What is correct:     1) Books and music makes life even better   or     2) Books and music make life even better   (saw a quote #1 and t-shirt with #2)
I was surfing the internet the other day when I found this phrase: Instead your precious time and attention is wasted. To my ears, it sounds wrong. But I'm not a native English speaker, so I consulted with a number of them, and some of them said that it was "is" because the adjective modifies only the noun "time" and not "attention". Others said it "is" because that's just how it is. But I still believe it should be "are". Any help is appreciated.
"Stay home" or "stay at home" – which is correct and why? Image, pre-image, and injection proof verification Just wanted to verify this proof was correct. Trying to make sure I have a handle on these subjects before the exam. Any style comments also more than welcome.    Statement: Let $f : A \mapsto B$ be a function. $f$ is injective if and only if for all $X \subseteq A$, $f^{-1}(f(X)) \subseteq X$.  Proof:  $\Rightarrow$ Suppose that $f$ is injective. Let $X \subseteq A$, and let $x \in X$. Since $f$ is injective, $f^{-1}(f(X)) = \{x\} \in X$, so $f^{-1}(f(X)) \subseteq X$.   $\Leftarrow$ Suppose that for all $X \subseteq A$, $f^{-1}(f(X)) \subseteq X$. Let $a_1, a_2 \in A$ and $X = \{a_1\}$. Suppose $f(a_1) = f(a_2)$. If $a_1 \neq a_2$, then $f^{-1}(f(X)) = \{a_1, a_2\} \not \subseteq X$, a contradiction. Thus $a_1 = a_2$, so $f$ is injective. Tor browser not opening How can I change my Minecraft username? proof relating to limit definition of e I'm studying the book A Primer for the Mathematics of FinancialEngineering, along with it's solution guide. I've ran into trouble with the solution to question 7 in chapter 1.    The problem is:  Show that $(1+\frac{1}{x})^x &lt; e &lt; (1+\frac{1}{x})^{x+1}$ .   Specifically, I'm having trouble with one step in the solution.    It says that  $$x\ln\left(1+\frac{1}{x}\right)&lt;1&lt;(x+1)\ln\left(1+\frac{1}{x}\right)$$  can be written as   $$\frac{1}{x+1} &lt;\ln\left(1+\frac{1}{x}\right)&lt;\frac{1}{x}, \forall \ge 1.$$  How can the first equality (or is it inequality?) be written as the second? I found a problem with an application on Ubuntu.   Questions :   How do I best report the issue?  What sort of information should I provide? I have a  with a fingerprint reader:    How to make Ubuntu recognise it and use it for login?  I already tried:  sudo add-apt-repository ppa:fingerprint/fingerprint-gui sudo apt-get update   ... but this GUI did not recognizes my device. Does anyone knows any other option? O-Rings vs. Washers for Garden Hoses? How can I retrieve data within my widget I have a Widget which I am creating but my quesiton is how do I access my custom table which I created via my plugin. I am attempting to fill the dropdown from the table called tfp which contains the column liters which I wish to popluate the values into the drop down   class my_plugin extends WP_Widget {  // constructor function my_plugin() {         parent::WP_Widget(false, $name = __('Thomsons Fuels Widget', 'wp_widget_plugin') );  }  // widget form creation function form($instance) {  //Check values if( $instance) {  $title = esc_attr($instance['title']);  $dropdown= esc_attr($instance['dropdown']);  $textarea = $instance['textarea'];  } else {  $title = '';  $textarea = ''; } ?&gt;   &lt;p&gt; &lt;label for="&lt;?php echo $this-&gt;get_field_id('dropdown'); ?&gt;"&gt; &lt;?php _e('Liters',   'wp_widget_plugin'); ?&gt;&lt;/label&gt; &lt;select&gt; &lt;option value="volvo"&gt;Volvo&lt;/option&gt; &lt;/select&gt;  &lt;/p&gt;   How I created the table in the plugin   global $wpdb; global $custom_table_example_db_version;  $table_name = $wpdb-&gt;prefix . 'tfp'; // do not forget about tables prefix  // sql to create your table // NOTICE that: // 1. each field MUST be in separate line // 2. There must be two spaces between PRIMARY KEY and its name //    Like this: PRIMARY KEY[space][space](id) // otherwise dbDelta will not work $sql = "CREATE TABLE " . $table_name . " (   id int(11) NOT NULL AUTO_INCREMENT,   liters VARCHAR(100) NOT NULL,   price VARCHAR(100) NOT NULL,      postcodearea varchar(20) NULL,         dft varchar(20) NULL,   PRIMARY KEY  (id) );";  // we do not execute sql directly // we are calling dbDelta which cant migrate database require_once(ABSPATH . 'wp-admin/includes/upgrade.php'); dbDelta($sql);  // save current database version for later use (on upgrade) add_option('custom_table_example_db_version', $custom_table_example_db_version); Completely clear all output from a Terminal window Loading a .X model in DirectX 9 How can I improve Light Armor as an Archer? I play as an archer, which means sneaking and killing foes off at long range. Problem is, once a creature gets too close to me, I am in a world of troubles. (A random dragon encounter is fair game if I can snipe it off, but a random bear encounter is the thing I fear mostly. Three strikes of such a vicious beast and I drop dead.)  At short range, I use a one-hand sword with shield, but I do not want to put much perks into those skills, as I want to be a sneaky archer first.  Which leaves Light Armor. But to get certain perks I need some skill points, e.g., 30 points are required for the "Custom Fit"- and 40 for "Agile Defender 2/5"-perk. Yet I have no clue how to accumulate those points.  Many enemies won't even see me, so I seldom will be hit. Getting hits means getting skills point. Letting some enemies come close to me and let me hit me on purpose sometimes helps, but since I cannot stand much damage I mostly die erasing any hard earned process.  So is there a teacher for Light Armor like there is for other skills? And if not, how should I go on to improve the Light Armor skill? I want to be able to have LinkedList.contains() return true for a custom comparator.  Suppose that I have 1 LinkedList and 2 objects  LinkedList&lt;MyObject&gt; myList = new LinkedList&lt;MyObject&gt;();  MyObject a = new MyObject("HELLO"); MyObject b = new MyObject("HELLO");   Technicaly, both objects are identical in terms of comparison (MyObject implements Comparable)   ( a == b ) == true  however, when I do the following, myList does not return true for myList.contains(b)  myList.add(a) myList.contains(b) // == false   I think its because contains will check object reference and see that a and b are 2 distinct objects. Is there any way I can make it so I don't have to extend LinkedList to compare those objects? I am a graduate student in mathematics who would like to learn some classical mechanics. However, there is one caveat: I am not interested in the standard coordinate approach. I can't help but think of the fields that arise in physics as sections of vector bundles (or maybe principal bundles) and would love an approach to classical mechanics or what have you that took advantage of this.  Now for the questions:   Is there a text book you would recommend that phrases the constructions in classical mechanics via bundles without an appeal to transition functions?   What are the drawbacks to this approach other than the fact that it makes computations less doable? (if it does that)   Are there benefits to thinking about things this way, ie would it be of benefit to someone attempting to learn this material to do it this way? "Hope you won't" vs "Hope you don't" What is the difference between "Hope you don't mind" and "Hope you won't mind"? What could be a contextual difference between the two? In a situation like the following, which one seems more appropriate?        Expect me to knock on your door sometimes. Hope you don't mind -or- Hope you won't mind (my knocking on your door) $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ Finding minimum bounding extent of given pixel value within raster? Upgrade to the latest PHP version in Ubuntu I am using  in my server and NextCloud informs me that:     You are currently running PHP 7.0.32-0ubuntu0.16.04.1. Upgrade your   PHP version to take advantage of performance and security updates   provided by the PHP Group as soon as your distribution supports it.   So, I tried to upgrade me OS (Ubuntu 16.04), by executing:  apt-get update  apt-get dist-update  Then I restarted the server and I re-executed the above commands. After all these, when I connect from terminal I am getting:  Welcome to Ubuntu 16.04.5 LTS (GNU/Linux 4.4.0-83-generic x86_64)   * Documentation:  https://help.ubuntu.com  * Management:     https://landscape.canonical.com  * Support:        https://ubuntu.com/advantage  0 packages can be updated. 0 updates are security updates.   and my PHP version is still PHP 7.0.32-0ubuntu0.16.04.1 (cli) ( NTS ).  This means that PHP 7.0.32 is the latest possible version that I can install in ubuntu 16.04; number of trailing zeros Securely erase hard drive using the Disk Utility