Mathematics - 2015-12-07 (page 2 of 2)

Jack Smith

18:12

hey any on here

i need some help

hello i need some help

no one wants to help really

Mike Miller

You haven't said anything about what you need help on. Nobody could possibly help.

Jack Smith

ok

what i need help on

is

or 1 add to the back of 1

Clarinetist

19:09

0

Q: $\frac{\Gamma(n_T + n_C - 2)}{\sqrt{\frac{n_T+n_C-2}{2}}\Gamma\left(\frac{n_T+n_C-3}{2}\right)} \approx 1 - \frac{3}{4(n_T+n_C+2)-1}$

In this answer to a question I asked (which derives the variance of Cohen's $d$), the approximation $$\frac{\Gamma(n_T + n_C - 2)}{\sqrt{\frac{n_T+n_C-2}{2}}\Gamma\left(\frac{n_T+n_C-3}{2}\right)} \approx 1 - \frac{3}{4(n_T+n_C+2)-1}$$ is used. We can reasonably assume that $n_T, n_C> 0$ are inte...

Frank Science

@MikeMiller Did you read Fomenko & Fuchs, Homotopic Topology?

MickLH

@Clarinetist know about stirling's approximation?

Clarinetist

@MickLH sigh I was wondering if that was used. I know of it, but I've never actually found a formula online that I've understood

ILoveChess

Hello, everyone.
Could someone help me quickly with geometry? Only one question.

Huy

Yes.

MickLH

19:13

@Clarinetist I'm not sure if that's how it was derived, but I read you weren't sure where to start. It's a lead, at the very least.

oh

ILoveChess

Is it possible to post pictures on this chat?

Clarinetist

@MickLH I know it's some sort of limit equation. However, browsing through Wikipedia and Wolfram haven't led me to it

Axoren

Use the upload button @ILoveChess

As for equations, use MathJax

Andrew Thompson

Using the (Hatcher) homology definition of (global) orientation in homology, how would one go about showing that, for instance, real projective plane is not orientable?

MickLH

@Clarinetist this is the simple form that I've found to be "good enough" whenever an approximation cuts it: $$\log(n!) \approx n\cdot\log(n) - n$$

Clarinetist

19:15

@MickLH Do you happen to know what the limit statement is? I should really just write it down

Balarka Sen

@AndrewThompson There is no obvious way to do it. You can prove that if $M$ is a closed compact orientable $n$-fold without boundary, then $H_n(M) \cong \Bbb Z$.

Using that you can show $\Bbb{RP}^2$ is not orientable.

Clarinetist

@MickLH Oh, I found it.
$$\lim_{n \to \infty}\dfrac{n!}{(n^n/e^n)\sqrt{2\pi n}} = 1$$

ILoveChess

Balarka Sen

@iwriteonbananas The cellular boundary formula is the nonobvious part.

ILoveChess

How can I prove that the vertex C will be of the form C(d; d) ?

Andrew Thompson

19:18

Ahhyes, that I do know, of course. Thanks, @BalarkaSen.

MickLH

@Clarinetist I believe this is a stronger form than what I posted, also I just found the same on Wikipedia :P

Clarinetist

-searches-

Oh, it's just not written out with the $\lim_{n \to \infty}$ next to it. Gotcha

MickLH

yeahhhh Weirdapedia writing math as English with embedded math lol

Balarka Sen

@AndrewThompson No problem :)

Clarinetist

Thanks @MickLH. I really should add Stirling to my toolset, but I've never used it. Let's see if it works out

Mike Miller

19:20

@AndrewThompson: Suppose you have one and find a loop that reverses the orientation. You can verify that it does so by working in, say, two charts, one at a time.

Clarinetist

For those of you who want some points

0

Q: $\frac{\Gamma(n_T + n_C - 2)}{\sqrt{\frac{n_T+n_C-2}{2}}\Gamma\left(\frac{n_T+n_C-3}{2}\right)} \approx 1 - \frac{3}{4(n_T+n_C+2)-1}$

In this answer to a question I asked (which derives the variance of Cohen's $d$), the approximation $$\frac{\Gamma(n_T + n_C - 2)}{\sqrt{\frac{n_T+n_C-2}{2}}\Gamma\left(\frac{n_T+n_C-3}{2}\right)} \approx 1 - \frac{3}{4(n_T+n_C+2)-1}$$ is used. We can reasonably assume that $n_T, n_C> 0$ are inte...

statistics distribution-theory gamma-function

Balarka Sen

Oh yeah, orientation double cover idea works.

Mike Miller

I didn't say work with a double cover, but sure.

@FrankScience: No.

Andrew Thompson

Hm, yes, I suppose that would work.

Balarka Sen

@MikeMiller Would you mind if I post your proof of this as an answer? Namely, cutting the 3d Hawaiian earring into two pieces of reduced cone over the earring, both contractible?

Then vkTing on thickened nbhd of the two pieces would give me $\pi_1 = 0$

It's a pretty neat proof which I have never seen before.

MickLH

19:31

@Clarinetist I must be screwing something up, because I am failing to see how the rhs even resembles the lhs in overall shape at all...

Mike Miller

@Balarka: It's not correct. A thickening of the two neighborhoods will contain one of the small soheres.

Balarka Sen

Yikes, that's true. Oh dear.

Frank Science

@MickLH Could you please reduce the size of your image/webpages?

@MickLH No, not deleting, but like this way.

> [this](https://i.sstatic.net/nEBrF.png)

MickLH

I've lost the URLs now :P

Frank Science

@Clarinetist It seems to me that flooding with one's post isn't a good idea. When we need to refer to something again and again, we usually do like this, which reduces the area in the chatroom.

Huy

19:46

@MikeMiller: by any chance do you know how I can legally obtain Hsiang's Lecture's on Lie groups (for free)?

Chantry Cargill

Hello ladies.

user174558

Hello.

Chantry Cargill

What's new?

user174558

@Huy Usually the only such way is if it is made available on the author's website.

Huy

@JasperLoy: there are sites like springerlink.

Mike Miller

19:48

Your local library?

user174558

My answer has no upvote, sad panda.

user2154420

Is this a good counterexample to the intuition that secant lines must approach the tangent line? Let f be continuous at zero. Then if f has the property that lim x->0 [f(x)-f(g(x))]/(g(x)) = M for all nonzero x and g(x) -> 0 as x tends to 0, does f'(0) = M? I've been working with g(x)=x/3 and can't seem to prove f'(0)=M so I'm guessing this is false?

Chantry Cargill

So, coke or pepsi?

user174558

Pepsi.

Huy

Coke, obviously.

Balarka Sen

20:02

@ChantryCargill Yes.

- Logician.

Chantry Cargill

@BalarkaSen I was waiting for you.

user174558

I post a brilliant answer that gets 0 votes and a silly answer that gets 3 votes, lol.

user174558

@BalarkaSen Not funny, lol.

user2154420

Any ideas?

Chantry Cargill

Coke is winning in stars.

user174558

20:12

Haha, someone upvoted a wrong answer, lol.

Alec Teal

Pepsi max.

How have a sequence, $(x_n)_{n=1}^\infty$ with the property that $\forall\epsilon>0\forall n,m\in\mathbb{N}[m>n\implies d(x_m,x_n)\ge \epsilon]$ although it obviously has no convergent subsequence I'm not seeing how to prove it.

@JasperLoy they're fake internet points, don't covet them.

user174558

@ChantryCargill An.

user41796

@ChantryCargill Watch the language please

Alec Teal

@ChantryCargill dubious claim there....

user174558

@GlenH7 Rep whore is often used on this site.

Chantry Cargill

20:24

Okay, fine. Jasper is an upvote queen.

user41796

@JasperLoy I realize where the term comes from. Chat flags are seen network wide. And commentary like that is a quick way to get a suspension from someone not familiar with your site.

Alec Teal

I remember once when I got banned for calling someone's mum a const whore - it seems no one realised that was actually a complement.

user174558

Yes, and I got suspended many times, which is fine for me!

Chantry Cargill

I'd be okay with it.

Alec Teal

@ChantryCargill your mother is a PHP programmer who enjoys the language. Not a const whore.

Chantry Cargill

20:28

@AlecTeal I guess it runs in the family.

I also like Ruby.

Alec Teal

So that sequence question.....

Chantry Cargill

@AlecTeal Pffft. This isn't a math chat.

user174558

I think flagging should be removed from chat. Star if you agree.

Chantry Cargill

Popular opinion.

user136984

I am an evil hungry Panda! The next one of you to flag something will end up in my belly (unless it's a valid flag which it probably won't be)! >:)

2

Huy

20:33

Flag me 1v1

Alec Teal

Can we not have crazy fetishes in here please @ParanoidPanda

Chantry Cargill

But they're sooo cuddly.

user136984

@AlecTeal: You just won a ticket to my belly!

Chantry Cargill

I just went to google and typed in jobs and hit enter

Huy

what happened next o_______________o

user136984

20:35

For god sake this is ridiculous!

Chantry Cargill

It fetched me some jobs .________________.

Huy

no way ö.ö

user136984

Anyway, I'm out of this clearly unfriendly chat room!

Huy

a bit paranoid, are we

Chantry Cargill

Aww, look what you guys did.

GBeau

20:37

when are the 2015 putnam problems allowed?

Alec Teal

Bloody furries. :P (There was a "panda" doing stuff....)

After running for a couple of months more or less unnoticed online, IBM's "hack a hairdryer" campaign suddenly attracted a barrage of criticism by Twitter users who called it patronising and sexist - and the company has now apologised.

With reactions like:

Chantry Cargill

Explain further how it is sexist.

Alec Teal

I dunno.

"Surely if anyone is equipped with the knowledge to improve the design of a hairdryer .... statistically speaking the users are....."

Chantry Cargill

I hair-dry (hairdry? hair dry? oh nooo ...) my beard all the time.

Alec Teal

There's a reason you don't see much of:

Huy

20:42

wat

Alec Teal

I didn't say pretty woman @ChantryCargill

Chantry Cargill

Touche.

Alec Teal

They should have gone with "Hack-a-Hoover" then when women got up set IBM could go "$\mathbb{P}i$s$ off, Dyson was a guy.

Also it's aimed at encouraging women to get into STEM, if you've already got a career in STEM why are you even looking at it?

Chantry Cargill

People have the right to be offended by anything. It doesn't mean their offence is justifiable. Although, now that I know it was aimed at women directly, it wasn't exactly a smart move by IBM lol.

Mike Miller

@GBeau: Test is over now everywhere.

Alec Teal

20:52

@ChantryCargill how are they supposed to encourage women to go into STEM fields?

user174558

Hi @OFFSHARING I just answered a series question, LOL.

OFFSHARING

@JasperLoy Really? :-) Hi. Good for you!

Chantry Cargill

@AlecTeal I'm not saying what they did was or wasn't wrong. I'm just saying, as a company, it wasn't good business sense.

user174558

@OFFSHARING It's only a finite series, not infinite, LOL. My brain is finite, while yours is infinite, LOL.

Chantry Cargill

@AlecTeal Interesting question though. I'm not exactly sure what can be done about that or if we should be doing anything.

Alec Teal

20:54

Careful that fence post doesn't hurt your ass @ChantryCargill

OFFSHARING

@JasperLoy Just a simple person here --- from the countryside :-)

user174558

@OFFSHARING I am just a banana, LOL.

Chantry Cargill

@AlecTeal Not a lot of twitterers and tumblrers in here, I hope.

OFFSHARING

@JasperLoy How is it going these days for you? :-)

user174558

@OFFSHARING Not too good, but I am trying to start studying on 1/1.

Chantry Cargill

20:56

@AlecTeal Good thing they didn't use a vacuum cleaner or an oven though.

Alec Teal

@ChantryCargill I already made that joke.

OFFSHARING

@JasperLoy awesome awesome awesome!!! :-) Waiting to see if you keep your word! :D

Huy

I think people should stop trying desperately to get more women into STEM. Those who want to, will. Those who don't want to, shouldn't.

Chantry Cargill

Oh, that you did.

Yeah, I'm kind of curious why it is such a big movement.

user174558

What is STEM?

Alec Teal

20:58

@Huy you're a guy though, it's easy for us to be like "lol today I will do this" apparently it isn't so for girls.

Chantry Cargill

Male privilege D:

Huy

I've never seen movements trying to encourage men to study say literature (which probably has the lowest men:women ratio over here). Why?

Alec Teal

This is backed up by a lot of evidence. Women are paid less for the same jobs also, there's a very different treatement.

Huy

@AlecTeal: This heavily depends on the country and on the job though.

Alec Teal

In countries where women are allowed to hold jobs it holds.

I don't think your case of "how can they be paid less if they are not allowed jobs?" really is a good defense.

Huy

21:00

What case?

Chantry Cargill

I was under the impression that less women go into high paying jobs in america, not that they got paid less. That's just my impression though.

Huy

I know of many jobs where women over here earn the same as men.

Alec Teal

They're both true.

N3buchadnezzar

Heya

Huy

Yeah, I have the same impression as Chantry.

Probably mostly because women are more likely to be family oriented.

Alec Teal

21:00

@Huy asking for jobs you know if is an awful bias. You need to look at a random sample at least.

Chantry Cargill

Hi @N3buchadnezzar

Huy

@AlecTeal: Can you provide a random-job-generator that I can use to get a random sample?

Can't be one you programmed though, would be biased.

Alec Teal

No @Huy, you need to get facts rather than going "I know what women are paid near where I am", grade wise they on pair with males all through compulsory school in the higher ends, something happens after that.

OFFSHARING

@JasperLoy I'm singing some songs with Ramanujan now ... (extremely happy now)

Chantry Cargill

Women actually do better in school then men.

Huy

21:02

@AlecTeal: Sorry, I have no idea what that last message is supposed to mean.

Alec Teal

@Huy do you know what a census is. Also income is recorded as well as job for taxation purposes in ... pretty much everywhere.

It's okay, I'm guessing you live in Syria or something :P

Huy

@AlecTeal: Can you put these words into context?

I'm not dedicating my life to evaluating women's vs. men's wages, so maybe I don't know quite as much about it as you do, if that makes you proud.

Chantry Cargill

So then you have data about job to job vs gender somewhere? I'm actually interested. I don't know what to think.

Alec Teal

@Huy neither have I! UK has the office for national statistics for that. Not every country is the same as yours, some are organised.

@ChantryCargill lmgtfy.com/?q=incomes+associated+with+jobs

Huy

@AlecTeal: Mine has too, and I agree that in some jobs such a difference is very noticable, but not in many of them - at least not in my country.

Alec Teal

21:05

tl;dr shush now.

Chantry Cargill

Okay then.

OFFSHARING

@JasperLoy To be honest, not sure if Ramanujan wouldn't be scared by my last creations. I consider that if I don't reach his performance during this life I failed in all my mathematical activity.

Alec Teal

Not you @ChantryCargill

user174558

@OFFSHARING Aha. Good luck. I think you may solve the Riemann hypothesis.

Alec Teal

I meant the one from the country stuck in phase 2 of geographyfieldwork.com/DemographicTransition.htm

Chantry Cargill

21:08

@OFFSHARING Your confidence is admirable.

@AlecTeal Oh, I didn't take offence. I was was referring to the google link.

Alec Teal

@ChantryCargill what it basically means is "do your own research", I could cherrypick for example, like people who argue "guns are safe" do, or the people who claim "vaccines cause autism"

Look stuff up yourself don't just rely on what someone with a stance already tells you.

user174558

Antidepessants may not work.

user174558

Most religion may be evil.

user174558

Most humans might be stupid.

Huy

or just accept that other people might have a different opinion, @AlecTeal

Chantry Cargill

21:11

@AlecTeal Fair enough. I would have accepted data from a reputable source. I just don't have the time or interest atm to go looking for myself.

user174558

AIDS might not exist.

Alec Teal

@Huy if someone has the opinion that vaccines cause autism .... they're just wrong, there's no "you believe what you want" there's "you contribute to herd immunity unless a doctor deems otherwise"

Mad Scientist

@JasperLoy It does

Alec Teal

If you haven't already @Huy go to the nearest WHO van and get jabbed.

Huy

@AlecTeal: sure

Chantry Cargill

21:13

@AlecTeal Well, you can be wrong about something less obvious though.

N3buchadnezzar

If $y[0] = x$ and $$y_{n+1} = 1 - \frac{\sin y_n}{x}$$ What is $$\lim_{x \to 0} y_n ?$$

Alec Teal

I can't but I'm sure others can.

Chantry Cargill

Hah.

Huy

oh, that claim again ;-)

Alec Teal

@ChantryCargill I had a crazy art teacher (who was really racist and also taught RE, 50 minutes of why Muslims were evil. I do not know how she was allowed to teach (specifically RE....)) she had year 9s make a poster against windfarms and told them that studies have shown windfarms kill sheep AND cause cancer (and so do substations).

Huy

21:17

maybe they do

Chantry Cargill

@AlecTeal Is this USA?

Alec Teal

No UK

(just ignore the troll)

OFFSHARING

@JasperLoy What will you do on the new year? Some parties?

Chantry Cargill

Ah, not sure how stringent the requirements are there.

Huy

well clearly not stringent enough, considering how bad people can turn out

Chantry Cargill

21:19

I'm certified to teach in Canada, but I can't just walk into a classroom. There's constant interaction with administration for the first couple years (if you even get a job)

user174558

@OFFSHARING I have no mood for parties. I will be studying. If I don't begin, I will need to wait another year, as you know.

Alec Teal

Everyone knew she was crazy, it was just like "Oh there goes Miss [name] at it again" and we'd laugh.

Chantry Cargill

@JasperLoy What are you studying for?

Alec Teal

She got the only black kid at school detained on a school trip and it's a story we all laugh about.

user174558

@ChantryCargill I am studying to apply to grad school in a few years time.

Chantry Cargill

21:20

Do you already have an undergrad?

user174558

@ChantryCargill Yes, I do.

Alec Teal

We used to tease her by getting said black kid to read books on mining and chemistry in the library. Or speak in Star Wars languages on his phone (and she'd call the police who'd try not to laugh)

Huy

@ChantryCargill: How cold is it in Canada these days?

OFFSHARING

@ChantryCargill Thanks. I think in mathematics one needs to trust his/her powers 100%, needs for a strong mind that resists all challenges.

Chantry Cargill

@JasperLoy I have similar ideas. I feel like I need to spend a few years to prep.

user174558

21:21

@ChantryCargill I have been spending the last 8 years doing nothing but struggling with severe mental problems.

Chantry Cargill

@Huy I'm currently living in Australia (doing casual relief teaching), but it's chilly in Canada right now.

@Huy I don't think they have snow yet though, which is ridiculous.

OFFSHARING

And don't forget to be crazy enough to do things that no one never did before you.

Huy

@ChantryCargill: Why did you get a teaching certificate if you want to go to grad school?

Chantry Cargill

@JasperLoy Oh, sorry to hear. Doing a masters degree could be a very rewarding experience for you though.

@Huy It was a decision made later in my education. That's part of the reason I need to revisit my course work, but I was doing that already anyway.

Huy

@ChantryCargill: Ah, so in Canada you can get a teaching certificate without a MSc?

Chantry Cargill

21:24

@Huy Yeah, you need an undergrad then you do a bachelor of education.

Huy

Ah, ok.

Chantry Cargill

@OFFSHARING You can apply that to anything I think. Without the will to succeed, you would never spend the time and effort required to really master something.

Huy

@ChantryCargill: Just BTW, I see you're interested to learn about manifolds. We're starting a reading group soon about Lee's Intro to Smooth Manifolds.

OFFSHARING

@ChantryCargill For climbing the mountain of gods you need more than will :-)

Chantry Cargill

@Huy Ah, you saw my profile. I may be a bit out of my depth for that at the moment. I have not studied topology at all. Who is involved in the reading group?

Huy

21:29

@ChantryCargill: What, no topology at all?

Just some people from MSE and r/math.

Chantry Cargill

@Huy It wasn't part of my undergrad. I could make an attempt anyway if you think it's possible.

Huy

@ChantryCargill: I would have said it's possible to jump right into smooth manifolds with very little knowledge about manifolds. Without topology, I don't know. Will be a lot harder for sure.

user174558

I reached 500 points. I hope to reach 1000 points this year, yay!

Huy

@ChantryCargill: But we have a very comfortable pace planned, IMO. You can try and you'll probably learn a thing or two or even more.

user174558

I always study on my own.

OFFSHARING

21:33

Celtic Music - Wolf Blood

►

Loudly!

@JasperLoy ^^^

user174558

I also have no idea why kids come here for their homework. They can ask their teachers or classmates, can't they?

Chantry Cargill

@Huy I'll give it a shot. How can I keep up with the progress of the group?

Huy

@ChantryCargill: The first step would be to join the chatroom. :D

user174558

These division by zero questions are so silly they get so many votes.

catfish

Ring theory should be a prerequisite for college algebra.

user174558

21:39

Prerequisite? Isn't ring theory already part of college algebra?

catfish

Only implicitly, unfortunately :(

Huy

@JasperLoy: what's your current holy list?

Ashley Davies

21:56

Super basic question but in the set of R for real numbers, R^2 represents the set of tuples (x,y) for all x,y in R (to my understanding), similarly for R^3 etc. Is R^1 == R in this respect? That is, does a tuple (x) = x for x in R?

Alec Teal

@AshleyDavies for two sets $X\times Y=\{(x,y)|x\in X\text{ and }y\in Y\}$

You should know that $(x,y):=\{x,\{x,y\}\}$ (this is one way of viewing a pair)

$X^n$ is a short hand for $\underbrace{X\times X\times\ldots\times X}_{n\text{ times}}$

user174558

I got 245 points today, thank you.

Alec Teal

Isn't the cap 200?

user174558

3 accepts.

Alec Teal

Damn, math.stackexchange.com/users/287321/jasper-loy?tab=reputation he's right

Ashley Davies

22:06

Ah better install mathjax

or whatever the extension is called

user174558

Bounties and accepts are not subject to the cap @alec.

anon

@AshleyDavies one can choose to interpretly them differently as technically different sets with different elements, or one may choose to "identify" them which means interpreting them as the same sets with the same elements

user174558

@Huy Still working on it.

Alec Teal

@AshleyDavies yes, and it's just a button you click to render maths

Chantry Cargill

@JasperLoy Diff eq textbooks, go@@@

Alec Teal

22:09

@AshleyDavies anyway technically $X^1=\{\{x\}|x\in X\}$ - notice it contains a singleton. So $X\ne X^1$ however it is easy to go between them. ($\{x\}\mapsto x$ and $x\mapsto\{x\}$) this may seem like "a bit of a hack" but

user174558

@ChantryCargill What do you mean?

Alec Teal

If you take $A\times B\times C$ as $(A\times B)\times C$ you elements of the form $((a,b),c)$ and if you do $A\times (B\times C)$ you get $(a,(b,c))$ but it's easy to move between these and thus not a problem.

Chantry Cargill

@JasperLoy It's the last topic on my study list. I need a decent differential equations book to restudy.

@JasperLoy Typical undergrad + a bit more if possible

user174558

@ChantryCargill The best is Teschl's Ordinary Differential Equations and Dynamical Systems.

Ashley Davies

@AlecTeal That's really helpful! Thanks :]

user174558

22:11

@ChantryCargill That book covers classical ODEs, discrete DS and continuous DS all in one.

Chantry Cargill

@JasperLoy Thanks. You're my hero.

user174558

@ChantryCargill To evaluate before buying, see author's website for legal free PDF version.

Alec Teal

@AshleyDavies gotcha back.

Ashley Davies

We finished the last lecture of our linear algebra course today and I couldn't be more relieved :') still catching up with lectures from 2 months ago

Chantry Cargill

@JasperLoy Even better.

user19405892

22:53

hi

can one of you help me with a venn diagram question?

65 kids at a school voted for their favorite ice-cream flavor.They can vote for up 2 flavors and the choices are vanilla,chocolate,and strawberry.10 kids voted for strawberry,35 voted for vanilla,and 25 people voted for chocolate.Let A be the amount of kids that voted for only vanilla,B be the amount people hat voted for chocolate,and C be the amount of people who voted for both.What is
ab/c ?

Chantry Cargill

That is a terribly written question.

Samuel Yusim

Does anyone in here know the Jacobson density theorem and feel like they can explain what it's for to me? I'm trying to learn it and the statement just seems unmotivated and confusing.

Chantry Cargill

@user19405892 $A = 35$ and $B = 25$. Let $D$ be the amount of people who voted for strawberry. We know that $A + B + D = 70$. But there are $65$ kids. So ...?

TomSIR

23:58

hello

hi everyone

Transcript for

$Mathematics$ Mathematics