Mathematics - 2015-10-04 (page 1 of 2)

Karim Mansour

01:03

@anon given a sylow p subgroup of G of prime order not power of the prime is intersection of two sylow p subgroup then trivial ?

anon

@KarimMansour what would you guess?

btw sylow theory is irrelevant to your question

Karim Mansour

I would guess yes they should be trivial

I am trying to prove it atm

since they are of prime order so they are cyclic

by lagrange theorem

so suppose x and y are generators those two p-subgroups respectively

anon

Suppose H and K are different subgroups of G, and each of them have no nontrivial proper subgroups. What can you say about their intersection (call it M)?

Karim Mansour

their intersection must be p or 1

yeah

since the intersection is a subgroup of M and Q respectively

anon

since M is a subgroup of H, either M=1 or M=H. similarly, M=1 or M=K. so either H=K or M=1.

Karim Mansour

01:09

yeah

but if the intersection is H that means both of them are equal

so yeah

same thing for M = K

so yeah good I can use that the # of non-identity elements is n_p ( p - 1)

good

DemCodeLines

02:01

Anyone here good at discrete math?

skill patrol

02:16

218

Q: Thinking and Explaining

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you're thinking? Please give either personal examples of how your thoughts and words differ, or describe how they are connected for you. I've been fascinated by the phenomenon the que...

DemCodeLines

0

Q: Expressing propositional function without quantifiers

I have been following "Discrete Mathematics and its Applications" textbook by Rosen, 7th edition. I have come across an exercise question (1.4, #20) that I am not sure how to answer. The book gives me the question and a bunch of choices that apply, but I'm not sure how I would solve and arrive a...

discrete-mathematics

Silent

03:26

@robjohn, why $S$ in bijection $f:\Bbb N\rightarrow S$ where $S\in \Bbb R$ does not always preserve well ordering?

anon

@Silent huh?

Silent

@anon, I want to understand , e.g. while N has well ordering while $\{1/n\}$ does not, why?

anon

@Silent start drawing the set {1/n} on a number line. clearly it has no minimum element.

Silent

@anon, but that i can't understand why, i mean which property a set must have to be well ordered?

anon

do you know what "well-ordered" means?

Silent

03:36

yes

anon

then you know what property a set must have to be well-ordered

get a feel for how ordinals looks. all well-orders are essentially ordinal numbers.

dunno what else to tell you

Silent

ok thanks

and all ordinal numbers are well ordered?@anon

anon

look them up

Silent

ok

Shahab

I am looking for an interview of a famous mathematician (perhaps it was Atiyah) where he propogated the thesis that the reason for doing maths was two fold: getting new definitions (making theories) and proving theorems on them. He then goes on to compare the relative importance of each.

Karim Mansour

03:45

if we have

nvm it is true

if we have a subgroup of normal group, then it will be normal.

no

what I am saying isn't true

1 second

Akiva Weinberger columbus

04:28

@Silent A set is well-ordered if every subset of it has a minimum. So every finite set is well-ordered. $\Bbb N$ is well-ordered. $\{0,1,2,3,\dots,0',1',2',3',\dots\}$ is also well-ordered, where we define $0<1<2<3<\dots<0'<1'<2'<3'<\dots$.

@Silent $\Bbb Z$ isn't well-ordered, as it doesn't have a minimum element. $[0,\infty)$, the set of nonnegative real numbers, isn't well-ordered, as the subset $(0,1)$ has no minimum element.

The Substitute

04:45

off topic. is there a way to plot multiple (overlapping) graphs in WolframAlpha?

nevermind doh

Martin Sleziak

09:38

When I saw this post in the close review queue and saw that for the most part it consist of the picture I have edited it. I was doing so in good faith that I am helping a relatively new user.

Only then I noticed that the OP was not seen at the site since 2014. This was a bit annoying - I basically spent my time in wain.

I am used to seeing mostly recent question in the close votes review queue. (Although if some users vote to close old posts which are really bad in order to clean up the site, it is a commendable effort.)

Next time I should keep in mind to look on the age of the question, too.

Agawa001

10:41

no interesting questions these days

this seems a good one but fits to be in different stack-section

Understand

11:44

Can anyone help me understand what a prime subfield is? It says it is a subfield generated by the multiplicative identity

Why does that not just give back the field itself?

Hi @Rememberme can you answer my question above? I have to leave soon

Remember me

@anon Mind checking a proof of mine
Q). Prove that a star convex set is simply connected.
Consider points $a_0,a \in A$ where A is star convex. Now by the definition of star convex there exists a path between $a, a_0$ lying in A. That is,
$F(a,t)=(1-t)a+t(a_0)$. Consider a path $p:I \to A$ . Then the composition defined by $f:I \times I \to A$, $f(s,t)=F(p(s),t)$ such that $f(s,0)=p(s), f(s,1)=a_0$ is a path homotopy between the constant map and p. Since the straight line homotopy is the path homotopy here, $\pi_{1}(A,a_0)$ is trivial. Also A is path connected . These two show that A is sim…

Ghost

12:16

hello?

Remember me

12:27

Hey @Huy

Huy

hi

Remember me

Are you free @Huy?

Huy

maybe

Ghost

good evening!

Remember me

Can you check this once:Consider points $a_0,a∈A$ where A is star convex. Now by the definition of star convex there exists a path between a,a0 lying in A. That is,
$F(a,t)=(1−t)a+t(a_0)$. Consider a loop $p$ in A. Then the composition defined by $f:I×I→A, f(s,t)=F(p(s),t)$ such that $f(s,0)=p(s),f(s,1)=a_0$ is a path homotopy between the constant map and $p$. Since the straight line homotopy is the path homotopy here, $\pi_{1}1(A,a_0)$ is trivial. Also A is path connected . These two show that A is simply connected.@huy

Huy

12:31

no

you should be able to check it easily

Remember me

I mean just tell me is there any mistake. I will find the mistake myself if there is

@Huy I don't think so I have any error. Am I right

Remember me

12:49

Really nice question:

3

Q: Is Homeo$(X)$ metrizable?

If $(X,d)$ is a metric space then is Homeo$(X)$ (the group of homeomorphisms of $X$ with itself) endowed with the compact open topology metrizable? At first I thought I could define a metric on Homeo$(X)$ using the metric $d$ but I can't find a good way to do that. I am not certain how to prove ...

general-topology metric-spaces

Mary Star

13:13

Could someone of you take a look at my question:

0

Q: The solutions are linearly independent and algebraic

The Grothendieck problem for differential equations (I think it is called Grothendieck-Katz conjecture) is the following: $$\alpha_n(x)y^{(n)}(x)+\dots +a_1 (x)y'(x)+a_0(x)y(x)=0, a_i \in \mathbb{Z}[x]\ \ \ \ (*)$$ We suppose that for almost each prime $p$, $(*)$, modulo $p$, has $n$ linearly...

abstract-algebra differential-equations differential-algebra grothendieck-topologies

?

Remember me

13:26

Hello@Karim

quantum

13:39

any russian mathematicians around?

gideon

14:50

I don't want this to sound like the typical question asked. I'm a programmer. I'm quite interested in math but I'm not very good at it. I'm slowly working my way through Khan Academy's Algebra and Trig and maybe break through the calculus barrier. My math pursuit is two fold, pure learning and getting better Programming jobs.

So for learning I can take my time, but I do need to get a better job sooner than later, I'm highly paid from where I live but I need the money. When I've tried for jobs with major companies many times I've got stuck at programming puzzles and that are quite mathy I'm wondering if anyone knows what I'm talking about? They're just puzzling and hard programs, say like google code jam Will studying math make me better at this?

I would think so but I would want a confirmation.

Pantelis Sopasakis

16:56

Hi everyone. I have a short question: Let $\{w_k\}_{k\in\mathbb{N}}$ be a random process in a probability space $\Omega, \mathcal{F}, \mathrm{P}$. Let $x_{k+1} = A(w_k)x_k$ be a random process driven by $w$ and let $\mathbb{E}$ be the expectation operator with respect to $\{w_k\}_k$. Let $\mathbb{E}_{[0,k]}$ be the expectation with respect to $w_0, w_1, \ldots, w_{k}$. Under what conditions is it $\mathbb{E}[x_k] = \mathbb{E}_{[0,k]} [x_k]$?

Lucas Henrique

Hello guys!

It's my first time here. It looks like the people don't talk too much :p

Huy

they talk if there's something interesting to talk about

what leads you to this place, @LucasHenrique ?

Lucas Henrique

I'm sorry to be a parasite like that but I came here because of a question I have

Huy

which is?

anon

@LucasHenrique the regulars aren't around

(cept me)

Huy

17:04

@anon :(

anon

Huy is occasionally regular

Huy

too late

Lucas Henrique

I know a bit of calculus and I was trying to get some physics defs

anon

heh

Huy

I'm offended now

Lucas Henrique

17:05

S = integral(integral(a)) (I don't know how to put it on notation

Huy

do you know how to use LaTeX, @LucasHenrique?

Lucas Henrique

We occasionally get S = So + vot + (at^2)/2

@huy sorry, I don't

Just the basics like $x^2$

About the problem: We also have that the space is the integral of time. Then we get S = So + vt

But if we use the definition of velocity in the second formula we get S = So + vot + at^2 which is not the same.

Huy

it depends on whether your body experiences acceleration or not

if it's not accelerated, the two formulae are the same since

a = 0

Lucas Henrique

:o

Huy

if it is accelerated, then they are obviously not the same

and no, the "space" isn't the "integral of time". you get position by integrating velocity

(with respect to time)

Lucas Henrique

17:11

Oops, I got confused there

But yeah, I know that

Ramanewbie

@lucas You French ?

Lucas Henrique

So what can I say about that? Why does it give the same formula (you've already answered that, then...)? How can I stop making these mistakes?

@ram Brazilian, but I'm using mobile

Why would you ask?

Huy

the problem is to obtain the first formula, you already assume that there is no acceleration

because if there was acceleration, then

Ramanewbie

@lucas Your name made me think that.

Huy

v'(t) = a, and then by integrating you get v(t) = at + v0 and integrating again you get s(t) = s0 + v0 * t + 1/2 * a * t^2

Lucas Henrique

17:15

@ram I thought you thought I was French cuz I have some problems to write

That's troublesome bro :p

Ramanewbie

@lucas You mean with your English ?

Lucas Henrique

Because if we hadn't the definition of acceleration it would keep s(t) = s0 + v(t)*t

@ram yup

Huy

idk what you mean by that

you have s''(t) = a

by Newton's laws

Lucas Henrique

yeah

Pantelis Sopasakis

Hi guys. Is there anyone to help me out with a (simple) question on stochastic processes?

Lucas Henrique

17:18

but that's what I mean

If we hadn't this relationship..

skill patrol

v'(t) = a

v(t) = at + v0

s(t) = s0 + v0 * t + 1/2 * a * t^2

Huy

idk what you mean

Lucas Henrique

I'm dying because of this cellphone. I'm going to the desktop

Okay, I'm back and now I can type normally

@skillpatrol I know this relationships and my question was about a "paradox" (which is a contradiction, actually)

lol

Huy

it's not. in one of your formula you're just setting a = 0

Lucas Henrique

Yes. You told me that and I got it.

skill patrol

17:28

@LucasHenrique where is the "contradiction"?

Lucas Henrique

@skillpatrol $S = S_0 + v_0t + at^2$

oh damn, I cant use latex

anon

@Rememberme how does that show every loop is contractible?

Huy

I don't see a contradiction

anon

(use underscores for subscripts @Lucas)

skill patrol

:-)

Lucas Henrique

17:31

thanks

skill patrol

ok, what's the contradiction about?

Lucas Henrique

If we only assume $S =\int v$, then $S = S_0 + vt$

We know that $v = v_0 + at$, then it comes to the formula

It should give the same formula...

skill patrol

there is no acceleration HORIZONTALLY right?

Lucas Henrique

?

Krijn

Is there anyone here with some knowledge of the Weierstrass-fucntion $\wp$?

Lucas Henrique

17:35

I don't know what do you mean by horizontally

It can be 1d, then...

skill patrol

which way does gravity act?

Huy

@LucasHenrique: that's only right if you assume

Lucas Henrique

Vertically

Huy

v to be constant

which it is not if it is accelerated

Lucas Henrique

Oh we're getting somewhere...

Huy

17:36

if you're integrating v(t) with respect to time, you can't be sure to get v(t) * t

Lucas Henrique

Let me think about what @huy said for a sec

yes

Huy

you only get v*t if v is a constant

skill patrol

^horizontally

anon

@Krijn what about it?

Krijn

I have almost solved an exercise on in it, but cannot prove the last step

Balarka Sen

17:40

@anon every loop is *nullhomotopic. :) /pointless nitpick.

anon

err, right

Krijn

We have $z_1, z_2 \notin \Lambda$ such that $z_1 + z_2 \notin \Lambda$. Then we can find $a$ and $b$ such that $f(z) = \wp'(z) - a\wp(z) - b$ has roots $z_1$ and $z_2$

Now I also need to proof that $f(-z_1 - z_2) = 0$

Huy

why does that function have roots z_1, z_2?

Krijn

Finding these $a$ and $b$ was easy, $a = \frac{\wp'(z_1) - \wp'(z_2)}{\wp(z_1) - \wp(z_2)$ and $b$ follows from that

$a = \frac{\wp'(z_1) - \wp'(z_2)}{\wp(z_1) - \wp(z_2)}$

Huy

ah ok different notation than I'm used to

anon

17:42

presumably you plugged in z1 and z2 and solved the linear system for a and b?

Krijn

Yeah

The only thing I could think of was using the fact that $\wp$ is even and $\wp'$ is odd to rewrite this to $f(-(z_1 + z_2)) = -\wp'(z_1 + z_2) - a \wp(z_1 + z_2) - b$

anon

there's got to be a better way than addition formulas (and I haven't checked if they work)

Krijn

The goal of the exercise was to prove to addition formula

By comparing these equations to the known cubic relation of $\wp'$ and $\wp$.

I was able to do that, but needed this last step

anon

okay, do you know that (sum of zeros) minus (sum of poles) is zero mod the lattice inside a fundamental parallelogram?

Krijn

Yeah

anon

17:49

f(z) has a pole of order 3 at the origin

so you get (z1+z2+?)-(0+0+0)=0 mod Lambda

Krijn

So it has 3 roots?

Ah. Wow!

Balarka Sen

cool idea, @anon

anon

wasn't my idea. it's textbook, I just had to remember it.

4

Krijn

That's very clean and easy, thanks!

Balarka Sen

wonder why that thing is getting highly starred.

Alessandro

17:57

good evening everybody

skill patrol

@BalarkaSen think about it

hello

Krijn

@BalarkaSen I guess it is a very recognizable feeling for mathematicians

skill patrol

it is recognizable once you read enough textbooks

Balarka Sen

what is a very recognizable feeling?

Huy

remembering textbook

Balarka Sen

18:00

oh, ok. fair enough.

skill patrol

:-)

Krijn

"I read this somewhere and it's easy, but where the hell did I read this"

Balarka Sen

haha, yes, indeed.

skill patrol

why re-invent the wheel?

Krijn

To improve understanding of the wheel?

3

skill patrol

18:02

but not every time

Agawa001

18:55

@gideon wth are u talking about ?

Karim Mansour

19:11

@BalarkaSen

I am trying to solve the following question

Let P $\in Syl_p(G)$ and assume N is normal in G. Use conjugacy part of sylow's theorem to prove that $P \cap N$ is a sylow p-subgroup of N.

Deduce that PN/N is a sylow p-subgroup of G/N

I guess since N is normal in G

so PN is a subgroup of G

P intersect N is a subgroup of PN

Lucas Henrique

Yo guys, let me make a little test

$\underset{a}{\overset{b}{\int }}f\left(x\right)=\sum _{i=a}^{b}i-20$

yeah, TexTablet didn't get it right

Huy

just learn the basics, it's not difficult really

and when you need to look up some symbol, detexify is amazing

Lucas Henrique

I actually have a Bamboo tablet

So I don't have much trouble

see:

$S={s}_{0}+{v}_{0}t+\frac{a{t}^{2}}{2}$

Karim Mansour

Hi @Rememberme

Lucas Henrique

Another test...

$\Delta ={b}^{2}-4ac$

Huy

19:23

that looks better

Lucas Henrique

Yeah, I don't have learn LaTeX :p

Huy

you should

it's easy and very useful

Lucas Henrique

i have enough stuff to learn, dammit :|

I have to improve my C# skills

and I'm on the National Physics Olympics

Huy

I want to improve my Swift skills

but I am never motivated enough to start

Lucas Henrique

I didn't think anyone actually started to program in Swift

Huy

19:25

wat

Lucas Henrique

I think the same about Azure

Huy

there's already swift 2

and I've actually heard good stuff about it from iOS developers

Lucas Henrique

hmm

I program in C++ (mainly), C, Python and Assembly

C++ and Python I would say

Huy

I know some basic C++, but I find Python more practical for my use

Lucas Henrique

I like C++ but Python has a lot of stuff when we compare them

not that C++ is a bad language, but Python has more "fame"

Huy

19:27

Python is just simpler

Lucas Henrique

Yes, that too

skill patrol

Learning LaTeX is a must...

Huy

^

Lucas Henrique

@Huy Everybody says that but C++ was my first language, so...

Huy

HTML was my first "language" :D

and then PHP

skill patrol

19:29

English was mine :P

Huy

I was forced to learn C++ in university, otherwise I would have left it with my Python knowledge

Ramanewbie

@huy HTML isn't a proper 'programming language', it's more like a 'descriptive language'

Huy

I know, hence the ""

Ramanewbie

@huy Yes !

Lucas Henrique

I really should D:

Huy

19:30

good job :D

it's really easy

you'll get the gist of it within less than two evenings if you talk here about maths

skill patrol

Practice

Lucas Henrique

meh, I should be studying

Physics zZzZzZ

Huy

are you at uni?

Lucas Henrique

?

oh, university

no, I'm 14

Huy

ah ok

then you have plenty of time to learn all those things

skill patrol

19:33

Great age to learn LaTeX

Lucas Henrique

"all those things": physics, programming, LaTeX? lol

Krijn

It'll take you some time to learn physics, I guess

skill patrol

Just have fun with it.

Huy

I learned LaTeX at age 16

I think everyone who likes maths should

that doesn't mean you should wait 2 years now

:D

Agawa001

latex is hell

skill patrol

19:35

Play around with it etc.

Agawa001

i dont want to learn it

skill patrol

Like a game.

Tobias Kildetoft

@Agawa001 Why not?

skill patrol

^

?

Why

Agawa001

just use editors they can handle it in my place

i find it just tiring

skill patrol

19:37

It gets easier like any skill

Tobias Kildetoft

@Agawa001 What editors? You mean like LyX?

Agawa001

no programming language take it in, it is just for human understanding

@TobiasKildetoft yes

there s alot of such simulators arround the net

skill patrol

Don't you want understanding?

Lucas Henrique

@Aga there are some, actually

Agawa001

i use codecogs

Tobias Kildetoft

19:39

@Agawa001 LyX is not bad as far as I know, but I doubt it is actually any faster than writing things yourself after a few weeks

Lucas Henrique

If you want you can implement something on R that receives LaTeX and returns a graph

Huy

yeah I absolutely hated LyX

and R too

Agawa001

i absolutely hate writing it key per key

A Googler

i use codecogs as well

skill patrol

Are you a fast typer?

Agawa001

19:41

not much :S

skill patrol

Ok

Huy

how fast do you type skillpatrol :3

Ramanewbie

@lucas are you in high school then

Lucas Henrique

@agawa buy a wacom tablet

Ramanewbie

typing-speed-test.aoeu.eu

Lucas Henrique

19:43

@Ramanewbie In Brazil the schools are "fundamental", "médio" and "universidade" (university)

IDK if média schools are the equivalent of high schools but if they are, I'm not. I'm on "fundamental" (last year).

Ramanewbie

@lucas How does Brazilian education system work ? Can you specialize in some subjects already ?

Huy

@Ramanewbie: i.imgur.com/0SxQmCU.png I'm typing on my laptop keyboard now because i broke my mechanical keyboard, hence the slow speed

Ramanewbie

@huy that is really fast

@huy I just finished doing it and got quite much less

Huy

remind me to do it again this week, I'll buy a new keyboard tomorrow

Ramanewbie

@huy But what is 'CPM' ?

Huy

19:46

so I can do it again tomorrow evening basically

Ramanewbie

@huy Alright

Huy

characters per min

I think I maxed out at around 720 CPM

Ramanewbie

That's alot

Huy

before I bought my MacBook, I went to the Apple Store and did typing speed tests on all MacBooks there to check the keyboard

people were looking me like I was some crazy kid

Boni

Just finished it: 81 WPM with 94%, 405 CPM

Ramanewbie

19:48

@huy lol I imagin the situation...

@Boni not bad

Tobias Kildetoft

I was around 200 cpm. Probably also approximately what I type when I actually type LaTeX though

Boni

My score's terrible, by today's kids standard, probably xD

Tobias Kildetoft

more importantly, I usually type somewhere between 3 and 5 pages per day when I spend most of my time typing

Huy

idk, I feel like todays kids are slower than "my generation"

typewise

:P

Lucas Henrique

@Huy I got ~70%, lol

Tobias Kildetoft

19:52

@Huy For most people the score on such a typing test is completely pointless (unless you often type things from paper to a computer).

Huy

for most, yea

skill patrol

Have you used a split key board?

Lucas Henrique

@Ramanewbie I can't NOW, but I will next year.

Huy

I used to do live coverages

Tobias Kildetoft

And for those where it is relevant, it would often need to include a lot of things that were not words to be really relevant

Huy

19:52

so I had to be able to write fast

Ramanewbie

@lucas What subjects do you study ?

Lucas Henrique

@Ramanewbie I like math, physics, programming. I'm also a pianist and I like drawing.

Huy

hey, I used to play some piano too

but I don't have space in my flat now, so I only play the guitar

Ramanewbie

@lucas Do you stidy programming with your school ?

@huy are you good at it ?

Lucas Henrique

@Huy Cool! How much time did you study?

Huy

19:55

piano not really, guitar a bit$

Agawa001

all matlab users can see this

Lucas Henrique

@Ramanewbie No, only @ home

Agawa001

a=input('');a=0;c=1;while(c-a>0.06)
a=toc
b=input('');
c=toc
end
fprintf('jackhammer detected');

Huy

I started taking guitar lessons at age 9

Ramanewbie

@lucas And what are you studying in maths ?

Huy

19:56

and stopped at age 17

and I took one year piano lessons

Ramanewbie

@huy why did you ?

Huy

just to learn some basics

Ramanewbie

@huy I mean why did you stop ?

Lucas Henrique

@Ramanewbie Well, I don't even care for school maths. I'm studying Calculus

Huy

@Ramanewbie: I don't have a consistent timeframe to practice like I used to in high school

Ramanewbie

19:57

@Agawa001 idk what that is, but why do you do a=input() and then a=0 ?

Lucas Henrique

I play the piano since when I was 5

Huy

so I had to stop taking lessons as soon as I started university

but I still play a lot

Boni

Learning the piano isn't cheap either.

Ramanewbie

@agawa at the end a=0 anyway

Agawa001

@Ramanewbie i suppose people use autohotkey to cheat and perform fake scores

Ramanewbie

19:58

@agawa I wonder if that works, they might have used javascript to avoid that

Lucas Henrique

@Boni :/

Ramanewbie

@Agawa001 And how do you know what key you have to enter ? I changes everytime you reload the page

Huy

@LucasHenrique: so you've played it for around the same amount of time as I did the guitar. :P classic or jazz?

Lucas Henrique

@Huy Classic :D

Agawa001

@Ramanewbie have you even tried it ? (my matlab)

Ramanewbie

19:58

What is calculus ? @lucas

Huy

@LucasHenrique: so I assume you don't have a clue how to improvise?

Ramanewbie

@Agawa001 You mean your algo ? What language is that ? I thought it was 'pseudo-code'

Lucas Henrique

I do play jazz also but I focus on classic

Agawa001

yes

Lucas Henrique

@Huy ?

what do you mean?

Huy

19:59

^^

exactly

Lucas Henrique

lol, damn xD

Transcript for

$Mathematics$ Mathematics