error in installing ffmpeg in Ubuntu 14.04
Is FFmpeg missing from the official repositories in 14.04?
Find all $x$ such that $$x^6=(x+1)^6.$$   So far, I have found the real solution $x= -\frac{1}{2}$, and the complex solution $x = -\sqrt[3]{-1}$.  Are there more, and if so what/how would be the most efficient find all the solutions to this problem? I am struggling to find the rest of the solutions. What's the difference between lists and tuples? What's the difference?  What are the advantages / disadvantages of tuples / lists? How do I remap the Caps Lock and Ctrl keys? I'd like to remap my keys such that Ctrl behaves as the Caps Lock key and vice-versa. Also, if possible I'd like the settings to be available only within the currently logged-in user. How can I achieve this?  I'm a vim user, unlike the other people who use this machine, so I'd like those settings only for my account. Is there a way to render an object with a subdivision surface modifier with a wireframe which is the original geometry as well as the wires that make the subdivision surface?  Example:   This wireframe here is curved. What if there was displayed the straight wireframe. The wires that make are made by the subdivision surface. Thats what I want to achieve. How to do it?  What I mean is - How to render the curved wireframe (which is the original geometry with the straight wireframe (which is the wireframe the is made by the subdivision surface)? How to secure my laptop so that hacking by physical access is not possible? Understanding etoolbox \ifdefempty and \ifdefvoid I am trying to understand the  \ifdefempty and \ifdefvoid macros. The documentation says that \ifdefempty     Expands to true if the control sequence is defined and is a   parameterless macro whose replacement text is empty, and to false   otherwise.   Similarly \ifdefvoid     Expands to true if the control sequence is undefined, if is a macro   whose meaning is \relax, or a parameterless macro whose replacement   text is empty, and to false otherwise.   From these descriptions I thought that \def\myempty{}, \def\myrelax{\relax}, and \def\myemptyempty{\myempty} would all be both "empty" and "void", but \def\myempty{} is the only one that is either "empty" or "void". What am I missing?  \documentclass{minimal} \usepackage{etoolbox}  \begin{document}  \def\myempty{} \def\myrelax{\relax} \def\myemptyempty{\myempty}   \ifdefempty{\myempty}{Empty}{Not empty}  \ifdefempty{\myrelax}{Empty}{Not empty}  \ifdefempty{\myemptyempty}{Empty}{Not empty}  \ifdefvoid{\myempty}{Void}{Not void}  \ifdefvoid{\myrelax}{Void}{Not void}  \ifdefvoid{\myemptyempty}{Void}{Not void}  \end{document} Is ∅ equivalent to {∅}? Ratio test and the Root test I have just started studying implication in mathematics. So, you'll probably have an idea of where my confusion lies right from the get go.  In the truth table, where $A \implies B$ we obtain this result:  A   B   T/F ___________ T | T | T T | F | F F | T | T F | F | T   Now, my confusion here is regarding why $A\implies B$ given A is false, and B true. The others I understand. The first and last one are obvious, the second one implies, to me anyway, that given A implies B, the truth of B rests upon the truth of A, B is false, A is True, which cannot be, thus not B given A is false.  Now... then, why is B true despite the fact that A is false? Or rather, why is the statement B given not A, True. The truth of B is implied from the truth of A, but A is a false statement. So it's very contradictory that this may be, and in fact, if you go through a real life example, you would find that the third statement seems to be false.  Say $A$ is the statement that it is dark outside, and $B$ the statement that the sun is not on our side of the earth. If it is not dark outside, than stating that the sun is on the other side of the planet must be wrong (in my example i'm going to claim that the sun is the only light source).  Side note:  I just had a thought, if A is false, does that mean you can conclude... mmm, whatever? I mean, B is implied via the truth of A, if A is false, B is NOT implied, but then B could be EITHER true or false, I suppose. Is this correct?  However, would that not mean that A does not imply anything when false. Would that not set the 3rd and 4th statement to be undefined? Cycle option when drawing between nodes in TikZ Cycle lets you close curves when drawing, and  \coordinate (a) at (0,0); \coordinate (b) at (1,0); \coordinate (c) at (0.5, -1); \draw (a) -- (b) -- (c) -- cycle;   works fine. Shouldn't also  \node (a) at (0,0) {}; \node (b) at (1,0) {}; \node (c) at (0.5, -1) {}; \draw (a) -- (b) -- (c) -- cycle;   give the same result?  The former gives a triangle, while the second doesn't close up. Is this a bug or am I missing something regarding the cycle option?  (Of course, as a workaround I could use the coordinates to draw the cycled path, and then draw the nodes at the same coordinates, but still...) See my edit below, this is not totally a duplicate of   My reverse-search function in the CLI is broken and I don't know how to fix it back...  When I hit ctrl+r and search a command I did earlier, find it then press the right arrow key to use it, the output is broken. Here is an example:  # I reverse-searched the word "test" then pressed right arrow yoshiji@x1carbon:~/path/to/git/folder (master) $ch)`test': rake test #                                              ^^^^^^^^^^ weird output #                                                     ^ cursor right there   It also "shifts" my cursor to a different position. If I press enter, the right command is executed (rake test in this case) so it means the text displayed is not the same as what is actually executed.  I know this is most-likely related to my PS1 export in my ~/.bashrc, so here are the last lines of this file:  # Git branch in prompt. git_branch() {   branch=$(__git_ps1 2&gt; /dev/null)   if [ "$branch" = " (master)" ]; then      echo -e "\033[33m${branch}\033[00m" # yellow   elif [ "$branch" = "" ]; then      echo -e "\033[90m (no git)\033[00m" # red   else      echo -e "\033[32m${branch}\033[00m" # green   fi } PS1='\u@\h:\w$(git_branch) \$ '   This is something I wrote to displays the git branch in orange (if master branch) or else in green (or no git in gray).  Do you guys have any idea on what is causing this weird behavior?    Edit: This is a different problem from the  in the way that I am using echo -e "some string" to return a string having color+name of the git branch from the function git_branch(). Using echo -e does not escape the characters \[ and \] (try it yourself in your CLI: echo -e "\[\033[33m\]test").  Ideally, I would like to keep those conditional colors based on the branch's presence &amp; name (gray if no branch, orange if master, else green). Can Xdebug be triggered by Drush commands? I'm running into an issue with my Features modules and installation profile when installing the site with drush si. There are a number of probably related issues in the Features issue queue, but none with good solutions. The interesting part (mentioned in some of the issues) is that it works fine when installing the site through the browser, but fails when installing with drush si.  I have an idea of what's wrong, but need to confirm it. The only way I can think of confirming it is to step through the code with a debugger (Xdebug is what I have set up). So, is it possible to trigger Xdebug from a command run with Drush? Specifically, can I get Xdebug to kick in when I run drush si? The work done against gravity is $mgh$, well at least that's what my textbook says. I have a question: I can apply a force say 50N, so total work done = $mgh + mah$. Where $ma$ = Force. But the truth is irrespective of the force applied, the work done against gravity is always $mgh$. Why?  For example, when I move an object with a force, the work done is more, so work depends on the Force. But in case of gravity it always depends upon the weight How to specify font size less than 10pt (or more than 12pt)? I'm trying to make a document that has a very small font throughout, I tried this:  \documentclass[0.5mm, a4paper]{article} \documentclass[7pt, a4paper]{article}   But it doesn't seem that they allow me to go anything below 10pt.  This hack make it work, but not for the section headers:  \fontsize{4mm}{5mm}\selectfont   Does anyone know any better ways to do this? Choosing power supply, how to get the voltage and current ratings? I have this question :  Proof if $f$ continuous in $x_0$ then there is a neighbourhood of $x_0$ so $f$ bounded.  I want to know if my proof is valid :  If continuous in $x_0$ then :  $$\lim_{x \to x_0} f(x)= f(x_0)$$  Therefore :  All $\epsilon&gt;0$ exists $\delta&gt;0$ so any $x$ that implies $|x-x_0|&lt;\delta$ implies $|f(x)-f(x_0)|&lt;\epsilon$.  Therefore for $\epsilon=1$ there is $\delta&gt;0$ so any $x$ that implies $|x-x_0|&lt;\delta$ implies $|f(x)-f(x_0)|&lt;1$.  $|x-x_0|&lt;\delta \rightarrow x_0-\delta&lt;x&lt;x_0+\delta$.  Lets choose $x_1,x_2$ that implies $x_0-\delta&lt;x_1&lt;x_2&lt;x_0+\delta$  Therefore in $[x_1,x_2]$ from Weierstrass from theorem bounded there. Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$   Here's what I did so far:  Let $\sup A, \sup B$, and $\sup (A \cup B)$ denote upper bounds of $A,B$, and $A \cup B$, respectively. If $x \in A$, then $x \le \sup A$. If $x \in B$, then $x \le \sup B$. In either case, $x \in (A \cup B)$. So either $x \le \sup A$ or $x \le \sup B$. In either case, $x \le \max \{\sup A, \sup B\}$. So $\max \{\sup A, \sup B\}$ is the upper bound of $A \cup B$, which means $\sup (A \cup B) \le \max\{\sup A, \sup B\}$.  I do not know if there's a better way to go at it, but all I did was show the inequality. Can I do this, and show the reverse inequality? If so, how can I go about doing that? How do I opt-out of the new Reply in Gmail? Today, when trying to reply to a message in Gmail, I was told that there is a new reply mode and then it was automatically enabled. I find it difficult to use, and it doesn't let you reply to the message in accordance with the netiquette I'm used to.  How do I opt-out of this brand new reply mode? It wasn't there yesterday. Getting key with maximum value in dictionary? Why do polarized sunglasses remove (most) reflections on car windows?  I know that both lenses of polarized sunglasses are polarized in the same direction and I can see that reflections in my own windshield and the windows of other cars appear, disappear, or change depending on how I tilt my head, but why?  Why is the light in those reflections polarized?  edit: And why is most of the light in the various reflections on the interior of my own windshield and various windows/windshields at what seem like a variety of angles all polarized in a sufficiently narrow set of ways as to make polarized sunglasses work?