Mathematics - 2014-12-11 (page 2 of 5)

Tom Cruise

08:00

if you take a slice out of it, isn't the rest connected?

Balarka Sen

i am not sure what you mean

Tom Cruise

slice the torus in half

Balarka Sen

if you slice $T_1$ in half then $T_2$ inside is no longer connected.

you won't get a connected space, no.

Tom Cruise

oh

you may be right but I am surprised

Balarka Sen

anyway give some thought to it @TomCruise. if not this, continuums are the place to be looked for such spaces.

well, now you have some food for thought at least

Tom Cruise

08:04

what if you just take a nested sequence of cylinders, one from each $T_i$

its intersection would be a proper closed connected set

Balarka Sen

an open cylinder? the intersection would just give you an open interval.

Tom Cruise

no you could do closed

Balarka Sen

oh a closed cylinder. then just a closed interval :P

Tom Cruise

yeah

so it doesnt have the property

Balarka Sen

it's a cute question to think about @TomCruise. i am beginning to appreciate it.

Tom Cruise

08:07

I can give you one example if you like

it takes a little time to work out the details though

Balarka Sen

ok?

Tom Cruise

do you know the Knaster continuum?

Balarka Sen

nope

Tom Cruise

you take the cantor set

Balarka Sen

oh that one

Tom Cruise

08:09

and then connect the points with these arcs

Balarka Sen

yes, yes, it's connected.

Tom Cruise

yeah

but it too has proper closed connected sets

it has intervals

Balarka Sen

mmyeah.

Tom Cruise

but you have $2^\omega$ of these loops such that no proper subcontinuum hits any two of them

to construct our space $X$ we choose a point from each of these loops in a special way

Balarka Sen

"special way"?

Tom Cruise

08:13

it is clear that no matter how we choose the points we will get a space with no nondegenerate closed connected sets

but we have to choose them so that $X$ will be connected

you take a bijection $\varphi$ from the set of $\mathcal C$ loops to the set $\mathcal S$ of closed subsets whose complements are disconnected. Then you choose one point from each $C\cap \varphi(C)$ and call this $X$.

like I said there are some details you have to check, but this does it

Balarka Sen

eh. i don't see why this would make $X$ connected

yeah, there's some work to be done i guess

but i believe you

Tom Cruise

yeah its not obvious

anyway, the interesting thing is that the answer to the problem I mentioned is yes for this $X$

Balarka Sen

ok i forgot what the problem was :P scrolls above

Tom Cruise

every proper subcontinuum of $\beta X$ is nowhere dense

Balarka Sen

right, right.

hmm.

skullpatrol

08:19

but, is it a rational belief @BalarkaSen? ;-)

/joke

Balarka Sen

@TomCruise i can't visualize $\beta X$.

Tom Cruise

yeah that's tough to do

it is not metrizable usually

Balarka Sen

indeed. if you can give me a sketch of the proof, i am interested.

skullpatrol

me too pal :D

runs for cover

Tom Cruise

well it turns out that the Knaster continuum has this property

and $X$ is dense in it

somehow $X$ inherits the property, and then $\beta X$ gets it

Balarka Sen

08:24

lol

Tom Cruise

I have a page or two of lemmas that lead to this

the Knaster continuum is indecomposable - that is the key

Balarka Sen

might be. OK, I gotta go. do think about the solenoid stuff i mentioned above - i am pretty sure that it's a space with the properties you want. not sure how the compactification looks like though.

skullpatrol

See you later my friend

Tom Cruise

but the solenoid contains closed intervals

Sawarnik

10:01

@Venus Speaker?

Venus

10:17

@Sawarnik Yup! :D

Kelly Blunie

Hi there

If the det of a set of vectors is zero, why does not span a vector space?and why there is at least one solution from the vector space that ins`ton the set?

This is linear algebra

Venus

10:42

@KellyBlunie I'm not good at linear algebra, maybe you should wait until this chat crowd enough & you may ask your question again. :-)

Just be patient

Lembik

11:50

hi

anyone interested in probability? math.stackexchange.com/questions/1059379/… has no answer

Balarka Sen

@TomCruise it contains something homeomorphic to the closed interval you mean? i don't see why that is true.

Sawarnik

13:01

@Venus I didn't understand :D

Venus

@Sawarnik I asked Anna yet you replied my comment. So, I suppose you as Anna's Speaker :D

Gennaro Marco Devincenzis

13:13

hi guys

is there anyone who knows a bit of conformal mappings?

Mike Miller

I know a bit. Not much, so don't expect much out of me!

Sawarnik

@Venus Oh lol :D

Gennaro Marco Devincenzis

yeah, it's probably a silly question anyway, so I encourage you not to expect much of me!

:P

can we talk in private?

Venus

This is so LOL

11

A: Ways to write "50"

We can use only two famous numbers in mathematics, $\large\pi$ and $\large e$, to produce number $50$. $$\bbox[8pt,border:3px #FF69B4 solid]{\color{red}{\Large \lfloor e^\pi \rfloor + \lfloor \pi^e \rfloor + \lfloor \pi \rfloor + \lfloor e \rfloor = 50}} $$ Click the box to see Wolfram Alpha's ...

skullpatrol

Why @Sawarnik does your avatar say "404"?

Sawarnik

13:16

@skullpatrol For no reason.

Mike Miller

There's no private rooms, @GennaroMarcoDevincenzis, unless you just mean going to a separate, less populated room. (Others can still see it, though.)

Venus

I've just answered this question about 3 hours ago & before that it has lots of good answers. I'm so lucky :D

The Artist

13:40

@Venus u there?

Venus

@TheArtist Yup

Gustavo Montano

@r9m. Last episode of Naruto is GREAT!!!!! I thought there was going to be a string of fillers. I'm glad that came to quick end.

The Artist

@Venus I got an idea for a question, dono if it's possible to ask it here properly

N3buchadnezzar

@GustavoMontano You know it has ended right?

r9m

@GustavoMontano haven't seen it yet ! ;) no spoilers please ! ;)

Gustavo Montano

13:46

Hahaha. I watch anime.

@r9m. Tell that to @N3buchadnezzar.

Hahaha :D!

Get to it! You don't want to miss it!

r9m

okay :D

Gustavo Montano

Wait, you have be on facebook, right?

The Artist

@Venus What do you think about adding a question and tagging the top users at Integrals, asking them to share how they became so good at it. What resources came into help the most....wouldn't that be very helpful for readers ? :D

Gustavo Montano

I don't remember if you added be before. WHATEVER YOU DO - DON'T LOOK AT MY COVER PHOTO!

r9m

@GustavoMontano I haven't checked fb yet ;) :P

N3buchadnezzar

13:48

@GustavoMontano meeeh. Mainstream people. Hipsters watched the anime/read the manga before it was cool ;)

The Artist

@Venus But then again :/ we are not sure if the users would answer it :/ what do u think? :D

Gustavo Montano

Hehehehe.

Venus

@TheArtist I have seen a similar question

Balarka Sen

Hello @GustavoMontano

Gustavo Montano

@BalarkaSen. How are you?

Balarka Sen

13:49

So-so.

Gustavo Montano

What did you get up to today?

N3buchadnezzar

@BalarkaSen many exams?

Balarka Sen

@N3buchadnezzar Finished.

Venus

33

Q: Some users are mind bogglingly skilled at integration. How did they get there?

Looking through old problems, it is not difficult to see that some users are beyond incredible at computing integrals. It only took a couple seconds to dig up an example like this. Especially in a world where most scientists compute their integrals numerically, I find it astounding that people e...

r9m

@GustavoMontano Madara Uchiha Rises .. ! I'm on it :D

Gustavo Montano

13:50

Woooooooo!

Balarka Sen

@Gustavo I'm fiddling with solenoids.

What kind of math are you doing right now, @GustavoMontano?

N3buchadnezzar

@BalarkaSen How many?

Gustavo Montano

Well, I recently finished Differential Geometry and Topology.

Balarka Sen

@N3buchadnezzar All of 'em. Even the results are out.

Gustavo Montano

I've actually completed my undergraduate pure math courses.

I however want to go over Real/Complex Analysis and Topology.

Balarka Sen

13:51

Topology is cool stuff.

Gustavo Montano

Perhaps some abstract algebra as well.

How about you?

N3buchadnezzar

@BalarkaSen What is the cardinal number to your exams ;) I have six this semester

Balarka Sen

I'm learning algebraic topology @GustavoMontano

Gustavo Montano

How is it? Any recommendations on books for it?

Balarka Sen

@N3buchadnezzar 7.

@GustavoMontano I'm studying Munkres.

It's good enough.

The Artist

13:52

@Venus but one answer ? Yes Ron Gordan is awesome. But it would be so cool if we can get so many users to answer a community wiki question, users like : soso45 , Chris's sis, Robjohn, Felix Martin, RON GORDAN, random variable, etc etc

@Venus Thanks for the link btw :D

Gustavo Montano

Awesome!

N3buchadnezzar

@BalarkaSen Isnt Munkres Point set topology?

Balarka Sen

@N3buchadnezzar There is also a Munkres for alg top.

N3buchadnezzar

Ah, nice

Venus

@TheArtist I doubt there's a user will answer such question as stated in Ron G's answer, he himself was reluctant to answer it.

N3buchadnezzar

13:54

@Venus Just practice. I have like 3-4 books on integration ^^

Venus

@TheArtist Try to set a bounty for that question instead of asking a new one because it will be likely closed as a dup

The Artist

@Venus exactly coz no one tagged them, if the OP has tagged the users and seem like they are addressing them, she would have got more responses .....

Venus

@N3buchadnezzar So answer in the main then :D

The Artist

@Venus He was reluctant to answer it because he didn't want to admit that he's awesome when it comes to Integrals ? :p

Venus

@N3buchadnezzar If I were asked such question, my answer would be three: 1. Practice 2. Practice 3. practice ^^

The Artist

13:57

@Venus and the answer by Ron Gordan is kinda generalised.....what I'm talking about is kinda like their lifestory (only about integrals) , how they achieved this. What books they read, etc etc :)

Venus

@TheArtist Just ask @Chris'ssis to answer it

The Artist

@Venus but a post where all the stated users answer would be so perfect and beautiful

Sawarnik

Hey @r9m did yous ee the RMO paper of thsi year? :P

Venus

@TheArtist Anyway, Ron G indeed mentioned some users that he considers as Integration Gurus on Math SE

The Artist

@Venus yes I read. I want all those users to give an answer :/ and some more users

@Venus can I do like this ? Set a bounty saying : For soso45 to answer ? :p after he answers then set another bounty for another user?

Venus

14:04

@TheArtist The experts tend to likely be humble. As the highest form of intelligence is knowing when to speak and to shut up ^^

@TheArtist I don't know. Let's ask our beloved moderator, @robjohn

@TheArtist If this is permitted, you must set 500 bounty to get a good response :D

Sawarnik

@Venus Are you on FB?

The Artist

@Venus I have 1k reputation , so I will only be able to get two users to answer

Venus

@Sawarnik FB?

Sawarnik

FaceBook.

Venus

@Sawarnik Not online right now

Why do you ask?

Sawarnik

14:09

Do you ave an account?

The Artist

@Sawarnik I do :p

Sawarnik

@TheArtist no thanks :p

Venus

Ave?

Balarka Sen

@Sawarnik Don't you have RMO coming up?

Sawarnik

@BalarkaSen Done.

Last Sunday.

:D

Balarka Sen

14:11

Ah. How did you do?

Sawarnik

3 solved.

Balarka Sen

Out of?

Sawarnik

Could have done 4, but didn't pay attention :( :((

Out of 6.

The Artist

@Venus we can start something like "bucket challenge" as "bounty challenge" , the user who gains the bounty must give it back by placing a bounty :p

Balarka Sen

Not bad at all, @Sawarnik. Don't fret about it.

Most barely do 2.

Venus

14:11

@TheArtist Instead you spend lots of rep to get answer for your question, why don't you email/ chat them one by one? Maybe they will answer it if you ask them personally

Sawarnik

Yeah, sure. Though the paper was easy this year, so cutoff is high and i won't qualify :O

Balarka Sen

The problems were all geometry?

Sawarnik

@BalarkaSen No it was peasy this year.

@BalarkaSen lol, no way!

Venus

@TheArtist That's not how the system here works

The Artist

@Venus good idea but how do I email them? Not like their email addresses are shown on the profile

Sawarnik

14:13

@BalarkaSen 2 geometry (both done easily), 2 number theory, 2 algebra.

Venus

Hey!? Since when I begin an expert on this site :D

Sawarnik

No combinatrnics this time :O :O :D :D

Balarka Sen

What were the number theory ones, @Sawarnik?

The Artist

@Venus but that's a one time exciting thing :D

Sawarnik

Both were really easy.

Balarka Sen

14:14

@Sawarnik combinatorics

Sawarnik

I solved NT :D

@BalarkaSen Yes, I know.

Venus

@TheArtist You can chat them here for users like Chris'ssis or robjohn. Ron G & sos440 can be reached by using simple Google search

r9m

@Sawarnik no .. do you have them ?

The Artist

@Venus okay :D thanks

Venus

^^

Sawarnik

14:18

@r9m not now :d

r9m

@Sawarnik you didn't appear for the test ? :o

Balarka Sen

you can't possibly forget all the questions @Sawarnik!

Sawarnik

@r9m no i did.

:O

Ok, the questions are:

@bala Prove there is no natural n<2310 such that n(2310-n) is a multiple of 2310. Such easy.

Balarka Sen

basic modular arithmetic.

Sawarnik

Even easier.

Balarka Sen

14:22

you just need to prove that n^2 is not a multiple of 2310 for any n < 2310

Sawarnik

@r9m The circumcircle of AOB intersects BC at X if O is the circumcenter. Prove that OX is perpendicular to AB. This was the easiest :D

@BalarkaSen Yup, exactly.

Balarka Sen

and note that 2310 is primorial 11.

Sawarnik

Yeah.

r9m

I don't understand .. is it rmo or primary school selection exam ?! -_-

Sawarnik

You did it in a whisper :O

Balarka Sen

14:23

it's basic.

Sawarnik

@r9m lol

RMO, actually.

It was so easy :O

Balarka Sen

never knew RMO was so easy

what was the other NT question?

r9m

@BalarkaSen I appeared in 2009 .. that year the paper was easy too (both rmo and inmo)

Sawarnik

How many did you solve?

@BalarkaSen Find the all three digit numbers that S(S(n))=2 if S(n) is the number of digits.

Balarka Sen

i am not going to take MOs.

Sawarnik

14:25

Takes time, but nothing special.

@BalarkaSen We know.

Balarka Sen

@Sawarnik Ah. That is slightly better.

r9m

@Sawarnik rmo ? all .. ;) inmo (didn't appear ... final school exams)

Sawarnik

@r9m Oh gawd.

Balarka Sen

use the explicit formula for number of digits, use some heuristics to bound up.

S(n) is the floor of log_10(n)

Sawarnik

@BalarkaSen simply divide into cases..

3 digit numbers are no big deal :D

Balarka Sen

14:27

so S(S(n)) is bounded above by log_10log_10(n)

r9m

@Sawarnik I remember a guy left the hall 15 mins before me =P ..

Sawarnik

@r9m Couldn't you have seriously requested the school to shift the dates?

Balarka Sen

it's even simpler, actually.

S(n) is a 2-digit number

The Artist

@Venus so what is your story :) You are good at Integrals too

Sawarnik

@BalarkaSen true.

r9m

14:29

@Sawarnik doesn't happen in my school (there were 4 others from my section who cleared the rmo .. two of them were prepared enough to ignore the school exams during the inmos .. ) but not me (I never studied the arts subjects)

Venus

@TheArtist Nah, I ain't good at it. Just learn from many gurus around here

Sawarnik

@r9m Why did you give it only once?

Other years?

Balarka Sen

well you have a whole load of n-s, @Sawarnik

r9m

@Sawarnik I was on 11th grade (2009) :-)

Balarka Sen

it's tedious, neither hard nor tricky.

one has to look for such numbers via case-by-case analysis

r9m

14:32

Naruto time BBL :D

Balarka Sen

@Sawarnik S(n) = 10 has solution n \in {10^9, ..., 10^10-1}. S(n) = 11 has n \in {10^10, ..., 10^11-1}, etc.

So your solution set is n \in {10^9, ..., 10^98-1} i guess.

Gustavo Montano

WOOOHOOO! Go for it :D

Balarka Sen

WAT @GustavoMontano

Gustavo Montano

Haha, talking to r9m. But I do not want to tag him as that will interfere with his current activity.

Balarka Sen

SHEESH. You guys are so serious with Naruto.

3

Gustavo Montano

14:36

I have been watching it for a very very very very VERY long time. It has become a part of me.

The Artist

@Venus are u studying in undergrad?

Khallil

Are you watching 391, @r9m?

r9m

14:53

@Khallil ya ! just finished watching :D

@GustavoMontano ;) :D !!

Gustavo Montano

What did you think?

r9m

@GustavoMontano there is no war without burning flesh and boiling blood !!! (evil grin) AWESOME

Gustavo Montano

So good!

Ok, with that - I am off to bed. Far toooo tired! Goodnight! Can not wait for next weeks episode.

r9m

@GustavoMontano cool ! good night ! :)

Venus

@TheArtist Yes

You?

Integrator

14:58

@Venus I've suggested your nomination!

Venus

I am expecting a good answer for @Chris'ssis's question but what I got is so disappointing

-1

A: Evaluating $\int_{0}^{\pi/4} \log(\sin(x)) \log(\cos(x)) \log(\cos(2x)) \ dx$

Mathematica cannot find an expression of this integral in terms of elementary functions. However, it can be integrated numerically, like this NIntegrate[Log[Sin[x]] Log[Cos[x]] Log[Cos[2 x]], {x, 0, Pi/4}] to yield the result -0.05874864

I downvote it

Transcript for

$Mathematics$ Mathematics