Mathematics - 2014-12-15 (page 2 of 10)

@ForeverMozart One is always in the list of top users for oneself, at least if one has any score in the tag. You're not in the list I see if that comforts you.

Alexander Gruber

@Behaviour Right

Forever Mozart

@DanielFischer ok yeah I figured that out. But I am in the list for top askers in the last 30 days, right?

Daniel Fischer

3:45 AM

@ForeverMozart Tenth place, if I haven't miscounted.

Forever Mozart

ok yeah

well that makes me feel slightly better

@DanielFischer Do you work in continuum theory at all?

Alexander Gruber

Oh no. The shame :(

5

user2780354

Hi guys, I'm new here, I had a question about revolving regions around axes. I am asked to revolve the region bound by y=(x^3)+1, y=2, x=0 about the line y=-1. So I know how to find the area of the region, which is done by: http://i.snag.gy/GP5pP.jpg
but how would I find the volume if it was revolved around y=-1? What would the volume be?

2

Daniel Fischer

@ForeverMozart Continuum as in (infinite) connected compact space? No.

3

Forever Mozart

darn

what about set theoretic topology?

Daniel Fischer

3:49 AM

@AlexanderGruber You can delete one of your answers. The tag badges don't stay.

Forever Mozart

@AlexanderGruber wear your shame

@DanielFischer set theoretic topology?

Daniel Fischer

@ForeverMozart Aka point set topology? I've forgotten stuff, but some I remember.

Behaviour

@AlexanderGruber Nothing like that in SEDE. Apparently, moderators have some access to such data, though.

Forever Mozart

but you are a top answerer in topology... what gives???

you have to be good at something... algebraic?

Daniel Fischer

@ForeverMozart I haven't forgotten everything, some I remember. Enough to get a couple of upvotes.

Forever Mozart

3:51 AM

oh ok

Mike Miller

@ForeverMozart There are lots of point-set topology questions that are much simpler than the kinds of things you think about, mostly asked by students taking their first topology class.

user2780354

Called a math chatroom, ask for help with math, nothing happens. Go figure. Thanks for the help (not really), I guess I'll try more to look it up or ask on math stack exchange

Forever Mozart

yeah I know, I am by no means an expert, but I recently discovered continuum theory and find it very interesting

teadawg1337

@user2780354 There's an active conversation going on, please be patient. I'm personally too tired to be of much help

Forever Mozart

@user2780354 wow, really? what was your freaking question?

Alexander Gruber

3:53 AM

@Behaviour Yeah I'm still doing a lot of it manually. Maybe if I moderate for 10 years they will give me an API

skullpatrol

6 mins ago, by user2780354

Hi guys, I'm new here, I had a question about revolving regions around axes. I am asked to revolve the region bound by y=(x^3)+1, y=2, x=0 about the line y=-1. So I know how to find the area of the region, which is done by: http://i.snag.gy/GP5pP.jpg
but how would I find the volume if it was revolved around y=-1? What would the volume be?

Forever Mozart

@user2780354 you need to use the washer method

Mike Miller

seems like the selfie hat requires you answer your own question without CW.

Forever Mozart

can you draw a picture of the region and then think of revolving it?

user2780354

I have been trying to read this http://www.math.utah.edu/lectures/math1210/30PostNotes.pdf
but I can't figure it out

Forever Mozart

3:56 AM

@user2780354 actually your area integral is incorrect

user2780354

@ForeverMozart how so?

Forever Mozart

The first step should be to draw a picture of the region

user2780354

I've done that

Forever Mozart

area will be given by $\int _0 ^1 2-(x^3+1) dx$

user2780354

How can I translate that to something legible instead of $_int etc

Forever Mozart

3:58 AM

go here and click startChatjax math.ucla.edu/~robjohn/math/mathjax.html

Mike Miller

@teadawg1337 just got spock; no idea why. what was your idea?

Behaviour

@AlexanderGruber You could put up a feature request either through Meta.SE, or informally through Teachers' Lounge.

user2780354

@ForeverMozart how do I input what you wrote into mathjax/chatjax

Forever Mozart

follow the instructions on that page. drag the link to your bookmark toolbar

then when you are on this tab, just click it

teadawg1337

@MikeMiller I got a different hat than the blue spock, I have no idea

Mike Miller

4:04 AM

oh, so there's fascinating, and fascinating, ma'am

Alexander Gruber

@Behaviour Ehh, too much to do. Winter bash is fun but causes problems for us

user2780354

@ForeverMozart I see what you did, however you did your area calculation through vertical slicing which is perfectly fine, and mine is through horizontal slicing, which is correct too. I guess I'll look into the washer method. Thanks for the suggestion!

Forever Mozart

no your integral is incorrect @user2780354

if you want to do right-left you have to integrate with respect to $y$

so it would be $\int _1 ^2 (y-1)^{1/3} dy$

user2780354

@ForeverMozart yeah I just figured that out, would have to show y as a function of x. My fault.

teadawg1337

Where's the network-wide rankings?

Mike Miller

4:08 AM

here

teadawg1337

@Mike Thank you

I'm heading off to bed, it's getting pretty late

Edward Jiang

Anyone figure out what the Chameleon is awarded for?

Mike Miller

Yup.

Forever Mozart

I want a new hat. Someone help me

Edward Jiang

@Mike What?

Mike Miller

4:14 AM

@EdwardJiang Either from modifying your profile or changing your avatar; I'm not sure which. Probably the latter.

2

Forever Mozart

hat?

Behaviour

@MikeMiller Yes, it's the avatar. Editing the bio text did not earn it. On the other hand, changing the avatar caused an avalanche of hats for me (61 SE accounts).

Edward Jiang

@Behaviour Yeah same LOL.

Mike Miller

Ah, I've discovered how to get Fascinating, Ma'am. But I need more votes to get it on Math.

Edward Jiang

Tell me how.

Mike Miller

4:25 AM

Not a chance, bub.

Edward Jiang

Oh I randomly just got it.

Behaviour

@AlexanderGruber Solution: propose the tag be nuked. It's too broad and used for weird reasons. I argued for this here and here.

Alexander Gruber

@Behaviour That would certainly raise the resale value of my now-antique bronze badge.

Kaj Hansen

Hello everybody

Mike Miller

greetings

Forever Mozart

4:37 AM

hiiiiii

Kaj Hansen

haha, @AlexanderGruber, I'm pretty close to that soft-question badge myself :P

Alexander Gruber

@MikeMiller Are we migrating math-history questions to HSMSE now?

Mike Miller

@AlexanderGruber I don't know. I hope so. It's a better fit there, I think.

From your comment I take it that's a reprimand.

Behaviour

@AlexanderGruber I think not. I usually comment "this would work well on HSM", but they are still on topic here.

That integral notation question, in particular. I voted to leave open.

Alexander Gruber

@Behaviour that is what I thought

Behaviour

4:39 AM

Unless OP wants to migrate, of course.

Alexander Gruber

@MikeMiller No, I was seeing if maybe there was a meta thread where the community had decided differently

But since there's not, I really shouldn't migrate it unless the OP asks me to, or unless there is another reason other than just being historical

Behaviour

I suggested updating on-topic page to move history of math from the "on-topic" list to "on-topic, but better elsewhere" list. WW commented that he'd like to wait.

By the way, HSM has moderators as of last week, including our friend HDE something, who shows up on meta frequently.

At the risk of disturbing the elephant so soundly sleeping in the middle of the room, I can't be the only one slightly jarred by seeing the name of this site abbreviated to "History of S&M", can I? Just putting this out there... — Ilmari Karonen Nov 16 at 16:56

Mike Miller

heh heh heh

Alexander Gruber

@Behaviour I'd say I agree with him. There are still only 200 or so questions, whereas the math-history tag on MSE has over 1,000. I would like to see how well HSM persists

but, maybe there is a place that it could at least be mentioned in the on-topic page, even if we don't move the topic yet.

Behaviour

On the line "History and development of mathematics" add (see also [link to site]).

Alexander Gruber

4:47 AM

@Behaviour that is what I am thinking.

Forever Mozart

I think I proved the conjecture

this one math.stackexchange.com/questions/1067342/…

it is in my head I just have to write it out

weeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

thanks to whoever just upvoted my question :)

usukidoll

5:20 AM

wow so many downvotes
http://meta.stackexchange.com/questions/214869/simplify-and-reduce-the-range-of-winter-bash-hats

yay I got a warm welcome hat

Forever Mozart

some folks have hatmania

no sane being views it as a competition

Karl Kronenfeld

I don't see a "I hate hats" link when I click the snowflake image.

Prototank

Hey guys... A discrete set with no accumulation points is closed, right? I'm going crazy right now.

Forever Mozart

You need to word it a little differently, but yes

you mean a discrete subspace of a given space

Prototank

5:36 AM

A discrete set $D\subset X$ with no accumulation points is closed in $X$?

Anonymous

@Committingtoachallenge You there?

Mike Miller

6:12 AM

@KarlKronenfeld bottom of the snowflake panel

Hat Man

6:24 AM

I don't like secret badges. What is "warm welcome" badge for?

usukidoll

upvoting a new user's question

Hat Man

6:37 AM

@usukidoll How do you know?

usukidoll

^ saw a thread about hats

Prototank

I think I have a proof that a metric space is a D-Space. Are there any topologists in the room that care to take a look?

Mike Miller

What's a D-space?

Prototank

A space is said to be D, or a D-space, if for every open neighborhood assignment $f:X\to \tau$ there exists a discrete set such that $f[D]$ is a cover of $X$.

An open neighborhood assignment is a function $f:X\to \tau$ such that $x\in f(x)$.

Mike Miller

Hm. Interesting. What's your proof?

Prototank

6:47 AM

Should I try to explain it here or make a post on the SE?

Kaj Hansen

So Jasper is back?

Jasper Loy

@KajHansen Yes. I am still not dead.

Kaj Hansen

Thought you left MSE though.

Mike Miller

Whichever you want, @Prototank. I'll take a look either way, for whatever it's worth.

Prototank

I just finished Texing it, so I think I can just copy/paste. It'll be few moments.

Jasper Loy

6:51 AM

@KajHansen I met one of my profs today. I told him about my plans. He told me how hard it would be to get accepted to grad school and how hard it is to find a job after that.

Forever Mozart

@Prototank

Prototank

Yes?

Forever Mozart

that is an unsolved problem, right?

Prototank

nah

I wish

Forever Mozart

oh nevermind the open problem is: Is every Lindelof space a D-space.

Prototank

6:53 AM

correcto

Metric is such a nice property. I have no doubt that this was solved very quickly.

There are really smart people out there

and stuff

Forever Mozart

I had to whip out my Open Problems in Topology II

Jasper Loy

@KajHansen You should be sleeping. If not you should be talking to me.

@usukidoll Are you angry with me? I hope not.

Forever Mozart

@Prototank

Prototank

Yeh?

Forever Mozart

Suppose $X$ is a nontrivial normal connected space whose connected subsets are precisely the cofinite subsets. Then every proper subcontinuum of $\beta X$ is nowhere dense.

that is the problem I am now working on

it is very slippery

Kaj Hansen

7:04 AM

@JasperLoy, was afk

Prototank

@fore

Forever Mozart

yes?

Prototank

@ForeverMozart, I do not know what a subcontinuum is. I also don't know what the difference between $X$ and $\beta X$ is.

Forever Mozart

thats ok you just need more topology. A continuum is a connected compact Hausdorff space and $\beta X$ is the stone cech compactification of $X$

that is an unsolved problem too, so get to work!

Prototank

connected compact Hausdorff is pretty sweet

Forever Mozart

7:08 AM

yes

there are lots of interesting theorems you can use in those spaces

Prototank

closed and bounded intervals in $\mathbb{R}^n$ have this property, are there more otherworldly spaces that are continuum?

Forever Mozart

Sure

Take any compactification of a connected space

you need the space to be T$_{3.5}$

@KajHansen!

Hey there Balarka

@BalarkaSen

7:11 AM

Yo @ForeverMozart

Hi guys

Sup

LEL @AlexanderGruber

This is what I have today: Suppose $X$ is a normal space whose connected subsets are precisely the cofinite sets. Then every proper subcontinuum of $\beta X$ is either nowhere dense OR is the union of two closed sets whose intersection is a nowhere dense copy of $\beta\omega$.

Balarka Sen

And 20 people starred Chat Guidlines? God, there really have been a fair bit of activity in here last night I guess.

@ForeverMozart I never had a feel for $\beta X$ :(

Forever Mozart

7:13 AM

well thats as far as I could get :(

Kaj Hansen

@BalarkaSen, I actually have the rep for a soft-question badge, but not enough responses under that tag :P

Prototank

@MikeMiller @ForeverMozart

http://math.stackexchange.com/questions/1068823/every-metric-space-is-a-d-space

Mike Miller

@Prototank Well, you've got Mozart on the case, and he's more of a point-set topology guy than I, so I'll bow out.

Forever Mozart

@Prototank I dont understand your well-ordering

Prototank

We well order each of the $L_n$'s, and then we splice them together such that $L_1$ is placed in front of $L_2$ etc. Is that allowed?

Forever Mozart

7:21 AM

yes

but I couldn't tell that's what you were doing

Prototank

Sorry, it is very unclear I understand. This is my first write up in a while, I apologize.

I think, looking at it now, there is a pervasive error in the proof involving $\mathit{d}(x)$. As $d$ is a natural number representing something specific and I am using it instead as the "size of the assigned ball around x".

Mike Miller

I now am the undisputed King of Hats. I have more hats than anyone else in the entire world, ever.

4

Balarka Sen

@MikeMiller $\Bbb R$ is a Hausdorff space covering the non-Hausdorff $\Bbb R/\Bbb Q$, not?

Mike Miller

Doubt that's a covering map.

Balarka Sen

I feel it is.

Mike Miller

7:27 AM

It's not.

Balarka Sen

Ok, rethink.

Forever Mozart

@Prototank I think that is ok

Balarka Sen

I am trying to answer some questions for collecting some hats :P

Forever Mozart

I would word things a little differently

Prototank

That's what the other guy said! haha. I'm not a topologist.

I don't know the familiar notations

skullpatrol

7:28 AM

You @MikeMiller are the overlord of hats :)

Forever Mozart

well thats a good proof. To me that is not trivial

would take some time to think about

Mike Miller

@BalarkaSen The exercise I mentioned gives the desired construction. (BTdubs - the quotient topology on $\Bbb R/\Bbb Q$ is indiscrete.)

Forever Mozart

the two tricks are the shrinking down to metric balls and the well-ordering

Prototank

yes sir

Forever Mozart

the first seems like a natural thing to do

Balarka Sen

7:30 AM

@MikeMiller I duncare about your exercise. I want to find one by myself.

Prototank

the second is not so natural. My professor gave us (my classmates and I) problems where we are to use Choice.

so I had a hint

but it could have been in lots of forms

Mike Miller

You wonder why I don't want to listen to what you have to say when you don't listen to what I have to say...

usukidoll

ooooooooo

Forever Mozart

I bet you could construct a different proof using just AC

Mike Miller

(But yes, I obvo support finding one on your own. One could just phrase it with a little more tact. :P)

Forever Mozart

7:32 AM

without using it to prove the WOP of course ;)

Balarka Sen

@MikeMiller Well, obviously you know a construction. I want to construct on my own.

Prototank

I was originally trying to Zorn things... but the union'd upper bound kept breaking

Balarka Sen

If you want me to see that problem, OK... opens up Hatcher

Mike Miller

Well, the problem tells you an explicit construction. If you don't want to know it, don't look.

Balarka Sen

Well you were complaining about me not wanting to listen to you, @Mike :P

Forever Mozart

7:34 AM

@Prototank

Prototank

yeh?

Forever Mozart

**Argument.** (no one is in another person's bubble) Let $x_\alpha,x_\beta\in D$. Since $X$ is well ordered, let $\alpha<\beta$. Then $x_\beta \notin f(x_\alpha)$ by construction. Hence, $\rho(x_\alpha,x_\beta)\geq \textit{d}(x_\alpha)$. But also, since $\alpha<\beta$, $\textit{d}(x_\alpha)\geq\textit{d}(x_\beta)$. Thus we have $\rho(x_\alpha,x_\beta)\geq \textit{d}(x_\alpha)\geq \textit{d}(x_\beta)\Rightarrow x_\alpha\notin f(x_\beta)$.\\

Prototank

I think all of those should be replaced with 1/d

Forever Mozart

Fix $\beta$. For all $\alpha<\beta$ show $x_\alpha \notin f(x_\beta)$.

I think that is all that's needed

Balarka Sen

Hatcher's formulation of the problem is BS

You are really looking at the covering map R \times R^+ \to R^2 - 0

Forever Mozart

7:37 AM

you are just making sure that at each stage of the induction you have a discrete set

Mike Miller

No you're not.

Balarka Sen

If you look at the collection of fibers over each point, you'll see it resemble the Riemann surface of log z

So Z, the monodromy group, acts on it.

Forever Mozart

@Prototank do you see what I'm saying?

Balarka Sen

That is the action of Z on R^2 - 0

Prototank

I'm processing your statement

Balarka Sen

7:38 AM

@MikeMiller I was referring to Hatcher's stupid action of Z on R^2 - {0}

Forever Mozart

I guess I would include that as part of the induction

Prototank

It results from the well ordering

Forever Mozart

oh maybe I'm wrong

Prototank

since the big sets were placed first in the well ordering

which is what the second half of the argument explains... but I messed up the notation

Forever Mozart

you also want to make sure the balls around the $x_\alpha$ with $\alpha<\beta$ do not hit the one around $x_\beta$

ok I understand

good job

I still have a problem with the wording here though: Let $X$ be well ordered such that if $x\in L_i$ and $y\in L_{j}$ with $i<j$ then $1/ \mathit{d}(x)<1/ \mathit{d}(y)$ with $X=\lbrace x_\alpha | \alpha\in\lambda\rbrace$.

the way you explained it to me makes sense, but the sentence here makes no sense.

Prototank

7:43 AM

its gross and I don't like it

Forever Mozart

lol

Prototank

I don't like having to define L_n

Forever Mozart

let me try...

Prototank

and I also don't like saying "Splice in the big guys first! :D"

haha

Balarka Sen

OK, @MikeMiller, why isn't R \to R/Q isn't a covering map?

haven't checked if Q acts properly disc on R

it probably doesn't.

there is a lot of pointless starring going on it seems. @skullpatrol is going star-crazy?

Mike Miller

7:45 AM

Because $\Bbb R/\Bbb Q$ is indiscrete, and no neighborhood of any point in $\Bbb R$ is non-Hausdorff.

Balarka Sen

oh ok

Forever Mozart

Enumerate $X=\{x_\alpha:\alpha<\lambda\}$ such that if $\alpha<\beta$ then either $x_\alpha,x_\beta\in L_i$ for some $i$ or $x_\alpha\in L_i$ and $x_\beta\in L_j$ for some $i<j$.

@Prototank

how's that?

Prototank

is the word enumerate allowed here

ensymbolate

Forever Mozart

yeah I use it in the place of well-order all the time

Prototank

@ForeverMozart I think its cleaner

Balarka Sen

7:48 AM

nope, @skull

Forever Mozart

usually we use "enumerate" when dealing with countable sets.

but here I am enumerating $X$ with $\lambda$ in effect

skullpatrol

ok :-)

Balarka Sen

sheesh this looks complicated, @Mike

Forever Mozart

@Prototank see the problem with what you wrote is you made no reference to the ordering of $X$ ...

we do not know the indexes on $x$ and $y$

Prototank

ahh. Yes, yours is much cleaner.

its a more readable sentence too

Balarka Sen

7:53 AM

oh wait there is a SES

$1 \to \Bbb Z \to \pi_1(X/\Bbb Z) \to \Bbb Z \to 1$

Mike Miller

Is that valid when $X/\Bbb Z$ is really messed up? I don't know off the top of my head.

I guess it is.

Balarka Sen

Z acts prop disc and freely on X

it's valid whenever X is connected and path connected (i.e., so is X/Z)

Prototank

@ForeverMozart so do you believe the proof?

Mike Miller

Sure.

Forever Mozart

yes I think so

Balarka Sen

7:55 AM

i guess all we need to do is to show it's abelian. pretty sure it's Z \times Z

Forever Mozart

is this for a topology class?

Mike Miller

Sure.

Prototank

Yeah. I'm a first year master's student.

it is a graduate topology class

I don't actually know if it is hard though... my school is so off the map that I have a hard time telling if my education compares to the rest of people who are first year graduate students.

usukidoll

woo got my sumo hat

and the star trek hats ^_^

Forever Mozart

it sounds like a good course

if you are proving theorems like that

I would almost put that into a set theoretic topology course

Prototank

7:59 AM

My professor is a very smart lady. She's going to Budapest next year... she won some award or something.

She's also a set theorist.

Forever Mozart

ok that figures

every topology professor teaches the graduate topology differently depending on his/her area of topology

some focus more on algebraic topology, others set theoretic topology, others continuum theory...

Prototank

I would really really like to see some algebraic topology.

I should just crack open a book probably

Mike Miller

@AlexanderGruber not that I disagree with the decision, but what's up with locking this post? something going on?

Alexander Gruber

@MikeMiller I'm afraid that one's classified.

Mike Miller

I see. 'preciate it.

Prototank

8:03 AM

Last year I was trying to graduate, but also my undergraduate math cirriculum was exhausted so I was taking my univeristy's graduate sections of real analysis and complex analysis. I think I ended up with a mediocre understanding of both, although I really liked each one. It was an unfortunate situation.

trying to graduate and trying to take graduate courses because they are interesting do not coincide.

well*

Mike Miller

I think the chameleon goes well on you, @AlexanderGruber.

Alexander Gruber

@MikeMiller It goes with my other hat.

Mike Miller

I think I dig the teeny lightbulb. It's probably what I'll stick to til I get Bill Lumbergh. Or Waffles.

Behaviour

@MikeMiller Eureka works the same as last year, I think: awarded manually by SE staff to those who figured out a secret hat.

Mike Miller

So I guess they're searching the chats for people who mention Chameleon etc?

One could really grate by singing Karma Chameleon in the channels of their choice.

Behaviour

8:09 AM

Yes. A bit of work, I imagine, but that's what they did last year.

Do I now qualify for Eureka-Eureka hat? :)

Mike Miller

We'll have to see.

Forever Mozart

I want a top hat

Behaviour

I'll stick with the crab; it fits my avatar. And I concede the site leaderboard to those who actually upvote things once in a while.

Mike Miller

I've doubts I'll ever get Breaking Bad (what closed post around here is ever salvageable?) or Red Baron, but otherwise, I've high hopes.

Behaviour

@MikeMiller I've edited and reopened a bunch, so it's doable. Also, the post does not have to be actually reopened. Close-edit-vote to reopen is all it takes.

Mike Miller

8:15 AM

And you can then retract your reopen vote, I assume?

Prototank

Goodnight everyone. Thanks for the help and input @ForeverMozart

Behaviour

You can't. And I wouldn't go out of my way for this hat. Reopening is serious business.

Forever Mozart

no problem, see you later

Mike Miller

That's a fair point.

Alexander Gruber