you are a blue plane. @Jonas

Ed Gorcenski

4:48 PM

using superscripts for indices should be grounds for jail time

Alpha

Hi, I had joined within an hour ago

Parth Kohli

Yes, Alpha, and you are fast!

Alpha

Maths Stackexchange is awesome

user19161

@JonasTeuwen Yes, we are both sexy.

Parth Kohli

Agreeage @Alpha ;-)

John Junior

4:49 PM

@Alpha Welcome

Jonas Teuwen

@WillHunting Imagine what would happen if you fuse use...

Alpha

@ParthKohli Thnaks

user19161

@Alpha Of course, the whole SE too.

Alpha

Thanks to all guys

Parth Kohli

... and what about girls? ^

Jonas Teuwen

4:49 PM

I am in terrible pain laughed the Belgian boy.

Alpha

Thanks to all girls too

user19161

@JonasTeuwen Is this your novel?

Jonas Teuwen

Sure is. Do you like it?

user19161

Yes, I might write one too in future!

John Junior

Where can I buy a copy?

Parth Kohli

4:50 PM

"I am in terrible pain," laughed the Belgian lad.

Ed Gorcenski

"In $Y$, we use the Euclidean scalar product, defined in the standard way by
$\langle p,q\rangle_Y = \sum_{1 \le i,j \le N} \left(p^1_{i,j}q_{i,j}^1+p_{i,j}^2q_{i,j}^2\right)...$ am I squaring $p_{i,j}$ or what...? *what is happening I don't even....*

Jonas Teuwen

You are postponing your whole life, Will!

Alpha

I had earned 14 reputation within an hour, maybe that is why my friend call me math master

sorry 24 reputation

Nimza

@ParthKohli today I was standing in traffic in bus and I saw a girl with a boy. Girl was telling her boy about horned sphere and boy was'n happy with interests of his girl. Bastard

user19161

@Alpha Erm, that is not much...

user19161

4:52 PM

How is your website @jonas?

Alpha

@WillHunting Its enough for a newbie

like me

Jonas Teuwen

@WillHunting Postponed.

user19161

@Alpha OK, you need at least 20 to chat.

user19161

It is raining heavily here.

Alpha

I am having 24 my friend

Parth Kohli

4:53 PM

I'm the n00b here.

user19161

@Alpha That is why you can post messages, silly!

Alpha

Yep, i thought you didn't got that

Ok, I g2g, bye friends

user19161

@EdGorcenski Which book is this? Just check for the definition.

Ed Gorcenski

It's a paper. It's undefined.

But, implicitly, it appears to be an index of an element in a vector

I'm trying to understand an algorithm for total variation regularization of a 2-D signal.

Unfortunately, most of these methods were developed for image processing, and so work on nice, uniformly spaced grids, which I do not have.

What is this "3568" that appears under my name on the left?

Jayesh Badwaik

@JonasTeuwen You have a new emacs convert. I have reached the conclusion that emacs is worth the effort of customization to be used as an editor for almost everything.
I have one more question. When I am writing BIG C++ programs with a lot of other header files, in KDevelop, whenever I hover over a function/class etc, it provides me with a complete overview of the function from its definition, and if I want, its uses. Is there something similar in emacs?

@EdGorcenski That is sum of your reputations from all chat accounts.

Jonas Teuwen

5:07 PM

@JayeshBadwaik Nice 8-).

@JayeshBadwaik There probably is.

Some .el file as always.

Jayesh Badwaik

@JonasTeuwen Ohh. 8-) Nice. I am searching for it right now, I don't know exactly how to search for it though, so taking a little time.

Jonas Teuwen

Yeah, there are many of those extensions right?

Jaakko Seppälä

Could someone say if it is correct to say that an elliptic curve is of the form y^2=x^3+ax+b as for example Qing Liu adds the privileged rational point to the definition? I'm just reading a popular article on ABC-conjecture.

Jonas Teuwen

Also check out emacs-org.

Jayesh Badwaik

@JonasTeuwen Hmm. BTW, this was the tipping point for conversion.

Jonas Teuwen

5:09 PM

Oh yes :-).

Check out the whole AucTeX suite...

(Was it for me too!)

Jayesh Badwaik

Yup installed that, exploring it correctly.
Awesome!

John Junior

hi @MarianoSuárez-Alvarez look who's back :-D

John Junior

5:32 PM

Ed Gorcenski

O_O this algorithm is shockingly simple once you cut through the heavy math

Jayesh Badwaik

@EdGorcenski Image processing algorithms generally are like that. :P

@MeAndMath Hello.

MeAndMath

hi!

John Junior

hi

Jayesh Badwaik

@JonasTeuwen I guess you use iPad and iPhone. Check out MobileOrg (if you don't already know about it that is. :P )

MeAndMath

5:46 PM

@JayeshBadwaik @JohnJunior How are you guys?

John Junior

Fine thanks and you?

MeAndMath

@JohnJunior I'm good.

@GustavoBandeira Are you woke up?

Gustavo Bandeira

@MeAndMath Yep. And curious...

MeAndMath

@GustavoBandeira about?

Gustavo Bandeira

Nothing. =)

How are you?

MeAndMath

5:51 PM

good

Parth Kohli

Hello!

Jayesh Badwaik

@MeAndMath I am good.

MeAndMath

a sec BRB

Jayesh Badwaik

@GustavoBandeira Everyone is curious around here. :P :P

Gustavo Bandeira

Actually, this is what happens when you divide by zero:

►

Me reading Barbeaur's Polynomials

Parth Kohli

5:55 PM

Heh, the way he dances.

Jayesh Badwaik

@ParthKohli Just for curiosity, you don't have to answer. What do you do?

Parth Kohli

@Jayesh: I am a student.

Gustavo Bandeira

@JayeshBadwaik OF COURSE HE HAS TO ANSWER! IF HE DOESN'T, I'M GONNA BAN HIM!

3

Jayesh Badwaik

@ParthKohli Okay.

@GustavoBandeira Heh.

Parth Kohli

@Gustavo: That's the misuse of theoretical moderation powers!

2

Ed Gorcenski

6:12 PM

I love when things work

I expected this to take me all day

Jayesh Badwaik

@EdGorcenski I'm curious, so can I ask what exactly you are reading?

Ed Gorcenski

The Chambolle Algorithm

citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.5226

Jayesh Badwaik

@EdGorcenski Hmm, every image processing algorithm uses that second set of images.

Ed Gorcenski

Lena?

Yes

Jayesh Badwaik

@EdGorcenski Yup, it is the standard image which is used for testing image processing algorithms.

Ed Gorcenski

6:21 PM

There is a history of that image

Jayesh Badwaik

Yup.

Ed Gorcenski

It was pulled from a copy of Playboy :D

Jayesh Badwaik

@EdGorcenski I know!

Matt

@JonasTeuwen No, I did not eat in France. I ate sushi, perhaps a mistake to do that outside Japan. Now sick.

user19161

@Matt Sushi here is pretty safe. It might even be that you just can't take raw food.

user19161

6:29 PM

@JayeshBadwaik Curious about what?

Jayesh Badwaik

@WillHunting Ask @GustavoBandeira why certain people are curious.

user19161

@JayeshBadwaik You are all so naughty...

John Junior

And you are not?

Jayesh Badwaik

@WillHunting Heehee.

user19161

@JayeshBadwaik What distro do you use?

Jayesh Badwaik

6:32 PM

@JohnJunior He is sexy enough that he does not have to be naughty.

Gustavo Bandeira

In mathematics the art of asking questions is

more valuable than solving problems.

Cantor (1867)

Jayesh Badwaik

@WillHunting ArchLinux.

Gustavo Bandeira

Yay! I'm done then!

user19161

@JohnJunior I am only curious about you. :-)

Jayesh Badwaik

@WillHunting You are also curious about anon.

user19161

6:33 PM

@JayeshBadwaik Same as Jonas. Wow now you both use Arch and Emacs.

user19161

@JayeshBadwaik Yes, I am curious about both anon and junior.

John Junior

Remember what it did to the cat.

user19161

@JohnJunior I am a dog, not a cat!

Jayesh Badwaik

@WillHunting Yeah, convergence of evolution I might say.

user19161

@JayeshBadwaik I use Debian and TeXworks.

Jayesh Badwaik

6:36 PM

@WillHunting I used to use debian, but it was not cutting edge enough for me. Never used TeXworks, so cannot comment.

user19161

@JayeshBadwaik How do you find Emacs and Arch so far?

Jayesh Badwaik

@WillHunting Arch I have been using for around a year, so it is quiet good. It is as good as Debian with the cutting edge stuff.

@WillHunting Emacs just starting to use now in full fledge. I am not satisfied with its GTK backend and hence corresponding GTK file selector dialog and stuff. But I guess I can live with it.

user19161

@JayeshBadwaik GNOME uses GTK! You may switch to GNOME!

Jayesh Badwaik

@WillHunting I am NOT satisfied with GTK! ;-)

I wish someone could re-write emacs in python. Then, you can use pygtk or pykde or wxwidgets as you wish and no one will have to force anythign upon you.

Ed Gorcenski

I am a Windows user, but Notepad++ is magical.

Jayesh Badwaik

6:49 PM

@EdGorcenski Whenever I am over at my friends room and have to show him some code stuff on his machine, I prefer notepad++, but I am not sure of any other alternatives which might exist as general purpose editors in Windows.

The stuff I miss the most whenever I am working on windows is the command line. I have tried powershell but I haven't completely adjusted to it.

Jonas Teuwen

@JayeshBadwaik Disable the GTK backend, you can do it without.

Ed Gorcenski

I need to learn more about dual constructions.

As far as I can tell, they're witchcraft.

Jonas Teuwen

Yeah they are. Stop doing that maaaaaaaaaaan.

Parth Kohli

Lambert W Function ?

Ed Gorcenski

What sort of class would one even learn about duals?

Transcript for

$Mathematics$ Mathematics