How to prove $\left(\sum_{i=1}^n x_i\right)^2 \le n\sum_{i=1}^n x_i^2$?
How to show $n\sum_{i=1}^n {x_i^2} \ge (\sum_{i=1}^n{x_i})^2$
Word meaning a job someone is installed in where they don’t do anything How can I check which songs or videos that I purchased from the iTunes Store have DRM restrictions?  All of the mobile OSes are very impressive to me at the moment, and I'm thinking about trying a non-iOS device again. I want to know now the impact it has on my Apple-sourced music collection though.  Is there a date cut-off for purchases when items went DRM free? Are the square roots of all non-perfect squares irrational? Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic? Birthday problem: why is this solution wrong? This question is about the birthday problem: the probability that in a group of n people, at least two of them have the same birthday ().  An easy way to calculate the probability is to calculate first the probability that no two people have the same birthday.  Let's say that I want to calculate the probability that in a group of 20 people, NO two people have the same birthday.  So, for 20 people with different birthdays, I can choose the first birthday in 365 ways, the second in 364 ways and so on, while for 20 people who can have the same birthday, I can choose the first birthday in 365 ways, the second also in 365 ways, and so on. At the end:  $p={365 \cdot 364 \cdot 363 \cdot ... \cdot 346 \over 365 \cdot 365 \cdot 365 \cdot ... \cdot 365}\approx 0.59$  This is the right method and I understand it. I don't understand why the following method is wrong:  The probability that in a group of 20 people NO two people have the same birthday is the ratio between the combination without repetition of 20 birthdays and the combination with repetition of 20 birthdays:  $$p={C_{365,20} \over C'_{365,20}}={\binom{365}{20} \over \left(\binom{365}{20}\right)}={\binom{365}{20} \over \binom{365+20-1}{20}}=\frac{{{365!}\over {20!\cdot(365-20)!}}}{{(365+20-1)!}\over{20!\cdot{(365-1)!}}}\approx 0.35$$  I understand the mistake is in the denominator (as the numerator is the same of the other method, after simplifying that 20!), but why? Isn't it right to calculate the k-combination with repetition of 20 birthdays?  Thanks for helping! Checking for valid floating point number To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$ My Approach. To prove the given statement it is sufficient to show that $$\exists \epsilon &gt; 0, \exists x \in [0,1], \forall N \in \mathbb{N}, \exists n &gt; N $$ $$ \Rightarrow | f_n(x) - f(x)| &gt; \epsilon$$    Let $\epsilon = \frac{1}{10}, x = \frac{1}{n}, n =N+1$. Hence $| f_n(x) - f(x)| = \frac{1}{2} &gt; \epsilon = \frac{1}{10}$. Hence, we have shown for every $N \in \mathbb{N}$, how to choose $n$ such that $| f_n(x) - f(x)| &gt; \epsilon$. Thus, $f_n(x)$ does not converge uniformly on $[0,1]$.    Is there any logical flaw or wrong steps in my proof. Any help would be appreciated. How to check if a column exists in a SQL Server table? How do I Sort a Multidimensional Array in PHP I have CSV data loaded into a multidimensional array. In this way each "row" is a record and each "column" contains the same type of data.  I am using the function below to load my CSV file.  function f_parse_csv($file, $longest, $delimiter) {   $mdarray = array();   $file    = fopen($file, "r");   while ($line = fgetcsv($file, $longest, $delimiter))   {     array_push($mdarray, $line);   }   fclose($file);   return $mdarray; }   I need to be able to specify a column to sort so that it rearranges the rows.  One of the columns contains date information in the format of Y-m-d H:i:s and I would like to be able to sort with the most recent date being the first row. Is it possible to have site-specific badges? How to connect to my web server? I have implemented a simple web server as a solution to a course assignment and I want to connect to this web server over the internet. I've set it up to listen on port 22881 and configured my router accordingly as the screenshot below shows    I'm able to connect to my web server locally using http://localhost:22881 and I can connect to the router's interface when I visit http://my.external.ip, but I can't connect to my web server using http://my.external.ip:22881 (I get a connection timeout). Any idea of what may be the problem?  Thanks in advance! How can I remap Caps lock to both Escape and Control? I generally run Linux. I use Vim a lot, so the Escape key is extremely important. I also use other keyboard shortcuts a lot, so Control is "key" as well. On Linux, I've solved this by using  to map the Caps lock key to Escape if pressed by itself, or Control if pressed in combination with another key. This puts the best of both worlds within quick reach of my pinky finger. Is there any way I can do this on a Mac? Why does Property Set throw StackOverflow exception? I know java and would normally put in getter/setter methods. I am interested in doing it in C# with the following code, but it throws a StackOverflow exception. What am I doing wrong?  Calling Code  c.firstName = "a";   Property Code    public String firstName; {     get     {         return firstName;     }     set     {         firstName = value;     } } was created on Server Fault, answered on Server Fault, I upvoted some of those answers on Server Fault, and then moved by consensus to Super User.  Now that the question is on Super User, I can upvote the same answers I previously upvoted on Server Fault. Rectangles around cells in table Do you have to take the second leg of a domestic flight? Say I want to book a flight from Fort Lauderdale to Chicago.  Say the airline also flies to St. Louis from Fort Launderdale but has a connecting flight through Chicago.  If I book that flights from FLL->ORD->STL and just get off in Chicago, what possible problems can I run into, assuming I didn't check any bags and only have carry on?  This scenario exist for Southwest, but I wanted this be more of a general question that would apply to all airlines. 2015 Macbook Air screen gradually dimming and dying This is not a problem at booting up. For a couple months now I'll be using my laptop when suddenly the screen dims to about 50% of normal. According to the brightness indicator the brightness is all the way up; I can make it dimmer, but not as bright as normal. The dimming isn't super even either, there are small areas of the screen that seem darker/brighter. In the past the problem easily goes away if I close the lid and reopen it... but now it's happening a lot and sometimes going completely black. Is this an easy/cheap fix? I'm traveling and can't do it myself. Is it worth bringing to the Mac store?  Thanks! Can inner classes access private variables? class Outer {      class Inner {     public:         Inner() {}         void func() ;     };  private:     static const char* const MYCONST;     int var; };  void Outer::Inner::func() {     var = 1; }  const char* const Outer::MYCONST = "myconst";   This errors out when I compile with class Outer::Inner' has no member named `var' What is the purpose of the EBP frame pointer register? Effective marketing strategies for independent game projects I would really like to hear how other independents generally approach marketing their game with limited resources. I know how critical marketing is since I've seen it first hand on several fronts. I've been part of teams that didn't put an ounce of marketing into their project and didn't come close to meeting expectations. I've also poured a lot of time into visiting forums to discuss our previous title which resulted in minor bumps over time.  I really think  is doing some amazing grass roots marketing with the way they are managing their community around their Blog. They've massed a following that is willing to pay (far in advance) them for their game before they finish it to help support them. That's awesome.  But how many people are really willing to divulge such information that early? Should that be a concern? Should I start talking about my next project before I really have anything implemented?   What has worked for you? I would be particularly interested to hear how people approach Apple's iTunes store. I believe we're looking at around 33,000 games on the store these days.