I just saw this symbol in an article of 1990 and was curious about how to display it in latex, but haven't found any answers after googling.  Does anybody know that or tell me it is actually rarely used nowadays?    It's at the end of the paragraph. Thanks a lot!
I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?
diagram software for Ubuntu? Proving that a list of perfect square numbers is complete Well, I have a number  $n$ that is given by:  $$n=1+12x^2\left(1+x\right)\tag1$$  I want to find $x\in\mathbb{Z}$ such that $n$ is a perfect square.  I found the following solutions:  $$\left(x,n\right)=\left\{\left(-1,1^2\right),\left(0,1^2\right),\left(1,5^2\right),\left(4,31^2\right),\left(6,55^2\right)\right\}\tag2$$     Is there a way to prove that this a complete set of solutions? So I mean that the solutions given in formula $(2)$ are the only ones?     My work:   We know that: $$ 1 + 12x^2 \left(1+x \right) \ge 0   \space \Longleftrightarrow \space   x \ge -\frac{1+2^{-2/3}+2^{2/3}}{3}   \approx -1.07245 \tag3 $$ So we know that for $x&lt;-1$ there are definitely no solutions. Manual/automatic line breaks and text alignment in TikZ nodes The Challenge  I have been trying to write a filter that applies (prepends a string) to (a) post titles of a certain post type and (b) to that same post type WordPress admin backend for use by an auto social sharing plugin.  I've gotten really close.  I've achieved: 1.  prepending only to custom post_type post titles 2.  prepending to custom_post type titles AND all nav menu items 3.  prepending to ALL titles (post, page, nav menu, and backend auto-sharing plugin)  The final, 3rd attempt got me very hopeful, but yet still, no matter the function, conditional statement, or combination I use, I can't get custom_post title AND backend social sharing plugin, but not nav menu items.  My Code - what I've tried  I've tried different conditionals, like is_admin() and !is_nav_menu with all nav menu IDs.  I've also tried comparing the ID of the post to the ID of the menu.  Finally, I've also tried adding the filter only to loop_start and that seems promising if combined with other statements.  I will clean up my code for your review but I leave it this way for now in hopes it helps to see what I've tried and maybe where I went wrong with any of those methods.  // , $id = NULL function append_album_review_to_title( $title ) {     global $post;     global $dont_apply_title_filter;     $text = 'Album Review: ';     $prepended_title = $text . $title; /*     $nav_menus_obj = wp_get_nav_menus();     $nav_menu_ids = '';     foreach( $nav_menus_obj as $nav_menu ) {         $nav_menu_ids .= $nav_menu-&gt;term_id . ',';     }     rtrim($nav_menu_ids, ','); */ //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; in_the_loop() ){ //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; $id == get_the_ID() ){ //  if ( !is_nav_menu( '32057,32058,35135,32054,32056' ) ) { //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; is_nav_menu( $id ) ) {     if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; !$dont_apply_title_filter ) {         //print_r( $nav_menu_ids );         //print_r( is_nav_menu( $nav_menu_ids ) );         return $prepended_title; /*     } elseif ( get_post_type( $post-&gt;ID ) == 'album_review'  ) {         return $title; */     } else {         return $title;     }; } add_filter('the_title', 'append_album_review_to_title'); //add_action('save_post', 'custom_post_type_title', 100); /* function set_custom_title() {     add_filter( 'the_title', 'append_album_review_to_title', 10, 2 ); } add_action( 'loop_start', 'set_custom_title' ); */ Graph Proof by induction. Can you prove via induction that there exists a node in a directed graph of n nodes that can be reached in at most two edges from every other node in the graph. Every node in the graph is required to have an edge with every other node that either points out or in (For every pair of nodes X and Y, either X points to Y or Y points to X). How did the word "Bollywood" originate? As we know, American film industry is referred as Hollywood. The American film industry is called so because the film industry emerged at the place called (Correct me if I am wrong). The place adopted the name Hollywood which is informally known as Tinseltown.  But my question is not about Hollywood but the . This is widely referred as Bollywood.   From the  page of Bollywood:      Bollywood is the sobriquet for India's Hindi language film industry, based in the city of Mumbai, Maharashtra. It is more formally referred to as Hindi cinema. The term "Bollywood" is often used by non-Indians as a synecdoche to refer to the whole of Indian cinema; however, Bollywood proper is only a part of the larger Indian film industry, which includes other production centres producing films in many other Indian languages. There is no place in India called Bollywood like the Hollywood.    Many people prefer calling it as Hindi film industry and against naming film industries with wood. There are other film industries in India too in other languages. Eg: Telugu film industry is named as Tollywood, Tamil industry is named Kollywood etc.,   is the list of Hollywood inspired nicknames.  My question:   Who is the creator of the word Bollywood? Since when did the word become popular? What are the main reasons the elves did not show up in force to defeat Sauron? During The Great Battle of the Last Alliance, there were an estimated 100,000 elves that fought with the armies of Isildur. This was one of the first scenes in the first LOTR movie. However, in the trilogy, it appears that only a small number of elves show up to Helms Deep and overall left the majority of the fighting to the humans. Why did the elves not participate during the rest of the war? Does there exist a bijective $f:\mathbb{N} \to \mathbb{N}$ such that $\sum f(n)/n^2$ converges? We know that $\displaystyle\zeta(2)=\sum\limits_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$ and it converges.        Does there exists a bijective map $f:\mathbb{N} \to \mathbb{N}$ such that the sum $$\sum\limits_{n=1}^{\infty} \frac{f(n)}{n^2}$$ converges.      If our $s=2$ was not fixed, then can we have a function such that $\displaystyle \zeta(s)=\sum\limits_{n=1}^{\infty} \frac{f(n)}{n^s}$ converges What does --shell-escape do? I stumbled upon an example, which needed to be compiled with the additional option --shell-escape. Using this option it worked just fine, but I'm curious:     Why or when is this option needed and what does it actually do? $$Rad(I)=\{a \in R | \exists n \in \mathbb{N} \text{ such that } a^n \in I\}$$   R is a commutative ring, I is an ideal.   To show that $Rad(I)$ is an ideal of $I$, we have to show that for $a,b \in Rad(I)$ it stands that $a-b \in Rad(I)$ and for $r\in R$ it stands that $a\cdot r\in Rad(I)$, right??   When $a,b \in Rad(I)$ we have that $a,b \in R$ and $a^n, b^m \in I$.   $a-b \in R$.   But how can we show that $(a-b)^x \in I, x \in \mathbb{N}$ ?? I've followed this tutorial to install Ubuntu 15.10:    After restarting my computer I got to the grub menu and chose Ubuntu. Shortly after that I got this error:  /run/lvm/lvmetad.socket: connect failed: No such file or directory WARNING: Failed to connect to lvmetad. Falling back to internal scanning.   These messages keep adding up on a black screen every second. After a while,  I get access to the initramfs ash console.  what am I doing wrong? Change default CSS of Google Chrome I would like to be able to change the default CSS used by chrome, such as removing the underlines for links, etc. However, I cannot find the default CSS file used by Chrome. Does anyone know where it is? Is it consistent with ZF for there to exist a set $S$ such that the power set $P(S)$ is countable? If so, what is the weakest form of the axiom of choice needed to prove that no such set exists? How do you join or create a server in multiplayer? I just got Minecraft Pocket Edition on my iPhone, but I'm having trouble figuring out how to start multiplayer. When I go to menu, there is only one button that says Play. How do I join or create servers? Given a file like this:  1,768,12,46576457,7898 1,123,435,134,146 2,345,6756856,12312,1311 5,234,567465,12341,1341 1,3245,4356345,2442,13 9,423,2342,121,463 9,989,342,121,1212   I would like to list all rows (in bash terminal) such that the value in column 1 appears at least twice (in column 1). The result should be  1,768,12,46576457,7898 1,123,435,134,146 1,3245,4356345,2442,13 9,423,2342,121,463 9,989,342,121,1212 How do I share variables between two functions? So...here is part of my code for a plugin.  I'm a newb of sorts so be kind.  I've read up on global variables but I can't seem to get it to work and I've read you shouldn't use them anyway.  So what would be the best way to write the code below without having to re-declare the variables for each function?  Here is the  if necessary.  // Display the product badge on the shop page  add_action( 'woocommerce_after_shop_loop_item_title', 'wc_simple_product_badge_display_shop', 30 ); function wc_simple_product_badge_display_shop() {     $title = get_post_meta( get_the_ID(), '_wc_simple_product_badge_title', true ); // badge title     $class = get_post_meta( get_the_ID(), '_wc_simple_product_badge_class', true ); // badge class     $duration = get_post_meta( get_the_ID(), '_wc_simple_product_badge_duration', true ); // badge duration     $postdate = get_the_time( 'Y-m-d' ); // post date     $postdatestamp = strtotime( $postdate ); // post date in unix timestamp     $difference = round ((time() - $postdatestamp) / (24*60*60));  // difference in days between now and product's post date      if ( !empty( $title ) &amp;&amp; empty( $duration ) || !empty( $title ) &amp;&amp; $difference &lt;= $duration ){ // Check to see if there is a title and the product is still within the duration timeframe if specified         $class = !empty( $class ) ? $class : '';         echo '&lt;span class="wc_simple_product_badge ' . $class . '"&gt;' . $title . '&lt;/span&gt;';     } }  // Display the product badge on the single page  add_filter( 'woocommerce_single_product_image_html', 'wc_simple_product_badge_display_single' );     function wc_simple_product_badge_display_single( $img_html ) {     $title = get_post_meta( get_the_ID(), '_wc_simple_product_badge_title', true ); // badge title     $class = get_post_meta( get_the_ID(), '_wc_simple_product_badge_class', true ); // badge class     $duration = get_post_meta( get_the_ID(), '_wc_simple_product_badge_duration', true ); // badge duration     $single_opt = get_post_meta( get_the_ID(), '_wc_simple_product_badge_single_page_option', true ); // badge on single page     $postdate = get_the_time( 'Y-m-d' ); // post date     $postdatestamp = strtotime( $postdate ); // post date in unix timestamp     $difference = round ((time() - $postdatestamp) / (24*60*60));  // difference in days between now and product's post date      if ( !empty( $title ) &amp;&amp; empty( $duration ) &amp;&amp; $single_opt === 'yes' || !empty( $title ) &amp;&amp; $difference &lt;= $duration &amp;&amp; $single_opt === 'yes' ){ // Check to see if there is a title and the product is still within the duration timeframe ()if specified) and the checkbox is checked to show on single page view         $class = !empty( $class ) ? $class : '';         echo '&lt;span class="wc_simple_product_badge ' . $class . '"&gt;' . $title . '&lt;/span&gt;';         return $img_html; }      elseif ( $single_opt === 'no' ) { // Check to see if the checkbox is unchecked to show on single page view         return $img_html;     }  } Retry a task multiple times based on user input in case of an exception in task Fast way to find period-n points of a tent map? I need to find a period-3 orbit for a tent map defined by $$T(x)=\begin{cases}2x &amp; 0\le x\le0.5 \\[2ex] 2-2x &amp;0.5 &lt; x \le 1 \end{cases}$$  So, what is a fast and efficient way of finding it? I only know how to do it by guessing-and-checking. For example, I picked a random point, $x = \frac{2}{7}$ and found that $$T\left(\frac{2}{7}\right)=\frac{4}{7}\\[4ex]T\left(\frac{4}{7}\right)=\frac{6}{7}\\[4ex]T\left(\frac{6}{7}\right)=\frac{2}{7}$$ which is a period-3 orbit. Is there any better way of finding a period-3 orbit , more specifically, a period-3 point? What levels-up Psi-abilities? Mortarboard badges being awarded as a result of bounties after recalc