Mathematics - 2015-03-10 (page 2 of 4)

Clement C.

14:02

@ABeautifulMind OK. That's going to sound ridiculous, but how do I do that?

(via flagging?)

A Beautiful Mind

@ClementC. It does not sound ridiculous. Ping one in chat, like @robjohn. Or flag one on the main site. I might be wrong.

Clement C.

tHANKS!

Oops. Thanks!

A Beautiful Mind

@ClementC. If the question has not received any answers, you can delete it and repost.

Clement C.

@ABeautifulMind @robjohn Well, that's maybe petty, but I am reluctant to do so because of the +200 bounty I put on it... if in any case it is to be lost, then I will go for that option.

Mike Miller

14:24

Nice question, @ClementC..

robjohn

@ClementC. We can't migrate it because of the bounty. As soon as the bounty has been given out, it can be migrated.

A Beautiful Mind

@robjohn Can the question be deleted keeping the bounty?

A Beautiful Mind

14:50

Wow that killed the conversation.

Clement C.

@ABeautifulMind I'm interested in the answer :) if it's not possible, I'll delete my question and incur the loss of the bounty: not too big a deal, I reckon.

A Beautiful Mind

@ClementC. Or you can wait.

Clement C.

(you mean, wait until the bounty ends? That's the crux: I am asking this as I need this to try and improve a proof in a paper in submission, for the full version that we plan on posting on arxiv. 5 days is a long period, under time constraints.)

Huy

I haven't done any calculus for years. How do I compute $$\int_{0 \leq \tau_1 < \tau_2 \leq \tau} d\tau_1 \, d\tau_2,$$ is it just $\tau^2/2$?

iwriteonbananas

@Huy $t^2/2$

Huy

15:01

@iwriteonbananas: Ok, so my reasoning was correct.

iwriteonbananas

maybe

Huy

@iwriteonbananas: If I have that integral, but as integrand some product of functions $f(\tau_1) \cdot g(\tau_2)$, can I also seperately compute the integral wrt. $\tau_1$ and then the integral wrt. $\tau_2$, multiply and divide by 2?

Mike Miller

it's just the area of a triangle

if you want you can split that into a double integral with multiple bounds

iwriteonbananas

@Huy yes, separate it into a double integral like mike said

it's the same as $\int_0^t \int_0^{\tau_2} d \tau_1 d \tau_2$

Clement C.

15:33

@ABeautifulMind @robjohn Funny thing -- I cannot even delete the question myself until the bounty ends. I assume cross-posting, even under these circumstances, would be frowned upon?

robjohn

@ClementC. I am finding out from MO whether it would be accepted there. If so, we will see what we can do.

Clement C.

Thank you!

robjohn

@ClementC. It is migrated. Go there, and make sure the tags are good.

Clement C.

I just saw it; thank you again. :)

Robert Cardona

15:56

Has anyone here worked trough "Essential Results" by Robert Zimmer?

"Essential Results in Functional Analysis"

Mike Miller

do you have a particular question about it?

Robert Cardona

nothing in particular

just wanted to see if anyone had worked through it and see how long it took them

I like to have a basic timeline for how long a book should take (Even though I know this varies from person to person)

Mike Miller

ah, can't say anything then, sorry

Vrouvrou

16:16

please : math.stackexchange.com/questions/1183927/…

is the sequence has a convergent sub sequence ? please

Vrouvrou

16:29

@robjohn can you help me please

someone here ??????

A Beautiful Mind

@Vrouvrou They will help if they can, relax.

Vrouvrou

16:59

@ABeautifulMind i juste want know now why this sequence has a convergent sub sequence

A Beautiful Mind

@Vrouvrou Sorry, I cannot help you. I am only a banana. =)

@Vrouvrou Are you doind a masters degree in math or something?

Vrouvrou

yes but i'm a big banana

A Beautiful Mind

LOL.

iwriteonbananas

@Vrouvrou can i write on u?

Theorem

@robjohn Hi, Did you have time to look into my problem ? :)

ta3920

17:08

Hey guys, any idea how I could prove the following:
Let W be a subspace of Rn and x_1, ..., x_k be vectors in W. Show that span(x_1, ..., x_k) is contained in W.

Sorry about no LaTeX but I think it's still readable.

A Beautiful Mind

@ta3920 This is trivial. Use the fact that W is a subspace and is closed uner linear combinations.

ta3920

Right, I kept thinking about how to establish that fact that these vectors won't leave W and forgot about W being a subspace. Thanks!

A Beautiful Mind

We often forget what is most important to us in life.

ɧɿρρԹʅȝՇԵՐՎԾՌ

@ABeautifulMind Brains

iwriteonbananas

@MikeMiller trying to prove: if $X$ is a path-connected space such that any map $S^1 \to X$ is null-homotopic, then $X$ is simply connected. if $f:S^1 \to X$ is any loop in $X$, how do we construct a homotopy to the constant path which leaves the base point fixed?

Mike Miller

17:17

two elements of the fundamental group are freely homotopic iff they're conjugate

prove that and use that

iwriteonbananas

what do u mean by freely homotopic?

Mike Miller

homotopic but not necessarily preserving the basepoint

iwriteonbananas

ok

A Beautiful Mind

Freely X means X in a free way.

iwriteonbananas

@MikeMiller once we've established that, do we use the isomorphism $\Phi: [f] \mapsto [ \bar{h} f h ]$ ?

Mike Miller

17:27

that's one way of phrasing it

the point is that the only element conjugate to the identity is the identity

so anything freely null-homotopic must be basepoint null-homotopic

iwriteonbananas

kk got it

robjohn

17:39

@Theorem No. I am not sure how to proceed on it.

iwriteonbananas

@MikeMiller if f, g are freely homotopic via $H: S^1 \times [0,1] \to X$, then $[ \bar{h} \, f \, h] = [g]$ where $h(t) = H_t(1)$, right?

Mike Miller

sounds reasonable

iwriteonbananas

i cant figure out the other implication

Mike Miller

that's the one I think is easier

draw pictures

iwriteonbananas

ok

iwriteonbananas

18:03

man oh man im retarded

Mary Star

Hello!!

I want to show that Insetion Sort is stable...
Is the invariant the following??

At the beginning of each iteration of the for loop, if $A[a]=A[b], a<b \leq j-1$, then $A[a]$ appears before $A[b]$.

Initialization:
We have to show that the invariant holds before the first iteration of the loop where $j=2$. In this case, the subarray $A[1 \dots j-1]$ consists of only the element $A[1]$, so there are no $a<b \leq j-1=1$. So, the invariant holds trivially.

Maintenance:
We have to check if the property maintains at each iteration. The body of the outer for loop shifts the elements $A[…

evinda

@AndrewThompson Are you familiar with the time complexity of algorithms?

Andrew Thompson

@evinda No, sorry.

evinda

A ok, no problem @AndrewThompson

iwriteonpeoplewhowriteonbanana

18:47

@iwriteonbananas :3

John Jack

hi @iwriteonpeoplewhowriteonbanana

iwriteonpeoplewhowriteonbanana

@JohnJack o/

John Jack

@iwriteonpeoplewhowriteonbanana Can I ask something simple. I just want to confirm the following basic fact of limits of a function:
$\lim\limits_{x \rightarrow a}f(x) = c \text{ iff } \lim\limits_{x\rightarrowa}|f(x)-c| = 0$

iwriteonpeoplewhowriteonbanana

please put one '$' on each side of the equation so that I can render it

yeah that's true

Gato

@Chris'ssis If someone (say a woman to a man ) offert a Mărțișor what does it means ?

John Jack

18:58

Thanks

Gato

@iwriteonpeoplewhowriteonbanana Encore un nouveau pseudo, j'espère que tu vas bien, je ne fais que passer :p.

iwriteonpeoplewhowriteonbanana

Mărțișor

Mărțișor (Romanian pronunciation: [mərt͡siˈʃor]) is a Romanian celebration at the beginning of spring, on March the 1st in Romania, Moldova, and all territories inhabited by Romanians. Alike, though not identical customs can be found in Bulgaria (see Martenitsa), while similar ones exist in Albania, and Italy. The name Mărțișor is the diminutive of marț, the old folk name for March (Martie, in modern Romanian), and thus literally means "little March". It is also the folk name for this month. Mărțișor, marț and mărțiguș are all names for the red and white string from which a small decoration is...

@Gato Ca va et toi ?

Chris's sis

@Gato It's about offering a Martisor.

Gato

@iwriteonpeoplewhowriteonbanana Je sais, mais entre ce que wiki dit et la réalité des fois..

@Chris'ssis ?

@Chris'ssis I ask for the meaning of offering a Martisor.

:-)

Chris's sis

@Gato " the one who wears the red and white string will be strong and healthy for the year to come"

Gato

19:08

@Chris'ssis I was not sure about the fact that it was the 'reality'

thanks

John Jack

@iwriteonpeoplewhowriteonbanana Lastly, would you say that the limit of $\frac{y^{2}-3}{y}$ does not exist?

iwriteonbananas

19:27

@JohnJack what does that mean?

what's the limit?

oh ur talking to someone else

damn you hippa

@iwriteonpeoplewhowriteonbanana you just might be the next best thing but not quite me

@ABeautifulMind that's pretty creepy

John Jack

@iwriteonbananas Sorry typo. $\lim\limits_{y \rightarrow 0}\frac{y^{2}-3}{y}$.

iwriteonbananas

@JohnJack it doesnt exist

John Jack

Thanks.

iwriteonbananas

but run it by @Chris'ssis just to be sure. he's a world class integrator/limit finder

teadawg1337

19:46

Chris'ssis is a woman

Ted Shifrin

hi bananas, @teadawg

teadawg1337

Hello @Ted!

Ted Shifrin

do we really know for sure, teadawg? :D

teadawg1337

Fair enough

Ted Shifrin

I see Hippa is continuing his obnoxious habits :P

teadawg1337

19:54

@Ted Any ideas for how to evaluate $\sum_{n=1}^{\infty}\frac{1}{16n^2-8n}$?

Ted Shifrin

Partial fractions?

teadawg1337

Nvm, nvm. Yeah, partial fractions and recurrence relations of the digamma function

It comes out to be... $\frac14\ln(2)$ I believe

Ted Shifrin

You know lots more special function stuff than I do, but I bet that, knowing about Euler's constant, I can get it.

teadawg1337

@Ted You mean $\gamma$, right?

Ted Shifrin

Yuppers.

Hmm ...

Yes, I get $\log(2)/4$, as well. Nothing too fancy.

That probably is one Chris'ssis would have done literally in her head in milliseconds.

OK, back to grading, since it's so silent in here ..

teadawg1337

20:04

Cya later @Ted

Vrouvrou

Someone has an idea for this :math.stackexchange.com/questions/1184270/…

@TedShifrin can you see my question please

Chris's sis

@iwriteonbananas That sounds nice. As regards math I'm in a competition with myself only, so this kind of recognition doesn't make much sense. I'm the person I wanna beat every day in the area of integrals, series and limits .

iwriteonbananas

hi there boys and girls, and ted

Alizter

Hi @TedShifrin

Do you still teach probability?

user159870

Hello @iwriteonbananas.......

iwriteonbananas

20:17

hey user

do you still use?

user159870

@iwriteonbananas Of course! Do you still write on bananas?

teadawg1337

@Chris'ssis How fast can you prove my simple (for you, anyway) series above?

iwriteonbananas

@Chris'ssis well well, sounds like you should team up with some other integratorz and get to the next lvl

Chris's sis

@iwriteonbananas Not really. I dream to become like Ramanujan, and keep in mind Ramanujan is from other world, no one can compare to him (so far).

iwriteonbananas

@user159870 yes, thanks for pouring salt into the wound. i live in a remote rainforest area and my circumstances force me to use bananas as writing material

Cortizol

20:20

Why is true that $|\cos(tx)-1| \leqslant t|x|$ for $|x|\leq N$ and $t$ small? I can't see...I'm too tired

Chris's sis

@iwriteonbananas Ramanujan is the god of all.

iwriteonbananas

@Chris'ssis everyone is a ramanujan lurking as i always say

user159870

After writing on them do u eat them? @iwriteonbananas

Chris's sis

@iwriteonbananas But I'm not everyone. ;)

iwriteonbananas

@user159870 no i eat them before

@Chris'ssis you're just an average joe

Chris's sis

20:21

@teadawg1337 $$\sum_{n=1}^{\infty}\frac{1}{16n^2-8n}$$?

teadawg1337

Yes

iwriteonbananas

could be working at burger king, spittin on my onion rings

but you compute integrals and series all day

trying to be like Ramanujan

Chris's sis

@iwriteonbananas aha, I see your point. Are you Romanian (btw)?

iwriteonbananas

no lol

Chris's sis

@teadawg1337 Well, partial fractions and then add 2 more partial fractions and grup all into 2 sums. All will very nicely flow.

teadawg1337

20:23

I already solved it

It's $\frac14\ln(2)$

Chris's sis

@teadawg1337 $$\sum _{n=1}^{\infty } \frac{1}{4} \left(\frac{1}{2 n-1}-\frac{1}{2 n}\right)$$

@iwriteonbananas Because, you know, if you were a Romanian I'd meet you and show you there in front of you if I'm good or not. (without pen and paper)

teadawg1337

@Chris'ssis Yes, and from there it's simple using recurrence relations of the digamma function

iwriteonbananas

@Chris'ssis 99% of the time i dont understand the comments you make

tthis is another one of those times

i believe u that ur the great :D

i dont need u to show me in person "without pen and paper"

teadawg1337

@Chris'ssis Keep an eye on me, I might surpass you one day :P

Chris's sis

@teadawg1337 Well, that would be great. I love to learn from those that know more than me. Really!

It's hard to do all alone, without learning from anyone, it's crazy hard. Ramanujan had almost no knowledge on complex analysis as Hardy mentioned.

teadawg1337

20:31

I also have hardly any knowledge of complex analysis, but I'm no Ramanujan... Far from it

I should get back to my work

Stan Shunpike

Why is it useful to have differentiability imply continuity? I am reading about the motivation for the total derivative in Apostol and he points out an example where the existence of all partial derivatives doesn't imply continuity. But I don't see why that matters.

iwriteonpeoplewhowriteonbanana

@TedShifrin >:c

robjohn

@Chris'ssis It would be good for a binary fireplace

Chris's sis

@robjohn :-)

Ramanewbie

@iwriteonpeoplewhowriteonbanana you're not on tox ?

robjohn

20:44

@Chris'ssis a quarter of a log is just about right

iwriteonpeoplewhowriteonbanana

@Ramanewbie hard connection problems

Ramanewbie

@iwriteonpeoplewhowriteonbanana ok ok

Chris's sis

@robjohn $\log(2)/4$

robjohn

@Chris'ssis That is what I meant :-)

@Chris'ssis Oh, I didn't see that you parted the fractions :-)

Chris's sis

MMMy screen is white, I see nothing.

Ramanewbie

20:47

@iwriteonpeoplewhowriteonbanana you quit already... :( hi @Chris'ssis

Chris's sis

DoDo you see anything?

iwriteonpeoplewhowriteonbanana

@Ramanewbie I told you, bad connection

iwriteonbananas

@Vrouvrou yes

robjohn

Interesting. I have 272 answers with a score of 0.

iwriteonpeoplewhowriteonbanana

@robjohn Now compare with the German Doctor

Alizter

20:50

@TedShifrin One hundred people line up to board an airplane. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats at random otherwise. What is the probability that the last person to board gets to sit in his assigned seat?

iwriteonpeoplewhowriteonbanana

low ? :D

robjohn

@iwriteonpeoplewhowriteonbanana which user?

Alizter

@iwriteonpeoplewhowriteonbanana Is that for the question?

Ramanewbie

@iwriteonpeoplewhowriteonbanana How did you change your name

robjohn

@Ramanewbie You can do that from your profile page

Chris's sis

20:52

I had to restart my comp.

iwriteonpeoplewhowriteonbanana

@Alizter Yeah :D

Alizter

@iwriteonpeoplewhowriteonbanana Work it out and be suprised

iwriteonpeoplewhowriteonbanana

@robjohn math.stackexchange.com/users/175066/dr-sonnhard-graubner

robjohn

@iwriteonpeoplewhowriteonbanana He has 290... just a bit above me

iwriteonpeoplewhowriteonbanana

@robjohn And with negative score ?

robjohn

20:54

@iwriteonpeoplewhowriteonbanana he has 272 with positive score

iwriteonpeoplewhowriteonbanana

Which leaves a lot of negative ones :/

robjohn

@iwriteonpeoplewhowriteonbanana and 60 with negative score

iwriteonpeoplewhowriteonbanana

@robjohn What about his average negative score ?

robjohn

:20473737 There is no search for that. I'd have to use the SQL for that, and that has some delay

Stan Shunpike

@PedroTamaroff why is it useful to have differentiability imply continuity? I am reading about the motivation for the total derivative in Apostol and he points out an example where the existence of all partial derivatives doesn't imply continuity. But I don't see why that matters. Any ideas?

teadawg1337

20:57

@Chris'ssis How about this one? $$\sum_{n=1}^{\infty}\frac{\sum_{k=1}^{2n}\frac{(-1)^{k-1}}{k}}{16n^2-8n}$$

robjohn

@Chris'ssis: I just computed the first three terms of the Laurent expansion for $\Gamma$ at negative integers for an answer.

Chris's sis

@teadawg1337 How can you write the numerator? What's the natural way to do it?

Stan Shunpike

@PedroTamaroff and just to be clear, the total derivative is the multivariable version for which differentiability implies continuity. And its the gradient for scalar fields and the Jacobian matrix for vector fields. Am I correct?

iwriteonbananas

@Vrouvrou nvm sry what i did is wrong

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$Mathematics$ Mathematics