I tried to search in the google. But everyone is explaining about inner join and when comes to outer join they are including full outer join /left/right. I just want to know only the difference between inner join and outer join.
Also how do LEFT JOIN, RIGHT JOIN and FULL JOIN fit in?
It's easy to check that for any natural $n$ $$\frac{n+1}{n}=\cfrac{1}{2-\cfrac{n+2}{n+1}}.$$  Now,   $$1=\frac{1}{2-1}=\frac{1}{2-\cfrac{1}{2-1}}=\frac{1}{2-\cfrac{1}{2-\cfrac{1}{2-1}}}=\cfrac{1}{2-\cfrac{1}{2-\frac{1}{2-\frac{1}{2-1}}}}=\ldots =\cfrac{1}{2-\cfrac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\dots}}}}},$$  $$2=\cfrac{1}{2-\cfrac{3}{2}}=\cfrac{1}{2-\cfrac{1}{2-\cfrac{4}{3}}}=\cfrac{1}{2-\cfrac{1}{2-\frac{1}{2-\frac{5}{4}}}}=\cfrac{1}{2-\cfrac{1}{2-\cfrac{1}{2-\frac{1}{2-\frac{6}{5}}}}}=\ldots =\cfrac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\ldots}}}}}.$$  Since the right hand sides are the same, hence $1=2$. How to test multiple variables against a single value? Should I flag/down-vote "Draft Answers"? Why can't I use a type argument in a type parameter with multiple bounds? So, I understand that the following doesn't work, but why doesn't it work?  interface Adapter&lt;E&gt; {}  class Adaptulator&lt;I&gt; {     &lt;E, A extends I &amp; Adapter&lt;E&gt;&gt; void add(Class&lt;E&gt; extl, Class&lt;A&gt; intl) {         addAdapterFactory(new AdapterFactory&lt;E, A&gt;(extl, intl));     } }   The add() method gives me a compile error, "Cannot specify any additional bound Adapter&lt;E&gt; when first bound is a type parameter" (in Eclipse), or "Type parameter cannot be followed by other bounds" (in IDEA), take your pick.  Clearly you're just Not Allowed to use the type parameter I there, before the &amp;, and that's that. (And before you ask, it doesn't work if you switch 'em, because there's no guarantee that I isn't a concrete class.) But why not? I've looked through Angelika Langer's FAQ and can't find an answer.  Generally when some generics limitation seems arbitrary, it's because you've created a situation where the type system can't actually enforce correctness. But I don't see what case would break what I'm trying to do here. I'd say maybe it has something to do with method dispatch after type erasure, but there's only one add() method, so it's not like there's any ambiguity...  Can someone demonstrate the problem for me? This works just fine:      protected void txtTest_Load(object sender, EventArgs e)     {         if (sender is TextBox) {...}      }   Is there a way to check if sender is NOT a TextBox, some kind of an equivalent of != for "is"?  Please, don't suggest moving the logic to ELSE{} :) How are Dementors created/born? This is inspired by some discussions in .  In the Harry Potter universe, how are Dementors born?  Or are they artificially created by some magical means? How do I make my rim brakes stop squealing? My rear rim brakes are squeaking loudly. I don't know what the problem is, but I am sure it has nothing to do with rain because it happens all the time even if it is dry.  Anybody have an idea what could be problem and how to solve it? It makes the rear brakes kind of useless, because if I use them I will scare the people or drivers around me. How to be granted root rights while browsing files/directories with Nautilus I'd like to know if there a way to be granted root rights while using Nautilus 2.30 ?   For example I'd like to move some old folders of long unused users from the home directory - remains of previous distros (Debian).   Of course I can open a terminal, but I want to know if it is possible to do that with a mouse in Nautilus. Calculation of $\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$ Calculation of  $\displaystyle \lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$  $\bf{My\; Solution::}$  Let $y=\displaystyle \lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$, Now taking $\log_{e}$ on both side  $\displaystyle \log_{e}(y) = \lim_{n\to \infty}\log_{e}\left(\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}\right)=\lim_{n\to \infty}\frac{1}{n}\cdot \sum_{r=1}^{n}\log\left(1+\frac{r}{n}\right)$  Now Using Reinman Sum of Integral ...  $\displaystyle \log_{e}(y) = \lim_{n\to\infty}\frac{1}{n}\cdot \sum_{r=1}^{n}\log\left(1+\frac{r}{n}\right) = \int_{0}^{1}\ln(1+x)dx = \log_{e}(4)-\log_{e}(e) = \log_{e}\left(\frac{4}{e}\right)$  So $\displaystyle y =\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}} =\frac{4}{e}$  But how can i solve above question using Stirling Approximation,  May I ask for help?  Thank you in advance! Dynamic Paint not showing in rendered image I would like to capture the contents of AJAX requests using Greasemonkey.  Does anybody know how to do this? Short story: people rediscover how to do math and want to put people in bombs Many years ago I remember reading a short story about an advanced civilization at war that rediscovers how to do math mentally. The reason I remember it is the guy tells it to government officials who are delighted because it means they can put people inside bombs or missiles instead of computers, which were thought to be more valuable.  I believe this is one of those stories I read in a science fiction anthology my father brought home on one of his business trips in the sixties or seventies. I know that to better balance paragon and epic level players against similar level monsters, WotC changed the math used for monsters for MM3, and I believe that they changed some of the types of powers they gave monsters.   If I want to update monsters from MM1 or MM2 to be in line with MM3 era monsters, what changes should I make? Fancy Chapter Headings Style I would like make a fancy chapter like the figure.    However, i made this code  \documentclass[12pt,a4paper]{book}   \usepackage{lmodern} \usepackage{titlesec} \usepackage{microtype} \usepackage{tikz}    \titleformat{\chapter}[display]   {\normalfont\bfseries\color{black}}   {%\filleft%     \begin{tikzpicture}     \node[       outer sep=-10pt,       text width=2.5cm,       minimum height=3cm,       fill=black,       font=\color{white}\fontsize{80}{90}\selectfont,       align=center       ] (num) {\thechapter};     \node[       rotate=0,       anchor=south,       font=\color{black}\Large\normalfont       ] at ([yshift=43pt,xshift=30]num.west)  {\textls[180]{\textsc{\chaptertitlename}}};       \end{tikzpicture}%  }    {-90pt}   {\titlerule[2.5pt]\vskip3pt\titlerule\vskip4pt\LARGE\sffamily \raggedright }    \begin{document} \chapter{The Singular Sturm-Liouville Problems in Spectral Parameter}    \end{document}      that produces this one    How can I produce the chapter like the First Figure? C++ virtual function from constructor Why the following example prints "0" and what must change for it to print "1" as I expected ?  #include &lt;iostream&gt; struct base {    virtual const int value() const {       return 0;    }    base() {       std::cout &lt;&lt; value() &lt;&lt; std::endl;    }    virtual ~base() {} };  struct derived : public base {    virtual const int value() const {       return 1;    } };  int main(void) {    derived example; } VirtualBox 5.0.40 crashes the whole host since update to kernel 4.13.0-26-generic I received the updates through normal Software Updater, 10-Jan-2018. After this VirtualBox would not start any VM, complaining about dkms and asking to make modprobe vboxdrv. Following the advice I reinstalled virtualbox-dkms with:  sudo apt-get --reinstall install virtualbox-dkms   After this and a reboot I tried to start a VM which freezed the whole machine and a hard reboot was necessary.  Is there a way to make VirtualBox work with the latest kernels?  EDIT:  As suggested by N0rbert, the command:  apt-cache policy `dpkg -S VirtualBox | head -n1 | sed -e 's/://g' | awk '{print $1}'`  gives:   virtualbox-qt:   Installed: 5.0.40-dfsg-0ubuntu1.16.04.2   Candidate: 5.0.40-dfsg-0ubuntu1.16.04.2   Version table:  *** 5.0.40-dfsg-0ubuntu1.16.04.2 500         500 http://fr.archive.ubuntu.com/ubuntu xenial-updates/multiverse amd64 Packages         100 /var/lib/dpkg/status      5.0.18-dfsg-2build1 500         500 http://fr.archive.ubuntu.com/ubuntu xenial/multiverse amd64 Packages   EDIT (on 29-Mar-2018): Issue is resolved for me, with the Ubuntu Ubdate from today. I have seen that it had some virtualbox-updates, therefore I tried to boot with the most recent kernel again. Then I had to run  sudo apt-get --reinstall install virtualbox-dkms  And after this my virtual machines in VirtualBox started working without crashing the whole computer. Finally! Removing small spaces (slivers) between polygons? I'm stuck in a teleporting loop. What can I do? Are there names for consonant-shifts when suffixes are added? Vectorization operator