Back in 30 min (need to prepare some latex cls file and make that horrible:D thing working)

@BalarkaSen @Rememberme Hey guys! Happy Diwali to the both of you! (where ever you are) ... make sure you scare the neighboring cats with enough crackers until it calls out for it's nanny :P

bbl

@r9m btw, I prepared a series problem for a magazine you would cry seeing. I myself almost cried for pleasure. Keep the date 11 Nov in mind to tell you about my problem when is published.

Remind me of it once in a while.

hey, @Huy

no physics for me tonight

@r9m What's a Diwali?

Kali pujo

What's a Kali pujo?

Bulerka is ded

rip Bulerka

you was true frand

rolls all 3 eyes

Hey, I finally sprouted an extra eye.

@Chris'ssistheartist 11th Nov! That's tomorrow :)

@BalarkaSen The day we decide to crack some crackers :P (especially because we have nothing better to do) :P

I am aware, but I was merely pointing out I don't care about it. Crackers are stupid, except the ones you eat.

@BalarkaSen you mean you don't like sudden explosions followed by light and fire everywhere?! poor soul :P

@r9m Yeap, precisely! Keep it in mind. :-)

Back in 30 min.

@Chris'ssistheartist okay! lemme know when to start shouting and start a chaos :P

@r9m :D

@r9m I just don't care for it, is all.

You guys call fireworks "crackers" over there?

Hi @JasperLoy

@JasperLoy what will you study soon

Cool

@JasperLoy Finals are in a month

Just like you @JasperLoy

I am ugly

@Chris'ssistheartist I took a little detour and worked out $m = 2$ $$1+{{\sqrt{e}}\over{2}}-{{\sqrt{\pi}\,{\it erfi}\left({{1}\over{\sqrt{2}}}\right)}\over{\sqrt{2^5}}}$$

@Jasper Subjunctive, indeed. <3

damn they star things here more than ninteeth byte

You think I didn't notice, Jasper?

@Balarka, you're weird.

June

@MickLH wow! :) How did you get that? :)

Why does the sequence a_n=\frac{n+1}{n} converge to 1?

I can't see it

@Jasper Ah, yes I've confused methods I think

@Jasper I inserted int into the definition of convergence of sequences $|a_n-1|\le \epsilon$, then I get $\frac{1}{n}$, which converges to 0, not 1

hi

I'm studying an interesting combinatorics problem today. I feel like my life has become just one combinatorics problem after another as of late ...

@SohamChowdhury physics is cool.

@PerplexedGuest Coursework?

@MickLH 'kay! Nice :)

nice!

@jukka.aalto - not coursework, but part of my research.

The problem is currently, "How many ways can $n$ unlabeled objects be placed into $k$ labeled bins such that bin 1 contains at least $a_{1}$ objects, bin 2 contains at least $a_{2}$ objects, ..., and bin k contains at least $a_{k}$ objects, such that $\sum_{1 \leq i \leq n} a_{i} \leq n$?"

That sum does not look as pretty as I want it to. xD

@MikeMiller I haven't been able to resolve the problem you gave me about whether a diffeomorphism of $S^n$ always extends to a diffeomorphism of $D^{n+1}$. Seems like it should be true, as diffeomophism is a strong condition on the map. Are there two nonhomotopic homeomorphisms $D^{n+1} \to D^{n+1}$ which are extensions of the same self-homeo of $S^n$? Seems like there shouldn't.

Oh, and in the PL category, taking cone over a triangulation gives you a triangulation so the cone method works fine, I think.

@BalarkaSen: I don't see the relevance to your first couple sentences to your last couple.

When you say "nonhomotopic", you mean in different path components of $\text{Homeo}(D^{n+1})$?

Here's a stronger statement: the space of homeomorphisms that restrict to $f$ on the boundary is contractible. So certainly any two homeomorphisms of $D^{n+1}$ that restrict to a given one are isotopic :)

@MikeMiller Yeah, they are not strictly related I should have put an "on a different note" before starting the second question. How it sprouted up : I wondered a bit about what are the self-homeos of D^n+1 which extend a self-homeo of S^n. If one can classify this, one can check if any of these maps are C^1. I thought about this before realizing that there are uncountably infinitely many of them, so that approach is hugely unreasonable, of course.

But then the follow-up question came up : can one classify them modulo homotopy?

I see.

@MikeMiller whoa. I have no idea/intuition why that should be true.

Not sure if you want me to give you the keyword or not. It's almost trivial once you know it.

Well, I won't tell you the keyword, since googling it seems to tell you how to answer the original question even if you're not looking for it, but I can explain the proof.

OK, I think I would like to know the proof.

Cone off, again. If you have a homeomorphism $f$ that restricts to the identity on the boundary, let $f_t(x)=tf(x/t)$ for $|x| \leq t$, and the identity for $|x| \geq t$. I'm squeezing the homeomorphism onto smaller and smaller shells.

mhm.

That's it.

What I've actually done, of course, is defined a null-homotopy $I \times \text{Homeo}(D^n \text{ rel } \partial) \to \text{Homeo}(D^n \text{ rel } \partial)$.

Oh. Of course.

Oh, I think my formula is wrong, but whatever.

Replace the $t$s by $(1-t)$s. Inconsequential.

Yeah. Meh, I feel silly for not seeing it.

Thanks.

It has a name. It's a very clever idea.

I'm not going to say the name because any discussion on it invariably mentions the version for diffeomorphisms.

(Of course what we just did works for PL maps.)

Oh hey I think I figured out my problem. :0

${n-\sum (a_{i}-1) -1 \choose k-1}$

That's kinda nasty lol. xD

hi @Jasper

good evening everybody

Good evening! :)

I am in a good mood, I just discovered a powerful new tool. :D

Hello! I have a question/topic to ask your viewpoint.

redd.it/3satb7 Do you always do every exercise in textbooks or do you (already) develop the ability to recognize crucial exercises?

Related post on the main: Should I do all the exercises in a textbook?

@r9m that series has such an awesome form! The only thing I can say is that I totally love it. :-)

@Chris'ssistheartist the one you posted in chat above? :)

Unfortunately I'm caught with my research in a certain corner of infinite series from which I get amazing results, one after another. I'm still there digging. :-)

@r9m Yeah :-)

@Chris'ssistheartist okay!! :)

$$\Huge{\text{I LOVE INTEGRALS, SERIES AND LIMITS!!!}}$$

:D

Just another awesome day!!! :-)

@r9m listen to this one loudly youtube.com/…

It's perfect while working on such math stuff. :-)

@Chris'ssistheartist that could be your book title .. potentially :)

@r9m lollll :-)))))))). That was good!!!

@Jasper It might be! I already have in mind a title. :D

@Jasper How are you doing?

hi @Jasper

@Jasper possibly because of the treatment? Try to rest often, and go some jogging, it might help.

@Chris'ssistheartist Nice! :)

@r9m :D

hey guys!

I've been struggling with an apparently easy problem for hours...

@Mircea Hello! How are you?

@r9m I'm good, thank you! Could you help me with a limits problem?

@Mircea what is the problem?

@r9m I wanna prove that if f(xn)->l where xn is a sequence than tends to a then lim f(x) = l as x approaches a

@r9m Sorry for the format, I suck at Latex

@Mircea you mean you are given a particular sequence $(x_n)$? (in which case we need continuity assumption on $f$) .. or do you mean for all sequence $(x_n)$?

@r9m for all

@Mircea look up sequential criteria for continuity for limit of a function!

* sorry misread .. sequential criteria for existence of limit of $f$ (not continuity assumption)

@r9m ok, I'll look it up, thank you!

Heine theorem

@Chris'ssistheartist it's for uniform continuity .. we are just doing seqn criteria for limit here :)

@r9m Not sure if the statement is properly written.

hi

Does anyone know any good introductory materials for Chevalley group?

@r9m ^^^

.

@Jasper You're back :D (I'm Hippalectryon)

@Jasper I haven't covered Ado's, but you can try the internet first, eg

My advice too pal :-)

@Jasper btw, any idea on that one ?

Yum :D

Gods aren't online for now :( oh wait, anon IS on. He's never here when i'm online usually so I didn't notice

@anon god, are thou here ? ~ starts incantation ~

?

hmm, diagonalizable bases

Damn it, the "show which rooms you are in" panel keep displaying the physics chat, although I have been trying to close it for ages (yesterday, in fact).

feeling tainted?

"are thou" :D classical english

@anon no doubt.

Tainted love

I see the méchant one has returned

omelette du fromage

@TedShifrin :(

@TedShifrin

du ou au?

hi @Karim

au

I got 87 % in my topology midterm :S

I really hate you know time stress

quelle faute, alors, M le méchant

I make stupid mistakes

My students rarely scored that high on my exams, @Karim; you shouldn't complain.

I have to get used to past tense.

yeah but you know what bothers me is that if I did the exam in my own time I would have aced it

instead of time pressure

87% is an A

Not when I was in primary school!

its my last year @skullpetrol so I want to do really good

I typically gave tests in upper-level courses where the best students scored 60-80.

Different style of teaching/examining.

Well, depends on the course. Not so much in first semester algebra, but in second semester, topology, differential topology, even differential geometry.

@AinzOoalGoal M le méchant: I only have patience for 3 minutes of that.

I mean exams should test how much you know a subject

not how fast you think

Define "know a subject."

Memorize definitions?

I got the lowest midterm score in my real analysis class but nobody passed either :(

:(

Neither is a point of pride, mr eyeglasses.

I guess knowing a subject also depends on how fast you think aswell

so yeah I am contradicting myself

i must get used to classic english

Depth of understanding often increases speed, @Karim.

@TedShifrin I have tried to help him as much as I can on algebraic topology. Let's see how he does in topology.

You've cursed him, @Balarka.

yeah

Of course, I'm waiting to see how you do on Inverse Function Theorem :D

help who @BalarkaSen ?

@TedShifrin I recall I came across a term (I think it was) "locally isomorphic" [groups] in Lie theory. But google doesn't provide any actual definition. What should I assume it means?

@Karim: mr eyeglasses

this is the last month of classes

I don't ever recall seeing that, @anon, but I would assume it means two groups having the same lie algebra.

I should like setup like some study camp at home so I don't fuck up in anything

That sounds better than what I was thinking

Can you give me context?

I don't remember any context

glares :)

@TedShifrin I was going to ask you for chapter 5 exams.

I m not gonna even do any other activity other than studying and eating this last month

@TedShifrin Our second lecture proving the inverse function theorem was today. He didn't finish because he forgot how to prove near the end of the proof

best I can do is remember it being applied when one group was a cover of another (which relates to having the same lie algebra)

LOL, great, mr eyeglasses ... That is one of my all-time favorite proofs.

Right, @anon. Exactly.

Is it hard to prove?

Well, you'll get there, if you ever get moving again, @Balarka.

It's a shame that I can't accept two answers :c I have two, and both are as good as the other

I don't write exams chapter by chapter, @Balarka. Only three exams a semester, plus a final.

I have done chapter 5, but I just haven't had anything to ask you/send you.

The proof seems really technical and boring to me. My favorite proof so far this semester in analysis was probably Stone-Weierstrass

Le méchant: Reward the answerer with lower rep.

The proof is wonderful, @morphic. At least the right proof is.

stone weierstrass proof is very long

Stone Weierstrass is quite technical.

@morphic: You can see the proof I like in the videos.

its amazing how actually Stone Weierstrass came up with his proof

Um, @Karim. Those are two different people.

oh

Stone abstracted Weierstrass's original theorem.

lol

I thought it was one guy