What is $\lim\limits_{n\to\infty}(\sqrt2-\sqrt[3]2)\cdots(\sqrt2-\sqrt[n]2)$? How to approach?
Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$
Compiz Problems (Plugin Missing, Performance Issues, Development) I've recently set up the compiz cube again, and I was very happy to find that that flickering window glitch is gone! However, the cube reflection and deformation plugins are also gone.  I am running a fresh 12.10 install, and I have every compiz plugin package installed (including compiz-plugins-extra, which supposedly contains everything that compiz-fusion-plugins-extra package used to have), but those two plugins are still missing. I haven't been able to find anyone with the same problem.   Any ideas? (thanks!) Is (rest) mass conserved in special relativity? I don't understand why it is said that the (rest) mass of a system is not conserved in relativity. I mean, the momentum of a system is conserved (i.e.: it remains constant in a frame of reference without any external influence). Also the energy of a system is conserved in relativity: it doesn't change without any external agency  and the (rest) mass of a system is just  $$m^2=E^2-p^2$$  $E$ is constant, $p$ is constant, how can $m$ change?  For example, entropy is not conserved in a system, that means that the entropy of the system will increase spontaneously with time, which is really the case. But, is this true for mass?   here is the problem from Griffiths and exact solution as given in the Griffiths,  Two lumps of clay, each of rest mass $m$, collide head-on at $3c/5$ and they stick together. Question: what is the rest mass $M$ of the composite lump?  Solution: In this case conservation of momentum is trivial it is zero before and zero after. The energy of each lump prior to the collision is $$mc^2/\sqrt{1-v^2/c^2} =5mc^2/4.$$ The energy of the composite lump after the collision is $Mc^2$ (since its at rest). so the conservation of energy says: $5mc^2/4 + 5mc^2/4 =Mc^2$ and hence $M=5m/2$.  Notice that this is greater than the sum of the initial masses! Mass was not conserved in this collision; kinetic energy was converted into rest energy, so the rest mass increased. Implementing support for nested transactions using JDBC 3.0 our legacy application uses JDBC 3.0. it supports transactions by implementing its own transaction manager that is capable of returning the same JDBC connection for each thread. The problem I recently discovered is that it doesn't support nested transactions: if a transaction is started inside an another transaction, then every SQLs running in the context of the inner transaction will be executed using the same db connection, and when it's commited or rolled back it will automatically commit or roll back all the changes starting from the outer transaction.  As far as I understand I can implement the support for nested transaction using JDBC 3.0 savepoints: whenever a nested transaction is started, I can set a new savepoint for the current connection. Afterward, if the nested transaction is rolled back, I will just rollback to this savepoint. If, on the other hand, it is commited, I will just do nothing. Only the commit of the most outer transaction will save the changes to the db.  Is this correct? Does this approach have any flaws? If yes, what are my possibilities?  Thanks. Why does this stream return no element? Why is this true?  $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$ Multiple Inheritance #include&lt;iostream&gt; using namespace std;  class A  {    int a;    int b;    public:    void eat()    {       cout&lt;&lt;"A::eat()"&lt;&lt;endl;    } };  class B: public A {    public:    void eat()    {        cout&lt;&lt;"B::eat()"&lt;&lt;endl;     }  };  class C: public A {     public:    void eat()     {        cout&lt;&lt;"C::eat()"&lt;&lt;endl;     }  };  class D: public B, C {  };  int foo(A *ptr) {  ptr-&gt;eat();  } main() {  D obj; foo(&amp;(obj.B)); //error. How do i call with D's B part.  }   The above foo call is a compile time error.  I want to call foo with obj's B part without using virtual inheritance. How do i do that.   Also, in case of virtual inheritance, why the offset information need to be stored in the vtable. This can be determined at the compile time itself. In the above case, if we pass foo with D's object, at compile time only we can calculate the offset of D's A part. What are the differences between $$, \[, align, equation and displaymath? How to Logout of an Application Where I Used OAuth2 To Login With Google? Is there a proof that the ratio of a circle's diameter and the circumference is the same for all circles, that doesn't involve some kind of limiting process, e.g. a direct geometrical proof? I'm looking for a way to search files where two word instances exist in the same file.  I've been using the following to perform my searches up to this point:  find . -exec grep -l "FIND ME" {} \;   The problem I'm running into is that if there isn't exactly one space that between "FIND" and "ME", the search result does not yield the file.  How do I adapt the former search string where both words "FIND" and "ME exist in a file as opposed to "FIND ME"?  I'm using AIX. Can a multi-class Bard/Wizard write spells known from Bard, into Wizard spellbook? For you that have tested this, should we use Ubuntu and install different Desktop Environments (KDE/XFCE...) or we should install different distributions (Kubuntu/Xubuntu...). Are there any notable issues in performance / CPU consumption?  PS:  I know how to install them (already did), I wanted to know if anyone has any problems regarding the performance and what is better to install the desktop or to use the ditribution Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$? How can I solve this functional equation, where $x,y$ are any real numbers and $f:\mathbb{R}\to \mathbb R$ is a function such that : $$f(x+y)+f(x-y)=2f(x)\cos y$$    I tried substituting $x=0$ to get $f(y)+f(-y)=2f(0)\cos y$ . Taking $x=y$ gives $f(2x)+f(0)=2f(x)\cos x$. I similar get some more relations like that, but its not really helping me in finding anything useful. I also think the function must either be $\sin$ or $\cos$ looking at the product to sum formulae. Can anyone tell me how should I solve this? Downgrading from SQL Server 2008 to 2005 In ZFC set theory, every element object is a set. We know or feel that if $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set.  My question is: Why if $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set? Fix formatting errors of page number > 99 in table of contents? This is a follow up question of .  The formatting problem has nothing to do with cleanthesis.sty.  The problem is that if I use the charter font, page numbers greater than 99 are not formatted correctly in the table of content.  \documentclass[draft=on]{scrbook} \usepackage{blindtext} \usepackage{charter}  \listfiles  \begin{document} \tableofcontents \section{Section 1} \blindtext[100] \section{Section 2} \blindtext[500] \section{Section 3} \end{document} How to prevent an email from accidentally being forwarded? Where are the Unity desktop wallpapers located? Please see the picture below. Where are the Unity desktop wallpapers located? How to create tagged PDF such that they will be:   good enough for PDF/UA "reflowable" on smaller screens and ebook readers   Any syntax &amp; any engine are of interest, but I'm most interested in using LaTeX with [Xe|pdf]latex engines. I just rememebered a case when I was still in school: we had to write an essay about a specific topic and one guy put big parts of his essay on Wikipedia before handing it in. When the teacher checked for plagiarism she indeed found big parts of his text in the Wikipedia article and thus accused him of plagiarism.  How would that situation be with journal papers (or other "official" ways of publishing)?  Can I reuse part(s) of texts I wrote myself but that are available publicly/online like on Wikipedia, my Blog, university homepage, etc.?  (Maybe consider that pseudonyms are used on Wikipedia, Blogs, etc.)