$\sqrt[3]{2}$ satisfies $x^3-2=0$ Show that there is no polynomial $P(x)$ of degree less than 3 with $P(\sqrt[3]{2})=0$
Elements of $\mathbb Q(2^{1/3})$
See the revision history on , where the  tag was edited in (and subsequently edited out after I started this discussion).  I think, by adding this tag, you're making assumptions about the OP which they could find a little bit offensive.  Particularly with this question, there's no mention of the level of PHP knowledge — it's more a math question than it is a programming question. Someone could be excellent at a particular language whilst not being particularly great at math, so isn't it a bit insulting to make the assumption they're a beginner? It's also interesting to note  tag, which currently stands at 7,784 on SO.  Compare this to , which only has 18 questions, most of them being &quot;discussiony.&quot;  Why do users retag questions as &quot;beginner&quot; but not &quot;expert&quot;? UPDATE, , .  Related   (thanks @Ralph) Is fractional scaling ( ) available in 18.04 LTS yet? I am waiting until this is available before I install. Here's an example of a Google Docs Spreadsheet script that sends emails using Google spreadsheets. I want the email Sent in HTML not plain text. Can someone help me out?  function sendEmails() {   var sheet = SpreadsheetApp.getActiveSheet();   var startRow = 2;  // First row of data to process   var numRows = 2;   // Number of rows to process   // Fetch the range of cells A2:B3   var dataRange = sheet.getRange(startRow, 1, numRows, 2)   // Fetch values for each row in the Range.   var data = dataRange.getValues();   for (i in data) {     var row = data[i];     var emailAddress = row[0];  // First column     var message = row[1];       // Second column     var subject = "Sending emails from a Spreadsheet";     MailApp.sendEmail(emailAddress, subject, message);   } } Probability of continuous random variable How can I separate multiple quote blocks? I have a series of quotes which I want to display in two separate quote blocks.  &gt; Are questions about Microsoft Word Online on-topic here? I don't &gt; really see any posted here, but perhaps I am not searching correctly. &gt; - mweiss &gt;  &gt; Yes, they are. We even have a specific tag: [tag:word-online]. -ale &gt;  &gt; Thanks! I'm sorry I missed that tag. -mweiss   When I try to add these to my post, they display as a single combined quote.     Are questions about Microsoft Word Online on-topic here? I don't   really see any posted here, but perhaps I am not searching correctly.   - mweiss      Yes, they are. We even have a specific tag: . -ale      Thanks! I'm sorry I missed that tag. -mweiss   How can I separate quotes so that they aren't combined into a single quote block? bilinear form - proof I have to prove that the mapping $f(x,y)={\displaystyle \sum_{i=1}^{n}}{\displaystyle \sum_{j=1}^{n}}x_{i}y_{j}{f}(e_{i},e_{j})$  is a bilinear form, that is, inter alia, the condition: $f(x+y,z)=f(x,z)+f(y,z)$  I have: $f(x+y,z)=f\left({\displaystyle \sum_{i=1}^{n}}x_{i}e_{i}+{\displaystyle \sum_{k=1}^{n}}y_{k}e_{k},{\displaystyle \sum_{j=1}^{n}}z_{j}e_{j}\right)=f\left({\displaystyle \sum_{i=1}^{n}}{\displaystyle \sum_{k=1}^{n}}\left(x_{i}e_{i}+y_{k}e_{k}\right),{\displaystyle \sum_{j=1}^{n}}z_{j}e_{j}\right)=\ldots$  and what's next?  Help! proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$ I am currently working through Velleman's book How To Prove It and was asked to prove the following  $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$  This is my work thus far  $(P \to Q) \wedge (Q \to P)$  $(\neg P \vee Q) \wedge (\neg Q \vee P)$ (since $(P \to Q) \equiv (\neg P \vee Q)$)  $\neg[\neg(\neg P \vee Q) \vee \neg (\neg Q \vee P)]$ (Demorgan's Law)  $\neg [(P \wedge \neg Q) \vee (Q \wedge \neg P)]$ (Demorgan's Law)  At this point I am little unsure how to proceed.   Here are a few things I've tried or considered thus far:  I thought that I could perhaps switch some of the terms in step 3 using the law of associativity however the $\neg$ on the outside of the two terms prevents me from doing so (constructing a truth table for $\neg (\neg P \vee Q) \vee (\neg Q \vee P)$ and $\neg (\neg P \vee \neg Q) \vee \neg (P \vee Q)$ for sanity purposes)  I can't seem to apply the law of distribution since the corresponding terms are negated.  Applying demorgans law to one of the terms individually on step 2 or 3 doesnt seem to get me very far either.  Did I perhaps skip something? Am I even on the right track? Any help is appreciated The scroll bar is hidden on MacBook if the user doesn't move the mouse for some time.  This pattern is also used in other devices too, for example Android devices.  The scroll bar does not take much place but it informs a user of where on page he is.  Is it a good approach hiding the scroll bar when the user is presumed viewing the content? Python scope: "UnboundLocalError: local variable 'c' referenced before assignment" I am trying to figure out this:  c = 1 def f(n):     print c + n  def g(n):     c = c + n  f(1) # =&gt; 2 g(1) # =&gt; UnboundLocalError: local variable 'c' referenced before assignment   Thanks! I'm working on the question     Let $G$ be the group of invertible real matrices of the form $\left [\begin{array}{c c}a &amp; b\\ &amp; a^2\end{array}\right ]$. Determine the Lie algebra $L$ of $G$, and compute the bracket on $L$.   I'm familiar with how to derive the Lie algebra for a linear group like $U_n$, $SU_n$, etc. but I'm not sure what to do in a more explicit case like this. System.QueryException: List has no rows for assignment to SObject I have this controller but I am getting this error      System.QueryException: List has no rows for assignment to SObject   public class MyController {     private final Account account;      public MyController() {         account = [SELECT Id, Name, Site FROM Account                     WHERE Id = :ApexPages.currentPage().getParameters().get('id')];             }      public Account getAccount() {         return account;     }      public PageReference save() {         update account;         return null;     } } Make the network profile editable on the main Stack Exchange page Currently, the Stack Exchange Network Profile links to all the network accounts and acts as a centralized profile page. Seeing that the ability to edit the profile is available from the profile pages of all *.SE sites, I think the ability to edit profiles should be available on that Network Profile page as well.  It will be consistent with the nature of the centralized profile page and will better the user experience.   EDIT: As the current Network profile, is actually the oldest profile on the Network, providing an edit option on the Network profile which links to the oldest profile edit page, would be one way to implement this. Why is everything floating in space so cold? Of course there is pretty hot stuff too. For example Suns.  But isn't the vacuum of space the perfect containment for heat? And shouldn't the rare collision with particles even heat up an object that floats around in space?  Why aren't they hot from time to time? Is it because they loose their heat by radiant heat?  And if so does radiant heat emission always occur until the object is the same temperature as the surrounding or does it depend on other factors? What is a one-word synonym for "science lover"? I'm searching for a one-word synonym for "science lover". In my case, I love science and I self study it, but I never got a degree in Physics or Chemistry or any of these related subjects (except computer-science). But I enjoy experimenting stuff and see what's going on.  So, what would be a one-word good alternative for "science lover"?  The best one I found is learner, but that's more general I guess. Scientist is probably too much in my case. I saw sciencophile in another post, but I don't really like it–it sounds too complicated. WordPress and Git Workflow I know this question has been asked a thousand times, but I'm really trying to work out how to get the best out of Git when working with WordPress.  I've scoured the web and read dozens of articles, all that seem to cover the topic briefly. Here's a few of the most notable one's I've read recently.        Currently, my workflow looks like this.   Install WordPress locally Develop Theme Export WordPress Databases from local server Import WordPress Database to remote server Upload WordPress files and theme via FTP Client makes changes Download WordPress files and theme via FTP and export WordPress Databases from remote server Replace files locally Make development changes Re-upload via FTP, export and import database to remote server   I realise Git can streamline this process. It seems the best way to do this is to have a .gitignore file that ignores certain directories that don't need to be tracked, as well as having both a local and remote wp-config.php file.  But how do you handle the databases? Clients will usually make changes (posts/pages/plugins). Do I still need to export from the remote database and import back on my local server?  Can someone suggest the best workflow for me here? And walk me through the steps.  Also, I'd probably like to use Bitbucket as private repos with them are free, unlike GitHub.  Any help would be appreciated.  Thanks in advance! Someone needs to set the record straight on what exactly antiderivatives vary by: constants functions or piecewise constant functions. I tried to upgrade from Ubuntu 16.04 to Ubuntu 18.04. First, after downloading and installing of packages, I was unable to login. Login screen hanged completely and it showed Failed to authenticate. But then I logged into tty1 and then logged in Ubuntu. It was saying that I am in Ubuntu 18.04. Then it asked for reboot. So I rebooted Ubuntu from terminal. It got stuck at something like /dev/sda4 : Cleaning files. After trying for a few times, I got into tty1 and here I logged in as root user and tried to update and upgrade. But now I am getting errors like unmet dependencies and broken packages. I have done sudo dpkg -- configure -a. I don't want to do a reinstall of Ubuntu. How do I get access to my Ubuntu Desktop? Inspired by question :  When do I need to invoke \phantomsection?  In what condition is invoking \phantomsection necessary? How do I disable search-as-you-type text in Ubuntu 17.10 and later? I cannot find enable-interactive-search in    gsettings set org.gnome.nautilus.preferences enable-interactive-search true.     I searched using    gsettings list-recursively | grep search     and    gsettings list-recursively | grep interactive     but no such option.  Can you help me disable this in Ubuntu 17.10 and later? I am facing problem to enable wifi on my Lenovo G50-30 Below are the command out put please help me out   lspci | grep -i wireless:  02:00.0 Network controller: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter     nm-tool:  NetworkManager Tool  State: disconnected  - Device: eth0    Type:              Wired   Driver:            r8169   State:             unavailable   Default:           no   HW Address:        28:D2:44:81:36:0B    Capabilities:     Carrier Detect:  yes    Wired Properties     Carrier:         off   - Device: wlan0   Type:              802.11 WiFi   Driver:            rtl8723be   State:             unavailable   Default:           no   HW Address:        14:2D:27:21:8D:47    Capabilities:    Wireless Properties     WEP Encryption:  yes     WPA Encryption:  yes     WPA2 Encryption: yes    Wireless Access Points      nmcli nm:  RUNNING         STATE           WIFI-HARDWARE   WIFI       WWAN-HARDWARE   WWAN       running         disconnected    disabled        disabled   enabled         disabled       sudo rfkill list:  0: ideapad_wlan: Wireless LAN     Soft blocked: no     Hard blocked: yes 1: ideapad_bluetooth: Bluetooth     Soft blocked: no     Hard blocked: yes 2: hci0: Bluetooth     Soft blocked: no     Hard blocked: no 3: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no