Mathematics - 2012-09-05 (page 1 of 4)

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12:00 AM

$x^{-y}=(x^y)^{-1}$

On iPad no mathjax.

user19161

$a^{-1}=\frac{1}{a}$

12:28 AM

An idle question for the regulars: do you think that the question limit has changed anything?

Hi! If $F$ is an infinite field, what is the cardinality of $PSL_n(F)$?

I suspect that it has the same cardinality as $F$, but I know little about these things

12:44 AM

@DylanMoreland Nah

Though, I haven't asked many questions lately, and I haven't seen anyone complain.

@PeterTamaroff I seem to recall that Matt was having some issues with it. Maybe I'll dig up that thread.

@DylanMoreland I think he is OK now.

1:04 AM

Is anyone familiar with mathematica? Its giving me trouble

Gustavo Bandeira

@math101 Tell me.

@math101 I'm on a very elementar level, but maybe I can help

math.ysu.edu/~faires/Numerical-Analysis/Programs/programs/…

open ALG023.MA

I then evaluated the notebook

Then a dialog box appears and u have to enter the function

Gustavo Bandeira

Yep.

.5+.25x^2-xSin[x]-.5Cos[x]

Gustavo Bandeira

I opened one of them and I cant close the window, let me try

Ok

1:09 AM

I am having specific issues with ALGO23>MA

@math101 Have you tried turning it off and on?

Turning what off an on

It works for other functions

I am just having difficulties with this particular one

Gustavo Bandeira

I'm evaluating it but nothing happens

thats weird

Gustavo Bandeira

The evaluation keeps running ad infinitum.

Let me restar mma

1:14 AM

ok

like on the mathematica bar ontop there should be an option for evaluation

Gustavo Bandeira

Now it's ok.

a drop down bar appears

Gustavo Bandeira

What function should I input?

.5+.25x^2-xSin[x]-.5Cos[2x]

The initial approximation =15.5

The tolerance = 10^-7

The number of iterations=50

Gustavo Bandeira

I got this while using Cos[x]

user image

1:18 AM

Ya it works with other functions

But smth is going wrong with this specific one

Also I pressed 2 the option to see all the approximations

Gustavo Bandeira

Answer only or all aproximations?

all approximations

Gustavo Bandeira

Formating notebook contents...

ya so its gonna crash in a sec

u shld exit it b4 it crashes ur comp

hmmmmm

wonder what happened

Gustavo Bandeira

@math101 Let it bang

1:26 AM

huh?

Gustavo Bandeira

It's eating a lot of memory.

did it crash?

Gustavo Bandeira

Yep.

idk what I am doing incorrectly

Gustavo Bandeira

But it still didn't crasehd the rest of the system.

1:28 AM

Oh It froze my comp twice today

Gustavo Bandeira

Mathematica - 4k RAM
Math Kernel - 2k RAM

It almost froze mine.

ughhhhh I seriously dont want to do all the computations by hand

Gustavo Bandeira

I closed it now.

I guess you're asking too much - I mean, it was eating 75% of my RAM.

I guess this process is a litle lengthy.

little*

well like i have to evaluate it this function at 3 diff initial approximations

i did one by hand

and then right after I was able to get mathematica to compute it

but now its refusing to listen to me

Gustavo Bandeira

Let's try to ask it on the Mathematica chat?

1:32 AM

whats the link?

Gustavo Bandeira

Wolfram Mathematica

Welcome! This is the main Mathematica chat room for mathematic...

Thankssssssssss

@MarianoSuárez-Alvarez Hello Mariano. Hola?

@GustavoBandeira Alrighty I posted my question. Thanks

Gustavo Bandeira

I want a remix of this: Ask stack exchange.

1:50 AM

y wld someone downvote my question

Like seriously I provided all the information I cld

Gustavo Bandeira

Maybe it's something so trivial, dunno.

user image

Perhaps a poor title.

ohhhh ya it is a poor title

i cldnt think of nething better

uughhh The guy said my coding is the issue

user19161

2:28 AM

@gustavo So you play the piano?

Gustavo Bandeira

@WillHunting I usually say I study it.

user19161

@GustavoBandeira How is your skill?

Gustavo Bandeira

As I'm a newbie, I like to stuck with that.

There's a graded list, let me try to find.

But I'm gradr 4 - 5.

grade*

The biggest music I played had 6 pages.

Not much, Totentanz has 31.

And a lot of advanced moves.

Look:

user19161

@GustavoBandeira From the pic alone it is hard to tell the sex of the person.

Gustavo Bandeira

Haha. Women.

Valentina Lisitsa.

@math101 It seems they solved your problem

@WillHunting Look this: youtube.com/…

I recommend you to see the one about the double notes.

The technique for that is ill.

Gustavo Bandeira

3:00 AM

This is topology, right?!

Yes the solved it. Everyone down voted my question

Thanks @GustavoBandeira

Gustavo Bandeira

3:51 AM

@math101 You're welcome. =)

2 hours later…

5:58 AM

Does anybody know about percolation thoery here??

Gustavo Bandeira

@RamanaVenkata A new weird name added to my list.

@RamanaVenkata I guess I've seen the application of this theory on minecraft - accoerding to the few things I read now.

Names from India will be wierd to Europeans or Americans or any non-Indians I suppose

I want to study about introdution to percolation

Gustavo Bandeira

@RamanaVenkata Sorry, It wasn't your name, it was percolation theory.

theory

Okay sorry

Gustavo Bandeira

In portuguese, I can visualize your name as a name, and "percolation theory" as a name.

Actually, I think they're different objects, but at that moment, It was how I could express it. I said that because I usually hear unusual names on mathematical fields here, some days ago, someone told me about surgey theory.

@RamanaVenkata mit.edu/~levitov/8.334/notes/percol_notes.pdf

Do you know this?

6:11 AM

Nope

Gustavo Bandeira

Look it

@FortuonPaendrag Hello!

I was kinda talking bout you. You said me about surgery theory.

@RamanaVenkata I've found several pdf's on google, want me to show them to you?

Actually I asked here because there is good probability of getting a good advice Google will give too many results I just want one or two which are good.

Gustavo Bandeira

@RamanaVenkata Since it seems to deal with probability theory, maybe it could be nice to ask on cross validated SE.

Okay

1 hour later…

7:28 AM

@JayeshBadwaik - hi there

@JohnSenior Hi. How are you?

@JayeshBadwaik Fine, thanks - and yourself?

I'm good too. I am just going now actually. Lunch awaits :-)
See ya in a bit.

@JayeshBadwaik Later

Gustavo Bandeira

John

@JohnSenior Can you help me with a notation?

7:32 AM

@GustavoBandeira I will try :)

Gustavo Bandeira

What's the meaning of this: $f:X\to \mathbb R$? Is it Function of x for all x contained in R?

@GustavoBandeira It means that $X$ is any set (need not have anything to do with $\mathbb{R}$ necessarily) and $f$ is a function which gives a real number for each possible element of $X$

For example, $X$ could be the set of all vectors, and $f$ could be the function which gives the length of a vector

Gustavo Bandeira

Yep.

You answered the question I would ask now.

Really?

Bzz.

7:38 AM

@JonasTeuwen Good morning - hope you are feeling better

Gustavo Bandeira

Yep.

You said: "Any set" I thought they could be only sets of numbers.

@GustavoBandeira Ah right - in the notation $f : X \mapsto Y$, both $X$ and $Y$ can be any kind of set - neither need to be numbers (but they often are)

Gustavo Bandeira

@JohnSenior Thanks.

@GustavoBandeira Glad to be some help :)

Gustavo Bandeira

Saying that "a number is not an algebraic function of x." means that this number can't be generated through algebrical methods, right? I mean, I've seen a lot of algebra names, I thought some of them could do this.

7:54 AM

@GustavoBandeira I would say that the statement "a number is not an algebraic function of $x$" is a slight abuse of notation - it would be better to say either "$x$ is not an algebraic number", or " a function is not an algebraic function"

but basically I agree with what you said :)

Gustavo Bandeira

@JohnSenior This is a naive question but: what are their sources then?

@GustavoBandeira sorry - sources of what?

Gustavo Bandeira

@JohnSenior Of transcendental numbers?

@GustavoBandeira Ah - you mean where do transcendental numbers come from?

Gustavo Bandeira

Yes.

7:59 AM

Probably best to think of them like this: they are the real numbers which are left after you have accounted for all the algebraic numbers

"Most" real numbers are actually transcendental, but it tends to be extremely hard to prove that a particular number like $e$ or $\pi$ is actually transcendental

Gustavo Bandeira

I've seen the source of the Euler's number, which I guess is this one:

$$e = 1 + \frac{1}{1} + \frac{1}{1\times 2} + \frac{1}{1\times 2\times 3} + \frac{1}{1\times 2\times 3\times 4}+\cdots$$

Why it's not an algebraic number?

@GustavoBandeira Correct - that is known to be transcendental - but the proof is a bit tough

the proof starts by assuming that there is an algebraic (polynomial) equation with $e$ as one of its roots, and then derives a contradiction, I think

Come to think of it, I don't think I've ever seen a proof of that. I have seen a proof for $\pi$ though.

@ZhenLin interesting - I saw a proof for $\pi$ which started by proving something about $e^x$ and then using the fact that $e^{2\pi i} = 1$

Yeah, but you don't need to know $e$ is transcendental.

8:05 AM

here is the theorem I was thinking of

Oh, that's cheating :p

it proves quite a lot of numbers are transcendental

I'm thinking of Cartwright's proof.

I seem to recall being a bit baffled by Hilbert's proof many years ago - but can't remember the details

Hilberts proof for $\pi$ seemed short and mysterious

Oh wait, that only proves irrationality. Hmmm. I don't think I've seen a proof of transcendence.

8:08 AM

Morning! Can anyone in here do knot theory?

@Matt Sorry - no :(

:,(

Knot theorists are underrepresented on SE.

@Matt maybe knot theorists are under-represented amongst mathematicians in general - I think I only ever met one

@GustavoBandeira It's interesting that my son skyped me that video and a second part last night.

Gustavo Bandeira

@robjohn What video?

8:17 AM

5 hours ago, by Gustavo Bandeira

Gustavo Bandeira

@robjohn See? I'm your son.

@GustavoBandeira long way from school in Chicago, then....

Gustavo Bandeira

@robjohn But it's a cool video - I was wondering on how topology should be, this helped me a little.

user19161

9:08 AM

@jonas How are you feeling today?

9:28 AM

@JohnSenior Lindemann–Weierstrass is one hell of a long proof.

@robjohn how did you quote @GustavoBandeira post? If you did this just using "Reply to Message" then that feature does not work properly for me I guess.

:6030717

testing the feature once again.

Can you guys see the Gustavo's video here? I cannot. I just see :6030717.

@JayeshBadwaik This is just a string of numbers.

@peoplepower Yup, but the original intent was to quote the video which Gustavo had posted.

@GustavoBandeira I hope this works.

No, it doesn't. This one as done using link to chat feature.

Use the permalink

7 hours ago, by Gustavo Bandeira

Like this?

:)

9:44 AM

Okay! I have tried using permalink before, they did not work though, so I thought it was not the correct method. May be I was missing the "http://" when I copied the link from the firefox address bar instead of the dropdown arrow. Firefox likes to hide "http://" I dunno why. and I might not have added it on my own.

I don't think I had http:// in it though.

okay. Let me check without it once.
http://chat.stackexchange.com/transcript/message/6032911#6032911

4 mins ago, by Jayesh Badwaik

7 hours ago, by Gustavo Bandeira

Ah, when I copy it from the url bar, it adds http://

Ah, well when I copy paste it from ff address bar, it does not work, however when I copy paste it from the permalink link, it works. Strange. sigh

10:26 AM

yay sphere eversion

ooh did i coin "eversity"? english.stackexchange.com/a/41012

"well if you can't have corners... and you can't pull loops tight... then i think it's impossible to..." "i'll explain."

I'm sure, if given the chance, I would have made that argument and swept the problem aside. :)

but how does that change anything? spheres don't have saddles!

gangnam style! youtube.com/watch?v=9bZkp7q19f0

10:43 AM

@JayeshBadwaik Oh yes - it is a tough theorem - I wouldn't expect an easy proof of transcendence, unfortunately

Meow.

2

user19161

@JonasTeuwen Hey! I just had some coffee.

"The Mercurial repository can be cloned using hg clone ssh://hg@bitbucket.org/jjbteuwen/ratparser. "
This is incorrect, since my public key is not registered with your account. Instead, you need
"hg clone https://hg@bitbucket.org/jjbteuwen/ratparser"

@JonasTeuwen

@WillHunting Me too.

@JayeshBadwaik Huh, does your public key need to be registered with my account or with bitbucket?

I thought the last one.

10:59 AM

@JonasTeuwen Actually there is no need for the public key to be registered, general users can directly download using the https protocol instead of ssh.

I know. But I don't like https.

It think it should work if your public key is registered with bitbucket (and not with my account).

@JonasTeuwen Hmm, yup it works. But then, people who just want to test out your stuff will need to create a bitbucket account. Of course they can go to the repo site and take https url and download anyway but still...

Why are people trolling me when I am sick? What have I done to them 8-(.

@JayeshBadwaik Well. They should understand how that works. I didn't mention what a repository was either.

So first they can grow a brain and then do that, yes.

Also, not much parser there.

@JonasTeuwen :P Yup, that I noticed.
Go back to sleep, I won't disturb you anymore.

8-).

You are not disturbing me, but thanks for mentioning. Perhaps there was something I missed.

11:04 AM

:-)

Or let me state it differently, you are allowed to disturb me. And most other regulars here too. 8-). I won't see it as being disturbed. Yeah.

8-)

user19161

@JonasTeuwen You feeling very bad today?

Don't know.

user19161

@JohnSenior You are quiet today.

11:07 AM

@WillHunting I took that testyourvocab.com test. Got a score of 29100. I did not know I knew so many words! :P

I am not even sure if I have even heard so many different words.

@WillHunting He's an old retired man. He needs to rest a lot.

@WillHunting "Sometimes I just sits and thinks ..."

user19161

@JayeshBadwaik Or maybe you got half the meanings wrong.

hey

@WillHunting Naah, of that I am sure.

11:07 AM

@WillHunting "... and sometimes I just sits" :)

@JohnSenior "This John... Sometimes it just sits and thinks".

user19161

@JohnSenior Who said that?

@Rushil hi

Pondering about life and such.

Also what beer to drink.

@WillHunting Dunno - but it is becoming my motto, now that I have retired

user19161

11:09 AM

I have been trying to work out solutions to my life problems. It is very difficult. I am afraid sometimes that there will be no solution.

I got my "old person's railcard" this morning - I now qualify for cheap travel :P

@JohnSenior Does the card apply to UK or to full Europe?

user19161

Sometimes, I wish I don't wake up from my sleep. I am not sure how long more I have to carry these heavy burdens.

@JayeshBadwaik Just UK - I think

@JonasTeuwen How does the software calculate the parameters?

11:11 AM

Calculating is a good thing.

user19161

@JohnSenior Ah, we call them senior citizens here.

@WillHunting I think that is my official title here too

user19161

I know of some people who mysteriously died in their sleep. No doctors knew why.

@Jayesh, I took Meyers-Briggs today, got INTP as usual, I dunno why it's always the same.

user19161

It was not suicide or disease of any kind.

11:14 AM

@DanBrumleve Okay, I am taking one right now.

user19161

openSuse 12.2 will be released in an hour.

@WillHunting Old People?

user19161

@jayesh must be having internet problems again.

user19161

@JayeshBadwaik No, a teen.

user19161

So, the availability of Lee's smooth manifolds book second edition has been postponed to end of this month on Amazon.

11:17 AM

@WillHunting No, I deleted the first message this time, because now I am practicing using the reply to this message and other links on a normal basis. You are often telling me to do that, and I guess, it becomes easier for other people.

user19161

@JayeshBadwaik Of course. I only tell people about best practices you know!

user19161

@JayeshBadwaik By the way, the verb is spelled as practise in BrE.

user19161

In AmE, license and practice are both verb and noun.

user19161

In BrE, there are practice/practise and licence/license.

@WillHunting I know. And about spellings, my english is a hopeless mix of british, american, india, so I won't even try to correct it now.

user19161

11:20 AM

@JayeshBadwaik Indian English just follows British English spellings.

@WillHunting I know. And about spellings, my english is a hopeless mix of british, american, india, so I won't even try to correct it now.

now or never?

a fellow INTP, certainly.

Who is?

What did you call me?

j/k talking about @Jayesh.

11:33 AM

I didn't call you anything. Do you want me to call you something? I have a whole arsenal of words.

"American!"

I seem to recall I had to do this test for work and I was INTP too. Let me check it out.

i guess u are INTP too. it is common in my profession and i assume among mathematicians as well.

Holy cow the first sentence already contains intuition.

i am barely I (almost E) and barely T (almost F). but very strong N and P!

Seems to fit quite well. Or would it be like those horoscopes? Everything fits.

"You might have had a hard time in your life".

"Yeah yeah! So right, continue! UR GENIUS".

It is fun to troll those people.

"So... do you mean I am not allowed to eat little children? But... when they are so young you are not really attached to them yet right?"

That is usually when they understand they are being trolled with.

As if I am voluntarily going to tell those work related -ologist people about my internal wirings.

i think i was a more definite type when i was younger. i've relaxed on the I and the T a bit.

11:39 AM

I usually do not contemplate so much about... these things. Does it yield interesting information you do not yet know?

T->F may be a function of contemplating mathematical logic. i mean how do we really know PA or ZFC is consistent except that we believe it, or feel it?

This gets a bit too cloudy for me.

You assume it is, if you turn out to be wrong it means you have been doing bullshit all the time.

Like most people.

I need to find a way to map kil[l..l] to kill in my shell.

I->E maybe comes from work and trying to understand and empathize with people. still i'm 56% I.

Sometimes I get dragged away a bit with killing things.

mostly BS i guess :)

11:42 AM

@DanBrumleve Perfect.

kill is a builtin in your shell

The fuq... apt-get install ipython requires me to install 200MB of stuff?

imma rap that.

That's just a wrapper to... python, right?

idunno i'm a perl guy

11:45 AM

I'm sorry to hear that. Nobody's perfect, you know.

It is too easy to write code in Perl even Indians would shy away from!

2

gotta go baby crying

Good luck. Bye bye.

12:10 PM

@JayeshBadwaik the same way I am replying to this message. The very first thing on the line is :6032840.

It's knot funny anymore : /

Tumeni Seifert thingies.

@JonasTeuwen ipython is a wrapper to python but includes scipy and numpy and other libraries as dependencies. So, probably, there is that dependency lot that is getting installed.

Yes. I know. But whyyy.

12:26 PM

@JonasTeuwen Well, mostly because the the following are its objectives

IPython provides a rich toolkit to help you make the most out of using Python, with:

Powerful Python shells (terminal and Qt-based).
A web-based notebook with the same core features but support for code, text, mathematical expressions, inline plots and other rich media.
Support for interactive data visualization and use of GUI toolkits.
Flexible, embeddable interpreters to load into your own projects.
Easy to use, high performance tools for parallel computing.

Yes. Why. Why. Can do it as a module. What the monkey.

It is an addition over the python interpreter enviornment, not just the functions,

Also, your quote about Indians and Perl is demeaning.

user19161

12:40 PM

Wanna learn a new chat trick?

@WillHunting Yup. Anytime.

user19161

Look for the left downwards arrow of a message, click and drag it into the box. Then it will be quoted quickly without having to copy link location.

user19161

44 secs ago, by Jayesh Badwaik

@WillHunting Yup. Anytime.

31 secs ago, by Will Hunting

Look for the left downwards arrow of a message, click and drag it into the box. Then it will be quoted quickly without having to copy link location.

Nice!

user19161

I knew about the copy link location method, but this new method is faster.

12:43 PM

It does not work with scroll though. I cannot drag and scroll at the same time.

user19161

openSUSE 12.2 is out!

@DanBrumleve I just took the test, turns out I am an INTJ. I am now reading what it means now.
@WillHunting :-) I used to wait with same expectations for the Fedora release. Now ArchLinux has taken out all the euphoria of a release.

@JayeshBadwaik does that not work for you?

@robjohn Sorry. I did not respond to you earlier. Using the "reply to this message" provides a link back for me alright. However, to quote, I need to copy paste permalink.

I verified this with others and this seems to be the normal behaviour.

@JayeshBadwaik Oh, yes... that's true.

user19161

12:52 PM

@rob I remember you use openSUSE right?

@WillHunting Nope, MacOS and Unix

user19161

@robjohn Oh OK. Well I guess the UCLA server uses openSUSE then. That's how I got that impression after visiting your chatjax site.

@WillHunting I have no idea what that server uses.

@WillHunting how? I mean how did you infer that the site is hosted on opensuse?

@WillHunting never mind. I never thought of trying to change the link by a little.

user19161

@JayeshBadwaik Because openSUSE is written there.

12:55 PM

:P

user19161

At least it was on one of those sites when I visited it in the past.

@WillHunting Yup. It is.

1:20 PM

Hello World!

$10\sqrt{15}-10\frac{\sqrt{15}}{5}$

How do I solve this?

@DantheMan "Hello, World!"

Michael Greinecker

@DantheMan Shouldn't there bes ome equality somewhere?

@DantheMan Isn't that simply $8 \sqrt{15}$?

@MichaelGreinecker No. I mean, how do I subtract this.

How do I get rid of the $\frac{\sqrt{15}}{5}$

the $\frac{}{5}$

@DantheMan Does $10 \frac{\sqrt{15}}{5}$ mean $10 + \frac{\sqrt{15}}{5}$ here?

Michael Greinecker

1:27 PM

What Jayesh wrote.

No. $10 \times \frac{\sqrt{15}}{5}$

That's multiplication...

:P

You can use \times to show the "x" you want.

ah ok

Thanks

Apart from that, you can just cancel $5$ with $10$ in the numerator to leave $2$ in the numerator.

Ah yes... I don't know why I didn't think of that

Thanks

Why do they prefer to rationalize the denominator instead of the numerator?

1:37 PM

@DantheMan To make getting a common denominator easier.

@JohnJunior Ah cool.

I forget... What is the order of a radical? I can't find it on Wikipedia.

Is it the index?

Could you give an example?

Since $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = (\sqrt{a})^2 - (\sqrt{b})^2 = a -b$, the order of any two conjugates is rational if the radicals are of order 2.

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