Mathematics - 2013-02-06 (page 4 of 4)

user19161

8:01 PM

@rob I am still having the display problem, but I am installing another OS now, so the problem should be resolved after that. But it's really strange...

robjohn

@JasonBourne Is it more than that post?

skullpatrol

Which OS?

user19161

@robjohn Yes, everywhere fractions appear in big form with parenthesis.

user19161

@skullpatrol I am installing Debian over Fedora now. Fedora is more cutting edge but also more buggy.

robjohn

@JasonBourne $\left(\frac12\right)\displaystyle\left(\frac12\right)$

user19161

8:04 PM

@robjohn The second one displays wrongly.

user19161

@skullpatrol This is not applicable.

skullpatrol

Sorry :(

robjohn

@skullpatrol playing tricks on Jason

user19161

Haha, this is yet another mystery in my life...

user19161

Weird things keep happening to me...

robjohn

8:06 PM

@JasonBourne It's because your rep is 15900...

user19161

@robjohn Haha, yes, a multiple of 5.

robjohn

@JasonBourne a multiple of 100

skullpatrol

When will the OS be installed?

robjohn

@JasonBourne: you've restarted your computer since this started, right?

user19161

@robjohn Yes, many times.

user19161

8:10 PM

@skullpatrol Well, I will install it later on.

user19161

Anyway, I just took a look at Shifrin's Linear Algebra for the first time.

user19161

Hmm, not my type of book, too many pictures.

skullpatrol

You don't think in pictures?

user19161

I do, but I can draw them myself.

user19161

I also prefer the typesetting to be less spacious.

user19161

8:14 PM

Jonas knows my style, we call it "phonebook" style, squeezing many things into a small space.

user58512

for example?

user19161

Hmm, take a look at Federer's Geometric Measure Theory.

skullpatrol

Look at a phonebook.

user58512

ok

user19161

That book is written for robots.

devWaleed

8:16 PM

Hi again...

skullpatrol

hi...again

devWaleed

How many terms of the series -9-6-3-... must be taken to amount 66?

Does it mean that -9-6-3-...66, Sn=66 ?

user19161

@skull What is your favourite sport you play or watch?

devWaleed

just explain the question please...

Jonas Teuwen

C IS FOR COOKIE! THATS GOOD ENOUGH FOR ME.

user58512

8:17 PM

-9-6-3-0+3+6+9+12+15+18+21=66

user19161

@devWaleed You mean you are adding all those terms?

user19161

Ah, see user's answer.

user19161

This is just an arithmetic progression.

devWaleed

umm, It further says explain the double answer...

user19161

One can use the sum to n terms of an AP formula to solve.

user19161

8:19 PM

@devWaleed What is double?

user19161

@skullpatrol OMG! You are a strong man!

Tobias

@JonasTeuwen Cookie cookie cookie starts with C

skullpatrol

@JasonBourne and silent ;-)

devWaleed

@JasonBourne the answers are double...

skullpatrol

@JasonBourne What is your favourite sport you play or watch?

user19161

8:22 PM

@devWaleed I don't understand what you mean by the answers being double.

user19161

@skullpatrol I like to watch tennis and table tennis. I don't play any sports, but I like running which I have not done for a long time.

devWaleed

The question is:
How many terms of the series -9-6-3-... must be taken to amount 66? Explain the double answer.

user58512

lol

user19161

@devWaleed HAHAHAHA

user19161

Well, then I dunno what it means.

devWaleed

8:23 PM

what?

skullpatrol

@JasonBourne OMG! You are a fast man!

user19161

There is only one answer, not two answers.

user19161

I really don't know what double answer means there.

devWaleed

book is giving me two answers

user19161

It is poor writing at best.

user19161

8:24 PM

And what are the two answers?

Jonas Teuwen

@Tobias Damn right.

user58512

do you get double marks for a double answer

devWaleed

-4,11

user19161

@devWaleed How can one get a negative number as an answer?

devWaleed

dunno, it says to explain, the answer is from book...

skullpatrol

8:26 PM

@user58512 No double marks for double answers, but you will lose half your marks if you don't find them :)

user19161

There is only one answer if I understand the question correctly, full stop.

user19161

Also, the fact that the phrasing is "double answer" suggests that the book is poorly written.

devWaleed

-.-

okay I will ask my teacher that thing what you said

user19161

All this is assuming you typed the question correctly.

devWaleed

yes

skullpatrol

8:29 PM

It should be "multiple or double root."

user19161

Also, "amount 66" should be "amount to 66".

user19161

The question is crap.

devWaleed

yes "amout to 66" actually

user58512

i agree

devWaleed

sorry for that...

user19161

8:32 PM

OK I think I know the problem @dev

user19161

When you apply the formula do you get a quadratic equation to solve?

devWaleed

and?

user19161

Perhaps you get a quadratic equation with 2 roots, and you have to reject the negative root, because the solution is positive.

user19161

Even then, the question is poorly phrased and misleading.

user58512

this is frustrating a lot, I have to sort out my notes but I can't figure out how ot do

if I don't get things organised I will fall behind

user19161

8:35 PM

@dev Who told you to get this book?

devWaleed

Its our college book :P

user19161

OK, I am sorry to say, I think it is very poorly written.

devWaleed

A boy has 231 marbles, He arranges them in rows so that each row contains one marble less than the preceding. The last row consists of one marble only, which forms the vertex of a triangle.How many marbles are there in the base of the trianble?

^_^

user58512

21

devWaleed

Jason It might be that you don't understand my last question or I poorly wrote it cause book can't be wrong, can be?

WTF

how fast you are?

user19161

8:37 PM

@devWaleed I am saying, that question should not be written that way.

devWaleed

@user58512 how do you solve these so fast?

user58512

@devWaleed, A boy has a large square based pyramid of cannonballs, he rearranges them into a perfect square... how many cannonballs does he have?

devWaleed

I am sorry @Jason

user19161

Well, it's just sum 1+2+3+...

devWaleed

I dont know :(

user58512

8:39 PM

@devWaleed, I mean like this thegrandoldgame.com/Features/SJA/BrassMonkey01a.jpg

user19161

@user58512 You should teach him how to solve it before posing a new problem.

devWaleed

I don't know, I am currently trying to use Sn formula :( for my question...

user58512

I don't know how to solve it

devWaleed

really?

then how'd you solve it?

user58512

@devWaleed, I know the answer though

devWaleed

8:40 PM

o.0

user58512

it's a famous problem

devWaleed

do you know answer for all questions?

oh

user58512

lol

user19161

@dev Do you know how to solve that marbles question now?

devWaleed

no

the problem is

user19161

8:41 PM

Have you learnt arithmetic progressions?

devWaleed

I know the correct formula to use in that case

but

dunno where do I make wrong move...:*(

user19161

You need to know how to model it: convert the word problem into an equation.

devWaleed

I did, I made the triangle too

user19161

So really it is summing 1+2+3+... until you get 231.

devWaleed

Sn=n[2a+(n-1)d]/2

user19161

8:43 PM

Now just apply the formula.

devWaleed

From the last, a=1 ; d=1

Sn=231

trying...

user19161

Yes.

devWaleed

I need to find n, right?

user19161

Yes.

devWaleed

ok

what should be the possible next step here?
231=n(1+n)/2
should it be:
231 x 2 = n+n² ?

user19161

8:48 PM

@devWaleed Yes.

devWaleed

462 = n² + n now use quadratic formula ?

user58512

hi

user19161

@devWaleed Yes, or you can just factorise.

devWaleed

I would go with Quadratic formula...

user19161

Factorisation is easier.

user19161

8:50 PM

@argon So happy to see you!

Argon

@JasonBourne :) Hi Jasper!

skullpatrol

@Argon hey

user19161

@Argon What's up?

Argon

@JasonBourne Not much. School is annoying, but everything is fine.

How's by you?

user19161

Same, hmm perhaps I should email you soon to tell you some new secrets...

Argon

8:51 PM

@skullpatrol Hullo!

o.O!

O.o!

O.O!

-_-

|_|

T_T

8:53 PM

here, see there are two answers @JasonBourne but marbles can't be counted as negative so its 21 :)

Argon

+_+

skullpatrol

Red marbles can be counted as negative.

devWaleed

how?

not yellow or blue ?

skullpatrol

-1, -2, -3, -4,...

devWaleed

So, you have -2 marbles? can I have 1 please....???

skullpatrol

8:58 PM

yellow could be positive marbles and blue could be negative marbles

devWaleed

uh ?

If somebody ask me what is my weight, Can I say my weight is m or W ?

@user58512 Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 7 ?

user58512

66661

devWaleed

wrong ^_^

try again

skullpatrol

Don't troll.
Show what you have tried so far, please.

devWaleed

@skullpatrol ^_^ He is right!

I was testing him

sorry...

ok, I have to go, 2am here ^_^ 8am college time sharp ^^

Bye all!

user58512

9:05 PM

bye

skullpatrol

L8er

zero

@skullpatrol $\Huge\text{Yo Mama}$

skullpatrol

@zero Whatever.

user58512

0

Q: Is $\sum_{n=2}^\infty \frac{\zeta'(n)}{\zeta(1/2 + i \cdot n)}$ convergent?

Consider the sum $$\sum_{n=2}^\infty \frac{\zeta'(n)}{\zeta(1/2 + i \cdot n)}$$ PARI/GP returned approximatly $-1.952441353 - 1.021043166 \cdot i$. I would like to see a proof of convergence of this series.

Nimza

9:28 PM

Hello

user58512

hi

Nimza

@user58512 good day/night/don't know what time is it in your city

Help me please, how do I imagine a path in topological space $X \times X / \left[ (x_1,x_2) \sim (x_2,x_1) \right]$ and in more general case of product of $n$ spaces: $X^n / S_n$ ?

user58512

@Nimza, if X = [0,1], I think it's just a square folded diagonally

Nimza

@user58512 and $\mathbb{R}^2 / S_2$ is just $\mathbb{R}^2_{+}$ right? but what in general?

@user58512 wiki writes "A path in the n-fold symmetric product is the abstract way of discussing n points of X, considered as an unordered n-tuple, independently tracing out n strings." I have a problem with it

@JasonBourne nice day JB!

user19161

@Nimza Hi Cookie Monster!

user19161

9:38 PM

@devWaleed Yes, easier to factorise than use quadratic formula. Also note that the sum to n terms formula is also n(a+l)/2 where l is the last term.

user58512

@Nimza, you could think about "points" in X^3/S_3 being sets instead {(a,b,c),(a,c,b),(b,a,c),(b,c,a),(c,a,b),(c,b,a)} so its like a kaleidoscope

Nimza

@user58512 wow, yup, that is :D the best word in this situation

@user58512 but why independently then?

user58512

I dont know

Argon

How does one solve $$|x-3|+|x-2| = 1$$

user58512

@Argon, you can split into 4 cases

Argon

9:42 PM

@user58512 So I get 3 as and answer, 2 as an answer and ..?

user58512

I mean for each abs value split into cases for it positive or negative

one case is impossible so there are 3 to look at

its not very fun to actually do ... but it works

Argon

Right, so I get 3, 2, all numbers and no numbers (?)

user58512

case 1: x-3 > 0, x-2 > 0. problem reduces to 2x - 5 = 1

Argon

right, so x=3

user58512

case 2: x-3 <= 0, x-2 > 0. problem reduces to 5 = 1

Argon

9:46 PM

so no numbers

Link

Hey

user58512

case 3: x-3 > 0, x-2 <= 0. problem reduces to -1 = 1

case 4: x-3 <= 0, x-2 <= 0. problem reduces to -2x + 5 = 1

Nimza

@Link hello

Link

@Argon, do you know something about extrema?

Or Nimza?

Argon

@user58512 So just 2 and 3, but the answer should include all in between

Nimza

9:48 PM

What, Link?

Argon

@Link Single variable?

Nimza

I know that extrema is an ice cream here, in Moscow :)

Argon

hehe

Link

Lol, no like absolute max and min

and relative max and min

Nimza

aha

Argon

9:49 PM

Ok, shoot

user58512

@Argon, I did case 2 wrong

Argon

@user58512 Does it end up as 1=1

?

Link

So, guys

I'm given this graph

wolframalpha.com/input/…

user58512

case 2: x-3 <= 0, x-2 > 0. |x-3| + |x-2| = |x-3| + (x-2) = -(x-3)+(x-2)=3-2=1

Link

The question is asking how many crit numbers there are

user58512

9:50 PM

so every x such that x-3 <= 0, x-2 > 0 is a solution

Argon

@user58512 So is that what was missing?

Link

I guessed 1, since it seems to be that the tangent line is flat only at the top

but there are 2 criticial numbers

user58512

i.e. 3 >= x > 2

Argon

@Link Two? Which two?

Link

Why?

@Argon, thats the question, I know that one critical number at the top is the absolute max

but whats the other? Is it also at the top for relative max?

Nimza

9:52 PM

@Link "In calculus, a critical point of a function of a real variable is any value in the domain where either the function is not differentiable or its derivative is 0" if you use such definition, then only one critical number

Argon

@Nimza What about the roots?

Link

@Nimza, I know that, but for some reason my book says there's two,

Argon

@Link Could your book be wrong?

Nimza

@Argon hm? I can't understand what do you mean)

Link

No idea.

Argon

9:53 PM

@Nimza I mean, it isn't differentiable at $x=0, 4$, is it?

Nimza

@Argon why? it has one-sided derivatives so belongs to C^1[0,4] by definition of this space

Argon

@Nimza Hmm, yes

Nimza

I think there is a mistake in your book

Link

I'm going to ask my prof

Time to star the question

Theorem

critical point is defined as the number of points where the function takes 0 . so 2 would be the correct answer .

Nimza

10:02 PM

Hm, did anybody think about "asymmetry" in relations of general topology and measure theory? :D Why do we have a Borel sigma-algebra (measurable structure generated by topological structure) but we don't have the asymmetric thing: topology, generated by sigma-algebra? Or do we have such thing?!

user58512

@Nimza, difficult.. I searched and found this math.stackexchange.com/questions/51222/…

Nimza

@Theorem strange definition, where did you get it? I think it's usually called "zero of a function"

Theorem

@Nimza : i have heard it many years back .

Nimza

@user58512 hm, I didn't find an answer in this topic

Theorem

i have a question

on sylow's theorem , related to it

anyone interested ?

user58512

10:16 PM

yes

Theorem

i am trying to prove that a group of order 231 has a sub-group of order 11 lying at the center of the group

user58512

do you mean every group of order 231?

Theorem

yes

user58512

231 = 3*7*11

Theorem

from sylow's theorem it follows directly that there is a subrgoup of order 11 which is normal .

yes

now subgroup of order 7 is also normal .

user58512

10:19 PM

why is it normal?

Theorem

because its unique .

ie there is no other subgroup of order 11 .

user58512

cool, I didn't know that ty

how do you know there is only one?#

Theorem

yes , if a group has a subgroup of a order which is unique then its normal .

user58512

so does that mean we can write the group as LxH where L is the 11-Sylow subgroup?

Theorem

according to sylow's theorem , the number of subgroup of order 11 must be congruent to 1 mod 11 and it should divide the order of the group

so u have only one choice , ie 1 .

implies that there is only one subgroup of order 11 .

user58512

10:22 PM

ohh

I see

Theorem

now my point is to show that product of the subgroup of order 7 and 3 make a normal subgroup .

user58512

right because when we conjugate N by g we get another group of size 11, therefore it's equal to N.. so N is normal

Theorem

what do u mean ?

user58512

I was just checking that the 11-Sylow group N was normal

the same argument for 11 works for 3 and 7 doesn't it?

Theorem

yes

user58512

10:32 PM

oh wait

1+3*2 divides 7*11

Khromonkey

Hi guys

user58512

so there might be 7 conjugate 3-Sylow groups?

Theorem

oh ya

u got it

user58512

so what do we do now??

Theorem

may be go to bed :D

user58512

10:37 PM

what about the problem

"i am trying to prove that a group of order 231 has a sub-group of order 11 lying at the center of the group"

Theorem

i am thinking ,

where are u from ?

Jonas Teuwen

I always think.

user58512

the center of a group is the subgroup of elements c such that forall g, cg = gc

Theorem

@Hi Jonas

user58512

so why would we expect the 11-Sylow group to be in the center?

Khromonkey

10:40 PM

this game is awesome kongregate.com/games/2DArray/the-company-of-myself

Theorem

@user58512 : thats what the question says ,

user58512

no I'm asking it

Theorem

@JonasTeuwen : any new post ?

Link

Hey, can you have an absoulute extrema on a slopped line? Like 2x-3?

user19161

@Link That has no global maximum or global minimum.

user19161

10:46 PM

Of course, the domain matters. Here we assume it is the function on the whole real line.

Theorem

gnt everyone

user19161

If we restrict it to say the closed interval from -1 to 1, then of course it has a global maximum and also a global minimum.

Orange Harvester

@Theorem good night.

@JonasTeuwen Good evening Sir.

user19161

If we use say the open interval from -1 to 1, then there is no max or min either.

Jonas Teuwen

Sir.

Link

10:47 PM

Hmm, okay

what if it's something like [-1,1), then is it only a min?

user19161

Nowadays, the downvote can come because of a typo you try to fix within the first minute of posting.

user19161

Or maybe it can come because there is a comment on the answer already which is similar to your answer.

user19161

Just my guesses.

user19161

Lots of nutcases around.

skullpatrol

like me

user19161

10:49 PM

Yes.

Link

@JasonBourne, what about closed to open interval?

user19161

@Link You mean like [-1,1)?

Link

yea

user19161

Just draw the graph and you will see.

user19161

So the function matters and the domain matters.

user19161

10:51 PM

@skullpatrol I am getting pissed with this site too, perhaps it is time to delete my account, HAHAHAHAHA.

Link

@JasonBourne, yup I got it now, thanks!

user19161

@Link So what is your answer there?

skullpatrol

@JasonBourne Go for it.

user19161

@skullpatrol HAHAHAHAHA

skullpatrol

@JasonBourne HEHIHOHUHY

user19161

10:56 PM

Really, these downvoters are nuts.

skullpatrol

Who said they're not?

Orange Harvester

@JasonBourne I hear ELU are separating sites into ELU and ELL?

user19161

@OrangeHarvester Not separating, they are two sites from the start.

Orange Harvester

@JasonBourne okay.

Khromonkey

Hi link

@Link

Bartek

11:38 PM

Hello. I have a question about this answer. Could someone please help me?

Khromonkey

what's the question?

Bartek

I don't understand how the residue theorem is used there.

Why is only one zero of $f$ considered in it?

If there are four zeros in the unit disk, doesn't it mean that we should have four residues?

The zeros of $f$ are exactly the poles of $f'/f$, right?

Khromonkey

I don't know

I think @robjohn knows

by the way, is every number coprime with one?

Bartek

Oh. :( That's OK!

Yes.

Well, every natural number.

OK, I'll wait here. I do hope he knows!

Khromonkey

or mabye @anon knows

Orange Harvester

11:50 PM

@Bartek Yes four residues each contributing to the final integral.

Bartek

@OrangeHarvester But there's only one residue in the answer!

In this line: ${1\over 2\pi i}\int_D {f'(z)\over f(z)}\,dz=\text{Res}(f'(z)/f(z),0)=4.$

Orange Harvester

@Bartek ?? Each of the pole of a function contributes a $2\pi i$ to the closed loop integral around all the poles of the function.

The total residue is the sum of all the contributions.

Bartek

I don't understand. What is a total residue?

@OrangeHarvester I know about residues at particular poles.

Orange Harvester

sum of residues at particular poles is the toal residue.

Bartek

OK. So why would each pole contribute $2\pi i$? In the residue theorem I know, each pole contributes its residue.

$\int=2\pi i\cdot\text{sum of residues at the poles}$

@OrangeHarvester And the answerer only calculates the residue at $0$...

Transcript for

$Mathematics$ Mathematics