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3:00 AM
Does anyone have a recommendation for a good introduction to statistical theory textbook?
 
If I shared the secret to a secret hat, it wouldn't be so secret anymore would it?
 
you probably dont even know how you got it
 
I have a good guess
brb, dinnertime
 
you meanie
 
I'm waiting to share my guess with a mod or something
 
3:06 AM
got Chameleon. looks gross; not changing
mods don't know
 
Wow, really?? Hehehehehehe.....
Confirmed, hats do not work on mobile
 
they're meant to, I think. update your app.
 
It is updated
 
annoyed it still has me wearing the chameleon hat
 
I am going to prove this conjecture if it kills me
of course it may be false
in which case I am wasting my time
 
3:17 AM
@MikeMiller No hats in Android app, no hats on mobile site either. Not surprised.
 
Tragic but unsurprising, because as you mentioned, they take resources.
 
i saw an Android hat
 
Heh heh heh
 
"On the Road, Bugdroid"
 
I suddenly had deja vu
 
3:21 AM
top of the list
 
I remember someone having that hat last Christmas
@teadawg1337
did you get to make your own hat @skullpatrol ?
it fits very well
 
@ForeverMozart i got the whole avatar off the web
3
 
@ForeverMozart This hat is distinct from the "Fascinating" hat. This one is called "Fascinating, Ma'am"
3
 
got warm welcome somehow. no ida how.
got a guess, tho
 
@MikeMiller Upvoted a post by new user?
I figure this is one of the hats I'm less likely to get, just going by its name.
 
3:31 AM
Both of those seem likely.
 
Btw @Mike, I saw yours :P
 
I didn't see yours. I suppose it will be more fun if we don't give away the deep secrets of the Stack Exchange empire.
@Behaviour Clever of them to make secret a habit they don't want happening en masse.
 
@Behaviour If that's true, I won't be able to get that one until tomorrow. I've used my upvotes for the day
 
Erm...... THat's a first, I accidentally posted an answer....
 
3:37 AM
"Accidentally", eh
 
A key got stuck, and my elbow slipped and moved across the trackpad
 
Its ok, we all had to delete incorrect answers from time to time ;)
 
Or you could delete an answer and then undelete it after getting a hat... Frankly, that particular hat looks like a pretty dumb idea.
 
It blows my mind that I am on the lists for top answerers in General Topology
 
Hey, @Behaviour
 
3:42 AM
you making fun of my hat?
 
Is getting mean review times over all users within the scope of SQL/data explorer?
 
@AlexanderGruber You mean the mean time a particular user spends on a review?
 
@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.
 
@Behaviour Right
 
@DanielFischer ok yeah I figured that out. But I am in the list for top askers in the last 30 days, right?
 
3:45 AM
@ForeverMozart Tenth place, if I haven't miscounted.
 
ok yeah
well that makes me feel slightly better
@DanielFischer Do you work in continuum theory at all?
 
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
 
@ForeverMozart Continuum as in (infinite) connected compact space? No.
3
 
darn
what about set theoretic topology?
 
3:49 AM
@AlexanderGruber You can delete one of your answers. The tag badges don't stay.
 
@AlexanderGruber wear your shame
@DanielFischer set theoretic topology?
 
@ForeverMozart Aka point set topology? I've forgotten stuff, but some I remember.
 
@AlexanderGruber Nothing like that in SEDE. Apparently, moderators have some access to such data, though.
 
but you are a top answerer in topology... what gives???
you have to be good at something... algebraic?
 
@ForeverMozart I haven't forgotten everything, some I remember. Enough to get a couple of upvotes.
 
3:51 AM
oh ok
 
@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.
 
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
 
yeah I know, I am by no means an expert, but I recently discovered continuum theory and find it very interesting
 
@user2780354 There's an active conversation going on, please be patient. I'm personally too tired to be of much help
 
@user2780354 wow, really? what was your freaking question?
 
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
 
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?
 
@user2780354 you need to use the washer method
 
seems like the selfie hat requires you answer your own question without CW.
 
can you draw a picture of the region and then think of revolving it?
 
I have been trying to read this http://www.math.utah.edu/lectures/math1210/30PostNotes.pdf
but I can't figure it out
 
3:56 AM
@user2780354 actually your area integral is incorrect
 
@ForeverMozart how so?
 
The first step should be to draw a picture of the region
 
I've done that
 
area will be given by $\int _0 ^1 2-(x^3+1) dx$
 
How can I translate that to something legible instead of $_int etc
 
3:58 AM
go here and click startChatjax math.ucla.edu/~robjohn/math/mathjax.html
 
@teadawg1337 just got spock; no idea why. what was your idea?
 
@AlexanderGruber You could put up a feature request either through Meta.SE, or informally through Teachers' Lounge.
 
@ForeverMozart how do I input what you wrote into mathjax/chatjax
 
follow the instructions on that page. drag the link to your bookmark toolbar
then when you are on this tab, just click it
 
@MikeMiller I got a different hat than the blue spock, I have no idea
 
4:04 AM
oh, so there's fascinating, and fascinating, ma'am
 
@Behaviour Ehh, too much to do. Winter bash is fun but causes problems for us
 
@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!
 
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 $\int _1 ^2 (y-1)^{1/3} dy$
 
@ForeverMozart yeah I just figured that out, would have to show y as a function of x. My fault.
 
Where's the network-wide rankings?
 
4:08 AM
 
@Mike Thank you
I'm heading off to bed, it's getting pretty late
 
Anyone figure out what the Chameleon is awarded for?
 
Yup.
 
I want a new hat. Someone help me
 
@Mike What?
 
4:14 AM
@EdwardJiang Either from modifying your profile or changing your avatar; I'm not sure which. Probably the latter.
2
 
@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).
 
@Behaviour Yeah same LOL.
 
Ah, I've discovered how to get Fascinating, Ma'am. But I need more votes to get it on Math.
 
Tell me how.
 
4:25 AM
Not a chance, bub.
 
Oh I randomly just got it.
 
@AlexanderGruber Solution: propose the tag be nuked. It's too broad and used for weird reasons. I argued for this here and here.
 
@Behaviour That would certainly raise the resale value of my now-antique bronze badge.
 
Hello everybody
 
greetings
 
4:37 AM
hiiiiii
 
haha, @AlexanderGruber, I'm pretty close to that soft-question badge myself :P
 
@MikeMiller Are we migrating math-history questions to HSMSE now?
 
@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.
 
@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.
 
@Behaviour that is what I thought
 
4:39 AM
Unless OP wants to migrate, of course.
 
@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
 
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
 
heh heh heh
 
@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.
 
On the line "History and development of mathematics" add (see also [link to site]).
 
4:47 AM
@Behaviour that is what I am thinking.
 
I think I proved the conjecture
it is in my head I just have to write it out
weeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
thanks to whoever just upvoted my question :)
 
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
 
some folks have hatmania
no sane being views it as a competition
 
I don't see a "I hate hats" link when I click the snowflake image.
 
Hey guys... A discrete set with no accumulation points is closed, right? I'm going crazy right now.
 
You need to word it a little differently, but yes
you mean a discrete subspace of a given space
 
5:36 AM
A discrete set $D\subset X$ with no accumulation points is closed in $X$?
 
@Committingtoachallenge You there?
 
6:12 AM
@KarlKronenfeld bottom of the snowflake panel
 
6:24 AM
I don't like secret badges. What is "warm welcome" badge for?
 
upvoting a new user's question
 
6:37 AM
@usukidoll How do you know?
 
^ saw a thread about hats
 
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?
 
What's a D-space?
 
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 $x\in f(x)$.
 
Hm. Interesting. What's your proof?
 
6:47 AM
Should I try to explain it here or make a post on the SE?
 
So Jasper is back?
 
@KajHansen Yes. I am still not dead.
 
Thought you left MSE though.
 
Whichever you want, @Prototank. I'll take a look either way, for whatever it's worth.
 
I just finished Texing it, so I think I can just copy/paste. It'll be few moments.
 
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.
 
@Prototank
 
Yes?
 
that is an unsolved problem, right?
 
nah
I wish
 
oh nevermind the open problem is: Is every Lindelof space a D-space.
 
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
 
I had to whip out my Open Problems in Topology II
 
@KajHansen You should be sleeping. If not you should be talking to me.
@usukidoll Are you angry with me? I hope not.
 
@Prototank
 
Yeh?
 
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
 
7:04 AM
@JasperLoy, was afk
 
@fore
 
@ForeverMozart, I do not know what a subcontinuum is. I also don't know what the difference between $X$ and $\beta X$ is.
 
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!
 
connected compact Hausdorff is pretty sweet
 
7:08 AM
yes
there are lots of interesting theorems you can use in those spaces
 
closed and bounded intervals in $\mathbb{R}^n$ have this property, are there more otherworldly spaces that are continuum?
 
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 $\beta\omega$.
 
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 $\beta X$ :(
 
7:13 AM
well thats as far as I could get :(
 
@BalarkaSen, I actually have the rep for a soft-question badge, but not enough responses under that tag :P
 
@MikeMiller @ForeverMozart

http://math.stackexchange.com/questions/1068823/every-metric-space-is-a-d-space
 
@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.
 
@Prototank I dont understand your well-ordering
 
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?
 
7:21 AM
yes
but I couldn't tell that's what you were doing
 
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".
 
I now am the undisputed King of Hats. I have more hats than anyone else in the entire world, ever.
5
 
@MikeMiller $\Bbb R$ is a Hausdorff space covering the non-Hausdorff $\Bbb R/\Bbb Q$, not?
 
Doubt that's a covering map.
 
I feel it is.
 
7:27 AM
It's not.
 
Ok, rethink.
 
@Prototank I think that is ok
 
I am trying to answer some questions for collecting some hats :P
 
I would word things a little differently
 
That's what the other guy said! haha. I'm not a topologist.
I don't know the familiar notations
 
7:28 AM
You @MikeMiller are the overlord of hats :)
 
well thats a good proof. To me that is not trivial
would take some time to think about
 
@BalarkaSen The exercise I mentioned gives the desired construction. (BTdubs - the quotient topology on $\Bbb R/\Bbb Q$ is indiscrete.)
 
the two tricks are the shrinking down to metric balls and the well-ordering
 
yes sir
 
the first seems like a natural thing to do
 
7:30 AM
@MikeMiller I duncare about your exercise. I want to find one by myself.
 
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
 
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...
 
ooooooooo
 
I bet you could construct a different proof using just AC
 
(But yes, I obvo support finding one on your own. One could just phrase it with a little more tact. :P)
 
7:32 AM
without using it to prove the WOP of course ;)
 
@MikeMiller Well, obviously you know a construction. I want to construct on my own.
 
I was originally trying to Zorn things... but the union'd upper bound kept breaking
 
If you want me to see that problem, OK... opens up Hatcher
 
Well, the problem tells you an explicit construction. If you don't want to know it, don't look.
 
Well you were complaining about me not wanting to listen to you, @Mike :P
 
7:34 AM
@Prototank
 
yeh?
 
**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 $\rho(x_\alpha,x_\beta)\geq \textit{d}(x_\alpha)\geq \textit{d}(x_\beta)\Rightarrow x_\alpha\notin f(x_\beta)$.\\
 
I think all of those should be replaced with 1/d
 
Fix $\beta$. For all $\alpha<\beta$ show $x_\alpha \notin f(x_\beta)$.
I think that is all that's needed
 
Hatcher's formulation of the problem is BS
You are really looking at the covering map R \times R^+ \to R^2 - 0
 
7:37 AM
you are just making sure that at each stage of the induction you have a discrete set
 
No you're not.
 
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.
 
@Prototank do you see what I'm saying?
 
That is the action of Z on R^2 - 0
 
I'm processing your statement
 
7:38 AM
@MikeMiller I was referring to Hatcher's stupid action of Z on R^2 - {0}
 
I guess I would include that as part of the induction
 
It results from the well ordering
 
oh maybe I'm wrong
 
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
 
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.
 
7:43 AM
its gross and I don't like it
 
I don't like having to define L_n
 
let me try...
 
and I also don't like saying "Splice in the big guys first! :D"
haha
 
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?
 
7:45 AM
Because $\Bbb R/\Bbb Q$ is indiscrete, and no neighborhood of any point in $\Bbb R$ is non-Hausdorff.
 
oh ok
 
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?
 
is the word enumerate allowed here
ensymbolate
 
yeah I use it in the place of well-order all the time
 
@ForeverMozart I think its cleaner
 
7:48 AM
nope, @skull
 
usually we use "enumerate" when dealing with countable sets.
but here I am enumerating $X$ with $\lambda$ in effect
 
ok :-)
 
sheesh this looks complicated, @Mike
 
@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 $y$
 
ahh. Yes, yours is much cleaner.
its a more readable sentence too
 
7:53 AM
oh wait there is a SES
$1 \to \Bbb Z \to \pi_1(X/\Bbb Z) \to \Bbb Z \to 1$
 
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.
 
Z acts prop disc and freely on X
it's valid whenever X is connected and path connected (i.e., so is X/Z)
 
@ForeverMozart so do you believe the proof?
 
Sure.
 
yes I think so
 
7:55 AM
i guess all we need to do is to show it's abelian. pretty sure it's Z \times Z
 
is this for a topology class?
 
Sure.
 
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.
 
woo got my sumo hat
and the star trek hats ^_^
 
it sounds like a good course
if you are proving theorems like that
I would almost put that into a set theoretic topology course
 
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.
 
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...
 
I would really really like to see some algebraic topology.
I should just crack open a book probably
 
@AlexanderGruber not that I disagree with the decision, but what's up with locking this post? something going on?
 
@MikeMiller I'm afraid that one's classified.
 
I see. 'preciate it.
 
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*
 
I think the chameleon goes well on you, @AlexanderGruber.
 
@MikeMiller It goes with my other hat.
 
I think I dig the teeny lightbulb. It's probably what I'll stick to til I get Bill Lumbergh. Or Waffles.
 
@MikeMiller Eureka works the same as last year, I think: awarded manually by SE staff to those who figured out a secret hat.
 
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.
 
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? :)
 
We'll have to see.
 
I want a top hat
 
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.
 
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.
 
@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.
 
8:15 AM
And you can then retract your reopen vote, I assume?
 
Goodnight everyone. Thanks for the help and input @ForeverMozart
 
You can't. And I wouldn't go out of my way for this hat. Reopening is serious business.
 
no problem, see you later
 
That's a fair point.
 
8:28 AM
This I think is what I was thinking about the other day
 
mm?
 
8:50 AM
Morning all! I just noticed the Winter Bash. Did it start up yesterday? ^_^
 
Greetings
@robjohn are you there? See my proof below.
@robjohn I wonder if Ramanujan had a better proof than mine, just curious to know.
 
9 hours ago @KhallilBenyattou
Greetings
 

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