How to show that $f_n(x) \to f$ pointwise?
Prove that $f_n$ converges uniformly on $\mathbb{R}$
When programming interfaces, I've found I'm doing a lot of casting or object type conversion.  Is there a difference between these two methods of conversion?  If so, is there a cost difference or how does this affect my program?  public interface IMyInterface {     void AMethod(); }  public class MyClass : IMyInterface {     public void AMethod()     {        //Do work     }      // Other helper methods.... }  public class Implementation {     IMyInterface _MyObj;     MyClass _myCls1;     MyClass _myCls2;      public Implementation()     {         _MyObj = new MyClass();          // What is the difference here:         _myCls1 = (MyClass)_MyObj;         _myCls2 = (_MyObj as MyClass);     } }   Also, what is "in general" the preferred method? How to show this equality of $\rho(X,Y)$ Let I have $(S,\Sigma,\mu)$ be a probability space, then $X,Y \in \Sigma$. Define $\rho (X,Y)$ by $\rho (X,Y)$ = correlation between random variable $I_X$ and $I_Y$, where $I_X$ and $I_Y$ are the indicator function of $X$ and $Y$. Express $\rho (X,Y)$ in term of $\mu (X)$, $\mu (Y)$, $\mu(XY)$. Conclude that $\rho(X,Y)=0$, if and only if $X$ and $Y$ are independent.      How to show that: $$\rho(X,Y)= \frac{\mu(XY)\,\mu(X^cY^c)-\mu(XY^c)\,\mu(X^cY)}{(\mu(X) \,\mu(X^c)-\mu(Y) \,\mu(Y^c))^{1/2}};0&lt;\mu(X)&lt;1;\,0&lt;\mu(Y)&lt;1$$ Modifying agsm.bst package bibliography output I would like to change the URL output from:  URL: the html link  into:  [Online]URL: [Accessed on]  I am using:  \usepackage[comma]{natbib} \bibliographystyle{agsm} sed : Ignore line starting whitespace for match how to set camera to the same view as I turn my cursor? I want to turn the camera to get the view I want, but everytime I turn the camera, I need to go to render window to check if it's the view I want. I turn the view with my mouse cursor, but that does not affect the actual camera view in rendering, can I set the camera view the same as I turn my cursor? What is the "rootless" feature in El Capitan, really? I have just learned about the "Rootless" feature in El Capitan, and I am hearing things like "There is no root user", "Nothing can modify /System" and "The world will end because we can't get root".  What is the "Rootless" feature of El Capitan at a technical level? What does it actually mean for the user experience and the developer experience? Will sudo -s still work, and, if so, how will the experience of using a shell as root change? Please add TeX rendering in titles on the iOS app TeX support works fine in question and answer bodies, and comments can be rendered manually by tapping and selecting Render MathJax. See related question .  However, the titles are not rendered which makes the browsing experience less than perfect. See screenshot below.   Are there any plans to implement MathJax support in titles?  (I'm running Stack Exhange iOS App Version 1.0.0 on an iPhone 4S with iOS 7.1.1)    EDIT: I was just informed about  asking for the same functionality for the Android app. I guess I shouldn't hope too much then... Why is it considered a bad practice to omit curly braces? Why does everyone tell me writing code like this is a bad practice?  if (foo)     Bar();  //or  for(int i = 0 i &lt; count; i++)     Bar(i);   My biggest argument for omitting the curly braces is that it can sometimes be twice as many lines with them. For example, here is some code to paint a glow effect for a label in C#.  using (Brush br = new SolidBrush(Color.FromArgb(15, GlowColor))) {     for (int x = 0; x &lt;= GlowAmount; x++)     {         for (int y = 0; y &lt;= GlowAmount; y++)         {             g.DrawString(Text, this.Font, br, new Point(IconOffset + x, y));         }      }  }  //versus using (Brush br = new SolidBrush(Color.FromArgb(15, GlowColor)))     for (int x = 0; x &lt;= GlowAmount; x++)         for (int y = 0; y &lt;= GlowAmount; y++)             g.DrawString(Text, this.Font, br, new Point(IconOffset + x, y));   You can also get the added benefit of chaining usings together without having to indent a million times.  using (Graphics g = Graphics.FromImage(bmp)) {     using (Brush brush = new SolidBrush(backgroundColor))     {         using (Pen pen = new Pen(Color.FromArgb(penColor)))         {             //do lots of work         }     }  } //versus using (Graphics g = Graphics.FromImage(bmp)) using (Brush brush = new SolidBrush(backgroundColor)) using (Pen pen = new Pen(Color.FromArgb(penColor))) {     //do lots of work }     The most common argument for curly braces revolves around maintance programming, and the problems that would ensue by inserting code between the original if statement and its intended result:  if (foo)     Bar();     Biz();     Questions:   Is it wrong to want to use the more compact syntax which the language offers? The people that design these languages are smart, I can't imagine they would put a feature which is always bad to use. Should we or Shouldn't we write code so the lowest common denominator can understand and have no problems working with it?  Is there another argument that I'm missing? Disable chat migration notification if one of the users has insufficient rep? A smooth vector field on $S^2$ vanishing at a single point I need to find a vector field as described in the title.  I was given a couple hints, and this is what I have so far. Let $\varphi:S^2\setminus\{N\}\to\mathbb{R}^2$ be stereographic projection ($N$ is the north pole). Let $Y$ be a smooth, non-zero vector field on $\mathbb{R}^2$ that dies off to $0$ "at infinity." Since $\varphi$ is a diffeomorphism, we can push $Y$ forward along $\varphi^{-1}$ to get a smooth vector field $(\varphi^{-1})_*Y_{\varphi(p)}$ on $S^2$. But this vector field is not zero at the north pole... it's undefined. So can I just define my vector field on $S^2$, call it Z, to be the pushforward of $Y$ (as above) away from $N$ but $0$ at $N$? And if so, do we still have smoothness? Zooming in to inspect texture details in 3D view clips some closer faces like shown in the image. It's not the camera view so changing camera settings doesn't help.   Where can the distance to the clipping plane be adjusted? In which situations is it OK to omit articles in short sentences? Recently, in many new online software I often see that developers omit articles in short sentences, especially on action buttons or tooltips.     For instance: "Add new task" (not "Add a new task"), "Create project" (not "Create a project"), but often in the same software I can see "Make a copy". What are situations it can be justified? When to use "click" and "click on" What amp rating of 24vac transformer for LM317T? I want to know what size transformer for LM317 at full 30 VDC. I know its a 24 VAC center tapped transformer but is 1 A or 5 A transformer best suited for a linear power supply of 1.5-30 VDC?  I will be using a standard LM317 variable power supply circuit with the 2200 uF 50 V smoothing and the 240 ohm drain resistor and potentiometer. I have a homemade oversized aluminum heat-sink that is quite large. Why is my USB drive showing corrupted data when plugged as an internal SATA drive? I have a 3TB Seagate Backup Plus Desktop USB 3.0 drive, which works fine when in its enclosure, but when I get it off its enclosure and directly plug it as an internal SATA drive, it's just not properly recognized (it works again when used in the enclosure). My systems’s motherboard is an , which has two SATA 6.0 Gb/s and four SATA 3.0 Gb/s ports.  When used as an internal SATA drive Windows 7 asks if I want to format the drive, as if it didn’t have a proper filesystem, and if I use the DISKMGMT.MSC tool (typing that in the start menu) I get completely wrong information about the drive.  It says the drive has 3 partitions (349,31GB of RAW data and two unassigned partitions of 1698,68GB and 746,52GB). This information is plain wrong, since the drive, when used in the USB enclosure, works as a single NTFS partition (2794,52GB). How come it’s shown as 3 partitions without filesystem when connected through SATA?!  Is Seagate using some proprietary way of storing the data when using the drive in its provided USB 3.0 enclosure? I didn’t use any kind of encryption. I just plugged the drive with USB 3.0 and started using it straight away, since it apparently came pre-formatted with an NTFS filesystem. Can suspended users post comments? Get notifications? What happens to their reputation? How can I correct a reviewer's opinion? My edit to an answer was accepted by two of the three reviewers, with the third rejecting with a claim that part of my edit was incorrect.  In fact, my proposed edit was entirely and demonstrably correct, and the reason given for rejecting is invalid.  How can I let that reviewer know about their error, and have them change their review to "Accept" - changing stats for both of us?  Please note:  This is not the same question as asking for an appeal of an edit that was rejected.  It's asking what I can do about one of the three reviewers, a dissenter who voted against my edit based on their incorrect information. How can I update all Snap packages? I know that I can update a snap package using  sudo snap refresh &lt;package&gt;   But is there a way to update all snaps, like   sudo apt dist-upgrade With biblatex, is it possible to replace one author of an author list by a bibnamedash or idem string? With biblatex, the author can be replaced by a dash (or “idem”) in the bibliography. Is it possible to have this replacement also if there are multiple authors, and the first of these multiple authors is the same as the author of the book listed before? (It is somewhat difficult to describe, see the attached example instead, where “Buchautor, Hans-Wilhelm” should be replaced in book3 as well.)   I assume that it should be possible by customising \DeclareNameFormat, but I don’t know how.  Minimal example:  \documentclass{scrartcl} \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} \usepackage[english]{babel} \usepackage{csquotes} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @BOOK{book1,   author = {Buchautor, Hans-Wilhelm},   title = {Irgendein Buch},   location = {Buch am Wald},   date = {2000} } @BOOK{book2,   author = {Buchautor, Hans-Wilhelm},   title = {Ein anderes Buch},   location = {Berlin},   date = {2001} } @BOOK{book3,   author = {Buchautor, Hans-Wilhelm and Zweitautor, Zoran},   title = {Noch ein Buch},   location = {London and New York},   date = {2010} } \end{filecontents}  \usepackage[ style=authortitle, backend=bibtex8 ]{biblatex} \bibliography{\jobname}  \renewcommand*{\bibnamedash}{%   \bibstring[\mkbibbold]{idem\thefield{gender}}}  \begin{document} \nocite{*}  \printbibliography \end{document}   Edit 15/02/2011 17:14   I should have added that there was a feature request for biber which pointed back to biblatex. See .  Edit 21/06/2011 9:26  Is this somehow possible now with biblatex 1.4/1.5? I played a bit with uniquename/uniquelist, but I could not get it to work. Merge two PDF files containing even and odd pages of a book I have two searchable PDF  documents, say even.pdf and odd.pdf which contain even and odd pages of a book, respectively.   I can decompile each PDF to separate files 001.pdf 002.pdf 003.pdf, et cetera. The question is how to merge them?  They are both even and odd sequences numbered 1, 2, 3. If the numbering in the decompile process with pdftk were different, e.g. 1, 3, 5 for even and 2, 4, 6 for odd instead of 1, 2, 3, 4, I could simply merge them.  Can I do this any other way?