Proving a group where every element's square is identity is Abelian
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
How to download, modify, build and install a Debian source package? If I want to make minor changes to the source code of a Debian package, how do I go about downloading, incrementing the package version, building the (modified) source, and installing it on my computer? I have an Ubuntu 12.04 machine on which I have installed VirtualBox with Ubuntu 12.04 as the guest OS.  How can I share files between the host and guest?   I have installed the guest additions also but still it’s not able to mount the sf_shared folders if even it’s mounted. This means I'm unable to retrieve the file from the host. I have two passports/nationalities. How do I use them when I travel? I am a citizen of two different countries, and have two passports.  How should I use my passports when traveling? Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice? I'm currently reading a little deeper into the Axiom of Choice, and I'm pleasantly surprised to find it makes the arithmetic of infinite cardinals seem easy. With AC follows the Absorption Law of Cardinal Arithmetic, which states that for $\kappa$ and $\lambda$ cardinal numbers, the larger infinite and the smaller nonzero, then $\kappa+\lambda=\kappa\cdot\lambda=\max(\kappa,\lambda)$.  I was playing around with the equation $k+\aleph_0=\mathfrak{c}$ for some cardinal $k$. From the above, it follows that $\mathfrak{c}=k+\aleph_0=\max(k,\aleph_0)$, which implies $k=\mathfrak{c}$.  I'm curious, can we still show $k=\mathfrak{c}$ without the Axiom of Choice? Is it maybe possible to bound $\mathfrak{c}-\aleph_0$ above and below by $\mathfrak{c}$? But then I'm not quite sure such algebraic manipulations even mean anything, or work like that here. Certainly normal arithmetic does not! Thanks. How can I prevent Chrome from offsetting newly opened Window? When I open a new Window in Chrome on Windows 7 (by pressing CTRL+N), the new window does not exactly overlap the existing window.   Instead it is offset to the right slightly.   So, immediately after opening a new window I have to manually move it to the left so that it uses the full screen real estate.   Is there a way to prevent this offset? What does the [Flags] Enum Attribute mean in C#? From time to time I see an enum like the following:  [Flags] public enum Options  {     None    = 0,     Option1 = 1,     Option2 = 2,     Option3 = 4,     Option4 = 8 }   I don't understand what exactly the [Flags] attribute does.  Anyone have a good explanation or example they could post? UV coordinates on a deformed plane I added a plane to a scene, subdivided it, and deformed it with proportional editing:    I'd like to UV unwrap this plane, making the mapping what the would have been without the edit mode deformations. In other words, I'd like my UV map to look like a square grid.  Is it possible to UV map this deformed plane to a square grid? Or do I need to start from scratch, and make sure I unwrap it before I do the edits? What can I do to give the players the same feel their characters would have about wilderness travel? fontawesome icons are getting too big using XeLaTeX The following example must be compiled with XeLaTeX to reproduce the issue.  % arara: xelatex \documentclass{article} \usepackage{fontawesome} \begin{document} Text Text \faMobilePhone\ Text Text \end{document}   Normally I am using TeXworks to compile and view the output. With the internal viewer I am getting the desired result. The following image demonstrates it:    However if I open the pdf with Preview (viewer of Mac) the scaling of the icon fails.     If I open the pdf file with Adobe Acrobat Reader the icon is still scaled correctly. If I print the page my printer is also not able to scale the icons correctly.   If I use LuaLaTeX everything seems to work correctly.   Can you reproduce the issue and do you know a solution? How does some of the black hole (BH) mass escape the event horizon (EH) of either BH, or the merged EH of two merged BHs? I'm looking for a site, similar to StackOverflow, but with possibility to ask opinion based questions Since opinion based questions are not allowed neither here nor on stackoverflow, I would like to ask if any of you, know some other web page (outside Stack* ecosystem), where we can ask questions like:  "Which Java Web framework would you recommend to learn"   or any other, which by nature are opinion based.  EDIT1:  Allow me to explain a bit more - I know there are webgroups, forums and mailing lists BUT most of those are for single programming language or framework and I'm looking for something more generic. Stackoverflow is great because there are experts from all sort of programming languages and frameworks, so if it would be allowed to ask:   "Best web frameworks similar to ASP.NET MVC4"  I would get a lot of opinions, from different languages and frameworks, and that exactly what I'm looking for. Explicit construction of a finite field with $p^n$ elements Add parenthesis as an accepted Markdown ordered list delimiter The Markdown editor knows that an empty line, followed by a number, followed by a period, followed by a space, is a list item.  This works great It's almost magic  The problem is that I almost always use a close parenthesis for my lists. I think it's a pretty common practice, but the problem is that the editor / Markdown parser doesn't accept parenthesis as an acceptable list delimiter:  This fails horribly This is on the next line I swear Question 1: Why are irrational numbers uncountable and rationals countable?  I really struggle to understand this. I initially thought it had something to with the fact that between any two numbers there will always be a irrational number. But now it has come to my attention that the same holds for rational numbers. So I can't really see the difference between them. What is it that makes the difference? Why can we line up all rational numbers one-to-one with the natural numbers, but not the irrationals with the naturals?  Sorry for a perhaps basic question, but I really, really struggle with it. Thanks. let $a,b,c$ be postive real numbers ,and such $$ab+bc+ac=3$$   show that   $$\dfrac{a^2}{a+2b^2}+\dfrac{b^2}{b+2c^2}+\dfrac{c^2}{c+2a^2}\ge 1$$   This problem is from Secrets In Inequalities volume 1  page 30,example 1.24. the comment.the  author this case is a bit more diffcult,But this author can't post solution.Thank you If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc? How can I update my OpenGL to 3.0 or higher I need to prove the following identity:  $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$  I know that -   $\sum_{k=0}^{n}{n \choose k}2^{k}=3^{n}$  but don't know how to continue. Wired connection not working Ubuntu 12.04 (Ubuntu 13.04 with GNOME Shell, upgraded, GNOME version 3.8) Recently, I upgraded Ubuntu to 13.04. the default desktop is gnome-shell. Except Nautilus, other software border doesn't disappear when I make them to be maximized. I checked the problem for these software:  LibreOffice Firefox Rhythmbox thunderbird GNOME-Terminal  On the other hand there are three bars on maximized mode:  GNOME Shell panel  Title-bar for software which contains - + x (minimise, maximise, close) buttons.  Software menu-bar  Number &quot;2&quot; is extra. Is a package missing?