Prove that sum of product of binomial coefficients is equal to 0
Asymptotic of a sum involving binomial coefficients
Java Access Denied When I'm on my mod site I have my diamond dropdown:    But on Meta.SE and other sites, I have the StackBurger:    This doesn't show on my mod site, so I can't switch between sites easily. How do I put an image texture on a material in Cycles? I am creating a model of a glass and I would like to put a drawing on it (a png picture).  I know how to do it using Blender Render, but not with Cycles Render. Help :) Which equals operator (== vs ===) should be used in JavaScript comparisons? I'm using  to go through JavaScript, and it's returning many suggestions to replace == (two equals signs) with === (three equals signs) when doing things like comparing idSele_UNVEHtype.value.length == 0 inside of an if statement.  Is there a performance benefit to replacing == with ===?   Any performance improvement would be welcomed as many comparison operators exist.  If no type conversion takes place, would there be a performance gain over ==? Minimum value of $ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $ If $x&gt;0$, $y&gt;0$, $z&gt;0$ and $x+y+z=6$ then find the minimum value of    $$ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $$   Thanks in advance. How does friction stop a car? I'm unable to understand how friction causes motion in cars and also is responsible for stopping them. When it starts the impending motion of tyres is in the backward direction that's why friction is in the forward direction and the car starts moving. But when the car engine turns off, the car stops after some time, but the condition of tyres are the same as in the previous case and friction must be in the forward direction. What is the cardinality of the set of the empty set? Given set $ A = \{  \emptyset   \}$ what is $|A|$? I just learned about sets today in class and I'm unsure how to answer this. $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ Let $f:[a,b]\to  R$ be integrable and continuous on $(a,b)$. Prove that: $$\lim_{h\to 0} \int_a^b\frac{f(x+h)-f(x)}{h} \,\mathrm{d}x = f(b)-f(a).$$  What I've tried so far: make a change of variables, which didn't help. I also thought of using the intermediate value theorem inside the integral, but the function being differentiable is not specified. Any help, tips? Thanks in advance! Proof for Property of Complex Numbers Is the inequality $\lvert z_1 + z_2 \rvert \ge \lvert z_1 \rvert - \lvert z_2 \rvert$ incorrect, where $z_1$ and $z_2$ are any two complex numbers? I need an example to prove that it is. And in case it is correct, can you please give the proof? Thanks for any help. I am currently working on an update of tkz-euclide and new documentation but I just met the following problem. If I compile this code with pdflatex or lualatex and pgf 2.1 (The library babel does not exist with pgf 2.1) then the code compiles fine but with 3.0 pgf I must comment on the call \usetikzlibrary{babel} (pgf doc gives so I recommend to always load this library by saying \usetikzlibrary{babel}).  I'd like to know where the error occurred. Especially I would like to work around this problem.   With \usetikzlibrary{babel} I get the error Latex Error: ./untitled 2.tex:46 Undefined control sequence. l.1 \tkz@line@start  Bug in babel, bug in tikzlibrary{babel} bug in my code. I would like to keep  \usetikzlibrary{babel} but to avoid the error.  %!TEX TS-program = pdflatex \documentclass[a4paper]{article} \usepackage[french]{babel} \usepackage{tikz}  \usetikzlibrary{calc} %\usetikzlibrary{babel}  \makeatletter \pgfkeys{%     tkzdrawline/.cd,     start/.code         =  {\gdef\tkz@line@start{#1}},%     end/.code           =  {\gdef\tkz@line@end{#1}},%     start style/.code   =  {\tikzset{tkzstartstyle/.style={#1}}},%     end style/.code     =  {\tikzset{tkzendstyle/.style={#1}}},%    /tkzdrawline/.unknown/.code ={\let\searchname=\pgfkeyscurrentname\pgfkeysalso{%                          \searchname/.try=#1,/tikz/\searchname/.retry=#1}}}  %&lt;--------------------------------------------------------------–&gt; %                              Draw line %&lt;--------------------------------------------------------------–&gt; \pgfkeys{tkzdrawline/.cd, start/.code       =  {\def\tkz@line@start{#1}},% end/.code         =  {\def\tkz@line@end{#1}}, start style/.code =  {\tikzset{tkzstartstyle/.style={#1}}}, end style/.code   =  {\tikzset{tkzendstyle/.style={#1}}},   /tkzdrawline/.unknown/.code   = {\let\searchname=\pgfkeyscurrentname                                  \pgfkeysalso{\searchname/.try=#1,                                 /tikz/\searchname/.retry=#1}}}%         %&lt;--------------------------------------------------------------–&gt;  \def\tkzDrawLine{\pgfutil@ifnextchar[{\tkz@DrawLine}{%                                   \tkz@DrawLine[]}}%   \def\tkz@DrawLine[#1](#2,#3){%  \begingroup   \pgfkeys{tkzdrawline/.cd,start = {}, end = {}, start style={}, end style={},}   \pgfqkeys{/tkzdrawline}{#1}   \draw[ /tkzdrawline/.cd,#1] (#2) to%     node [at start,left,/tkzdrawline/.cd,tkzstartstyle] {\tkz@line@start}%     node [at end,right,/tkzdrawline/.cd,tkzendstyle] {\tkz@line@end} (#3);  \endgroup  }%   \makeatother   \begin{document}    \begin{tikzpicture}      \node (A) at (0,1) {};       \node (B) at (5,2) {};       \tkzDrawLine[end = {$\alpha$}](A,B)       \end{tikzpicture}  \end{document} One definition of an  is:     An abbreviation formed by (usually initial) letters taken from a word or series of words, that is itself pronounced as a word, such as RAM, radar, or scuba; sometimes contrasted with initialism.   An  is:     A term formed from the initial letter or letters of several words or parts of words, but which is itself pronounced letter by letter.   If I pronounce an initialism, as a word, and not just as letters, does that 'make' it an acronym? My code runs inside a JAR file, say foo.jar, and I need to know, in the code, in which folder the running foo.jar is.  So, if foo.jar is in C:\FOO\, I want to get that path no matter what my current working directory is. Is it worth it to buy an FD-EOS adapter, or is it better to exchange a misbought lens? I recently bought a manual-focus (since manual doesn't bother me) . However, I didn't notice at the time of purchase that it was an FD lens. (I'm a hobbyist; I didn't know Canon had actually changed lens mounts at some point.)  On the one hand, I kind of want to experiment with this guy. And quality FD lenses are relatively cheap on the used market, so if the adapters were worth it, I could probably get more (and more varied) glass. On the other hand, everything I read about the FD-EOS adapters is highly contradictory. As in, some people swear by them, and others think they're outright tripe.  I am still within the exchange period, and can easily exchange this lens for this  that I'd been tossing up about buying anyway, as they are the same price.  Which would be the wiser choice? Is there a better way of getting this result? This function fails if num has more digits than digits, and I feel like it should be in the library somewhere (like Integer.toString(x,"%3d") or something)  static String intToString(int num, int digits) {     StringBuffer s = new StringBuffer(digits);     int zeroes = digits - (int) (Math.log(num) / Math.log(10)) - 1;      for (int i = 0; i &lt; zeroes; i++) {         s.append(0);     }     return s.append(num).toString(); } Support anchor names in posts I admit this feature request is probably somewhat limited in useful scope, but I'm throwing it out there anyway. Inspired by , and because I want to use it on , I'm requesting that name be supported on a tags in posts.  On very long answers, such as the closing/migration guidance answer, this would allow direct linking to the specific closure reason. This would then allow us, when someone , to link directly to the appropriate reason and description thereof.  I recognize the limited scope of this, however, I have seen other long answers that could stand to have that kind of "deep" linking ability as well.  (The original incarnation of this post had either name or id, but preferenced name. Per Koper's answer, which I agree with, I took out the idea of supporting id, because Koper's right -- too dangerous.) ViewParam vs @ManagedProperty(value = "#{param.id}") How do you get the index of the current iteration of a foreach loop? Is there some rare language construct I haven't encountered (like the few I've learned recently, some on Stack Overflow) in C# to get a value representing the current iteration of a foreach loop?  For instance, I currently do something like this depending on the circumstances:  int i = 0; foreach (Object o in collection) {     // ...     i++; } Let $a &lt; b$ and $f:[a, b] \rightarrow \mathbb R$ be a Riemann integral function. Suppose that $f(x) \geq 0$ for all $x \in [a, b]$. I want to show whether $\int_a^bf(x) = 0$ implies $f(x) = 0$ or not, but I'm not sure where to start. I don't know much about Riemann integral functions in general. I only know that $$\underline \int_a^b f= \overline \int_a^b f.$$ Also, I know the fact that if $f$ is continuous, then $f(x) = 0$ for all $x\in [a, b]$. Can anyone provide any hints for me, because I'm really confused about this whole thing. I plan to attach my 2014 and 2015 annual leave letters to prove I was on leave, and a letter from my sales manager who was in charge of the business during my vacation.  I intend to explain all my sources of income in additional letter because the ECO calculations of my income were different from mine.   How else can I improve my new application? When is "self" required? I have been using classes for only a short while and when I write a method, I make all variables reference self, e.g. self.foo.  However, I'm looking through the wxPython in Action book and notice that "self" isn't used all the time. For example:   import wx  class TextFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Text Entry Example',             size=(300, 100))         panel = wx.Panel(self, -1)         basicLabel = wx.StaticText(panel, -1, "Basic Control:")         basicText = wx.TextCtrl(panel, -1, "I've entered some text!",             size=(175, -1))         basicText.SetInsertionPoint(0)         pwdLabel = wx.StaticText(panel, -1, "Password:")         pwdText = wx.TextCtrl(panel, -1, "password", size=(175, -1),             style=wx.TE_PASSWORD)         sizer = wx.FlexGridSizer(cols=2, hgap=6, vgap=6)         sizer.AddMany([basicLabel, basicText, pwdLabel, pwdText])         panel.SetSizer(sizer)   The one below does use "self".  import wx class ButtonFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Button Example',             size=(300, 100))         panel = wx.Panel(self, -1)         self.button = wx.Button(panel, -1, "Hello", pos=(50, 20))         self.Bind(wx.EVT_BUTTON, self.OnClick, self.button)         self.button.SetDefault()     def OnClick(self, event):         self.button.SetLabel("Clicked")   If I remember correctly, "self" is reference to a particular instance of the class, so when is it not necessary? Is there a general rule of thumb?