Mathematics - 2016-01-17 (page 1 of 3)

Julian Rachman

00:07

@BalarkaSen Will do.

Idle001

00:21

how can we tell if a number divisible by 11 isnt palindrome

fo example 121 is but 11*12 isnt

we have also odd digit palindromes, not all devisible by 11 like 848

and like einstein ever said, "nothing is random" some mysterious secret is hiding behind that i should demystify*

Tosh

Hello

When we say "f dependence of g", are we talking about f(g), or g(f)?

user303542

00:56

@Tosh don't we normally say "f depends ON g"?

means f(g)

Mary Star

01:42

I am looking at the following exercise:

If $S$ is a smooth surface, define the notion of a smooth function $S \rightarrow \mathbb{R}$.
Show that, if $S$ is a smooth surface, each component of the inclusion map $S \rightarrow \mathbb{R}^3$ is a smooth function $S \rightarrow \mathbb{R}$.

I have done the following:

For any point $p\in S$, there exists an open set $U\subseteq \mathbb{R}^2$, and open set $W\subseteq \mathbb{R}^3$, and a smooth function $\sigma:U\to \mathbb{R}^3$, such that $\sigma$ is a homeomorphism from $U$ onto $S\cap W$.

idonutunderstand

01:55

Does the word commutative in category theory have a different meaning than commutative in algebra of magmas?

Mary Star

@robjohn could you take a look at my question above?

Joe Stavitsky

02:36

If i integrate over a function above x-axis am I guaranteed a positive result, even if my limits are negative?

Stan Shunpike

03:49

Hello

dREaM

04:19

@Idle001 what project euler problem is it?

I remember seeing one like that.

Balarka Sen

05:49

Hi @Fargle.

Fargle

Hey @Balarka. How goes it?

Balarka Sen

About right. How's it with you? You haven't been here for a long time.

Fargle

I'm alive, anyway, haha. Been busy with family stuff, school stuff, and Magic: The Gathering.

Balarka Sen

Ah. How're studies? Also, what is Magic: The Gathering?

Fargle

Studies are alright. School starts again in a few days, so I'm happy about that.

M:tG is a really fun trading card game.

Balarka Sen

06:00

Oh. Meh. :)

@Fargle Cool.

Fargle

Haha, I enjoy it. I've always had an affinity for card and board games, both for the mechanics involved and for the social aspect.

Balarka Sen

Nice. I like board games, but haven't ever really tried out card games.

Fargle

I find them more compact, although the lack of a board almost seems to allow for greater complexity as well.

Balarka Sen

Fair enough.

Ugh, I seem to have caught an annoying sort of cold.

Fargle

Oh no! My condolences to your sinuses.

Balarka Sen

06:14

:P

Mike Miller

@Fargle It's more often true than not.

Fargle

@Mike, what is?

Mike Miller

Balarka being sick.

Fargle

Ah. That's a tenuous ground state to have.

Balarka Sen

It's a feature for version 2.0's.

Fargle

06:20

Guess I'll wait for version 2.1, then.

Balarka Sen

Do you really want a Balarka version 2.1 on this chat? Another one?

I'd think one is enough.

Fargle

I dunno. You're much more tolerable than you give yourself credit for.

Balarka Sen

I'm not sure whether to take that as a compliment. :P

Fargle

I meant it well, haha.

Anyway, I'm finally going to take an actual course on complex analysis. I am extremely excited.

Balarka Sen

Sounds good. I don't know much about complex analysis.

Fargle

06:28

I don't either! I mean, I know that $i^2 = -1$, but past that, all I have is trivia.

Balarka Sen

:)

Oh, strange coincidence: math.stackexchange.com/questions/1614973/…

Mike Miller

heh

Balarka Sen

wonder what was the $\phi$ he found.

Mike Miller

06:48

Probably not a very good one.

Balarka Sen

Apparently.

Stan Shunpike

Sup yall?

Balarka Sen

Inf, @Stan.

4

Stan Shunpike

What does that mean? Lol

Fargle

That joke gets a perfect 5/7, @Balarka

Balarka Sen

06:53

en.wikipedia.org/wiki/Infimum_and_supremum.

Stan Shunpike

hahahahahhahahaha

Caught me off guard

I even thought infimum but i never thought it would be a punch line

Balarka Sen

There's a harsh truth behind this joke.

Fargle

The chrysanthemum is defined to be the ugliest prettier bound of any set of flowers.

Balarka Sen

That doesn't even make sense.

Fargle

I blame 1 AM.

In light of that, goodnight, chat.

Balarka Sen

07:04

@Fargle Making weird rhymes in everything you say is the 1st sign of madness.

Well, sleepiness, I mean.

Julian Rachman

07:41

@Balarka mathoverflow.net/q/228605/82691

Look at it periodically and tell me what your think.

usukidoll

08:55

hello?

robjohn

09:06

@MaryStar did you define the notion of a smooth function $S\to\mathbb{R}$?

Balarka Sen

@JulianRachman The current answer doesn't appeal much to me. You should improve your question, e.g., define "informal" correctly.

The correct word, as I said before, is non-formal, not informal.

i.e., not formal mathematics like logic and set theory.

@JulianRachman Just to let you know, I wasn't really quite so interested in looking for an answer to that question. I just conversationally asked whether you were aware of one. So it's unlikely I'd check the MO thread frequently. However if you are interested in an answer, that's fine by me.

Feel free to let me know if there are any other answers.

@iwriteonbananas There is a geometric interpretation for the snake map, however. I don't know how explicit that is in the de Rham context.

Huy

09:55

@BalarkaSen: what's the fastest argument you know to show that $SL_n(\mathbb{R})$ and $SL_n(\mathbb{C})$ are connected?

iwriteonbananas

@BalarkaSen True, but of course one cannot say in general whether it's surjective/injective/..

Mary Star

How do we do that? Maybe as follows?

Let $f:S\rightarrow \mathbb{R}$ a smooth function, i.e., each of its components have continuous partial derivatives of all orders.

Or what does it mean to "define the notion" ? @robjohn

Balarka Sen

10:15

Sorry, was away.

@iwriteonbananas True.

@Huy Uh.

Vrouvrou

i have that f: E\rightarrow \mathbb{R} a application, if we have that for all \lambda\in \mathbb{R} the two sets $A=\{x\in E, f(x)<\lambda\}$ and $B=\{x\in E, f(x)>\lambda\}$ are open , how to prove that f is continuous?

have an idea please

Balarka Sen

If $A$ is some square matrix with det = 1, it's related to the identity matrix by a finite number of elementary transformations, yeah? So all you need to do is to show that elementary matrices belong to the same component as identity.

I think it's even true that SL_2 is path connected. Given an elementary matrix, can you join it through a path with I?

Huy

over $R$, they're the same anyways

or am I misremembering?

Balarka Sen

what are the same?

Huy

path-connected and connected

Balarka Sen

10:19

What do you mean by they are the same? I don't understand you.

Huy

ah

Vrouvrou

is that have a relation with my question ?

Balarka Sen

Path connectedness is a stronger property.

Huy

yeah, I think in $R^n$ they might be the same when the set is open

Balarka Sen

yes, it is

well, "same" is a bad choice of word.

but connected open subsets of R^n are all path connected, yes.

But I don't know what this has to do with SL_2

Huy

10:23

yes, I was remembering the condition for equivalence incorrectly

Balarka Sen

By the way, I do think the elementary matrices can be joined through path with I. Any elem. sym. matrix is a matrix with bunch of 1's along diagonals and a single nonzero entry somewhere, right? Call that entry $m$.

Huy

yes, they can

Balarka Sen

Consider the sequence of matrices with $m$ replaced by $mt$, $t$ running through $0$ to $1$.

Huy

it works for any $SL_n$ even

Balarka Sen

Right.

Same logic shows why GL_n has 2 path components.

namely, the subspace consisting of matrices with + det, and the subspace with - det.

Vrouvrou

10:30

i have that f: E\rightarrow \mathbb{R} a application, if we have that for all \lambda\in \mathbb{R} the two sets $A=\{x\in E, f(x)<\lambda\}$ and $B=\{x\in E, f(x)>\lambda\}$ are open , how to prove that f is continuous?
Can i say that $A=f^{-1}(]-\infty,\lambda[)$ and $B=f^{-1}(]\lambda,+\infty[)$ then the preimage of an open sets is open so f is continuous

Huy

@BalarkaSen: wouldn't it be easier to - once we know SL_n is connected - argue that you can get all of GL_n by "scaling" +- SL_n (two connected components) and since the determinant is continuous, those can't be connected?

@Vrouvrou: You have to show that the preimage of all open sets is open.

Idle001

10:57

moaning

PVAL

11:26

2

Q: Components of the space of immersions 2-manifold into $\mathbb R^3$

Let $M$ be a $2$-sphere with $g$ handles. Consider the space of maps $M\to \mathbb R^3$, which are immersions [i.e. smooth maps with nondegenerate differential in each point $x\in M$], with compact-open topology. It is well-known that for $g=0$ this space is path-connected; and how about the same...

Rudy the Reindeer

11:54

Screenshot of tangent limit thread:

Though it's not the most broken layout I've ever got on MSE.

Daniel Fischer

@RudytheReindeer The good old "double rendering" bug. Happens from time to time. Reloading the page usually helps. May or may not yet be reported on meta.

Rudy the Reindeer

Once it somehow managed to write text over text so that it was completely unreadable. This is just a little off to the side.

Reloading, huh. It did not occur to me : )

I have something else I want to share here.

Daniel Fischer

@RudytheReindeer Reloading is for browsers what rebooting was for Windows.

Rudy the Reindeer

Are you guys up for a picture of my Kleenex box?

Daniel Fischer

I wasn't.

Rudy the Reindeer

11:59

Sorry : )

As for the Kleenex box: I haven't managed to decide whether I am disturbed or amused by this text.

Daniel Fischer

What the … is that? A Mickey Mouse advertisement on a kleenex box?

Rudy the Reindeer

I mean, who would write this about Micky Mouse on a box of Kleenex?

Daniel Fischer

Beats me.

(below the belt)

Rudy the Reindeer

@DanielFischer Well, no, not an ad. It's... decorative, I guess. But thank you for being disturbed by it too : D

Owatch

Hello. All.

Rudy the Reindeer

12:03

See you all later!

Daniel Fischer

Hello. One.

Owatch

Hello Diamond.

Daniel Fischer

Hello Seal.

Owatch

I am a ghost.

But ghosts can be anything, so a Seal as well.

Balarka Sen

12:16

@Huy that'd be the argument I had in mind.

Urgh, I am sleepy. And sneezy.

Can't decide whether I should sleep before I sneeze or whether I should sneeze before I sleep.

Huy

12:58

@BalarkaSen: does the "Casimir element" come up in algebra? If so, what is its meaning and purpose there?

Balarka Sen

I don't even know what the Casimir element is.

Huy

I don't either

I was hoping you could help

Balarka Sen

If it's about Lie theory, unlikely I can ever help you.

Huy

ever?

@TobiasKildetoft: Can you ping me if you have some time at some point? It's about some Lie algebra stuff.

Balarka Sen

@Huy: I try not to set my goals too high. $\infty$ is a reasonable amount of time after which I can learn and understand Lie theory and help you if you want.

Huy

13:02

very good

I'm looking forward to it

Balarka Sen

your welcome in advance

Huy

*you're

Balarka Sen

your aware of the fact that im lazy, aren't you?

:P

Huy

*you're, I'm

*-___-

man this is some next level feeling stupid

when you read a proof and don't understand what exactly it has to do with the statement

Balarka Sen

something weird is happening to my toes

Huy

13:07

call an ambulance

Balarka Sen

right.

it seems like an allergy localized at my toes

Huy

maybe they are allergic to your feet

Balarka Sen

dude, you just made me forget a sheaf joke i had about the sheaf of allergies on the spectrum of toes

but maybe probably for the best

it's going away. yippie.

Superstar Monica

13:21

@robjohn do you wanna see something awesome?

Huy

@SuperstarMonica: don't ask to show, just show

Superstar Monica

@Huy in my bad days I don't wanna see anything. :D Better to ask first. :-)

Robjohn is probably sleeping now.

Huy

is Ronjohn his twin brother?

Superstar Monica

@Huy Who is Ronjohn? :-)

Huy

you know ;-)

Superstar Monica

13:28

@Huy No, I don't ;)

Let see what we have new about my bounty!!!

Andrew Thompson

@BalarkaSen You might know something about this: is it easy to compute the group cohomology of $\mathbb{Z}/2$ with integer coefficients without mention of $\mathbb{R}P^{\infty}$?

I don't know much about group cohomology other than the definition, but I suspect one should be able to read it of the canonical free $\mathbb{Z}[G]$-resolution of the integers.

Balarka Sen

@AndrewThompson I don't know many ways to compute group cohomology other than computing singular cohomology of $K(G, 1)$'s :)

Andrew Thompson

Ah, alright.

Superstar Monica

5

Q: Convergence of $\sin{\pi\sqrt{n}}$

Revising for an exam: Let $a_n = \sin{(\pi\sqrt{n})}.$ Show that: (i) $a_{n+1} - a_{n} \rightarrow 0$ (ii) The sequence $(a_n)$ is bounded. (iii) $(a_n)$ does not converge. My attempt: (i) ??? (ii) min($\sin(x)$) = -1, max($\sin{x}$) = 1, so $-1 \leq a_n \leq 1, \forall n ...

calculus real-analysis sequences-and-series trigonometry radicals

Balarka Sen

Yes, certainly there are abstract ways using the Ext definition.

Superstar Monica

13:29

Nothing new!

Andrew Thompson

Yup, which is what I want to do (as a fun example in undergradthesis.)

user303542

What could possibly be the twin of the mean square. @Huy?

Huy

where did you read that?

user303542

You said it.

Ronjohn

:-)

When meanness is squared are there any extraneous roots?

Superstar Monica

@user303542 Very relaxed today! Besides that my research is amazing, more than happy to say! :-)

user303542

13:34

Cool :-)

Superstar Monica

;)

@user303542 Do you consider yourself a happy person?

Really, who from here consider happy?

I'm extremely happy in general! And I hope that would NOT affect anyone's mood, just because the mood might be different.

Smile!!! :D

@Huy Are you happy in general? :P

Huy

very

user303542

I wouldn't consider myself an overly bubbly happy person.

Superstar Monica

@Huy Awesome!

Huy

I agree

Superstar Monica

13:46

To explain: it's not anything related to my personality that makes me extremely happy, maybe you misunderstood me ...

My math makes me extremely happy, my every day results!

Amen.

:-)

OK, back to some more reserch.

user303542

Have fun :-)

Superstar Monica

:D

user303542

*research

Balarka Sen

@Huy why so serious, eh?

Huy

what's serious about that

the weather is ridiculous today

one minute it's like the worst snow storm and the next minute the sky is blue

user303542

13:51

Who is ronjohn? @Huy

Balarka Sen

@Huy it was a rhetorical question.

also, referencing joker.

Huy

@BalarkaSen: you're not very rhetorical

I know joker

Balarka Sen

not much interesting questions on the main today

Huy

@BalarkaSen: do you listen to Taylor Swift?

user303542

Was it rhetorical

Balarka Sen

13:54

@Huy who's that?

Huy

do you want to know how I got these scars?

Balarka Sen

I don't listen to random gibberish from random people.

user303542

Country chic

Balarka Sen

@Huy I already know that.

Huy

do you want to clean my flat for me?

Balarka Sen

13:55

no thanks.

Huy

ragequit induced

user303542

Listening to country music will scar you for life. :P

Balarka Sen

@Huy I'm glad you're not the Joker, Huy.

You're infuriating.

:P

Huy

if only you knew

user303542

Knew what?

Huy

13:57

that my father was a drinker and a fiend

user303542

:O

Balarka Sen

apparently he's suffering from grandiose delusions

user303542

srsly?

Huy

@BalarkaSen: if I flag that, you'll surely get banned

user303542

-_-

Balarka Sen

13:59

for a year, @Huy?

Huy

more than that

Balarka Sen

I'll take my chances.

Huy

you've been warned

see you in your dreams

user303542

9000 years

Balarka Sen

aha, knew @user303542 sounded like skull from the very beginning

Huy

14:00

;)

I created a different account too

one of my first answers got more upvotes than any of my answers on this account

that made me sad

Balarka Sen

lol!

Huy

and yet it wasn't accepted

ABcDexter

hello everyone.

Huy

@BalarkaSen: you know about solvable Lie algebras?

Balarka Sen

I don't know any Lie algebras, @Huy.

Huy

14:05

-_________________________________________-

Balarka Sen

You're on your own. Sorry.

Huy

-_______________________________________-

becko

14:16

Can I use Lagrange multipliers with redundant constrains?

Or do I have to find an independent set of constrains first and use those with the Lagrange multipliers?

Huy

why would you want to use Lagrange multipliers with redundant constraints

Ilya_Gazman

Hey guys

Is it ok if I refer to my question here? It got pure attention.

Huy

pure people $\neq$ poor people

Ilya_Gazman

@huy does it mean you are willing to help me?

Huy

I have no idea why you'd think that

Ilya_Gazman

14:29

@Huy is it: "No, I have no idea why you'd think that" or "Yes, I have no idea why you'd think that I'm not"

Huy

Yes, at least one of those two is true.

Balarka Sen

troll :P

@Huy Also, the correct reply should have been "Yes".

Ilya_Gazman

@Huy do I get to choose which one?

Balarka Sen

Truths are universal. You don't get to choose whether a statement is true or false.

It is either true or false depending on the ambient axiomatic logical system.

Tobias Kildetoft

@Huy I am on my phone, so I won't be typing complicated stuff. But try me.

Ilya_Gazman

14:32

@BalarkaSen it's only true until the universe is changed by it self, in such case you are missing the attitude of time.

0

Q: Find the minimum function

During my work I came to some problem, please take a look on the next table. a b c -------------- 818 610 5 819 615 7 820 622 9 821 631 11 822 642 13 823 655 15 824 670 17 825 687 19 826 706 21 827 727 23 ...

number-theory functions

@TobiasKildetoft rescue me please

Balarka Sen

Sorry, but that doesn't make any sense. But I'm stepping away from being a troll. :P

Ilya_Gazman

Tnx, it was nice trolling with you.

Huy

@TobiasKildetoft: I literally just started cleaning my flat. I'll write a question once I'm done and have looked through my stuff again.

Tobias Kildetoft

Ok

Balarka Sen

You're switching implications. I was the troll, you were the trolled.

Julian Rachman

14:54

@Balarka Gröbner bases in Commutative Algebra

Balarka Sen

@JulianRachman Cool. What's the result there?

That is to say, how does the lemma apply?

Julian Rachman

Here is the example I was provided: arxiv.org/abs/0908.1777

Owatch

What would you say the solution to: $9\frac{d^{2}y}{d^{2}x} - 12\frac{dy}{dx} + 4y = 0$ is?

I have: $y = c_{1}e^{\frac{2}{3}x} + c_{2}xe^{\frac{2}{3}x}$

Transcript for

$Mathematics$ Mathematics