localStorage.setItem() not working on page load
How to execute a JavaScript function when I have its name as a string
What is wrong with this fake proof $e^i = 1$? Prove Or Disprove: tr(AB)=tr(A)*tr(B) $\mathrm{tr}(AB)=\sum\limits_{i=1}^n \sum\limits_{j=1}^n a_{ij}*b_{ji}$  $\mathrm{tr}(A)*\mathrm{tr}(B)=\sum\limits_{i=1}^n a_{ii}*\sum\limits_{i=1}^n b_{ii}$  Therefore $\mathrm{tr}(AB) \neq \mathrm{tr}(A)*\mathrm{tr}(B)$  Is the proof valid? Filling triangle doesn't seem to work with PGF/TikZ I was wondering if anyone had any clue on why my triangles are not filled in red within the following piece of code:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{calc,3d}  \usepackage[active, pdftex, tightpage]{preview} \PreviewEnvironment[{[]}]{tikzpicture} \newcounter{number}  \begin{document} \begin{tikzpicture}[x  = {(-0.5cm,-0.5cm)},                     y  = {(0.9659cm,-0.25882cm)},                     z  = {(0cm,1cm)}] \begin{scope}[canvas is yx plane at z=0] \foreach \x / \y / \label in {1 / 0.4 / 1, 0.9 / 0.4 / 0, 1 / 0.5 / 1, 0.7 / 0.3 / 0, 0.8 / 0.4 / 0, 0.9 / 0.5 / 0, 1 / 0.6 / 1, 0.7 / 0.4 / 0, 0.4 / 0.4 / 0, 0.6 / 0.4 / 0, 0.5 / 0.4 / 0, 0.8 / 0.5 / 0, 0.9 / 0.6 / 0, 1 / 0.7 / 1, 0.7 / 0.5 / 0, 0.5 / 0.5 / 0, 0.4 / 0.5 / 0, 0.6 / 0.5 / 0, 0.8 / 0.6 / 0, 0.9 / 0.7 / 0, 1 / 0.8 / 1, 0.7 / 0.6 / 0, 0.6 / 0.6 / 0, 0.5 / 0.6 / 0} { \addtocounter{number}{1} \pgfmathparse{\value{number}}\let\k\pgfmathresult \draw (8 * \x, 8 * \y) node[inner sep=0, outer sep = -0.1pt,color=black,fill,circle] (node-\k) {}; };  \foreach \x / \y / \z / \trash in { 4/5/8/0, 9/11/16/0, 9/16/17/0, 11/10/18/0, 11/18/16/0, 10/8/15/0, 10/15/18/0, 8/5/12/0, 8/12/15/0, 5/2/6/0, 5/6/12/0, 2/1/3/0, 2/3/6/0, 17/16/24/0, 16/18/23/0, 16/23/24/0, 18/15/22/0, 18/22/23/0, 15/12/19/0, 15/19/22/0, 12/6/13/0, 12/13/19/0, 6/3/7/0} { \draw[fill=red]  (node-\x) --  (node-\y) --  (node-\z) -- cycle; } \end{scope} \end{tikzpicture} \end{document}) SQL to find the number of distinct values in a column I can select all the distinct values in a column in the following ways:   SELECT DISTINCT column_name FROM table_name; SELECT column_name FROM table_name GROUP BY column_name;   But how do I get the row count from that query? Is a subquery required? If I have a Windows executable, how can I find out which dlls it will load?  I'm just talking about which ones that will be loaded statically, not ones it might load dynamically with something like LoadLibrary. Show that $f(z)=0$. Suppose that $f:\mathbb{C}\rightarrow\mathbb{C}$ is analytic on the open unit disc and continuous on the closed unit disc. Assume that $f(z)=0$ on an arc of the circle $\{z\in\mathbb{C}:|z|=1\}$. Show that $f(z)=0$. How to increase Scrollback lines in Ubuntu(14.04.2) server edition? I can see only limited lines on terminal by using shift+ pageup. in Ubuntu desktop version, there is option to make scroll-back lines unlimited. how to do it in Ubuntu server version. please suggest. Incorrect icons on hot network questions I see the same problem has occurred in the past, the most-linked one being   Is this happening for anyone else?   I've marked the icons I could recognize as incorrect.  This exists on every page, is on both chrome and firefox (from Ubuntu 16.04), and persists after hard-refreshes in each.  Edit: The icons in Meta's Hot Network Questions tab appear to be consistently accurate. Every other page I checked (including Unix, Workplace, English Language &amp; Usage, Money, and Sci-fi) have a handful of incorrect ones, even for some of the same questions that are displayed correctly in Meta.  Further note: if it matters, the icons are also incorrect in the drop down community-search feature on the right end of the header. Again, they appear correct on this Meta page, and incorrect on all other pages I've checked. Some of the ones that are consistently incorrect:   computational science constructed languages movies and TV raspberri pi rpg russian language science fiction and fantasy sitecore skeptics super user latex workplace   That distribution seems skewed, but I may just be disproportionately familiar with the sites at the end of the alphabet. Many others could be wrong, those are just the ones I could recognize.    Last edit: apparently my Google skills were lacking -  was asked an hour prior. How can I reduce screen brightness below the minimum without an app? I have an Optimus Elite, and it has a minimum brightness setting. In certain apps, I can reduce the brightness below the safe minimum, but when I leave the app, the brightness is increased to the system-wide minimum.  Using , I can permanently set the brightness below the safe amount, and it will stay even after going to other apps. Or using , I can accomplish almost the same thing even without needing root (it displays a translucent 'filter' over the whole screen, reducing brightness/contrast but not actually changing the backlighting power amount).  What I want to know is where the minimum screen brightness is stored. I have a rooted phone with CyanogenMod 9, so I have permissions to edit anything and could change a config or sqlite entry, but I don't know where this value is stored. What I would like to do is use the status bar brightness slider to be able to slide to the actual minimum of the screen, rather than the OS-controlled minimum. Having an app is useful, but having the functionality without the app seems to be within reach, if only I knew where the OS is getting it's safe minimum setting.  Where is this "safe minimum brightness" setting stored? If I can change it, I can remove my apps and use native controls. The web is littered with any number of pages () giving an existence and uniqueness proof that a pair of squares can be found summing to primes congruent to 1 mod 4 (and also that there are no such pairs for primes congruent to 3 mod 4).  However, none of the stuff I've read on the topic offers any help with actually efficiently finding (ie other than a straight search up to sqrt(p)) the concrete values of such squares.  What's the best way to actually find them ? A doubt on the definition of limit of a function definition I want to prove the definition of limit of a function from definition (1) to definition (2).  (1) A function $f(x)$ is said to have $f^*$ as the limit as $x$ tends $x^*$ iff for every sequence $\{x_n\}$ with limit $x^*$, the limit $\lim_{n-&gt;\infty}f(x_n)$ exists and is equal to $f^*$. (2) A function is said to have $f^*$ as the limit as $x$ tends $x^*$ iff for each $\epsilon &gt;0$, there exists a $\delta_\epsilon &gt;0$ such that $|f(x)-f^*| &lt;\epsilon \forall |x^*-x|&lt;\delta_\epsilon$  I am confused about the steps. Suppose I am given an $\epsilon &gt; 0$ and $x^*$. I have to show the existence of a $\delta_\epsilon &gt;0$ such that for all $x$ satisfying  $|x^*-x|&lt;\delta_\epsilon$ I can construct a sequence $x_n$ which converges to $x^*$ and $x_n=x$ for some $n \geq N$. Then I can say that $f(x_n)-f^*=f(x)-f^* &lt; \epsilon$. I think I may have made some mistake about the steps.  My main confusion is the following : Suppose I choose $\delta_\epsilon=\epsilon$. Then if a sequence $\{x_n\}$ converges to $x^*$ then $x_n=x$ (where $x$ satisfies $|x-x^*|&lt;\epsilon$) for some $n\geq N$. Now, $\lim_{n-&gt;\infty}f(x_n)$ exists implies there exists an $M$ such that $\forall n\geq M$, $f(x_n)-f^* &lt;\epsilon$. Now, I need to show that for some $n \geq M$ indeed $x_n=x$. How do I show that ? This $M$ and $N$ are different. Why Oracle discontinued Oracle Java (JDK) Installer PPA? How to check if a row exists in MySQL? (i.e. check if an email exists in MySQL) Post for clarifications on the updated pronouns FAQ Badge progress reports Is there a way to view your own progress towards certain badges? For example:   Tumbleweed - What value constitutes low views for a week? Fanatic  – Is there a way to view how many days in a row you currently have? Beta – Is it even possible to get this badge anymore? Here are some examples.  "Until the Son of God appear" What I was taught: Subjunctive of indefinite future.  "It is required that the applicant be 18 years old and possess a valid driver's license." What I was taught: mandative subjunctive.  "Where be ye going," said the false knight on the road?" What I was taught: subjunctive of direct discourse.  "If I were you, which we both are thankful I am not, I wouldn't do that. What I was taught: The subjunctive mood is used for supposition contrary to fact.  "I dreamed I were a fireman in my Maidenform bra." What I was taught: The subjunctive mood can be used with words like dream.  "God bless you." I don't remember, so obviously I wasn't taught.  I can live with Pluto's not being a planet, but I must say it's irksome to find that so much of what I was told about English turns out to be nonsense. Is there a way to remove sites permanently from (my personal) Google search results? I regularly find sites that copy content from elsewhere (mailing lists, etc) while not providing any added value. Quite to the contrary, they are pretty heaped with ads.  I'd like to remove those sites as permanently as possible from my Google search results. Any ideas? Port forwarding with UFW I realize UFW is mainly just for enabling/disabling access on particular ports, but I'm trying to forward one port to another. I want any connection to port 1724 to be forwarded to 1723.   The file /etc/default/ufw already has DEFAULT_FORWARD_POLICY="ACCEPT". And I believe I need to uncomment net/ipv4/ip_forward=1 in /etc/ufw/sysctl.conf. Finally I need to edit /etc/ufw/before.rules to add an iptables rule.   And here is where I get lost because I can't find any documentation for this file. Where do I add the rule? And how exactly?  In particular:   On exactly which line do I add the rule? Do I put anything before or after it? Remove empty elements from an array in Javascript Prove $\lim_{x\to0}\sqrt{4-x}=2$ using the precise definition of limits. (Epsilon-Delta) Prove $$\lim_{x\to0}\sqrt{4-x}=2$$ using the precise definition of limits. (Epsilon-Delta)  I am not sure how to link $0&lt;\left |x  \right |&lt;\delta$ with $\left |\sqrt{4-x}-2\right |&lt;\epsilon$ .  EDIT (Trying it out now)  I worked till here, then I basically got stuck.