How to show that the composite function of two injective functions is injective
Is the composition of two injective functions injective?
How can I write a unit test to determine whether an object can be garbage collected? How can I edit/create new launcher items in Unity by hand? Will Unity allow making custom launcher icons from .desktop files or via menu editing system? (Right now the launcher doesn't give the option to "keep in launcher" on all programs.  For some programs I use, I have to make custom launchers or .desktop files.  For instance, daily blender builds are generally just folders with an executable.  In basic Gnome or KDE, I can make a new menu entry with the menu editing system. Then, I can also add it to Docky either from the menu or by dragging a .desktop file to it. Unity launcher doesn't support drag and drop, so thats not a bug or anything, but when I open a .desktop file, it has unpredictable results. Most time it will not have "keep in launcher". Sometime it will have a pinnable item without the .desktop's icon, and if I pin the item to the launcher, it will not call upon the program again after closing it. I've also gotten it to just work with a .desktop file for celtx. Tag info not updated regularly on profile? From my , I learned that all tag related info on profile will be updated daily at UTC 03:00.  However, something is wrong here. It's now UTC 05:00+, but my tag number, say 93 (c++) is not updated against yesterday. I am pretty sure about this and I did earn some more points throughout the day. Sorry for not be able to capture the screenshot yesterday, but I did check this number 10 hours ago (which belongs to yesterday, also 93).  Is there a bug happening here? Or updating time different?    UPDATE: As of 24 Jan, the tags are still not updated with the proper values.  UPDATE2: Fixed around 25 Jan, UTC 03:00, at least for me. $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ Let $f:[a,b]\to  R$ be integrable and continuous on $(a,b)$. Prove that: $$\lim_{h\to 0} \int_a^b\frac{f(x+h)-f(x)}{h} \,\mathrm{d}x = f(b)-f(a).$$  What I've tried so far: make a change of variables, which didn't help. I also thought of using the intermediate value theorem inside the integral, but the function being differentiable is not specified. Any help, tips? Thanks in advance! Two circles intersection Could you tell what are all the four points in following? Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is the argument about the other two missing points ? How do I add custom validations to Webform? I have created the country and state fields with the Webform module, and I want to add a field validation for the state field when user select US as country.   How can I achieve this? What does "Warning: untrusted X11 forwarding setup failed: xauth key data not generated" mean when ssh'ing with -X? How does one create, caption, label and refer to a subfigure? Can "it" be used with plural subject? Several years ago I heard of something called dummy subjects in high school. It was then stated that, for example, it is a dummy subject when it starts many instances of sentences, e.g.        It is rainy today.   It is hard to imagine how hard is to live alone.   It is not my university degree that matters here.     My question is if we can use it with plural subjects? For example in       If some think that in Mahmoud Dowlatabadi’s works it is only social themes that matter and the writer is ignoring fictional arrays and artistic techniques, at least, endings of his stories show wrongness of this idea.     My question deals with the italicized part. If this usage is OK, can we also write they are social themes that matter? I mean can they also play the role of a dummy subject? This is my first post on this forum :)  I've been trying for a while to solve this problem about symmetric difference of two sets:     Given two sets $A$ and $B$, we call symmetric difference of $A$ and $B$ the following:      $$A\mathrel{\triangle}B = (A\cup B)-(A\cap B)$$      Show that if $A\mathrel{\triangle} B = \emptyset$, then $(A\subset B) \vee (B\subset A)$.   I don’t know where to start; thank you very much for the help :) MySQL not using indexes with WHERE IN clause? I have written code like below and all works fine, but while submitting the form I get the error below. I am trying to filter the second dropdown based on the first drop down selection.     An illegal choice has been detected. Please contact the site administrator.   How do I overcome that error?       function dynamic_location_dropdown_form_alter(&amp;$form, $form_state, $form_id) {   if($form_id == 'product_node_form') {    $location_options = array();    if(isset($form['field_destination']['und']['#default_value'][0])) {     $destination = $form['field_destination']['und']['#default_value'][0];   }   else {     $destination = 0;   }    $location_options = dynamic_location_dropdown_locations($destination);    $form['field_destination']['und']['#ajax'] = array(     'event' =&gt; 'change',     'wrapper' =&gt; 'squadron-wrapper',     'callback' =&gt; 'dynamic_location_dropdown_ajax_callback',     'method' =&gt; 'replace',   );   $form['field_product_location']['#validated'] = true;   $form['field_product_location']['und']['#prefix'] = '&lt;div id="squadron-wrapper"&gt;';   $form['field_product_location']['und']['#suffix'] = '&lt;/div&gt;';   $form['field_product_location']['und']['#options'] = $location_options;   } }  function dynamic_location_dropdown_ajax_callback($form, $form_state) {   $country_id = $form['field_destination']['und']['#value'];   $form['field_product_location']['#validated'] = true;   $form['field_product_location']['und']['#options'] =  dynamic_location_dropdown_locations($country_id);    return $form['field_product_location']; }  function dynamic_location_dropdown_locations($destination_id) {   $nodes = array();   $nodes[''] = '- None -';   if($destination_id != '') {     $select = db_query("       SELECT node.title AS node_title, node.nid AS nid, node.created AS node_created       FROM {node} node       LEFT JOIN {field_data_field_location_country} field_data_field_location_country        ON node.nid = field_data_field_location_country.entity_id        AND (field_data_field_location_country.entity_type = 'node'        AND field_data_field_location_country.deleted = '0')       WHERE (( (node.status = '1')        AND (node.type IN  ('location'))        AND (field_data_field_location_country.field_location_country_nid = $destination_id)))       ORDER BY node_title ASC     ");     $nodes[''] = '- None -';     foreach ($select as $node) {       $nodes[$node-&gt;nid] = $node-&gt;node_title;     }   }    return $nodes; } How do I answer "Where do you work?" What are the main purposes to ask someone 'Where do you work?' apart from to find out the type of place he or she works in?  I can answer:     I work in a shop.   I work in a hospital.   I work in an office.   But what other things can (or should) I use as a reply to this question?    Extra question:  sometimes I see     I work at a shop.    I work at a hospital.    I work at an office.   What's the difference between 'at' and 'in' in this case? How to define a Bijection between $(A^B)^C$ and $A^{B \times C}$ Spacing before and after section titles I know this subject has been mentioned before, but I'm still having a problem in creating a space under a section title. I used the titlesec package and then tried using the command \titlespacing{\section}...  This is my code. Can anybody help?  \documentclass[10pt]{book} \usepackage[utf8]{inputenc} \usepackage{fullpage} \usepackage[compact]{titlesec} \usepackage{setspace} \usepackage{sectsty} \chapterfont{\huge} \sectionfont{\Huge} \begin{document} \chapter*{Kapitel 1} \section*{Einleitung} \begin{large} \subsection*{1.1 Motivation} Modifying list while iterating How can you programmatically tell an HTML SELECT to drop down (for example, due to mouseover)? How to enable hibernation? Is there a list of Windows special directories/shortcuts (like %TEMP%)? I'm looking for a reference list of shortcuts like %TEMP%.  When I'm using Windows+R or Windows Explorer and type %temp%, the Windows Explorer takes me to the Temp directory. Are there more of these shortcuts?  UPDATE: . Run cmd.exe in Administrator mode without explorer.exe I've recently had trouble with explorer.exe not working.  I found a possible solution , using .  The problem is that I cannot "right-click Command Prompt, and then click Run as administrator", since explorer.exe does not work for even a second without crashing.  I tried to use the  to open cmd as administrator, but I get an error 1327 because I have a blank password.    My question is, is there any other way to run cmd.exe with admin privileges?  If not, is there any way to run sfc.exe without admin privileges?  If not, does anyone have solution to my original problem of explorer.exe stopping and restarting ad nauseam?