Mathematics - 2014-09-21 (page 3 of 4)

Khallil

17:00

I've heard a lot of people using 'read' in place of 'study' when they refer to the course they're doing at university, @BalarkaSen. Doesn't it seem really out of place. I can never bring myself to say 'I read xx at blahblah'.

Balarka Sen

mmhmm

"reading" is vastly different than "studying"

I have another DBZ-theory @Khallil. Interested?

Sami Ben Romdhane

I think that saying read instead study is a direct translation from the native language of the speaker. In arabic language for example we may say I read something and it's a synonym of I study something. @BalarkaSen

Khallil

Is that you in your picture, @Sami?

Not really, @Balarka.

Balarka Sen

That's a valid point @SamiBenRomdhane

@Khallil =(

Sami Ben Romdhane

Yes it's my picture :-) why? @Khallil

Khallil

17:06

You're the man, right? I wanted to have a guess at where you're from, @Sami. Are you from Morocco or somewhere in the north of Africa?

Sorry, @Balarka. I'm doing a few things right now but I'd like to hear it later if you have time.

Balarka Sen

Eh, forget it @Khallil.

Sami Ben Romdhane

You're not far from in your guess, my country is the country of Hannibal and elissa;-) @Khallil

Khallil

Are you Lebanese, @Sami?

I just typed Elissa into Google and it came back with a Lebanese singer. =P

Sami Ben Romdhane

No this is her origin but she traveled to the north africa! @Khallil

Balarka Sen

@Alizter

Did you figure out that $\Bbb Q^\times$ problem?

Sami Ben Romdhane

17:11

Do you know Carthage? @Khallil

Khallil

I just heard of it. My mum said it's a place with a lot of history in Tunisia, @Sami.

I know hardly anything about Africa. I've lived in the UK my whole life, but my whole family is Moroccan, @SamiBenRomdhane. That's why I asked where you're from. ^_^

Balarka Sen

That's kind of obvious from you're name @Khallil.

Khallil

It is, @Balarka?

Balarka Sen

mmhmm. Does it not sound a bit Arabian?

Sami Ben Romdhane

I thought that you have an arabic origin from you noun. Do you know its meaning. @Khallil

Khallil

17:19

I think it means 'friend', @Sami. Somebody told me that my name means 'flute' in Hebrew.

Studentmath

@Khallil that would be me

Khallil

You're here!

Studentmath

And it means 'dearest friend' in Arabic

Balarka Sen

@Studentmath!

Khallil

I didn't see your avatar in the sidebar, @Studentmath. ^_^

Studentmath

17:21

@Balarka !

MickLH

wow, so the word for flute in hebrew is "studentmath"

Studentmath

I just came in.

MickLH

and it's also the word for dearest friend?

Balarka Sen

hahhaha

Studentmath

@Mick indeed

Khallil

17:22

Exactly that, @Mick.

MickLH

I can't play a studentmath

Balarka Sen

hello ~~pals~~ studentmaths

MickLH

hehe do I mean I can't play a flute, or do I mean I can't deceive my loved ones? (I can hijack the star board now)

3

Studentmath

I am working on some problem, and I have an issue with something. $\lim_{n\to \infty} (1-p)^n\to 0$, when $p\in (0,1]$.

MickLH

um

Studentmath

17:23

But what about when $p\to 0$ as well? $n\in N$

Oh wait.

There you go.

MickLH

lol ok thank you

Studentmath

I would think it would go to $1$.

But I really can't say.

Khallil

Why?

Balarka Sen

It goes to $1$

$0 < 1 - p \leq 1$

Khallil

You're looking at a number in the interval $[0,1)$ being raised to a very high power.

MickLH

17:26

I think it would go to 1 too, because actual 1 to any power would be you know...

Khallil

Hmm?

Studentmath

I think it won't go to 1. I think it's not determined.

Balarka Sen

Yes, @Khallil

That's what I meant

@Studentmath Well, prove your claim ;)

Khallil

That's the wrong inequality, @Balarka. My one is correct.

$p\neq 0 \implies 1-p \neq 1$

Balarka Sen

Ah I misread $(0, 1]$ as $[0, 1)$

Khallil

17:28

Yep. So wouldn't it tend to $0$, @Balarka?

Balarka Sen

But if $p = 1$, $1 - p = 0$

in that case limit would go 0.

yes, @Khallil. typo.

Studentmath

Yeah. But if $p\to 0$.

Hrm, I will look at different lines of approaching it, shouldn't be too hard

Balarka Sen

what is $\lim_{n \to \infty} 1/x^n $ for $x > 1$, @Studentmath?

Khallil

(Or more generally, $|x|>1$.)

MickLH

$\lim_{x\to i \infty } \, (1-\Re(x))^{\Im(x)} = 1$

Balarka Sen

17:30

blah overcomplications

MickLH

Well at least mathematica accepts that one

Khallil

Balarka Sen

hahaha

Khallil

You lose a turn trying to figure out why you're laughing, @Balarka!

80 damage inflicted!

Sami Ben Romdhane

Yes your name in Arabic means friend and precisely the intimate friend and the kh in Kallil is pronounced like ch in Banach in the German language so this letter does not exist in english:-)@Khallil

Khallil

17:35

Yep, that's why so many people here fail to say my name properly, @Sami. ^_^

nerdy

Let (X,d) be a metric space and A a subset of X. Define x to be a closure point of A iff for every open ball centered at x , it contains at least one element from A.
Define x to be a limit point of A iff for every open ball centered at x , it contains at least one element from A differently from x.
Define x to be an isolated point iff x is in A and x is not a limit point.

My question, if i know x is a closure point, does it mean that it either is a limit point or an isolated point ? Could it be something else ?

Jose Antonio

Hi. I have a question in semidirect product, someone could help me, please?

MickLH

@BalarkaSen oh, let me get your hopes up ever-so-slightly again

I've stabilized in my new job mostly, and last night I got a couple hours to work on the program :)

Studentmath

Hah. 1 it is!

@Khalil sometimes they write it as 7 (the kh, in arabic, over the net)

Jose Antonio

17:55

This says the following: Let $G$ a group and $N$ a normal subgroup of $G$. If $G$ it have a subgroup $H$ s.t. $H \cap N $ is the trivial subgroup and $H$ is isomorphic to $G/ N$ then $G$ is isomorphic to $N\rtimes H$ (semidirect product). I'm not completely sure here because if we let $g$ the composition of the canonical map from $G \to G/N$ with the isomorphism, is clear that its kernel is $N$ and permute the elements in H. But from here I'm not completely sure of how to proceed

Khallil

Ah, I see. There's a double l in my name, so I didn't get the ping, @Studentmath!

Jose Antonio

$G \to G/N \to H $ so if we let $g$ be the composition, then g it has N as kernel and permute the elements in H. So I have to show that all the elements in G are of the form NH, but is not clear to me that this really happens in this case? (If so, with that and the normality of N is sufficient)

Jose Antonio

18:09

someone?

at least that I have to show that g is the identity over H and that's it. But I'm not sure how to do it

Alizter

@Khallil I literally read.

@BalarkaSen Which one was that the noetherian one?

Khallil

I know what you're talking about. @Balarka and I went off on a tangent to do with something else.

Balarka Sen

say huh, @Khallil?

Khallil

Say wha, @Balarka?

Balarka Sen

@Alizter No. It was about deriving a structure theorem for $\Bbb Q^\times$.

Prove that $$\Bbb Q^\times \cong \Bbb Z_2 \times \bigoplus_{\text{primes p}} \Bbb Z$$

math101

18:32

Hi guys

When is the following statement true $x^{x!}=x!^{x}$ and $x \neq 0,1,2$

Daniel Fischer

@math101 Which primes divide $x^{x!}$, and which divide $(x!)^x$?

Balarka Sen

@math101 Look at $x^y = y^x$ in general.

Whoa @DanielFischer

You knew the answer ;) That could never have occurred to me.

math101

@DanielFischer what do you mean by that?

Daniel Fischer

18:50

@math101 If there is any prime dividing one but not the other, the two cannot be equal.

Alizter

@BalarkaSen You havn't showed me that before

What does $\bigoplus$ mean?

nabla blah

@DanielFischer How did you know that if there's any prime dividing one but not the other, the two cannot be equal?

GBeau

Does the division algorithm for $2/1$ proceed as $2=2\cdot 1+0$ or $2=1\cdot 1+1$

Balarka Sen

@nablablah Fundamental theorem of arithmetic.

nabla blah

Oh

Daniel Fischer

18:54

@nablablah That's the unique prime factorisation of integers. Every nonzero integer has a unique representation as the product of a unit ($\pm 1$ for $\mathbb{Z}$) and finitely many primes [unique up to order of the factors].

nabla blah

I don't know about that theorem

Balarka Sen

Every number can be decomposed into primes uniquely, @nablablah

Alizter

@BalarkaSen what does $\bigoplus$ mean

Daniel Fischer

Direct sum, @Alizter.

Balarka Sen

@Alizter Google direct sum.

Why... do I always get beat by @DanielFischer?

nabla blah

18:56

lol

Daniel Fischer

@BalarkaSen You're typing too slowly today.

nabla blah

What are your wpm typing speeds

Balarka Sen

wait typing speed can be measured?

nabla blah

@BalarkaSen Try some typing tests on the internet

math101

@BalarkaSen play.typeracer.com

nabla blah

18:58

Let's make a MSE room on there

Balarka Sen

whoa, @math101

nabla blah

Congrats, you just typed 122 wpm! We have to ask everyone who gets over 100 wpm in a race to take a short typing test. This is done to discourage cheaters.

lol

Chris's sis

@BalarkaSen On this site you might be suprised to find out some know things you haven't ever thought of. (for instance, some see what I was typing - before you see this message)

math101

@nablablah lmao Im like 40 WPM

Chris's sis

The same things happen if you use the latex editor of the site. They see everything you write there, no one tells you that. (I realized that due to a mistake of someone)

Balarka Sen

19:01

race booked. will come back and test my speed. ;)

math101

@DanielFischer So is this just by trial and error. How would you go about this?

Chris's sis

But don't ask me about those mistakes, I won't tell anything.

Daniel Fischer

@math101 Not trial and error. Generally, which primes divide $n^k$?

Alizter

71 wpm

on this clunky keyboard

Chris's sis

And I wanna add one more thing: I also know things some would have never ever thought of.

Now, this subject is closed to me.

Let me post a nice integral ... (hmmm)

Alizter

19:07

@Chris'ssis but first let me see your wpm

Balarka Sen

@Chris'ssis Oh?

Chris's sis

@BalarkaSen Please do not mention this anymore.

Balarka Sen

I don't think it's even true.

Alizter

I didnt see it damn

Balarka Sen

Why would anyone do that?

what makes you so sure?

Alizter

19:10

was it an integral?

Balarka Sen

I don't believe you have details.

nabla blah

lol

Balarka Sen

I mean, it's such a far-fetched idea.

Alizter

@Chris'ssis what is it Ahhhh

anon

interesting.

Balarka Sen

19:14

@anon?

darn it's 31 wpm

Alizter

@BalarkaSen :P

Daniel Fischer

@BalarkaSen You should have typed shorter words, Mr. Sesquipedalian.

Balarka Sen

throws tables at everyone

anon

catches table

Daniel Fischer

Logarithm tables?

math101

19:16

@BalarkaSen Why do i feel like im in a room with a bunch of highschoolers

Ice Boy

sets table for lunch

Balarka Sen

@math101 not sure. have been baby-sitting lately?

Alizter

@Chris'ssis don't post seeecreeets because I am now dying to know :P

Chris's sis

@Alizter It was nothing important, and not about math.

nerdy

nabla blah, that theorem is really intuitive

Balarka Sen

19:19

@anon throws a bench

nerdy

the decomposition of natural numbers HAD to be into numbers whose divisors are only 1 and itself ... it couldn't be otherwise

unique decomposition*

Daniel Fischer

@nerdy Why couldn't it be otherwise?

Balarka Sen

i like non-UFD rings

nerdy

it wouldn't be unique

anon

it fails in other number rings, and there's no eye-catchingly obvious reason why

Chris's sis

19:20

@Alizter A very nice integral here $$\int_0^1 \frac{\log(1-x) \log^2(1+x)}{1+x} \ dx$$

anon

it's true that factorizations into primes are obviously unique, but it's not necessarily obvious when they exist or if factorizations into irreducibles are unique or when the primes are irreducibles are the same (although we know PIDness is a good culprit to pin it on)

Balarka Sen

@nerdy it fails in many other number fields. is there any particular reason you see it to be true on $\Bbb Z$?

nerdy

yes

Balarka Sen

what is it? why do you think you can't generalize that reason to $\Bbb Z[\sqrt{-5}]$?

Chris's sis

and then $$\int_0^1 \frac{\log(1-x) \log(x) \log(1+x)}{1+x} \ dx$$

nabla blah

19:22

Hi @JasperLoy

Will Hunting

Hey @math101 so when do you graduate?

Daniel Fischer

@Chris'ssis Weren't these on main about sixteen times in the last three days?

Will Hunting

@nablablah Hello dear Bart.

math101

@WillHunting Im not sure yet. Depends how busy I get

But hopefully really soon

saadtaame

If we have a circle. Do all triangle that inscribe that circle have the same area?

anon

19:23

no

make the base of the triangle a diameter, then the altitude of the third point determines the area

Chris's sis

@DanielFischer I'd like to see any of them only one time on main in the last three days. Do you have a link?

Will Hunting

Hey @sarah, lol. Let's not post any more pics.

saadtaame

@anon if the base is the diameter parts of the circle will be outside the triangle!

Daniel Fischer

@Chris'ssis No, I just had the impression that I've seen them on main recently.

anon

@saadtaame oh, you want the circle inscribed in the triangle

answer is still no

Chris's sis

19:26

@DanielFischer There might be some similar like this one http://math.stackexchange.com/questions/408270/a-challenging-logarithmic-integral-int-01-frac-log1x-log1-x1xdx/938103#938103.
Anastasiya-Romanova answered it 2 days ago, but not following my requirements (I also talked about it here).

anon

think of isosceles triangles

sarah

chat.stackexchange.com/transcript/message/17783600#17783600

nabla blah

wat

saadtaame

@anon math.stackexchange.com/questions/940581/…

Balarka Sen

what's the message you're referring to @sarah?

Will Hunting

19:28

@sarah It's deleted. What is it?

anon

it was deleted for a reason

does it involve you in some way @sarah?

Will Hunting

@anon seems to know what happened.

sarah

Seeing if it would work

anon

okay

Chris's sis

@DanielFischer this one comes from personal research, I think it would require some time for someone to answer it $$\int_0^1 \frac{\log(1-x) \log(x) \log(1+x)}{1+x} \ dx$$

Alizter

19:29

@sarah what was it?

nabla blah

Let's give it to Cleo

Alizter

no, let's not

nabla blah

lol

Alizter

Cleo is just an advanced version of mathematica

Will Hunting

I think I should join okcupid, lol.

nabla blah

19:30

@JasperLoy It's not very fun

Chris's sis

@nablablah I was referring to a complete solution. Cleo's answers mean nothing to me.

Will Hunting

@nablablah You are the only person who pings me as that now, lol.

nabla blah

@JasperLoy what

Will Hunting

@nablablah My username is Will Hunting now.

nabla blah

@JasperLoy Oh

Why you keep changing your username

Will Hunting

19:31

Why do you still see the old username?

Did you refresh your browser?

nabla blah

@JasperLoy I see "Will" but I didn't pay attention to it until now

Alizter

@JasperLoy it still pings you

Will Hunting

@nablablah LOL

Daniel Fischer

@Chris'ssis I meant this and this. Not quite yours, but close enough to mistake one for the other if one isn't really interested.

Will Hunting

I think I will stop flagging the trio X, Y and Z. I have better things to do than get the Marshal badge, lol.

But the fact that X, Y and Z think their trivial answers are great shows how weak they are mathematically, lol.

nabla blah

19:34

I'm weak mathematically

sarah

@WillHunting I don't think being here shows you have better things to do

Will Hunting

@sarah LOL, thanks.

nabla blah

Shots fired

Will Hunting

I am desperate to find a gf, lol.

sarah

Unless porn + chat is open then touche

nabla blah

19:35

@JasperLoy why do you want one so badly

Aren't we enough for you

Will Hunting

Anyway, I have planned to study English, French and German in Oct, Nov and Dec resp.

nabla blah

I guess we're not good enough :(

Alizter

~~for cleaning~~ to help

Will Hunting

@nablablah Well, it's just natural, lol.

sarah

@Alizter at least girls can clean

Will Hunting

19:36

I got a copy of "The blue book of grammar and punctuation" to improve my English.

Alizter

@BalarkaSen

Chris's sis

@DanielFischer hmmm, very interesting the second one. I would have missed it. Thanks!

Alizter

lets run away to number theory

Balarka Sen

@Alizter

Will Hunting

I also got a copy of "Complete French" and "Complete German" to learn these two from scratch.

Balarka Sen

19:36

OK

Will Hunting

@sarah Are you in undergrad or grad?

sarah

Under. But I have a dominative personality.

nabla blah

lol

Will Hunting

OMG.

math101

@sarah AKA bitch

Chris's sis

19:38

I also think of $$\int_0^1 \frac{\log(1-x) \log(x) \log(1+x)}{1-x} \ dx$$

Will Hunting

@math101 OMG

nabla blah

topkek

Ice Boy

@math101 that's not a nice thing to say

math101

@IceBoy Shes a domineering personality she can handle a jab :)

Ice Boy

@math101 still...

Will Hunting

19:40

@math101 and @sarah make me laugh. You two can be my gfs, lol.

nabla blah

What if she dies like Harry Houdini did

Ice Boy

@math101 ...be nice

sarah

@math101 Theres no need for such language you bastard

nabla blah

lol

math101

@sarah hahaha why is everyone soo sensitive here

Will Hunting

19:41

Let's not invite the unwanted flaggers.

I sense they are coming to get us.

Ice Boy

no more name calling please @math101 @sarah

math101

@IceBoy Sure thing dad

Ice Boy

daddyo

sarah

@IceBoy ok mom

Ice Boy

:D

you guys can call me all the names you want np

nabla blah

19:43

Ice Boy

I prefer skullpatrol

sarah

not nice boy

@math101 fight me

nabla blah

Oh, you are @skullpatrol

I thought you disappeared

math101

@sarah atta girl

Ice Boy

@nablablah yep

sarah

19:44

picks up baseball bat

sticks nails in it

Ted Shifrin

Hi skull, @nabla, @sarah

Will Hunting

I just answered a lhf, upvotes please, lol.

sarah

hurts hand

Will Hunting

Hi @TedShifrin

Ted Shifrin

Oh, and Jasper

Ice Boy

19:45

Hi Professor @TedShifrin

math101

@sarah hahaha oh nooo not today

Ted Shifrin

Sarah is almost as violent as @Balarka

Will Hunting

Laura Ramsey plays @Sarah in The Covenant, lol

sarah

As shcawt once said: "Dad, I've got a gun in my room. It will be fun!".

Austin Powers

nabla blah

Hi @TedShifrin

Ice Boy

19:46

@sarah Janies got a gun?

Balarka Sen

@TedShifrin Moi!? Violent?!

Ted Shifrin

throws a table and chair at Balarka

sarah

one hits @sarah

@sarah swears really loud

Will Hunting

No more throwing tables, children.

@sarah You can't ping yourself.

nabla blah

(╯°□°）╯︵ ┻━┻)

Balarka Sen

19:48

@TedShifrin Look who's talking.

ahhhahaha, @nabla

Ted Shifrin

I was demonstrating @Balarka

Ice Boy

no more ~~name calling~~ violence please

Will Hunting

Guys, I notice I get more upvotes after I posted that post on meta, lol.

Ice Boy

talk math

Balarka Sen

My aim's real bad, @TedShifrin

nabla blah

19:49

/me divides by zero

Ice Boy

:-O

Balarka Sen

@Will You're getting famous.

Will Hunting

@BalarkaSen Do they know I am Jasper Loy? I wonder...

Ted Shifrin

I try, @skull. What post, Jasper?

sarah

@IceBoy

Will Hunting

19:50

24

Q: On mutual tactical serial upvotes and unconstructive comments

I notice that there are some groups of users on this site that like to leave unconstructive comments on each other's posts. For example, A writes "Great answer, +1" on B's posts and B writes "Short and sweet, +1" on A's posts. Often there are a few of these comments each day, accompanied by the u...

Hey any girls here looking for a bf you may consider me, lol.

Ted Shifrin

Ah, the incestuous upvoters ...

Will Hunting

My email is jasperloy at outlook dot com, lol.

Daniel Fischer

@IceBoy You mis-spelled "violins".

2

Ted Shifrin

That's inappropriate posting, Jasper ...

@DanielF !

Chris's sis

@DanielFischer This one seems from the same family

15

Q: How to evaluate $\int_{0}^{1}{\frac{{{\ln }^{2}}\left( 1-x \right){{\ln }^{2}}\left( 1+x \right)}{1+x}dx}$

I want to evaluate $$\int_{0}^{1}{\frac{{{\ln }^{2}}\left( 1-x \right){{\ln }^{2}}\left( 1+x \right)}{1+x}dx}$$ I run this integral on Maple, It does converge. How we get a closed form? Is that related to polylogs? $Li_{5}\left(\frac{1}{2}\right)$

calculus sequences-and-series integration summation

Will Hunting

19:53

@TedShifrin I am sorry I said Munkres is "terrible". I should have said I don't like it. But I think Willard is much better, really.

Chris's sis

@DanielFischer I finished it with a full nice solution today (very well explained). It requires some work, that's true.

Ted Shifrin

what an exhausting weekend ... Now waiting in the airport to fly back to drive 90 minutes home ...

Ice Boy

@TedShifrin get some well deserved sleep when you get home

Ted Shifrin

I don't know Willard, so I shan't debate.

Daniel Fischer

@TedShifrin Uh. I hope you don't need to lecture tomorrow morning.

Ted Shifrin

19:56

Of course, twice. To make matters worse, in probability it's a problem/test review day :)

Will Hunting

@TedShifrin Kelley is also good, but the language is a bit old.

Ted Shifrin

Too hard, too terse, and not nearly enough exercises.

Will Hunting

I like terse, lol.

The most compact book I have seen is Federer's Geometric Measure Theory. That book is like an address book, lol.

sarah

@TedShifrin I though you were talking about someone, lol.

Ted Shifrin

Clearly you lie. Lee is the opposite of terse.

Will Hunting

19:57

@sarah OMG

@TedShifrin OK, Lee is an exception.

Ted Shifrin

Even experts cannot read Federer.

nabla blah

What about Bourbaki

Ted Shifrin

It's a huge tome ... Far from compact.

Ice Boy

overly terse is useless

sarah

►

Will Hunting

19:59

@nablablah The level of generality kills.

sarah

halariows

Ted Shifrin

Ok, almost boarding time ... Y'all misbehave without me.

Ice Boy

later

Transcript for

$Mathematics$ Mathematics