Find the cardinality of the set $A_p$ defined as the following :
For any prime number $p$, let $A_p$ be the set of integers $d\in \{1,2,\dots, 999\}$ s. Then what is the cardinality of $A_p$?
how implement the jqueryUI in visualforce linear dependence proof using subsets How much of an $n$-dimensional manifold can we embed into $\mathbb{R}^n$? I observed some naive examples. Spheres, for example, when we cut out one point, can be embedded into $\mathbb{R}^n$. And if we cut out a measure zero set of a projective space, it can be embedded into the Euclidean space of the same dimension. So I wonder if all manifolds can be embedded into a same dimensional Euclidean space when we cut out a measure zero set? Can anyone prove it or disprove it by giving me some counterexamples? Change elements on different positions within a list XMLHttpRequest Origin null is not allowed Access-Control-Allow-Origin for file:/// to file:/// (Serverless) form in a .tpl.php file This is the code in my template.php file.  function studiga_theme_theme($existing, $type, $theme, $path) {         $items['add_property_form'] = array(         'render element' =&gt; 'form',         'template' =&gt; 'node--14',         'path' =&gt; drupal_get_path('theme', 'studiga_theme') . '/templates/node',     );      return $items; }    function custom_add_property_form($form, &amp;$form_state) {     $form['first_name'] = array(         '#type' =&gt; 'textfield',         '#attributes' =&gt; array('placeholder' =&gt; t('First name')),     );     $form['last_name'] = array(         '#type' =&gt; 'textfield',         '#attributes' =&gt; array('placeholder' =&gt; t('Last name')),     );     $form['address'] = array(         '#type' =&gt; 'textfield',         '#attributes' =&gt; array('placeholder' =&gt; t('Address')),     );     $form['city'] = array(         '#type' =&gt; 'textfield',         '#attributes' =&gt; array('placeholder' =&gt; t('City')),     );     $form['state'] = array(         '#type' =&gt; 'select',         '#options' =&gt; array(             'default' =&gt; 'State',             '...' =&gt; '...',         ),     );     $form['zip'] = array(         '#type' =&gt; 'textfield',         '#attributes' =&gt; array('placeholder' =&gt; t('Zip')),     );     $form['email'] = array(         '#type' =&gt; 'textfield',         '#attributes' =&gt; array('placeholder' =&gt; t('Email')),     );     $form['phone'] = array(         '#type' =&gt; 'textfield',         '#attributes' =&gt; array('placeholder' =&gt; t('Phone')),     );     $form['submit'] = array(         '#type' =&gt; 'submit',         '#value' =&gt; 'Submit',     );      return $form; }   This is the code in node--14.tpl.php.                                          Contact Information                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  &lt;div class="row"&gt;     &lt;div class="small-12 medium-12 large-8 large-offset-2 columns"&gt;         &lt;?php print render($form['submit']); ?&gt;     &lt;/div&gt; &lt;/div&gt;     But no fields are appearing - what am I doing wrong? You can't have a straight forward  in a tpl.php file can you? $m$ is the Lebesgue measure. I was thinking that: $\Bbb Q$ is dense and $m(\Bbb Q)=0&lt;1$ but it fails to be open, but maybe I could construct an open set from this fact, or also using that $(0,1)$ is a dense and open subset but $m(0,1)=1$.   Any hints or ideas will be very appreciated. Thanks. Miktex Package Installation I recently installed MiKTeX with the texmaker editor and cannot figure out how to update the packages. When I attempt to use the subfigure package with the following preamble  \documentclass[a4paper,12pt]{article} \usepackage[english]{babel} \usepackage{graphicx} \usepackage{subfigure}   I then get a prompt to install a new package, which I then set to the online directory at ctan. I then get the following error:   ! LaTeX Error: File `subfig.sty' not found.Type X to quit or &lt;RETURN&gt; to proceed,or enter new name. (Default extension: sty)Enter file name:! Emergency stop.&lt;read &gt;   How do I properly install packages to miktex? I'm absolutely confused. Thanks in advance for any help. How can I run ssh-add automatically, without a password prompt? I want to communicate between several computers on my network (static Ethernet), through SSH. In order to do that I need to run ssh-add every time I log in on a specific machine, how can I do it so that it's set up once and it doesn't ask me for the passphrase every time I log in or reboot my machine?  I know that there is a way that you should add some lines to the bash_profile file, but I still need to type the password every time I reboot/log in to a specific machine.  if [ -z "$SSH_AUTH_SOCK" ] ; then     eval `ssh-agent -s`     ssh-add fi How can I make sure that a certain OLEDB driver is installed when I start my application? I use ADO from Delphi and would like to display a descriptive error message if the driver is missing. The error that's returned from ADO isn't always that user-friendly.  There are probably a nice little function that returns all installed drivers but I haven't found it. Loopback to forwarded Public IP address from local network - Hairpin NAT Just ran the latest batch of updates on 20.04 (Xubuntu), and now I'm getting a GRUB error: symbol 'grub_calloc' not found  I'm dropped into the 'grub rescue' shell, but have no idea what to do there that might be useful. To me, 'symbol not found' implies some sort of build error with the grub package, but I don't really know how grub works. I noticed that this update also included 'firmware', not sure if that could be related. Is my best bet just to boot from a live CD and see if I can roll back the update to grub somehow? Edited to add: OK, thanks to lots of people ! Here's what I think I now understand.  On 'non-UEFI' systems, grub is installed in two separate parts. The first, most basic, part is the part that is started on bootup. But for most of it's functionality, it needs the second part. These parts must be aligned - neither part must require any functionality from the other part which is not actually there. The visible, run-time problem occurs when these parts are not aligned, and the function grub_calloc is not supplied. It's not 100% clear to me if grub_calloc belongs in the second, larger part or the first. I would have expected the second, but the grub build system is a work of considerable art, so I don't know :).  The root cause of the problem is that the grub update has not ensured that both parts have been updated. Ideally, failure to do this should cause grub installation to fail, and the system should be reverted to a safe state. This does not happen. This is actually still a bit of a mystery to me. All that the update needs to do by default is put each part where the current parts are, because obviously that worked. If the install locations/drives are configuration - driven, and one of these locations can't be reached, then somehow a mismatch has arisen between that configuration data and reality. This might not show up as a problem as long as no new dependency was introduced between the parts.   All flavours of solution involve reinstalling grub to ensure that the two parts are aligned. It's not actually necessary to go back to the previous version ( although that will work ), because it's not the grub runtime per se that is broken. There are numerous ways to achieve this, depending on your environment, but running the Boot-repair live disk worked for me. It may be useful, for the purpose of avoiding such a misalignment in future, to ensure that the grub installer on your system is configured to install to the correct devices. This update resolves some important bugs (). If you have reverted grub to resolve this problem, be aware that you are exposed to these issues. How do you pull first 100 characters of a string in PHP I am looking for a way to pull the first 100 characters from a string variable to put in another variable for printing.    Is there a function that can do this easily?  For example:  $string1 = "I am looking for a way to pull the first 100 characters from a string variable to put in another variable for printing."; $string2 = 100charfunction($string1); print $string2   To get:  I am looking for a way to pull the first 100 characters from a string vari Asymptotic of a sum involving binomial coefficients Calculating Image boundary / footprint of satellite images using open source tools? Ubuntu 18.04 bond with netplan duplicate MAC address after cloning Sound of a next scene starts one moment earlier than video How do I display the nth result of an ls command? I used this command to display the first result of files in my directory.    ls | head -n 1   My simple question is, how can I modify this command to display say the nth result?  Thanks! How to Detect workstation/System Screen Lock/unlock in windows OS using java? Due to my reputation on Stack Overflow, I have access to different review queues. I want to know if it will change my score/reputation or if it will only provide me some badges?  Maybe this part seems a bit odd, but I want to know why some users spend so much time in the review queues? Is it something about their passion about Stack Overflow or their passion to help others inside the community or does it have some other reasons which I've missed?  P.S. I have read some information like  and  but I will be grateful to have your answer about this.