PHP 7.0 - rounding and/or casting float to int gives incorrect values
Is floating point math broken?
If $p\in\Bbb Z[X]$ show that: $ \max\limits_{x\in [0,1]}\left|p(x) \right| > \frac{1}{e^{n}}. $ This is problem 10 from the International Mathematical Competition for University Students of 2015, from day 2, in Bulgaria. I think it is an interesting problem!     Let $n$ be a positive integer, and $p(x)$ be a polynomial of degree $n$ with integer coefficients. Prove that   $$ \max_{x\in [0,1]}\left|p(x) \right| &gt; \frac{1}{e^{n}}. $$   Proposed by Géza Kós, Eötvös University, Budapest. Turn off autocomplete in PhpStorm Can every non-simple group $G$ be written as a semidirect product? When people want to classify a group with certain (small) order, they seem to find a normal subgroup $H$ and a subgroup $K$, and then consider how many distinct $H \rtimes_\varphi K$ are there.  My question is: For any group $G$, does it always exist normal subgroup $H$, subgroup $K$ and $\phi : K \rightarrow Aut(H)$ s.t. $G\cong H \rtimes_\varphi K $?  Sorry if this question is too basic...  Thanks the comment and the answers. Then if the $G$ is not simple, can we have can $G\cong H\rtimes_\varphi K$ for proper subgroup $H$, $K$, with $H$ normal?  EDIT:  If we have a group $G$, that is not simple (then $G$ has at least one normal subgroup), are there always a non-trivial normal subgroup $H$ and a proper subgroup $K$ s.t. $G \cong H \rtimes K$. (Note that if $G$ is simple this is clearly not possible).  But the quaternion group and $Z_4$ given in answers have shown that we cannot always have it. I have created a 'control' using jQuery and used jQuery.extend to assist in making it as OO as possible.  During the initialisation of my control I wire up various click events like so  jQuery('#available input',              this.controlDiv).bind('click', this, this.availableCategoryClick);   Notice that I am pasing 'this' as the data argument in the bind method. I do this so that I can get at data attached to the control instance rather from the element that fires the click event.   This works perfectly, however i suspect there is a better way  Having used Prototype in the past, I remember a bind syntax that allowed you to control what the value of 'this' was in the event.  What is the jQuery way? The particle number on my settings appear in gray, I don't think i'm able to change the number even thought i need it, how can i make it white again? One word/phrase to describe the reaction when you eat a very spicy-hot food I've read the discussion here about .  I've also read this one: .  But I did not find any word or phrase that describes the reaction someone has when eating a too spicy-hot food. You know, they tend to sweat, catch their breath, and even sometimes shed tears; due to the spiciness of the food.  So my questions:        What do you say to describe the reaction someone has when being excitedly "suffered" by a very spicy-hot food? In Indonesian, we would call it kepedasan.   What do you say when you get that thing [the answer to question 1] with you, other than the list I enclose below:                Oh, spicy!     My God, it's spicy-hot!                      Is that it? Is the 64-Bit version of Ubuntu only compatible with AMD CPUs? I was told that computers with more than 2 gig's memory need a 64 bit operating system to utilize all RAM.  Is the 64bit Ubuntu download really JUST for AMD processors? I am asking because the disk image I downloaded says AMD64.  So will my new Intel 2.3Ghz Core i3 Dual Core processor work with 64 bit Ubuntu?  It runs the 64bit version of Windows without any qualm. Do Chinese citizens require a visa to go to Hong Kong for less than 7 days? Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic. Is there a better (or other) way(s) to prove the following statement? Also, the same argument works for multiplicative groups $\mathbb{R}-\{0\}$ and $\mathbb{Q}-\{0\}$, right?       Problem Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.   Solution By cantor's diagonal argument, there is no possible bijection between $\mathbb{Q}$ and $\mathbb{R}$. Since an isomorphism needs to be a bijection, there is no possible isomorphism between the additive groups $\mathbb{R}$ and $\mathbb{Q}$.    Thanks I am using the Service Console in Lightning Experience, and using the Chatter Feed component on the Case layout to display updates to the Case.  If I use the "Log a Call" Quick Action from the Chatter publisher, these calls are displayed in the Chatter feed.  This is the desired behaviour.  However, if I insert a Log a Call record related to the Case any other way - e.g. using the Developer Console, or my CTI system's custom components - the call does not display in the feed.  If I query the record, it looks exactly the same as the record that is created with the Quick Action.  It just seems that the Chatter post is never made in this situation.  I have checked my Feed Tracking settings:   Task has Enable Feed Tracking and Subject checked Case has All Related Objects checked   How can I enable calls created with a custom component (part of a CTI system) to display in the case feed? Word for killing off or attempting to kill off an entire bloodline? I would like to know if there is a word or phrase for a systematic campaign to annihilate every descendant of a particular ancestor.   We have the word 'genocide' for killing off an entire race, and plenty of words for killing people based on how they are related to you (fratricide, filicide, et. al.), but looking over the  and the , I couldn't find a term for systematically killing an entire bloodline.   My question is prompted by a US news story about the horrific murder of 8 members of the same family, but those murders are not an example of what I'm thinking of because the children of the victims were left alive, so the motive for the killings was not to kill off the bloodline. The sense that some group had coordinated an attack against just one family is what made me wonder what the "not an entire race, just one bloodline" version of 'genocide' would be called.   Searching the Internet for "kill off" and bloodline sends me straight into the land of vampires, Illuminati, reptilian overlords, and, naturally, Priory of Sion nonsense so I haven't had much luck finding a thread to pull.   It may be that there is no word for it in the sense of murdering a human bloodline, because we just don't attempt kill off our royals down to the last heir often enough to coin a term for it. Maybe there is a scientific term for culling a line from a test population as part of biological research? Prevent Windows 7 from sleep + power button hook I'm used to not shutdown Windows but to sleeping it. I set up power button (PB) action to do it. When I want to shutdown I must go to start -> Shutdown. That's OK.  Now I think of a mechanism that will be hooked up to a PB. Should be started after I press PB but before OS will go to sleep. Something that will check few conditions (i.e. running backup, running AV scan, ...) and if true (something is running) prevent go to sleep.  Optionally: It would be nice to start the same "mechanism" before restart and shutdown (invoked not only from Start menu, but also by other software (i.e. installers) but with option to allow some sources (i.e. UPS software)  Generally: How to run something after PowerButton but before Sleeping. How to code (C#.NET, vbs, batch (preferred)) sleep prevention (cancellation). Where to upload too big files? I have a big HTML file that causes no errors in most of the browsers. However, when I open it with, let's say, Google Chrome, the program shuts down and I cannot trace why this is happening.   This HTML file is quite big and cannot be posted to a question in SO, but it should be ran as a whole as I cannot trace where the problem is. What is/are the most appropriate file upload website/s to upload and paste the link into the question? Regex to validate date format dd/mm/yyyy Why is it sensical for a proposition with a false antecedent to validate to true? Render result is completely blank A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [ Is there a problem with the ClearBits data dump? I have some section where user can upload CV and profile images,  I'm using the native attachment functions,  $attachment_cv_id = media_handle_upload( 'candidate_cv', 0 ); if ( ! is_wp_error( $attachment_cv_id ) ) {     // We link this file to the post      // add_post_meta( $result , 'wpcf-cv-file', wp_get_attachment_url($attachment_cv_id)); } else {     $submit_candidate_errors[] = lang("Hubo error subiendo la CV"); }   Is there any way I can hide this files from the media section in the wp-admin? ( perhaps changing its folder )  Thanks  -EDIT-  i'm trying like Dave suggested, adding a meta: 'rrhh-file'  $attachment_id = media_handle_upload( 'apply_file', 0 );  if ( ! is_wp_error( $attachment_id ) ) {     // The image was uploaded successfully!     add_post_meta($attachment_id, 'rrhh-file', true); }   And even that it has the attribute:  var_dump(get_post_meta(1200)); // last id I uploaded die();   Prints out:  array(4) {   ["_wp_attached_file"]=&gt;   array(1) {     [0]=&gt;     string(20) "2017/06/image001.jpg"   }   ["_wp_attachment_metadata"]=&gt;   array(1) {     [0]=&gt;     string(666) "a:5:{s:5:"width";i:523;s:6:"height";i:122;s:4:"file";s:20:"2017/06/image001.jpg";s:5:"sizes";a:2:{s:9:"thumbnail";a:4:{s:4:"file";s:20:"image001-150x122.jpg";s:5:"width";i:150;s:6:"height";i:122;s:9:"mime-type";s:10:"image/jpeg";}s:6:"medium";a:4:{s:4:"file";s:19:"image001-300x70.jpg";s:5:"width";i:300;s:6:"height";i:70;s:9:"mime-type";s:10:"image/jpeg";}}s:10:"image_meta";a:12:{s:8:"aperture";s:1:"0";s:6:"credit";s:0:"";s:6:"camera";s:0:"";s:7:"caption";s:0:"";s:17:"created_timestamp";s:1:"0";s:9:"copyright";s:0:"";s:12:"focal_length";s:1:"0";s:3:"iso";s:1:"0";s:13:"shutter_speed";s:1:"0";s:5:"title";s:0:"";s:11:"orientation";s:1:"1";s:8:"keywords";a:0:{}}}"   }   ["rrhh-file"]=&gt; // &lt;-- here   array(1) {     [0]=&gt;     string(1) "1"   }   ["_edit_lock"]=&gt;   array(1) {     [0]=&gt;     string(12) "1498731595:1"   } }   With this action this attachment still shows up in the media library  add_action( 'pre_get_posts', 'wpse_hide_cv_media_list_view' ); function wpse_hide_cv_media_list_view( $query ) {     // Bail if this is not the admin area.     if ( ! is_admin() ) {         return;     }      // Bail if this is not the main query.     if ( ! $query-&gt;is_main_query() ) {         return;     }      // Only proceed if this the attachment upload screen.     $screen = get_current_screen();     if ( ! $screen || 'upload' !== $screen-&gt;id || 'attachment' !== $screen-&gt;post_type ) {         return;     }      // Modify the query.     $query-&gt;set( 'meta_query', [         [             'key'     =&gt; 'rrhh-file',             'compare' =&gt; 'NOT EXISTS',         ]     ]);      return; }   Any idea what i'm missing? 2.8 Why are collections grayed out? How can I open them? I've bought Cup models from Internet.   When opening .blend file I get Blender's Interface changed. To avoid this I've unchecked "Load UI" on opening the file.   But now I cannot see the objects of the project (I can see and render them when opening the file and leaving "Load UI" checked).   "Collection 1" on the "Objects Panel" (Don't know if it is it's name). is grayed out.   cup-models.blend with LOAD UI:    cup-models.blend without LOAD UI:    Blender 2.8: Layover at Tokyo Narita airport: can I travel outside, and what kind of visa would I need? I am travelling from Singapore to San Francisco and the airline has a layover of 7.5 hours at Tokyo Airport (NRT). I am wondering if I would be allowed to go out to experience the city for a while in some form a visitor visa.  I know Singapore has such facilities, but does anyone know if I can do it in Tokyo? Any suggestions or pointers are welcome. Note - I do not have a visa for Japan yet, but I am hoping that 1 day visitor visa could be possible at airport.