Mathematics - 2013-05-03 (page 1 of 5)

That's likely the problem - the question is motivated by lazy evaluation a la Haskell. So, union is meant to take a list of infinite sequences each monotone increasing, and produce a single sequence monotone increasing. But if not done carefully it just hangs.

skullpatrol

12:17 AM

@QuinnCulver This game has no rules, not even a guide

Charlie

@skullpatrol is that a line?

Quinn Culver

So far we have:
"As I was pondering the continuum,
I was wondering what to bring him
A cantor's hypothesis, it hasn't been proven"

@skullpatrol the lack of rules does not imply an impossibility of producing something nice

Charlie

@peter your turn

skullpatrol

@QuinnCulver But we should have some structure, no?

Quinn Culver

@skullpatrol It's not necessary, but might help. We've actually got some already, in the first two lines. So it's up to whoever writes the 4th to continue with that structure (relative to the 3rd)

minopret

12:21 AM

Thanks @QuinnCulver! I'll just manipulate the code a little to see what makes or breaks it. I always said that all problem solving boils down to trial and error anyway :-)

Peter Tamaroff

@Charlie What?

Charlie

@PeterTamaroff give us a line

3 mins ago, by Quinn Culver

So far we have:
"As I was pondering the continuum,
I was wondering what to bring him
A cantor's hypothesis, it hasn't been proven"

Quinn Culver

@minopret I have no idea how what you've said relates to the fact that 'productivity' and 'creativity' (as defined here) are not related to that function

Peter Tamaroff

@Charlie But that doesn't rhyme.

skullpatrol

This is free style.

whatever that means

Quinn Culver

12:26 AM

it means follow your heart

skullpatrol

listen to your heart

minopret

Well, if Bird said it's tricky to make it a "productive function" and was using the common meaning of the words, then I suppose he only meant that the programmer has to toy with the implementation a bit to achieve the one that enables the evaluator to make progress rather than spin uselessly.

Quinn Culver

@minopret What do you take to be the 'common meaning' of "productive"?

@skullpatrol good muthafuckin song

Peter Tamaroff

@Hurkyl

minopret

Producing anything. We want the code to produce integer after integer, on demand ("lazily"), not to do syntax tree rewriting silently and endlessly - as it very cheerfully will. @QuinnCulver

Peter Tamaroff

12:34 AM

@user1

Do you think this is useful? I'm starting to doubt. Specially in the shadow of Hurkyl's answer.

skullpatrol

14 mins ago, by Charlie

3 mins ago, by Quinn Culver

So far we have:
"As I was pondering the continuum,
I was wondering what to bring him
A cantor's hypothesis, it hasn't been proven"

and like Cantor's hypothesis it can never be proven

Peter Tamaroff

@user75064 Hello there.

skullpatrol

@QuinnCulver awaiting judgement...

Peter Tamaroff

@julien

Charlie

I read "cage of variable"...

Quinn Culver

12:40 AM

@skullpatrol i'm satisfied

who's next?

Charlie

@julien Peter :)

Peter Tamaroff

@julien Hello.

julien

@PeterTamaroff Oops... Hi Peter!

Peter Tamaroff

@julien Heh, thought it was a typo!

anorton

Quick question: For this answer, did I answer correctly? (i.e. I feel like my response was too easy for the way the question looked)

Peter Tamaroff

12:42 AM

@julien How is it going?

julien

@PeterTamaroff Pretty good, you? It takes me 1 minute to type 5 words correctly on average...

Peter Tamaroff

@julien Oh, don't worry. I will correct you.

Charlie

}:)

Peter Tamaroff

I'm OK. Learning multivariable calculus.

Charlie

@skull listen to this. I loved.

julien

12:44 AM

@PeterTamaroff You're a generous editor, I noticed. Multivariable? How far are you?

Charlie

depends, what's your definition of distance?

2

user74918

Can anyone help me with my bipartite issue?

Peter Tamaroff

@julien Hmm, I'm reading Apostol's mathematical analysis, but in my course we got to Taylor's polynomial of second order, namely $$T({\bf x})=f({\bf p})+\nabla f({\bf p})+\frac 1 2 ({\bf x}-{\bf p}){\bf H}f({\bf p})({\bf x}-{\bf p})^T$$

I'm still wondering where does the motivation for the generalization come from.

julien

@PeterTamaroff How come there is no mathjax on chat? Is there something I can do I am not aware of?

Peter Tamaroff

I mean, for Taylor in $\Bbb R^n\to\Bbb R^m$.

@julien Yes, there is.

@julien Here

Charlie

12:48 AM

@julien be aware

skullpatrol

@Charlie 8.5

Charlie

@skullpatrol nice, nice :)

user1

@PeterTamaroff I do prefer Hurkyl's answer, but I do not see exactly why. One thing is that your answer does not stay on topic (notice that Hurkyl only devotes a small paragraph at the end to point out the mistake in the arclength formula). I think that it would be worth mentioning that $\frac {dx}{dt}$ is regarded as a function of $t$, not a ratio of functions of $t$.

Peter Tamaroff

@user1 Yes, I agree.

julien

@Charlie @PeterTamaroff Thank you guys.

Peter Tamaroff

12:50 AM

@julien Apostol defines "higher order derivatives" as multilinear forms.

skullpatrol

Have you ditched Rudin?

Peter Tamaroff

@skullpatrol I am actually using it to, but for sequences and series of functions, Stone Weiertrass and stuff.

Charlie

@julien no problem :)

julien

@PeterTamaroff I have not applied multivariable calculus much. So I can't think of an enlightnening nontrivial motivation. But you already do multivariable calculus with holomorphic functions!

Peter Tamaroff

@julien Heh, I haven't studied complex analysis yet! =)

Specifically, $$f^{(n)}({\bf x},{\bf v})=\sum_{i_1,\dots,i_n} D{i_1,\dots,i_n}f({\bf x})v_{i_n}\dots v_{i_1}$$ or some ugly monster of the sort.

julien

12:55 AM

@PeterTamaroff Yes, that's the problem. It soon becomes ugly. But you'll get ued to it, I'm sure.

Peter Tamaroff

For example, $$f''({\bf x},{\bf t})=\sum_{i=1}^n\sum_{j=1}^n D_{i,j}f({\bf x})t_j t_i$$ is the product ${\bf t}\cdot {\bf Hf}({\bf x})\cdot {\bf t}^T$ where ${\bf Hf}$ is the Hessian of $f$.

@julien What do you do?

julien

@PeterTamaroff Professionally? I teach maths. Calculus I, typically. Or II.

Charlie

hmm

Peter Tamaroff

@julien Ah. You're a professor.

Charlie

"Ah! you're a cat!"

Peter Tamaroff

12:58 AM

@Charlie Your small talk is bad, and you should feel bad.

Charlie

@PeterTamaroff Alice

Peter Tamaroff

@julien And do you do any other math work apart from teaching?

julien

@PeterTamaroff No, I just teach. And I found myself spending a lot of time here since january.

Peter Tamaroff

@julien It's a nice place to be. =)

julien

@PeterTamaroff yes, it's great. It helps me remember lots of things I had almost forgotten. And even learn new ones.

Charlie

1:02 AM

@skull ;O

skullpatrol

@Charlie :-|

anorton

@Charlie You always seem to be able to find emoticons that I've never seen before! :)

Charlie

@anorton because I create them

@anorton :D

there's another i created with @skull

S2!

i don't wanna stay awake anymore

Peter Tamaroff

Hmm. I think I'll delete this one

Charlie

do it, do it

skullpatrol

1:07 AM

do it till your satisfied, whatever it is

Peter Tamaroff

@julien Are professors well paid in France?

julien

@PeterTamaroff I'm in Quebec. Yes, it's well-paid. Far from what doctors make. But way enough for me.

Charlie

@PeterTamaroff his profile says "Montreal"

Peter Tamaroff

@Charlie Yes, thank you. I already face-palmed.

@julien How nice.

Charlie

@PeterTamaroff good :)

Gnintendo

1:11 AM

aced my Linear Algebra final...now to study for my Differential Equations final

>.<

julien

@Charlie True. I did not lie on my profile.

Charlie

@Gnintendo oh noes!

X-(

user74918

can anyone point out some advice for how to count connected graphs?

Peter Tamaroff

@user74918 Mariano told you your problem was very difficult. Mariano told you your problem was very difficult.

Charlie

HAHAHAHAHHAHAHA

user74918

1:14 AM

It is very difficult

Doesn't mean it's not worth attempting

Peter Tamaroff

@user74918 True.

user74918

I have an approach that is almost working but I am getting the inclusion-exclusion wrong

skullpatrol

Have you posted what you have done so far on the main site?

user74918

yeah but it never pans out well

people just tell me it's hard and then that's that

Charlie

@skullpatrol I think I will sleep, Skull.

skullpatrol

1:21 AM

@Charlie later

Charlie

@skullpatrol byee byee! (I hope I can sleep now >:( )

skullpatrol

@Charlie bye

user74918

is there a term/definition for a graph that has at least one edge connected to each vertex?

may or may not be connected?

skullpatrol

6 mins ago, by skullpatrol

Have you posted what you have done so far on the main site?

user74918

vs. a graph that has some vertices without edges touching them

Charlie

1:23 AM

@skullpatrol byes

user74918

i already answered that above

skullpatrol

@Charlie bye

Ethan

1:37 AM

$$-1=\sum_{n=0}^\infty \frac{q^{-2^n}}{(1-q^{-1})(1-q^{-2})(1-q^{-4})(1-q^{-8})....(1-q^{-2^n})}$$

|q|<1

Alexander Gruber

3:36 AM

$\color{red}\star\color{blue}\star-\color{red}\star=\color{blue}\star$ :)

Gustavo Bandeira

@AlexanderGruber LJ account name?

Alexander Gruber

@GustavoBandeira TheTitsGroup

Gustavo Bandeira

Haha

Alexander Gruber

later :p

Quinn Culver

question of the day: math.stackexchange.com/questions/378284/what-is-this-all-about

Gustavo Bandeira

3:48 AM

@QuinnCulver Did he deface the question?

user1

@GustavoBandeira Depends on how you view the original material.

Gustavo Bandeira

@user1 I view it with my eyes.

user1

@GustavoBandeira I meant perceive, which I suspect is not an operation of the eyes.

Gustavo Bandeira

@user1 I know. I'm just kidding.

user1

@GustavoBandeira I probably should have gotten that. :)

amWhy

4:01 AM

My goodness, it's been quiet here (in chat) tonight... ;-)

Gustavo Bandeira

16

Q: Can rats pass on memories of a maze to their offspring?

A friend of mine told me once about a documentary movie he saw some years ago. On this movie he saw scientists talking about particular experiment. This experiment involved rats and probably electrical traps. The rat had to get to the cheese, there were traps on the shortest route to it, and obvi...

This is interesting.

Gnintendo

somebody come up with a simple 2nd-order DE that I can solve with basic laplace

(studying for DE)

>.<

Gustavo Bandeira

@Gnintendo I guess you should search problem books.

Gnintendo

yeah..................................................

Laplace seems really easy so I feel like I'm missing something

you just substitute for the ys, then make it look like stuff from a table..

Ethan

4:23 AM

@GustavoBandeira interesting

Gnintendo

hmm

I am noting that an easy way to solve an initial value problem given a solution to a homogeneous differential equation is to plugin the initial values into my wronskian and set up a matrix with the initial values on the right side and solve with linear algebra

for non-homogeneous equations with another answer part that is not a coefficient of a constant, can I simply subtract the value obtained from plugging in the appropriate initial value from the righthand side of that augmented matrix?

Ocena Pothik

4:42 AM

Hellow Guyz , I have a problem . Can u plz try to solve it ?
http://math.stackexchange.com/questions/379938/minimum-number-of-moves-for-numbering-vertices-of-cubes

Antonio Vargas

@OcenaPothik combinatorics is probably a more accurate tag than number theory. Mind if I re-tag it?

Ocena Pothik

no its ok .

Can u plz give me a idea to solve this problem ?

Antonio Vargas

@OcenaPothik Sorry, I don't have any ideas.

Ocena Pothik

I am too much curious to solve this problem .

Any other guyz ?

Gustavo Bandeira

6:27 AM

@Ethan What?

@Ethan Hey. I remembered of you today. My book on number theory is here, I've seen some of the stuff you type here. =)

skullpatrol

I think he found your Biology question interesting.

As I did also :)

Gustavo Bandeira

Yeah.

I had the idea of searching about it after watching stargate.

skullpatrol

I think there is a Science Fiction.SE also.

If you're interested.

Gustavo Bandeira

Yep.

Is this opening there?

skullpatrol

6:44 AM

Yep.

Gustavo Bandeira

I'm unable to access it. =/

skullpatrol

Norm (mathematics)

In linear algebra, functional analysis and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space, other than the zero vector (which has zero length assigned to it). A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector). A simple example is the 2-dimensional Euclidean space R2 equipped with the Euclidean norm. Elements in this vector space (e.g., (3, 7)) are usually drawn as arrows in a 2-dimensional cartesian coordinate system starting at the o...

Gustavo Bandeira

Yep. No need to worry - it's really not so necessary.

The book I'm reading just proposed the norm function and I was kinda confused about what it is.

I've been elucidated by the the portuguese version.

I'm just not sure of it's purpose.

skullpatrol

I wonder why you can't access it...

Gustavo Bandeira

I guess my ISP is having dns problems.

I was also playing league of legends and having lag spikes.

Rebooted PC and modem and it persists.

I have access only to a few sites.

Now I can!

Yay!

skullpatrol

6:53 AM

Great!

:D

awllower

Good day!

Gustavo Bandeira

The norm seems to be only the length of the vector.

Good day!

Hello!

:D

7:14 AM

Given a group G, Why is <a> the set generated by sucessive products not only on a, but on both a and a^-1

user1

@nerdy It has to be the group generated by a.

anon

by definition.

if you're wondering why it's defined that way, then user1's mentioned the idea: just including positive powers of a will not in general yield a group, since a group must have inverses (and hence negative powers of a)

nerdy

hm but if the group is finite

we dont even need negative powers of a to make sure we generate a rgoup

right ?

suppose after 6 operations on a, we get the identity

then we are certain that a^5 is the inverse of 5

anon

right

Dominic Michaelis

7:50 AM

hi

skullpatrol

huhu

How are you?

Dominic Michaelis

still waiting for an anwer

seems like the question is not that easy, or noone likes it

awllower

8:28 AM

@DominicMichaelis WOW You have asked a question with 92 upvotes!
Quite amazing indeed...

Dominic Michaelis

Well i still need 8 more upvortes but on this question there are some awesome answers

awllower

Yes!

Dominic Michaelis

But on this question math.stackexchange.com/questions/374442/… there are no answers yet

awllower

Maybe it is a little too subtle?

Dominic Michaelis

how do you mean it ?

awllower

8:33 AM

I think that I made that statement simply because my topology is very poor.

In any case, it might help by separating the question in an independent box!

skullpatrol

....or even considering a bounty :)

awllower

:)

A question worth of some thoughts.

Hello

hi!

...@

8:46 AM

what a bounty should i offer

robjohn

@DominicMichaelis depends on how much you are willing to part with and how much you want to get an answer.

awllower

@robjohn Excuse me. What does this mean? Thanks.

Dominic Michaelis

@robjohn math.stackexchange.com/q/374442/62278

robjohn

@awllower it is a rolling tumbleweed... symbolizing a deserted street

quietness

Vrouvrou

someone does it study the theory of Morse ?

awllower

8:51 AM

I see.
Thanks for telling me. :-) <-

Dominic Michaelis

my first 500 bounty :D

robjohn

@DominicMichaelis wow!

awllower

à.0

robjohn

@DominicMichaelis I wish I knew about filters :-)

skullpatrol

@DominicMichaelis Is it worth that much to you?

Dominic Michaelis

8:56 AM

@skullpatrol Well I still have more than 10k reputation so i still have moderator tools, and i thought a lot about that question

Vrouvrou

hey someone to answer me ?

awllower

I know no Morse theory. Sorry then.

@Vrouvrou But one of my seniors knows something about it. Maybe I can take a note of your question, and then ask him?

Vrouvrou

ah really

awllower

:)

Vrouvrou

so this is the question

awllower

8:59 AM

yes

Vrouvrou

0

Q: Question about theorem 3.2 from Morse theory by Milnor

THe demonstration of the theorem 3.2 in the book Morse theory by Milnor is given in the special case whene the manifold is the Torus , My question is : can i prove it in the case where the manifold is a manifold with dimension 1 ? Please Thank you

homework analysis functional-analysis manifolds morse-theory

awllower

OK
When I receive an answer, I shall tell you.

;)

Vrouvrou

thank you thank you

awllower

NP

Neo

Week before finals is worse than finals week

awllower

9:08 AM

indeed.

Lord_Farin

9:20 AM

Good morning colleagues.

skullpatrol

comrade

Lord_Farin

What's with the propagation of grammar slacking by a certain "Quinn Culver" being starred?

@skullpatrol Everyone picks at those, because nobody likes to be confronted with their errors (regardless of the cause). I always consider this to be under the "Don't shoot the messenger" policy.

skullpatrol

10:19 AM

...@

....@

.....@

......@

.....@

....@

...@

user1

$\implies$

skullpatrol

2 hours ago, by robjohn

@awllower it is a rolling tumbleweed... symbolizing a deserted street

quietness...

Chris's sister and pals

10:47 AM

Greetings

I was thinking of computing elementarily $$\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{kn (k+n+1)} $$ that according to Mathematica is $2$.

Ishan Banerjee

11:00 AM

@Chris'ssisterandpals maybe $k+n+1-k-n=1$, so partial fractions looks nice.

Dominic Michaelis

HI

Chris's sister and pals

@DominicMichaelis hello

@IshanBanerjee yeah, that could work.

Dominic Michaelis

finally i got at least a comment on my questio

Lord_Farin

11:12 AM

@DominicMichaelis Of course, that's the least that can be expected after deploying a sack of 500 goodies :).

I had contemplated adding a bounty for your question myself, but you beat me both in timing and size.

Dominic Michaelis

well we don't know if the bounty helps at all

user19161

The easier the question, the easier it is for me to give wrong answers.

Chris's sister and pals

@IshanBanerjee did you get the answer by going partial fractions way?

nonagon

11:32 AM

Please see here physics.stackexchange.com/questions/63140/work-done-by-tension

Jayesh Badwaik

What are we looking at? What is the big ball?

Dominic Michaelis

what are that for graphics ?

nonagon

It is path

the big circle

and small circle is ball

Dominic Michaelis

Made with paint ?

nonagon

yes :(

?

Jayesh Badwaik

11:36 AM

Why is horizontal velocity increasing? Tension is always perpendicular to the velocity, and hence only direction is changing.

nonagon

Because tension is there in horizontal direction , and it acts for a however small but finite amount of time , hence , since a=F/m , and for a small time it acts , hence it must increase velocity by a x t. where t is the time for which it acts and F here is tension and m is mass of the ball/stone which is rotating in circular path

Kindly see the edit too

And if only tension is there , then acc. to Work Kinetic Energy theorem , the Kinetic energy must not change , hence forth , speed must not change , but it is changing here according to newton's laws

?

(:

Jayesh Badwaik

@nonagon Are you familiar with calculus?

Frank Science

Nope.

Ishan Banerjee

12:00 PM

@Chris'ssisterandpals Sorry I wasn't at home for a while. I simplified it to $\lim_{N\to\infty}((H_N)^2-2\sum_{k=1}^N\sum_{n=1}^N\dfrac{1}{k(n+k+1)})$

TEX doesn't seem to be working for me in chat.

Lord_Farin

See the link on the middle right of your screen.

(The one with "$\LaTeX$ rendering in Chat")

Chris's sister and pals

@IshanBanerjee I see.

Frank Science

$$S=\sum_{j,k>0}\frac1{jk(j+k+1)}$$

Chris's sister and pals

@FrankScience it looks much better. :-)

Frank Science

It's a positive double sum, therefore we can rearrange the terms.

$$S=\sum_{n>1}\frac1{n+1}\sum_{0<k<n}\frac1{k(n-k)}$$

Note that $$\sum_{0<k<n}\frac1{k(n-k)}=\sum_{0<k<n}\frac1n\left(\frac1k+\frac1{n-k)\right)$$

where $H_n=1/1+1/2+\dotsb+1/n$

Note that $$\sum_{0<k<n}\frac1{k(n-k)}=\sum_{0<k<n}\frac1n\left(\frac1k+\frac1{n-k}\right)=\frac{2H_{n-1}}n$$

We have $$S=2\sum_{n>1}\frac{H_{n-1}}{n(n+1)}$$

Partial sum is $$T_n=\sum_{n=2}^N\frac{H_{n-1}}{n(n+1)}=\sum_{n=2}^NH_{n-1}\left(\frac1n-\frac1{n+1}\right)$$

Telescope, we have $$T_n=\frac{H_1}2+\sum_{n=3}^N\frac1n(H_{n-1}-H_{n-2})-\frac{H_{N-1}}{N+1}$$

Note that $H_{n-1}-H_{n-2}=1/(n-1)$, we can telescope the summation again.

$$T_n=\frac{H_1}2+\sum_{n=3}^N\left(\frac1{n-1}-\frac1n\right)-\frac{H_{N-1}}{N+1}$$

Therefore $\lim_{n\to\infty}T_n=1$. Q.E.D.

Charlie

12:22 PM

Good morning

Frank Science

Good morning.

Charlie

@FrankScience how are you?

Frank Science

@Charlie I'm fine.

Charlie

Great!

Frank Science

I'm worried.

Chris's sister and pals

12:24 PM

@FrankScience nice.

Lord_Farin

@Charlie Good morning.

Charlie

@FrankScience why??

Ocena Pothik

Hellow Guyz

I have a problem

Lord_Farin

Hello.

Ocena Pothik

Plz look at a galance to this problem

math.stackexchange.com/questions/379938/…

Charlie

12:25 PM

@Lord_Farin hi F! How are you? Did you sleep well? I did!

Frank Science

@Charlie There're some problems unsolved, and the mid-term exam is coming.

Lord_Farin

(Intermediary rant: RAAHHH @ this. Will it ever stop?!)

nonagon

@JayeshBadwaik Yes very much .

Lord_Farin

@Charlie Yes, though a little long for my liking. Glad to hear you slept well :).

Charlie

@FrankScience oh!! are you having many problems?

@Lord_Farin :D

user1

12:28 PM

@Lord_Farin Yes, a chance to fix a typo without being the one to bump it onto the front page. :)

Charlie

@Lord_Farin oh noes....oh noes!

Frank Science

Asymptotics

Lord_Farin

@OcenaPothik This seems like one of those problems where heuristics is the best we can do with current knowledge. But it's not my area of expertise...

Charlie

When my sister says: but I don't know! I say: you do know, keep trying. What shes thinking it's usually right. You just need to write. Ah! And think too.

Dominic Michaelis

asldfjla

oh you said i should htink too :D

Charlie

12:33 PM

Hi @dom

Lord_Farin

@Charlie A humongous number of points for homework and exams was lost in the mind $\to$ paper transition.

Dominic Michaelis

@Charlie Hi youtube.com/watch?NR=1&v=eRKJQNsFH7A&feature=endscreen

@Lord_Farin thats a forgetfull functor ;)

Lord_Farin

@DominicMichaelis :) Indeed it is. Sometimes it really helps to know the TA/professor somewhat; it can make them more tolerant regarding skipping "trivial" (IMO) steps :).

Dominic Michaelis

yeah i did TeX a 4 page homework for a freaking trivial problem which isn't worth 2 lines

Charlie

@dom hehehe

Tobias Kildetoft

12:38 PM

Remember that the point of homework exercises is not to prove something or even convince the reader that it is true. It is to convince the reader that you have understood why it is correct.

user19161

@JayeshBadwaik So that is your new email address, what you sent me yesterday?

Transcript for

$Mathematics$ Mathematics