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12:36 AM
Parseval's identity: $\sum_{n=-\infty}^{\infty}\lvert a_n\rvert^2=\lVert f\rVert^2$

How does one get $\sum_{n=-\infty}^{\infty}\lvert n\rvert^2 \left (\lvert a_n\rvert^2+\lvert b_n\rvert^2\right)=1$, by applying Parseval's identity to $\frac 1 {2\pi}\int_0^{2\pi}(x'(s)^2+y'(s)^2)ds=1$
 
12:56 AM
Hi chat
 
@KasmirKhaan hi
 
1:21 AM
@EricSilva Hey I have a question for you
 
1:34 AM
is it quick im v busy rn
 
probs not, can a stable totally geodesic minimal surface have singularities
 
no clue off the top of my head
 
2:03 AM
If somebody here wants a challenge, see this question: math.stackexchange.com/questions/2752487/…
 
What's a good intro topology book that proves alexander duality?
 
Hi. If I have 3 vectors a, b and u and a triple inner product ((a.u).b).a
is it acceptable to say something like a.u = |a||u|cos(a,u) a real number
so it becomes |a||u|cos(a,u) . a . b ?
 
@user537566 If you can't answer this question, then you might as well forget studying Alexander duality.u
 
@user330477 What question?
 
2:17 AM
@user330477 What's that question got to do with me? Isn't it your question?
 
@user537566 Yes, so what? If you help me with this, I will give you a good book recommendation
 
I'm still not convinced that all the "user######" anons aren't actually all the same person
2
 
@AkivaWeinberger It's all me! Two of my personalities are clashing right now due to a glitch!
 
multiple personality disorder.
 
2:33 AM
@0celo7 Stop putting your butt in other people’s affairs.
 
lol
 
@0celo7 puts his butt wherever he pleases. We have learned to get out of the way.
 
im a thicc boi
 
@0celo7 I apologise on behalf on my other personality. It's an issue that we're working on.
Nice butt, though.
 
2:37 AM
thank you
 
i like big butts and i can not lie
 
:D
 
How big are we talking.
 
refer to picture
 
@user537566 I am not your other personality.
 
2:40 AM
lol
 
@0celo7 Stop posting nonsensical and obscene photos or else.
 
bwahahaha
 
@user330477 relax
 
looool
 
someone thinks that you are being offensive @0celo7
 
2:41 AM
@s.patroller who are you to support him?
 
stop doing that, so that I can go back to ignoring flags
 
Lmao I was flagged?
 
@user330477 why not?
he's my pal
 
Also, to whoever was doing the flagging, Sir Mix a Lot hasn't been offensive since the 80s
(also, it took me way too long to Google whether or not Sir Mix a Lot should be hyphenated---based on his official website, it is correct as I have written it above)
 
oh come on, what is with these troll flags
 
2:43 AM
enough with the flags, children, before the mods show up
 
@user330477 Don't give up on me now! We've only a few more therapy sessions to go.
 
@XanderHenderson too late :(
 
Guys, enough...
2
 
Flags, flags everywhere.
 
"Anon" is actually what I'm gonna name my first child
"Untitled 1" is what it should be really
 
2:47 AM
This user has been automatically suspended for posting inappropriate content and cannot chat for 26 minutes.
 
It seems that one cannot counter-flag flags on their own content... that seems fair.
 
@AkivaWeinberger I didn’t expect this from the moderator. Just shows how incompetent this site has become.
 
Like, someone actually thought about the design of this chat!
but we still don't have basic IRC functionality :(
 
I've no idea what happened.
 
1 min ago, by s. patroller
This user has been automatically suspended for posting inappropriate content and cannot chat for 26 minutes.
 
2:49 AM
import IRC
 
/me shakes his fist a the sky, and shouts that these damn kids to get offa his lawn.
 
I need to do import Python first actually
 
#include IRC.h
does that work?
or maybe $\usepackage{IRC}$
 
I'm going to ask you to stop. This is getting out of hand.
I don't care if you're joking, it looks really horrible.
 
6
Q: What is a 'wavicle?'

Paul FitzSimonsWhat is a wavicle? I learned in electronics class that electrons are little particles. In physics they even say that the electron orbits the nucleus thus exhibiting angular momentum. But in chemistry they were little electron clouds. And physics deals with position and momentum in a probabilistic...

fun question^
:-)
he left
 
3:01 AM
Oh no
For a few seconds I had the upper hand.
 
Jekyll^?
 
22 messages moved to Trashcan
 
I am very confused at what happened here
 
This user has been temporarily suspended by a moderator and cannot chat for 59 minutes.
 
Thank you!
 
3:04 AM
When I ask someone to stop... I mean it. Have a good evening.
 
Consider $\displaystyle I = \int_0^1 \frac{\log(- \log(x))}{1+x+x^2}\mathrm{d}x, ~~ J = -\frac{1}{2}\int_0^1 \frac{\log(- \log(x))}{1-x+x^2}\mathrm{d}x$; what's $I+J$?
 
@Catija Stop doing what
 
Does anyone know whether this or a variant of this had been asked in the forum?
 
Were people flagging stuff?
 
3:06 AM
No, the geezer that came here to fight (strange enough) I think.
 
I mean, all I saw was everyone essentially acting normally, and him saying "fight me" for no reason
 
Lol I thought I was gonna get banned because our usernames are similar.
 
I said, jokingly, that I would name my first kid "Untitled 1", and he said "I do not expect that behavior from a moderator"
and I can't see what else I said that he could have been replying to
 
yeah, strange...
 
I thought I was gonna get booted out because of the similar usernames lol.
 
3:11 AM
...just some drive-by "user"
 
Yeah. Now it has changed.
 
welcome back @0celo7 :-)
 
What the hell was that
How could I get suspended for posting a clothed, nonsexual picture
 
it said "automatic" suspension
his says "by a mod"
 
The butt was too irresistible.
 
3:20 AM
he likes a juicy one
maybe he's in denial
 
conservatives can view anything as offensive
 
Lol he hates liberals too
@user330477 we could be allies ;)
 
can we be friends @user330477?
 
Guys, my personality won. Sorry, but @user330477 is no more!
 
so that was you?
 
3:25 AM
No, it was my other personality @user537566. It's...complicated.
 
just like life
 
Tell me about it.
 
3:28 AM
loool Classic repost then!
 
I clicked on your linked question and understood nothing but liked this! xD
 
the last answer is good
> In my first year of college teaching I watched a freshman chemistry student asked a recent Harvard Ph.D. how the electron in one lobe of a p-orbital could get to the other lobe if there was zero electron density at the node? The brilliant professor was stumped, and I felt bad for him. But I used that story for years to encourage my students who were also stumped, and to help them realize: "You're thinking about it all wrong: they're not particles! And they're not waves! They're wavicles!"
 
Very interesting!
 
if i say
can we settle this via email
to my teacher
is that consider not respectfull ?
he asked if we could meet at a particular time and i cant that time
 
3:33 AM
sounds ok to me
 
thanks patroller
is there other word
for settle this via email ?
 
set up a time via email
 
by that i mean , another way to say that :D
 
Can we do this via email?
 
no no i only meant this particualr thing we have to do
okay thanks multi :D
but settle and do
 
3:34 AM
Could we do this via email?
 
are the same meaning
because i learned that word when gangsters on the movies settle their issues
so it sounded very bad at first to me :D
 
"settle" is informal
 
It's all about context.
 
aha =p
okay I think ill go for could we do this via email
 
i would use "set up" a time
 
3:36 AM
thanks guys :D
 
I'm usually overly polite in emails, which can be just as uncomfortable as reading a rude email I imagine.
 
 
1 hour later…
4:51 AM
How can we prove these?
Is the proof of any one of them understandable (at high school level)?
 
@Abcd google taylor expansion, i think it can be understood at high school level , just computational stuff, it is just derivatives but not only first order, second order etc
@LeakyNun hey leaky :D
 
@KasmirKhaan Interesting, how did they get this^
 
@Abcd you know that one can approximate any function with a line right?
 
@KasmirKhaan no
 
but if we want a better expansion we need more than a line
okay
you know what a tangent is+
 
5:00 AM
yes
 
tangent to a curve e.g y =x^2
 
y=2x
 
if you draw a tangent line at the point ( 2,4 )
 
y = 4x
 
if you now look at a very very small intervall on the line near the point (2,4)
the line and the function y=x^2
behave kinda the same
but if we go far a way, the line and the curve arent close to each other anymore
you are right about y=2x +m part
that tangent line will have the slope = 2
but the y - intersept will be a bit below 0
but we only care about the nighberhood of the tangent line
the basic idea is, you take any function , and you want to find the y value of it, approximate that y-value
 
5:04 AM
Okay then?
 
what you do is take a tangent like to it at that point , and then you can approximate near by points
lets take a better function such as sqrt (x)
we know the sqrt (9) = 3
 
ok
 
but we dont know sqrt (10 ) right+
what we do here, we take a tangent line at the point (9,3)
 
yes
 
and from it , we can approximate the point (10 , y)
we just read on the x axis , x=10
and see how high the line is at x=10
this ofc will just be a line approximation
the line and the curve wont differ by much since we just went 1 unit
but if we try to approximate sqrt (20 ) with that point (9,3)
this will give us a very bad approximation
 
5:07 AM
yes
 
so far so good?
so from there, we can do better approximation
 
\yes
 
using second derivaties and third and etc
 
@KasmirKhaan why?
Didnt get that part
 
there is no stop for this, each derivative we take at that point will give us a better and better approximation
 
5:08 AM
how?
 
because we will apprixmate our function now with a second degree poly and third , which they will agree better and better with our function
a line approximation is easy but not very good
the more derivatives we take, the better the polynomial approximation will be
 
We tool y = x^2
y'= 2x
y''= 2
y'''= 0
Now?
 
well the first example is not what this is used for =p
because y=x^2 is allready perfect :D
we need to take a non poly function
e^x
ln x
etc those we can approximate by polynomilas
 
sin x
y' = cos x
 
becaue polys are easy to work with
 
5:11 AM
y'' = - sin x
 
yes now you getting it
 
y'''= -cos x
 
ok now loook at the taylor expansion for sin x
 
@KasmirKhaan Why?
 
why ?
 
5:11 AM
2 mins ago, by Kasmir Khaan
the more derivatives we take, the better the polynomial approximation will be
I didnt get this part
 
okay a line is a first degree polynomial
it is stright
but in general our cuves are more complicated and curvy
to capture this, we need to take higher order polynomials
okay do this on a papper
draw any exponential function, and draw a tangent line to it
 
then
 
you will see after a little bit from that point , the line and the exp function will be very far from each other
 
yes
 
now draw a parabola at the same point
the para will follow the exp a bit better than the line
that is the basic idea
 
5:15 AM
y'' gives the rate of change of slope but
How is that related to degree of polynomial
 
there is no need to think about that part
just look at it this way
each function, no matter what it is , it can be approximated using a polynomial
the higher degree of the poly , the better it is approximation this function
 
Yes then?
 
then you get taylor expansion of that function
the ones you just posted a pic of
 
ok thanks
 
np it is not that hard, when you do calculus you will understand this better
but for high school that is enough, you can now do the computational sutff and not worry about the theory of it
allthought the theory also is not that hard
 
5:21 AM
Where it says "students are advised to learn these expansions" they mean memorize @Abcd
The more terms you use, the better the approximation.
 
5:40 AM
Actually:
This is amazing.
I understood all of it.
 
cool
 
Isa
6:00 AM
Why the roots of $r^4=w^4$ are $r_{1,2}=\pm w$ and$ r_{3,4}=\pm iw$? with w>0. I thought it was just r=w.
Does someone here has experience with PDEs ??
 
6:34 AM
Fundamental theorem of algebra, thus it has 4 roots
plug those back in and you will see it solves the equation
 
I know that $\{e^{in}:n\in\Bbb N\}$ is dense in unit circle in complex plane. For what values of $\theta$, is the set \{e^{in\theta}:n\in\Bbb N\} dense in unit circle?
 
@Silent should be anything which isn't a rational multiple of $\pi$
 
6:50 AM
@Daminark thanks for your reply. why is that?
@Daminark, i see that if $\theta$ is rational multiple of pi, then $e^{in\theta}$ is $-1$ for some power. and they may be equal for different n's.
 
7:10 AM
@Daminark, oh! is that because if $\theta$ multiple of $\pi$, then $\{e^{in\theta}:n\in\Bbb N\} $ can take only finitely many values?
 
7:25 AM
useful complex plotter
 
@Secret nice
 
@Silent sorry I was out but the idea there is that if you rotate by a rational multiple of $\pi$ you end up being periodic
So yeah if you look at, say $e^{i\pi n\theta}$ for some $\theta = \frac{p}{q} \in \mathbb{Q}$, then for $n = 2qk$, you hit $1$
Then you just repeat
So there are only those values
Now, turns out the converse is true, if you are choosing $e^{i\pi n \theta}$ where $\theta\notin\mathbb{Q}$, the orbit should be dense
For this, note that you can identify the circle as $\mathbb{R}/\mathbb{Z}$, just using the exponential map, so you try to think about the stuff using addition mod 1
So okay, if you assume the orbit is a finite set, then you can find some $x$ such that $x = x + n\theta$ mod 1
But yeah since $\theta$ is irrational and $n > 0$ you're in trouble
So if your angle is irrational, your orbit is infinite, but by compactness there's a limit point, meaning you can find $x + n\theta$ and $x+m\theta$ within $\epsilon$ of each other, but then $(n-m)\theta$ is gonna be $\epsilon$-dense
 
7:54 AM
I want to examine the convexity of the following set $\{(x_{1},x_{2}):x_{2} \le e^{x_{1}}\}$, checking the graph i can see that it is not convex, but how can i check it in theory (method?). Most questions i found online were about functions with equality (like $f(x,y)=$ something), but here it is an inequality, how can i solve this?
In equalities i can use hessian matrix, what to do here?
 
8:11 AM
@Daminark I am so thankful for this elaborate reply.
 
8:35 AM
hello
@TobiasKildetoft hello
 
@Vrouvrou Hi
 
please can you see this question : math.stackexchange.com/questions/2752199/…
i think that the set of limits is $\{(x,y)\in \mathbb{R}^2, (x+2)^2+(y-2)^2\geq \sqrt{8}\}$ and not just
$\{(x,y)\in \mathbb{R}^2, (x+2)^2+(y-2)^2=\sqrt{8}\}$
what do you think about that ? @TobiasKildetoft
Have you an idea @TobiasKildetoft
 
@TobiasKildetoft, Conway says: " An open set $G\subset \Bbb C$ is connected iff for any two points a, b in
G there is a polygon from a to b lying entirely inside G.
" Can't we say this about any set $G\subset \Bbb C$?
 
8:51 AM
@Vrouvrou I don't really feel like thinking about topology right now
 
@Silent no, for example pick a circle for $G$
 
@mercio oh, ok. So, in metric space, a subset connected iff path connected, but polygonally connected may not hold, right?
 
no
there are also some connected subsets that are not path connected
 
Hi. Does anybody have an idea how I can show that the closure of a set $Y$ is closed without using limit points? My definitions are $\partial Y= \{x \in X \mid \forall \varepsilon \gt 0: B_\varepsilon(x) \cap Y \neq \emptyset \neq B_\varepsilon(x) \cap (X \setminus Y) \}$ is the boundary of $Y$, and $\overline Y = Y \cup \partial Y$ is the closure.
 
Can some one confirme me that the limits of $(\frac1n,0)$ are all $(x,y)\in \mathbb{R}^2$ such that $$(x+2)^2+(y-2)^2\geq 8 $$? here : math.stackexchange.com/questions/2752199/…
 
9:00 AM
and what is the definition of closed ?
yes @vrouvrou
 
A set is open if for every point in the set there is an $\varepsilon$-ball around that point which is contained in the set
and closed if complement open
Though I know the result that a set is open iff every convergent sequence whose limit is in the set has almost all of its elements in the set and a set is closed iff every convergent sequence which has all its elements in the set also has its limit in the set
does that help me?
 
@mercio my answer is correct right ?
 
yes
 
yes for me @mercio or for philmcole ?
 
hi guys, if $A \subset X$, $A$ convex and absorbing and $X$ vector space. Defining with $\mu_A(x) = \inf \left\{t : t^{-1} x \in A \right\}$ why is $\mu_A(sx) = s \mu_A(x)$, if $s \geq 0$?
in my book it is just said "it's obvious"
i don't see why
 
9:22 AM
@mercio ?
 
9:51 AM
26
Q: Shapes for an infinite animal?

SilverCookiesThis creature exists in an infinite world, a flat landscape that extends ad infinitum, where light rains from the sky from infinity during recurrent day-night cycles, and, similarly, the ground goes down continuously. All kinds of critters populate the cosmos including the skies and the undergro...

 
the worldbuilding.SE is completely bonkers
 
An organism with the shape of a network is really the most reasonable choice, since an infinite organism has to have all its digestive system and whatnot to be everywhere in order to not starve to death
which is why fungus sounds natural
You cannot have a infinite but bounded organism as approaching the limit, the thickness will soon become so small that its physical effects no longer matter
 
10:30 AM
Anyone who can help me with the "<=" part of a proof regarding linear algebra? math.stackexchange.com/questions/2752781/…
 
 
2 hours later…
12:54 PM
@Sirmimer the set M you introduce at the start of the question seems like a non sequitor
 
1:38 PM
Graph theory has like 9000 definitions wtf
 
graph theory has as many definitions as it has weird examples
and it's got a lot of weird examples
 
feels like topology :P
 
But topology is completely natural
 
Lies. Bornology is completely natural. Topology is silly.
Can I get an "AMEN!"?
 
Large scale shill
 
1:56 PM
Pft... "Big Topology" just wants you to believe that. At least bornologies can reasonably bound "Big Topology" and keep it in check.
And we all know that "Big Topology" has been in BED with the NSA for decades!
 
@XanderHenderson what does nonstandard analysis have to do with this
 
HA!
I was trying so hard to act all conspiracy-theorist with a straight face, but I just can't even respond to that last one.
It is too perfect
right... time to go
laters
 
bye
 
2:14 PM
Hey folks
Given a Grassmann algebra with an infinite number of generators
DeWitt says that there are non-nilpotent bodies in it
but gives no proof for it
Is that correct?
ie there are elements $$z = z_i \theta^i + z_{ij} \theta^i \theta^j + ...$$
such that $z^2 \neq 0$
this is false for any finitely generated Grassmann algebra, so I'm not sure how to prove it
might be useful
"If $\Lambda$ is infinit then there exists an infinite set of idempotent set of pairwise orthogonal idempotents"
 
2:37 PM
yo
trying to plot pos from spherical coordinates. In need of maybe a link to some info.
 
user131753
3:17 PM
0
Q: Homeomorphism via map between topologies

user 170039Background Theorem. Let $(X,\tau_X)$ and $(Y,\tau_Y)$ be two topological spaces and $f:(X,\tau_X)\to(Y,\tau_Y)$ be a homeomorphism between them. Then there exists a bijection $\varphi:\tau_X\to\tau_Y$. Sketch of the Proof. Define $\varphi:\tau_X\to\tau_Y$ by $\varphi(U)=f(U)$. Then the m...

 
user131753
@AaronHall: Sorry for bothering. I didn't read the earlier messages.
 
A noncommutative maze where you must found the starting point in order to transverse all the box
 
3:33 PM
@user170039 ok - sometimes images can be disruptive in chat, so the least destructive thing I could think of was to un-one-box it. Everybody please be respectful of each other. :)
 
I am confused on what happened here, what "earlier messages"?
 
@Secret I don't see why $\ce{SF2 } = 98^\circ$ and $\ce{HOF}= 97.2 ^\circ$ (bond angles)
I was expecting SF2 to be lesser
due to rehybridisation to $\ce {sp^{\approx 4}}$ owing to greater EN difference.
 
3:52 PM
S has a lot of electrons, I will expect the repulsion to be larger, whereas H ad F is tiny
 
Alfohrs is defining a family of functions that "uniformly converges to infinity" as uniformly convergent. Is that a common convention?
or is it weird
 
@Secret But there are only two lone pairs in both S and O. Sorry for disturbing, could you just elaborate a lil bit.
 

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