Where is the problem here:$-1=(-1)^1=(-1)^\frac{2}{2}=({(-1)}^{2})^{1/2}=\sqrt{1}=1$?
Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$?
Don't impose delay loading Close dialog when you haven't just loaded it Because of , clicking the "close" link on a question that's been edited (for me usually the edit comes in a half-second before, as I'm reaching for the link) reloads the question instead of opening the Close dialog. Clicking it again to actually open the close dialog says     You may only open the Close dialog every three seconds   I didn't open it, I refreshed the post.  And yes, there are lots of times when the post edit is so trivial it's obvious in less than a second that it doesn't affect the need to close the question. What's the "official" explanation for Harry's (and everyone else's) absence from muggle school? Is there a way to make sure that a deleted file can not be recovered?   As you know, deleting a file by pressing shift-del or using trash doesn't mean that file is gone forever. It resides somewhere in the computer.  In day to day life, law enforcement or thieves use recovery programs to reveal our private data or something else.   They can recover all data that resides on hard disk, in RAM, and even USB.  To protect us from these people, what should one do? Which program should one use?  Note: I don't want an answer like first use a recovery program then erase that file with shred. With just one program, I want to erase all unused/deleted files on my computer. Additive group contains exactly three elements of the set $\{p,p+q,pq,p^q,q^p\}$ Is there a schematic overview of Ubuntu's architecture? as enthusiastic, advanced Linux learner, I'd love to get an overview about Linux' architecure/structure in general. You know, like "the big picture".  I'm thinking of a large schematic graphic showing what is what, who is who, what system (e.g. X) comprises which subsystems (GDM/Gnome/Compiz) on the way from a to z, from boot to interactive desktop, including the most important background services (auth, network, cron, ...).   Maybe a bit like this:  but way more detailed. There's bootchart, which produces very comprehensive charts, but they again are too detailed and difficult to get the "big picture" from.  Is there such a thing? Possibly not for the whole System, but maybe for single subsystems?  I had trouble searching for this, because using search terms like "scheme" or "architecture" pointed to the wrong direction (a tool called "scheme" or CAD software for linux).  I appreciate any links. If there's interest in those schematic overviews and links, maybe someone could turn this post into a wiki post? is it possible to raise the tip while raising the back and lowering the center of the tongue when making /R/ sound? Following , this is how we correctly make the r sound:   Let the throat vibrate since it is voiced. Round the lip a little. Raise the tip of the tongue towards the hard bump behind the upper front teeth,  but do not let the tip of tongue touch the bump. This also makes the center of the tongue go down. The back part of the tongue is raised because you pull it into a tight ball Fold and raise the sides of the tongue so they touch the upper side-teeth.   If we follow the above requirement, our tongue should have an s shape when we pronounce the r sound as depicted in the following sketch:    Is it possible to raise the tip while raising the back and lowering the center of the tongue when making an r sound?   How do native speakers make an r?  P.S. My tongue is very short anyway! Say I have two Chrome windows open like this:   It seems that the most recently used window always appears on top. In other words, the &quot;Apply Digital Signatures&quot; was the window I had open last. If I were to switch to the window showing the new tab, then the order in which the windows are displayed in the task bar suddenly changes. Is there a way to keep them from shuffling around? I'd like to be able to order them however I want, like tabs in a web browser. (I'd also like to put them across different workspaces.) How to read dash files How can you draw more detailed/smoother images in pygame? Flowchart using Tikz I'm trying to create a fine flowchart that is a bit complicated. Therefore I need a block for a predefined process and a connector block as well as a data block. Can someone help me? In comment is what I'd like to see in my code to keep my code nicely arranged. The rest of the code is a simple example for the Tikz site.  \documentclass{article}  \usepackage[latin1]{inputenc} \usepackage{tikz} \usetikzlibrary{shapes,arrows} \begin{document} \pagestyle{empty}   % Define block styles \tikzstyle{decision} = [diamond, draw, fill=blue!20,      text width=4.5em, text badly centered, node distance=3cm, inner sep=0pt] \tikzstyle{block} = [rectangle, draw, fill=blue!20,      text width=5em, text centered, rounded corners, minimum height=4em] \tikzstyle{line} = [draw, -latex'] \tikzstyle{cloud} = [draw, ellipse,fill=red!20, node distance=3cm,     minimum height=2em]  %\tikzstyle{subroutine} = [draw,rectangle split, rectangle split         horizontal,rectangle split parts=3,minimum height=1cm]  %\tikzstyle{connector} = [draw,circle,...] %\tikzstyle{data} = [draw, trapezium, ...]  \begin{tikzpicture}[node distance = 2cm, auto]     % Place nodes     \node [block] (init) {initialize model};     \node [cloud, left of=init] (expert) {expert};     \node [cloud, right of=init] (system) {system};     \node [block, below of=init] (identify) {identify candidate models};     \node [block, below of=identify] (evaluate) {evaluate candidate models};     \node [block, left of=evaluate, node distance=3cm] (update) {update     model};     \node [decision, below of=evaluate] (decide) {is best candidate     better?};     \node [block, below of=decide, node distance=3cm] (stop) {stop};     % Draw edges     \path [line] (init) -- (identify);     \path [line] (identify) -- (evaluate);     \path [line] (evaluate) -- (decide);     \path [line] (decide) -| node [near start] {yes} (update);     \path [line] (update) |- (identify);     \path [line] (decide) -- node {no}(stop);     \path [line,dashed] (expert) -- (init);     \path [line,dashed] (system) -- (init);     \path [line,dashed] (system) |- (evaluate); \end{tikzpicture}   \end{document} Wiki-tag edit error is non-descriptive I've been editing some wiki entries on the new Expatriates site, and started to get the following error:    When I go to a normal post, I see what is presumably the proper explanation:    Can the Wiki Tag edit error be updated to show a more meaningful error message? Are black hole regarded as baryonic matter in cosmology? Black holes do not have any property as baryonic or non-baryonic matter, as is stated by the no-hair theorem. Regarding conventional theories, in different models of cosmology, like Lambda-CDM, are black holes regarded as baryonic matter, and does the black hole matter significantly affect the baryonic density? Do virtual particles actually physically exist? Unable to disable Hyper-V in Windows 10 Hi I installed Docker for Windows which enabled Hyper-V on my windows 10 machine. Unfortunately this caused Virtual Box to not work anymore, therefore I removed Docker again, but Hyper-V is still activated.  If I try to disable Hyper-V with any of those ways:  on the reboot it will first try to apply the changes and than say that the changes couldn't be applied and reverts, so Hyper-V is activated again.  Has anybody an idea what could be the issue here? how do you make clothes move along with your model? Do you rig the model first and then parent it to the body of the character then click cloth simulation? I am a little bit confused with the process. Thanks for the help. By the time, many files are still on my system and I don't need them anymore, so how to delete all files that are one year old at least? Associativity of symmetric difference of sets By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.) Reference request: Standard textbook for first-order predicate logic in english I am writing my bachelor thesis in english, but I have studied logic in my different native language. Since a rely on elementary results from first-order predicate logic (especially satisfaction in structures), I should reference the reader to a textbook for details.   Is there a standard textbook that starts with elementary propositional logic and goes to Incompleteness theorems? Nginx Subdirectory returning 404 I currently have a bunch of working static files at the domain name khairulslt.me (from NameCheap). Recently, I've tried setting up a subdirectory (khairulslt.me/RGBGame) as seen in the code below; However, I keep getting 404 errors. What am i missing out?  server {    server_name khairulslt.me www.khairulslt.me;    autoindex off;   location / {     root /var/www/khairulslt.me;     index circles.html;   }   listen 443 ssl; # managed by Certbot ssl_certificate /etc/letsencrypt/live/khairulslt.me/fullchain.pem; # managed by Certbot ssl_certificate_key /etc/letsencrypt/live/khairulslt.me/privkey.pem; # managed by Certbot include /etc/letsencrypt/options-ssl-nginx.conf; # managed by Certbot ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; # managed by Certbot  location /RGBGame {     root /var/www/khairulslt.me/RGBGame;     index colorGame.html;     try_files $uri $uri/ /var/www/RGBGame/colorGame.html?q=$uri&amp;$args;     autoindex off;   }  location /robots.txt { return 200 "User-agent: *\nDisallow: /\n";    }  }   server { if ($host = www.khairulslt.me) {     return 301 https://$host$request_uri;   } # managed by Certbot   if ($host = khairulslt.me) {     return 301 https://$host$request_uri;   } # managed by Certbot   listen 80; server_name khairulslt.me www.khairulslt.me; return 404; # managed by Certbot }   I've tried all the different settings like (alias vs root), try_files, autoindex(on, off). My main website www.khairulslt.me works fine and is serving the html/css/js files in /var/www/khairulslt.me perfectly fine. I'm just not sure why I can't replicate the settings for my other app (html/css/js files in folder /RGBGame). Could it be that I've missed out something that isn't related to the nginx config? Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$