$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial y}$
Problems with partial derivatives.
show that a distance function is continuous Let $X$ be a metric space with metric $d$. Define $d: X \times X \to \mathbb{R}$, show that $d$ is continuous.  I would like to show that the function is continuous the topology way (since it is a course on topology).   Let $(a,b)$ be a basic open set in $\mathbb{R}$, then $d^{-1}(a,b) = \{(x,y): a&lt;d(x,y)&lt;b\}$. Define $A= \bigcup_{x \in X} B_{b} (x)$, where $B_b (x) = \{y \in X| d(x,y)&lt;b$}. Clearly $A$ is open. Now define $C = \{(x,y):d(x,y)&gt;a \}.$ Essentially I hope that $A \cap C$ is open. But I am stuck in showing that $C$ is open.  Any help please? :) Given a list ["foo", "bar", "baz"] and an item in the list "bar", how do I get its index (1) in Python? Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$. The problem is:  Suppose that $f(z)$ is continuous on a domain $D$ that contains the unit circle, and that $f(z)$ satisfies: $$\vert f(e^{i\theta})\vert \leq M \; \forall \theta \, \in [0, 2\pi )$$ and $$\bigg \vert \int _{\vert z \vert=1} f(z) \text{d}z \bigg \vert =2\pi M $$ show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.  I've tried lots of different approaches such as defining a function $g(z)=\frac{f(z)}{\bar{z}}$ and trying to show that $g'(z)=0$ so that $g$ is constant on the circle, or trying to use some bounding theorems for analytic functions to show that $g$ is constant but this requires $g$ to be analytic. Some other methods were using the Cauchy-Riemann equations but I couldn't find any reason why $g$ should be analytic.  Any help would be greatly appreciated, thanks! I'm trying to split text in a JTextArea using a regex to split the String by \n However, this does not work and I also tried by \r\n|\r|n and many other combination of regexes. Code:  public void insertUpdate(DocumentEvent e) {     String split[], docStr = null;     Document textAreaDoc = (Document)e.getDocument();      try {         docStr = textAreaDoc.getText(textAreaDoc.getStartPosition().getOffset(), textAreaDoc.getEndPosition().getOffset());     } catch (BadLocationException e1) {         // TODO Auto-generated catch block         e1.printStackTrace();     }      split = docStr.split("\\n"); } Why couldn't they omit the Batgirl narratives and scene in The Killing Joke movie? I loved the comic book. I've read it multiple times. And given that the purpose of the book and consequently, the movie, was       for the Joker to prove that anyone can be driven mad simply because of "one bad day", all he needed was the Commissioner right?    Why would they need to have us, as viewers, bond with Batgirl emotionally for around 25-30 minutes, have her frolic around with Batman and try to prove herself to him, etc.?     Sure, you feel deep sorrow for Barbara when she gets shot and molested by Joker. And this obviously is what affects Commissioner Gordon (in part),   But it isn't essential to the crux and the essence of the movie in my opinion (and going by the book, so to speak). Did Sam Liu or Brian Bolland offer any explanation to this end? If $a^\phi = 1$ then the order of $a$ divides $\phi$ Check if a class is derived from a generic class I have a generic class in my project with derived classes.  public class GenericClass&lt;T&gt; : GenericInterface&lt;T&gt; { }  public class Test : GenericClass&lt;SomeType&gt; { }   Is there any way to find out if a Type object is derived from GenericClass?  t.IsSubclassOf(typeof(GenericClass&lt;&gt;))   does not work. I wish to print a Stack&lt;Integer&gt; object as nicely as the Eclipse debugger does (i.e. [1,2,3...]) but printing it with out = "output:" + stack doesn't return this nice result.  Just to clarify, I'm talking about Java's built-in collection so I can't override its toString().  How can I get a nice printable version of the stack? I use Microsoft Outlook 2013 for work and Google Calendar for everything else. I'd like to find an easy way to sync my work calendar to my personal calendar. Ideally, this would be a software application that sits in the background and automates the syncing.  Requirements   Syncing should be one-way only: Outlook to Google. Must support repeating calendar items. Must allow me to specify which calendar in Google to sync to. I will set up a separate calendar for work items. No intermediate server. Export is direct.   Nice to Haves   Automated. Syncs in real time or regularly (say, every fifteen minutes or so). How can Cooper communicate with his daughter before the time he went to space? In the movie Interstellar it's shown that after Cooper fell into the Black Hole, he communicates with his daughter Murph through some codes as Ghost. My doubt is how can he communicate to his daughter before he goes into space? I didn’t get the logic of that part. Can anyone please make it clear? Youtube says "This video is currently unavailable" Correcting for multiple kruskal wallis tests I am running a kruskal wallis test a number of times (37) and wanted to know if I have to adjust the p-values of the kruskal tests before I look any further into the post hocs? My computer wont shutdown If I try to shutdown my computer it simply takes me back to the login-screen. I looked around and found :  Type in terminal:   sudo gedit /etc/default/grub Find the line: GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" Change this to:GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi=force" Save the file and close the file.  Finally, in terminal: sudo update-grub   But now there is a new problem when I try step 5 it says:  *myname*@ubuntu:~$ sudo update-grub [sudo] password for *myname*:  /usr/sbin/grub-probe: error: cannot find a device for / (is /dev mounted?). *myname*@ubuntu:~$    I am new whit linux and dont know what to do. I want to show without using Sylow theorem that     Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)   My attempt: Since $|G|=2p,$ even $\exists~a\neq e\in G$ such that $a^{-1}=a.$ Then $H=\{e,a\}\leq G.$ Let $S$ be the set of all left cosets of $H$ in $G.$ Now $S$ forms a group w.r.t. the composition $g_1Hg_2H=(g_1g_2)H.$ The mapping $\sigma:S\to G:gH\mapsto g$ is an $1-1$ homomorphism. Then $S\simeq\sigma(S)\leq G.$ Thus $G$ has a subgroup of order $p.$  Please tell me whether I'm right!     I'm skecptical as I didn't use that $p$ is prime. If I take a screenshot, often the next action is to paint on it. Sometimes I paint a circle around something, sometimes I blank parts to anonymize them.  Below is an example of the window after the screenshot was taken:    It would be great if I could directly go to "edit image".  BTW, I use Pinta, not Gimp.  I guess this is impossible.  Off-topic but nevertheless relevant:  I know the terms "Wayland", "Xorg", "Gnome".  But my grand mother is a user, not a geek. She does not know these terms. And it would be great, if she could use ubuntu without learning these terms. Rep graph overview thing™ is white (only in latest Chrome) As you can see, if you go to the reputation graph on your profile on Stack Overflow, the bars in the bottom overview will be white. This makes them invisible unless they are selected.  Eeek!  This does not happen on meta or any other site. Also, I cannot seem to reproduce it on others' profile. Possibly a bug only on your own profile? EDIT: I think I've existed for too long. If I change the CSS on one of the bars to stroke: none, then it becomes green. I think the outline is covering the fill because the bars are too skinny. EDIT2: Confirmed hypothesis by reproducing on Jon Skeet's graph. Proposed solution: enforce minimum bar width and add horizontal scrollbar. EDIT3: Can only repro on Chrome 29.0.1547.57 (Official Build 217859) m (the latest version). Norepro on older versions of Chrome, IE9 (winces), all versions of FF, and all versions of Safari. EDIT4: Can be fixed simply by running the JavaScript $('rect').css('stroke-width', '0') or a userstyle rect { stroke: none }. I may make a user[style|script] to fix this. Film where aliens looking like humans are waiting in an airport closed due to snowstorm I saw the movie 6 - 7 years back on cable tv, from the looks of it it seemed to be made in the late 1990's or early 2000's. Unfortunately I could not see the complete movie. The story goes like--   Some people are waiting at a small airport because snowstorm activity has cancelled all flights in and out. There are two children in the group as well (one boy and a girl). Somehow they discover there are aliens looking like humans among them. They decide to check passengers through baggage scanners (checking the skeletal structure via x-ray). They find and kill 2 aliens.   and the big twist:      5. They then realize the two children are also aliens.   any ideas what the name of the movie is ??? How to use JACK and Pulseaudio/ALSA at the same time on the same audio device? Whenever I launch hydrogen it breaks my audio in all other applications which use Pulse, for example, I can no longer play videos in Chrome after having launched Hydrogen once, until I restart my PC or do sudo alsa force-reload. I have found people with similar issues, but no actual guide to fix this, often there are links to  (which has moved to  ) I am using Ubuntu Studio 14.04 64bit.  ALTERNATIVELY if this is truly impossible to achieve, can someone tell me how to use Jack on one soundcard and Pulse on another? This way I could plug in a USB sound card only when I need JACK.  Please don't make me use windows. Inheritance in Java - creating an object of the subclass invokes also the constructor of the superclass. Why exactly? I have a question about inheritance in Java.  I have two classes A and B , and class B, inherits from A:  public class A {      public A() {          System.out.println("Hi!");      } }   public class B extends A {      public B() {          System.out.println("Bye!");      }       public static void main(String[] args) {          B b = new B();      } }   When I run program B, the output is:  Hi! Bye!      Question : why the constructor of class A is invoked, when I create and object of class B ?    I know that B inherits everything from A - all instance or class variables, and all methods, and in this sense an object of B has all characteristics of A plus some other characteristics defined in B. However, I didn't know and didn't imagine that when I create an object of type B, the constructor of A is also invoked. So, writing this:  B b = new B();   creates Two objects - one of type B, and one of type A.  This is getting interesting,   can somebody explain why exactly this happens? I have a question about something I'm wondering about. I've read somewhere that L'Hopitals rule can also be applied to complex functions, when they are analytic. So if have for instance:  $$ \lim_{z \rightarrow 0} \frac{\log(1+z)}{z} \stackrel{?}{=} \lim_{z \rightarrow 0} \frac{1}{(1+z)} = 1 $$  Now i'm wondering if this is correct? Also if we take $|z|&lt;1$, is it then correct?  Thanks,