Mathematics - 2014-12-04 (page 5 of 9)

@MikeMiller I am not sure why so. Intuitively, you can "chuck out" the circles inside to pull it to outside and you'll get a bunch of circles wedged at a point.

Venus

@Chris'ssis OK, I will start to browse online catalogue then

@Hippalectryon Sorry, my bad. You seems care with her :P

Mike Miller

3:08 PM

That doesn't sound very continuous.

Hippalectryon

@Venus She's in my gold users list, with @Chris'ssis. They produce such nice Q&A :D

Balarka Sen

Might be @Mike. Hrmph. I forgot continuity in this mess.

Chris's sis

@Venus :D

Mike Miller

@Balarka Try to prove what I said about the fundamental groups involved.

Chris's sis

@Hippalectryon lol, gold users? Platinum users don't you have? :-)))

Hippalectryon

3:10 PM

@Chris'ssis Unfortunately not

Chris's sis

@Hippalectryon OK :-)

Balarka Sen

I was scared away by your $H_2$, @Mike. But if you say so...

Venus

@Hippalectryon You like her, like emo too. It's kind of a sign ^^

Mike Miller

@Balarka The first thing I said is completely unrelated to the letter $H$.

Balarka Sen

Ana might not be Anna but @Hipp is still Hipp, not Hip.

Venus

3:11 PM

@Hippalectryon How did you make a feature like that?

Hippalectryon

@Venus >.> What kind of reasoning is that (ノಠ ∩ಠ)ノ彡( o°o)

@Venus It's a chrome extension

Venus

@Hippalectryon Just kidding :D

@Hippalectryon Where I can get it?

Link please

Hippalectryon

On the deadly flower's profile

Venus

@BalarkaSen But she want us to call her Anna, not Ana

Hippalectryon

Warm Fuzzies

26.6k 3 58 108

Balarka Sen

3:14 PM

@MikeMiller it's evident that it's homotopy equivalent to $\Bbb R^2$ with $(0, 1/n)$s chucked out, so I guess I'd start from that.

Wait

Hippalectryon

@Venus chrome.google.com/webstore/detail/stack-user-filter/…

Balarka Sen

Path-ological spaces are confusing =(

Mike Miller

Is that evident?

Balarka Sen

No, @Mike.

Gustavo Montano

Best book for abstract algebra?

Balarka Sen

3:14 PM

That's why I said "wait".

@GustavoMontano Artin

But Dummit-Foote is also good @GustavoMontano

Mike Miller

OK. Don't try to give it other forms, just use the standard definition...

Venus

@Hippalectryon I have no chrome, haha

Gustavo Montano

I want to buy a good book on abstract algebra to read over the holidays.

Hippalectryon

:/

Gustavo Montano

Will have a look at these, thanks @BalarkaSen.

Balarka Sen

3:16 PM

It's not @Mike

Hippalectryon

@Venus What do you use ?

Balarka Sen

$\Bbb R^2 - \bigcup_{n} (0, 1/n)$ is deformation retractable to consecutive wedge of countably many circles, homotopy equiv to $\Bbb C - \Bbb Q$

Venus

Mozilla

Hippalectryon

Ah

Gustavo Montano

Hahaha, @WillHunting's starred comment made me laugh!

Balarka Sen

3:18 PM

@GustavoMontano Look at what?

The books.

Which books?

Artin & Dummit-Foote

I've studied those @GustavoMontano. Not sure what you mean.

Oh darn

I misread "Will have a look" as "Will you have a look"

Gustavo Montano

Hahaha :)

Balarka Sen

3:21 PM

This happened to me twice a day, probably I should shut up and think about the Hawaiian earring.

UserX

Did they change mathjax?

Mike Miller

@Balarka The countable wedge of circles is not homotopy equivalent to $\Bbb R^2\setminus $\Bbb Q$.....

Balarka Sen

I mean consecutive wedge.

Mike Miller

And I've my doubts it's homotopy equivalent to $\Bbb R^2 \setminus \{1/n\}$ either.

Balarka Sen

a bunch of circles arranged sidewise tangentially.

Mike Miller

3:23 PM

There's no such thing as a consecutive wedge.

Hippalectryon

@UserX ?

Mike Miller

Oh, I see. That's still wrong.

UserX

@Hippalectryon it renders differently now...

Balarka Sen

oh i am thinking about $\Bbb C - \Bbb N$

grr pathological spaces.

$\Bbb Q$ is dense in the x-axis.

Hippalectryon

@UserX I don't see any difference

UserX

3:26 PM

It doesn't become grey while rendering

Mike Miller

Yes, @BalarkaSen, and that $\Bbb C \setminus \Bbb Q$ has uncountable fundamental group is easy to see. Cardinality again...

Hippalectryon

Oh that

Yeah then @UserX

Daniel Fischer

13

Q: Mathjax 2.5 alpha

We have deployed the latest Mathjax 2.5 alpha on Math.SE. As with any beta release please post an answer to this question if you find any issues. We will be monitoring this thread closely along with the authors of Mathjax to ensure this release goes smoothly. This particular release has a new f...

support featured mathjax

Gustavo Montano

What's the difference between alpha and beta versions?

Mike Miller

How do I enable fast rendering?

Gustavo Montano

3:27 PM

Wait, is there such thing as a beta version? I am assuming there is.

Hippalectryon

@MikeMiller By reading the post

UserX

@MikeMiller it's the default I guess

You can turn it off if you want

Hippalectryon

@UserX no

Chris's sis

I have a simple question for you ... did you ever see this integral in closed form $$\int_0^{\pi/2} \arcsin(\tan(x)) \ dx$$?

Venus

@UserX It means you should buy a new laptop. It's holiday month, sales are everywhere :D

Chris's sis

3:28 PM

@Venus @Hippalectryon ^^^

UserX

@Venus I'm on my phone

Mike Miller

That didn't work when I tried it at home... bizarre. Maybe i'll clean my cache. Pleasant comment regardless.

UserX

98% of my answers and browsing are done with my phone

Hippalectryon

@Chris'ssis I don't have a good memory for that :/ BUT don't give me the closed form. It doesn't seem that awful.

Venus

@Chris'ssis The answer is NEVER :D

Balarka Sen

3:29 PM

I can't do it @Mike it's too complicated for me

I just can't think about these spaces.

Venus

Ask your guru @Chris'ssis :-)

Mike Miller

OK, let me know when you change your mind.

Chris's sis

@Venus I did it on my own.

Balarka Sen

i thought you'd reveal the solution @Mike

Mike Miller

No.

Balarka Sen

3:30 PM

heaves great sigh

Mike Miller

Yikes, fast preview is ugly. I guess that's why it's a preview.

Chris's sis

@Venus Don't understand me wrong, but I'll always appreciate someone that invested time and effort in me. He is and it remains a guru to me, but this doesn't mean I do not appreciate the others. I don't like when others want to think for me and speak about me as if they knew what my options are.

@Venus I love your answer, M.N.C.E.'s answers, you're on top, that's clear.

Mary Star

Hello!! What does it mean <<prove the correctness of the algorithm>> ??

Venus

@Chris'ssis I never get you wrong, seriously. I'm on your question anyway. That was only a joke

Chris's sis

@Venus OK :D

Venus

3:35 PM

@Chris'ssis I never get pissed off by anyone on internet. I'm always cool ^^

Chris's sis

@Venus That's great!

@Hippalectryon Did you manage to finish those series? Do they match numerically with the integral? I'll check the details when I return. I need to buy some food for my pets.

Back in 20-30 min.

Hippalectryon

@Chris'ssis I didn't work on them any further. I don't have mathematics, and I usually make stupid mistakes, so I thought it would be better if you could proofread it first.

Chris's sis

@Hippalectryon OK. I'll finish the job there (soon).

Hippalectryon

@Chris'ssis Make sure I didn't make a mistake in what I sent you though

Chris's sis

@Hippalectryon Sure. That's clear.

Hippalectryon

3:39 PM

It would be a shame to compute it, then realize it was wrong

@Chris'ssis sharelatex.com/project/547faac0566ab8e67923af4e

Balarka Sen

@MikeMiller It is clear that $\pi_1(\mathfrak{H})$ has a copy of $\prod \Bbb Z$ inside, but I don't see any other elements though.

Mike Miller

"It is clear" is not a proof.

You use those words too much.

Anyway, i've gotta teach. See ya.

Balarka Sen

OK, I am gonna use "if you don't believe me, I'll punch you" from now on.

Mike Miller

Anyway, if you can prove that group embeds, you're done... since $\prod_{\Bbb N} \Bbb Z$ is uncountable

Daniel Fischer

3:56 PM

@MaryStar It means "prove that the algorithm does what it is meant to do". Whether that is sorting an array, factoring a number, whatever.

Venus

@Chris'ssis $$\int_0^{\pi/2} \arcsin(\tan x) \ dx=2{\large\chi}_2\left(\sqrt{2}-1\right)-\frac{\ln\left(3-2 \sqrt{2}\right)}{2}\sinh^{-1}(1)-\frac{i\pi}{2 }\sinh^{-1}(1)$$

Hippalectryon

@Venus Nooooo :c

Venus

@Hippalectryon Hohoho...

Hippalectryon

31 mins ago, by Hippalectryon

@Chris'ssis I don't have a good memory for that :/ BUT don't give me the closed form. It doesn't seem that awful.

I wanted to try it before :C

Venus

It came from Santa

Hippalectryon

4:00 PM

Santa is mean

Venus

@Hippalectryon Didn't you know Santa? I mean Santa Claus

Hippalectryon

I know him :c

He never gives me what I want

Venus

@Hippalectryon Coz you're not a good boy *kidding

Hippalectryon

:C

Venus

I always get it every X-mas

Chris's sis

4:20 PM

OK OK OK, that one was far too easy

clap, clap, clap...

Hippalectryon

@Chris'ssis Which one ? The arcsin(tan) or arctan^3(sin) ?

Chris's sis

Let's see this one ...

@Hippalectryon $\arcsin(\tan(x))$

$$\int_0^{\pi/2} \arcsin^2(\tan x) \ dx$$

@Venus Good job.

Venus

@Chris'ssis I'm honored it came from you, but that was not easy for me

Chris's sis

@Venus How would you rate it as difficulty (on a sclae from 1 to 10)?

Venus

@Chris'ssis Do you always follow fashion trend?

I think it's 7

Hippalectryon

4:30 PM

Girl's stuff >.>

Chris's sis

@Venus What do you mean by "fashion trend"?

@Hippalectryon :D

Venus

@Chris'ssis Fashion like clothes, scarf, hat, etc

Chris's sis

@Venus Yeah, I know, but what is the meaning in this context? Do you refer to integrals or to clothes, scarfs and hats (and so on)?

@Venus I don't follow the trends posed by the others, never. I define for me the fashion trends as I like.

Venus

it's just a personal question. Please don't always talk about math

Chris's sis

@Venus hehehe, I was thinking of math. :D

Venus

4:34 PM

@Chris'ssis You're too serious :D

Chris's sis

@Venus You got me here! :-)

Venus

What kind of pet do you take care of?

Chris's sis

@Venus Dogs

Venus

More than one?

Chris's sis

@Venus I had $7$ some time ago, but now I only have $3$.

Venus

4:36 PM

@Chris'ssis What??

I envy you. I can keep dogs here T_T

Hippalectryon

plot twist : @Chris'ssis can't integrate, she just steals her dog's works

:D

Chris's sis

@Venus Yeah, I had $7$ dogs! I often prefer to talk to them, and they answer back to me barking. :-)

Integrator

Knock knock!

Chris's sis

@Hippalectryon :-))))))

Venus

@Chris'ssis Owww, that's very cutteee!!

Chris's sis

4:38 PM

@Venus yeap :-)

Integrator

@robjohn @UserX Any Idea about how much votes are required to trigger serial voting script?

robjohn

@Integrator couldn't say

Integrator

@robjohn okay!

@robjohn Any update about mod-elections, I need badge!

Anonymous

Anybody has a solution book to Linear Algebra and its Applicatins?

Anonymous

Thers's one guy on the web who claims he has solution books to many books,but demands money.Can I buy the book from him?

Integrator

4:48 PM

@AshwinGokhale I don't trust anybody!

Venus

@AshwinGokhale Never trust a man :D

robjohn

@Integrator you need a badge? any badge in partcular?

Anonymous

@Committingtoachallenge Are you taking any Physics courses?

UserX

@Integrator I get my first gold in 5 hours

teadawg1337

5:06 PM

I still need the Self-Learner Badge ;_;

Integrator

@robjohn math.stackexchange.com/help/badges/207/caucus math.stackexchange.com/help/badges/208/constituent

@UserX Which one? Electorate? Fanatic?

@UserX I think Fanatic!

@Venus I'm just a kid :P

teadawg1337

Grrr... I still only need one more upvote...

Chris's sis

@Hippalectryon I think something is wrong there since numerically the last series does not match the integral.

@Hippalectryon I'll go my way ... from scratch.

Integrator

@teadawg1337 I could have up-voted you but, I've reached my voting limit for today, and I'll need to spend my votes more wisely to earn a Sportsmanship badge! So, will help you after two days! @ least!

UserX

@Integrator fanatic. I won't probably get the upvoting ones soon as I'm too picky on my upvotes

Chris's sis

5:28 PM

@Hippalectryon

2 ((-1+Sqrt[2])^(-3+2 k+2 l+2 n) (1/(3-2 k-2 l-2 n)+1/(-1+2 k+2 l-2 n)+1/(-1+2 k-2 l+2 n)+1/(-1-2 k+2 l+2 n)))/((-1+2 k) (-1+2 l) (-1+2 n))

@Hippalectryon The calculations are not hard but pretty tedious, boring.

robjohn

@Integrator I see. I never thought that election badges (which are gotten quite easily when there is an election) were that important.

@teadawg1337 for?

Balarka Sen

@MikeMiller oh you just want me to prove that $\pi_1(\mathfrak{H})$ is uncountable? ~~that is pretty obvious~~ i'll punch you if you don't believe that's true.

@Venus everyone are too serious in here.

Mike Miller

I do believe it's true, but I assume you're trying to learn some math, and you don't do that by asserting things without proof.

Balarka Sen

@MikeMiller i was just joking.

Mike Miller

ok. ping me when you have a proof.

Venus

5:43 PM

@BalarkaSen I'm too serious to answer this one too

0

A: Proving $\frac{200}{\pi}\sum_{n=0}^{\infty}\frac{(-1)^{n}}{(2n+1)\cosh\left(\frac{\pi}{2}(2n+1)\right)}=25$

We will evaluate $$S=\sum_{n=0}^{\infty}\frac{(-1)^{n}}{(2n+1)\cosh\left(\frac{\pi}{2}(2n+1)\right)}$$ Since the series is alternating, use $f(z)=\pi\csc(\pi z)$ and we have $$\oint\frac{\pi \csc(\pi z)}{(2z+1)\cosh\left(\frac{\pi}{2}(2z+1)\right)}\,dz$$ The poles are at $z=-\frac{1}{2}, \;\ z=...

Balarka Sen

@Venus i don't see the context. i was just asserting that mathematicians in MSE chat are serious in general.

come along to the dark side. don't try to resist :P

Venus

@BalarkaSen I didn't see the chat because I was too busy to answer a question

Balarka Sen

eh? I was replying to this :

1 hour ago, by Venus

@Chris'ssis You're too serious :D

Venus

@BalarkaSen How do I even know that? You just mentioned my name, so I replied it

Balarka Sen

@Venus Click on the small arrow on the message.

^ do you see a small grey arrow?

UserX

5:52 PM

I created a cryptographed code. Anyone up for deciphering it?

Venus

What arrow? I can't see anything

UserX

@Integrator maybe you're interested

Balarka Sen

@Venus this is an example of a message with no arrow

@Venus this is an example of message with a arrow

Warm Fuzzies

@Integrator Your comments about election / badges / Sportsmanship suggest you took Jyrki's comment too seriously.

Mike Miller

@WarmFuzzies I like the new name. How do you change so frequently? I thought there was a monthly limit.

Balarka Sen

5:54 PM

wait @WarmFuzzies = care bear?

Venus

@BalarkaSen I get it now. I thought that arrow was meaningless

Balarka Sen

@Venus it's pretty useful.

Warm Fuzzies

@MikeMiller Join new SE site -> change name there & copy to the rest of network. A known workaround.

Mike Miller

Also = Raff, Rafflesia Arnoldii, this is much healthier, 900 sit-ups per day, Post No Bulls...

@WarmFuzzies Ah, so one day you'll run out of free passes.

Venus

@BalarkaSen How to type a chat contains arrow like that?

Warm Fuzzies

5:56 PM

No, because I can also delete those accounts. And new sites come up almost every week.

Mike Miller

Ah, I didn't know you could delete accounts.

Warm Fuzzies

This is super easy on a site where you never voted or posted: there is a delete button on the profile page.

Balarka Sen

@Venus mouseover a message you want to reply to, and clickon the downarrow that appears. you'll get a drop down list containing "reply to this message". click on it.

Venus

@BalarkaSen This!

It's so easy Haha

What kind of magic that I haven't known yet in chatroom?

Transcript for

$Mathematics$ Mathematics