difference between property with empty accessor or without accessor?  // Property with empty accessors public string Name { get; set; }  // Property without accessor public int Counter;   edit:  what implications beyond the compiler's statement implies such
I see a lot of example code for C# classes that does this:  public class Point {     public int x { get; set; }     public int y { get; set; } }   Or, in older code, the same with an explicit private backing value and without the new auto-implemented properties:  public class Point {     private int _x;     private int _y;      public int x {         get { return _x; }         set { _x = value; }     }      public int y {         get { return _y; }         set { _y = value; }     } }   My question is why. Is there any functional difference between doing the above and just making these members public fields, like below?  public class Point {     public int x;     public int y; }   To be clear, I understand the value of getters and setters when you need to do some translation of the underlying data. But in cases where you're just passing the values through, it seems needlessly verbose.
POSTFIX main.cf permission denied I am trying to set up a postfix server for smtp relay. Centos 5.5  I have followed  but am getting a FAILED error when trying to restart or reload postfix.  When I do:  cat maillog   I get:  fatal: open /etc/postfix/main.cf: Permission denied   Here is what I have tried:  chown postfix /etc/postfix/main.cf chmod u+rwx /etc/postfix/main.cf   After that, I do:  ls -l /etc/postfix/main.cf   Which gives me:  -rwx------. 1 postfix anotheruser 27531 Apf 29 12:19 /etc/postfix/main.cf   No dice. Same error. I even tried temporarily doing chmod 777 but got same error.  Any ideas on the permissions problem? I am assuming it is running the service as the postfix user.  Thanks Which way is up? (electric outlet) My house has electric outlets in both orientations.  Which one is correct?  Should the ground hole be at the bottom or the top?    OR How do the Chitauri "ships" propel themselves? In the 2012 The Avengers film, the Chitauri army arrives through the portal along with these big robot alien whale Chitauri dudes. Here's one chasing Iron Man:  These guys basically swim through the air like... giant robot alien whales. I don't see any means of propulsion. Other, more humanoid Chitauri soldiers fly around on things that seem to be mechanical &quot;speeders&quot; of sorts. What are these guys? Are they ships, creatures, or both? Is there an explanation anywhere in the Avengers universe for how they defy gravity and swim through the air? Setting controller variables not reliable from apex:commandButton I'm trying to set a variable inside my controller via an actionFunction, which is called by some Javascript, which is initially called by either by an actionPanel (with styleClass='btn') or a commandButton.  If the caller is the actionPanel then the variable updates reliably. However with the commandButton I can see the updated value flash briefly before reverting to its previous value. Maybe one out of every six clicks of the button actually causes the new value to stick. Sometimes it can take a dozen or more tries, regardless of click frequency.  Can someone please explain what's going on here?  PAGE  &lt;apex:page controller="MyController"&gt;     &lt;apex:form &gt;         &lt;apex:outputPanel id="panel"&gt;             &lt;apex:outputText value="MyString = {!MyString}"/&gt;             &lt;apex:actionFunction name="SetString" rerender="panel"&gt;                 &lt;apex:param name="param1" value="" assignTo="{!MyString}"/&gt;             &lt;/apex:actionFunction&gt;             &lt;script&gt;                 function JSetString() {                     SetString('{!MyString}' + '.');                 }             &lt;/script&gt;             &lt;apex:outputPanel onclick="JSetString()" styleClass="btn"&gt;                 Grow {!MyString} (works)             &lt;/apex:outputPanel&gt;             &lt;apex:commandButton onclick="JSetString()" value="Grow {!MyString} (unreliable)" rerender="panel"/&gt;         &lt;/apex:outputPanel&gt;     &lt;/apex:form&gt; &lt;/apex:page&gt;   CONTROLLER  global class MyController {      public MyController() { MyString = 'hello'; }      public String MyString {get;set;} } Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura Let $I$ and $J$ be ideals of a Noetherian ring $A$. If $JA_P\subseteq IA_P$ for every $P\in \operatorname{Ass}_A(A/I)$, then $J\subseteq I$.   I'm reading Matsumura's Commutative Ring Theory book on my own. This is exercise $6.4$ in that book, and I fail to prove it. Could you help me with this? Thanks in advance. Derivatives: enter "evaluated at" vertical bar with multiple values as subscripts Sorry for the long title, but how do I enter evaluated at (for a derivative), with multiple valuation criteria at the bottom of the the big | line?  Thanks! I have a question pertaining to the concept of acceleration and it's formula - Both seem to give me different answers.  I was asked:     A train is moving at a velocity of $20\ \mathrm{m/s}$. It hits the breaks and starts slowing down at the rate of $8\ \mathrm{m/s^2}$. How long does it travel before coming to a stop?    $a=-8\ \mathrm{m/s^2}$ $u=20\ \mathrm{m/s}$ $v=0$ $s=?$ (Displacement is asked)   According to the formula of $s= \frac{(v^2-u^2)} {2a}$, answer I got was 25 meters.  BUT!  My concept of acceleration explains me this :    According to my intuition of acceleration and velocity, when  an object is said to be accelerating at $-8\ \mathrm{m/s^2}$, it means that with every passing second, it's velocity will reduce $8\ \mathrm{m/s}$. So,   At 1st second - Velocity = $20\ \mathrm{m/s}$ - It'll travel 20 meters. At 2nd second - $v = 20\ \mathrm{m/s}-8\ \mathrm{m/s}=12\ \mathrm{m/s}$ -  Train travels 12 meters At 3rd, it travels 4 meters. At 4th, it halts.   So total is 20+12+4 = 36 meters. It travels 36 meters before halt.  Where am I going wrong in my conceptual understanding, I really don't understand! What's the difference between the following sentences?      (a) I wish they wouldn't make so much noise.   (b) I wish they were not making so much noise.    (c) I wish they did not make so much noise.   I'd appreciate your help. How long does it take for badges to be awarded? How are they generated? Do badges get calculated in real time, or do they get calculated by an external service? How long does it take for a badge to be awarded, once its requirements are met?  Does Stack Overflow use any external services to do things, like maintenance, e-mailing or badge calculation? How to highlight (color/draw attention to) a particular snippet in Minted I'm currently doing some work on error messages in programming languages. As such, I'm showing faulty pieces of code, alongside the compiler-errors accompanying them.  I'm using minted for the code snippets, but ideally, in addition to normal syntax highlighting, I'd like to highlight the sections of the code at which the error is located, by underlining them, putting a red box around them, shading their background, etc.  Is this possible using Minted? Let $X$ ~ $Bin(n,p)$ and $Y$ ~ $Bin(m,p)$ be two independent random variables. Find the distribution of $Z=X-Y$.   see also   I figured this out:  $$ P(Z=z)=\cases{\sum_{i=o}^{min(m,n)} Bin(k+i,n,p)*Bin(i,m,p), &amp;if $z\ge0$;\cr \sum_{i=0}^{min(m,n)} Bin(i,n,p) * Bin(i-z, m, p),&amp;otherwise. \cr}$$  I also validated it by Monte Carlo simulation. For $n=30$, $m=20$ and $p=0.5$, I get the following distribution, where the circles are the analytical probabilities and the line connects the MC estimates.    Because that looked to me pretty much like a binomial distribution, I gave it a try and figured out that its actually a binomial, just shifted by m to the left. This can be simply written as $P(Y=y) = Bin(y+m, m+n, p)$. Hence, given equal success probabilities, the sum of two independent binomially distributed random variables is binomial, but also their difference, just shifted to the left.  This question here  is actually the same as mine, but received no answer and only the comment that there would be no simple formula. But the above formula looks pretty simple to me.   Is it correct that for the case of equal success probabilities, the above equations actually describes the distribution of $Z=X-Y$? I read in a book that $Z$ could not be binomial distributed because it had negative support. Is it right to call it a shifted binomial? Can a git submodule be created retroactively? /var/log/syslog constantly logging errors, growing at 1 MB/s It seems to be the same three errors repeated:  $ tail -n15 /var/log/syslog Apr  5 23:32:01 detoo kernel: [ 6042.078785] ACPI Error: [PGRT] Namespace lookup failure, AE_NOT_FOUND (20150619/psargs-359) Apr  5 23:32:01 detoo kernel: [ 6042.078787] ACPI Error: Method parse/execution failed [\_GPE._L6F] (Node ffff8808554d42d0), AE_NOT_FOUND (20150619/psparse-536) Apr  5 23:32:01 detoo kernel: [ 6042.078788] ACPI Exception: AE_NOT_FOUND, while evaluating GPE method [_L6F] (20150619/evgpe-592)   I noticed something was wrong when I was getting low disk space warnings. I've flashed to the latest UEFI available, I've tried enabling/disabling the C states in my UEFI.  I'm running Linux Mint 17.3 Cinnamon 64-bit with kernel 4.2.0-34-generic. I have a skylake processor and z170 motherboard.  I'm quite new to linux and am at a lost as what I should do next.  EDIT: I have the same problem when booting from a USB with Ubuntu 16.04, and nearly identical error logs being constantly spammed:  Apr  6 01:01:48 ubuntu kernel: [  152.594053] ACPI Exception: AE_NOT_FOUND, while evaluating GPE method [_L6F] (20150930/evgpe-592) Apr  6 01:01:48 ubuntu kernel: [  152.594994] ACPI Error: [PGRT] Namespace lookup failure, AE_NOT_FOUND (20150930/psargs-359) Apr  6 01:01:48 ubuntu kernel: [  152.594996] ACPI Error: Method parse/execution failed [\_GPE._L6F] (Node ffff8808554e02d0), AE_NOT_FOUND (20150930/psparse-542) $\chi(G)+\chi(G')\leq n+1$ How to prove, that the sum of chromatic numbers of graph and it's complement is smaller then the number of vertices incremented by one?  $\chi(G)+\chi(G')\leq n+1$  The notes from my classes say to color the first graph using sequential algorithm with vertices ordered by their degrees (the ones with lowest appear first). We would get $k_1$ colors, then we color the graph $G'$ in the backwards order and get $k_2$ colors, and the sum $k_1+k_2$ in my notes is magically smaller than $n+1$, but I just don't see why... SEO in Stack Overflow We've been out of private beta for only two days, and stackoverflow.com is already ranking high in .  Are there any specific techniques applied in the site? I've been researching the subject for some time and haven't found it to be so easy.   even returns site-links.  () Is Java "pass-by-reference" or "pass-by-value"? Checking for a file and whether it is readable and writable I'm trying to write a script that will look for a certain .txt file saved to my desktop.  I want the script to be able to check if this file exists and then check to see if it is readable and writable.  Any hints? Combinatorics That Looks Similar to Vandermonde's Identity I want to prove that $\lim_{(x,y)\to (0,0)} \frac{\sin(x+y)}{x+y} = 1$  Is it sufficient to say that if $u = x+y$ then as $(x,y) \rightarrow (0,0)$ then $u \rightarrow 0$ and then evaluate $\lim_{u\to 0} \frac{\sin u}{u}$ which is 1 by L'Hôpital's rule?  I feel that this is somehow "cheating" and I would really like to prove it in a more rigorous way, i.e., by using an $\epsilon$ - $\delta$ argument.  I have tried for a long time to use the one variable version and prove that if $0 \lt \sqrt{x^2 + y^2} \lt \delta$ then somehow $0 \lt |x+y| \lt \delta$ and it would follow from the one variable case that $| \frac{\sin(x+y)}{x+y} - 1| \lt \epsilon$. However, because $|x+y| = 0$ when $y = -x$ I am not getting anywhere with this.  Any input on this would be helpful :) ..and I don't mean finding out why it doesn't compile, I mean serious debugging: breakpoints, figuring out value of variables at a given moment during run/compile, stepping, examining a stack (is there one?), etc. All the things that we take for granted when debugging a "real" programming language. Since TeX is "turing-complete", I would like to be able to really see what is going on internally.   I'm guessing that a GUI interface for the debugger would be too much to ask, but if it exists, I'd love to hear about it.