To show $Q(\sqrt{p}, \sqrt{q})= Q(\sqrt{p} + \sqrt{q})$, where p and q are prime with gcd 1.
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
How do I post code in chat? I would like to be able to post code in chat. I know that I can post inline snippets of code by using backticks, but I don't know how to post blocks of code, with the entire chat message formatted as code, and indentation respected. I am aware of . After reading the comments, I found out that I could format in "fixed width", but I can't see a "fixed width" button anywhere. What should I do? How to prove that compact subspaces of the Sorgenfrey line are countable? How to prove that every compact subspace of the  is countable? How to create a Facebook page without a personal account In the past, Facebook used to let business create pages or apps without a personal account. This account created in the page/app creation process had limited capacities and could be switch to a full personal account after—if needed (irreversible).  But today, if I want to create a page for a new brand, without having a Facebook account, it seems I can’t anymore. And I can’t find any communication from Facebook regarding this change.   Anybody has any info? Is it still possible (in a new way maybe)? I find it very strange that $$ e^x \geq x^e \, \quad \forall x \in \mathbb{R}^+.$$   I have scratched my head for a long time, but could not find any logical reason. Can anybody explain what is the reason behind the above inequality? I know this is math community, but I'd appreciate a more intuitive explanation than a technical one. Centering \vdots in a system of many equations I have a system of equations with an arbitrary number of equations (k). I'd like to use \vdots to compactly describe the system, like so:  \begin{align*}   R(-1) &amp;= \sum_{i=1}^m A(i)R(i-1) \\   R(-2) &amp;= \sum_{i=1}^m A(i)R(i-2) \\         &amp;\vdots                    \\   R(-k) &amp;= \sum_{i=1}^m A(i)R(i-k) \end{align*}     I'd like the dots, however, to be centered with = or the entire equation. Is there an elegant way of centering a column or row with AMSMath? I'm currently using an unholy combination of whitespace operators (\; \, etc.) to get the job done. What is the plural form of "Software"? Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$ Are there any drawbacks to using a wish spell to increase ability scores? If not then what would stop players from just using wish repeatedly and raising their ability scores to 30?  I'm just getting back into RPGs with D&amp;D 5e after not playing for years, and I seem to remember this being covered in the editions we played back then. SUMIF Horizontal I am searching for a column header and return a value under it.  Example:  _|A|B|C  1|X|Y|Z  2|1|2|3   If the value is Y, it must return 2. I tried =SUMIF(A1:C1,"B", A2:C2), but realized that IFSUM does not support searching horizontal.  I would appreciate an alternative solution! Lately I see a blue screen of death a lot and want to know why it appears. Where should I gather the information so the problem can be diagnosed best? Couldn't find anything in C:\Windows\Logs. how to change my hostname? My hostname is localhost, reported by hostname command, and terminal prompt root@localhost:~#.  How can i change it to mismis.com with mismis alias? and what is the proper configuration.  I confused after reading some articles on web.  My /etc/hosts:  127.0.0.1       localhost 127.0.1.1       srv345.myweb.com      srv345 178.162.231.61  janstone.mismis.com    janstone # The following lines are desirable for IPv6 capable hosts ::1     localhost ip6-localhost ip6-loopback fe00::0 ip6-localnet ff00::0 ip6-mcastprefix ff02::1 ip6-allnodes ff02::2 ip6-allrouters I know that $\operatorname{Spec} \mathbb{C}[x]$ can be identified with the set $\mathbb{C}\cup *$, where $*$ is a generic point via the correspondence  $$ \prod_{i}(x-a_i) \leftrightarrow \{a_i\}_i , \ \ \ \ (0)\leftrightarrow *. $$ This correspondence holds for any $\operatorname{Spec} k[x]$ with algebraic closed field $k$.   When $k$ is not algebraic closed, how should one understand $\operatorname{Spec} k[x]$? Are threads implemented as processes on Linux? I'm going through , Advanced Linux Programming by Mark Mitchell, Jeffrey Oldham, and Alex Samuel. It's from 2001, so a bit old. But I find it quite good anyhow.  However, I got to a point when it diverges from what my Linux produces in the shell output. On page 92 (116 in the viewer), the chapter 4.5 GNU/Linux Thread Implementation begins with the paragraph containing this statement:     The implementation of POSIX threads on GNU/Linux differs from the   thread implementation on many other UNIX-like systems in an important   way: on GNU/Linux, threads are implemented as processes.   This seems like a key point and is later illustrated with a C code. The output in the book is:  main thread pid is 14608 child thread pid is 14610   And in my Ubuntu 16.04 it is:  main thread pid is 3615 child thread pid is 3615   ps output supports this.  I guess something must have changed between 2001 and now.  The next subchapter on the next page, 4.5.1 Signal Handling, builds up on the previous statement:     The behavior of the interaction between signals and threads varies   from one UNIX-like system to another. In GNU/Linux, the behavior is   dictated by the fact that threads are implemented as processes.   And it looks like this will be even more important later on in the book. Could someone explain what's going on here?  I've seen this one , but it doesn't help much. I'm confused.  This is the C code:  #include &lt;pthread.h&gt; #include &lt;stdio.h&gt; #include &lt;unistd.h&gt;  void* thread_function (void* arg) {     fprintf (stderr, "child thread pid is %d\n", (int) getpid ());     /* Spin forever. */     while (1);     return NULL; }  int main () {     pthread_t thread;     fprintf (stderr, "main thread pid is %d\n", (int) getpid ());     pthread_create (&amp;thread, NULL, &amp;thread_function, NULL);     /* Spin forever. */     while (1);     return 0; } How to override Drupal.ajax.prototype.beforeSend? I need to add my own little if's and checks in 3 functions inside   misc/ajax.js (   Drupal.ajax.prototype.beforeSend,   Drupal.ajax.prototype.success,   Drupal.ajax.prototype.error )   How can I override them in my module? I can't find a manual and it's not in Examples for Developers. Sorry if it seems a dumb question, but I'm a php developer - I can work with js, but I'm not so fluent with it.   Can I simply write it in my module's js file? If 2 or 3 modules needs to modify them, how to avoid conflicts? I just got a question in the review queue that, though poor, I thought was potentially salvageable via editing.  However when I clicked the Edit button I got the deleted post error.  Since the post was gone, I clicked I'm Done (what is there do do with a deleted post?) only to get the review audit failed message instead.  The current behavior is also problematic in that, now that I know about it, it's a risk-free way to check if a question is an audit and not an actual review. That allows me or anyone else who knows about it to detect audits without having to recognize that the question is bad. CodeIgniter: A Class/Library to help get meta tags from a web page? The following you could have seen in  (sorry, I've commented there, so you won't see it anymore) in Chrome 35.0.1916.153 m (current version). Notice how the add comment link overlaps the bounty box:    The same you can observe with a comment box on other sites, e.g. at this time in :    Could you shift it a bit down ?  It seems that it happens on more than just Stack Overflow (maybe all sites ?). Upgrade or replace a Wubi installation? I've got Windows 7 with Wubi 11.10 installed. I would like to upgrade to 12.04 but I'm not sure what the best path would be.  I'm not skilled enough to use Ubuntu all the time, and my iPhone requires me to run some Windows version for the damn iTunes software. I would love to run Windows XP but I can't figure out how to install it via USB -- my computer has no cd drive.  I'd like to run Windows XP and Wubi 12.04 on top of that. Or, perhaps, Ubuntu 12.04 natively and Windows XP alongside of that. So I guess I have 2 questions:   (lazy) Should I upgrade my Wubi from inside Ubuntu, or should I remove Wubi 11.10 from within Windows and install a brand new Wubi 12.04? (proper) How can I install Windows XP and Ubuntu 12.04 alongside each other?   Update: I am going to create a separate question post about the above #2 question... I realize it's wrong to ask two questions in one post when they are that different. Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$ Prove via induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$ Having a very difficult time with this proof, have done pages of work but I keep ending up with 1/(k+2).  Not sure when to apply the induction hypothesis and how to get the result $1- \frac{1}{(n+2)!}$.  Please help! thanks guys, youre the greatest! Remove the flag notification in the top bar when I have done my job with it I have the moderator privileges on .  Even though it's quite rare that flags appear over there, it is still quite annoying that once I have done my job with a flag and therefore cannot do anything else with it, the flag in the top bar remains there. Why do I have to keep seeing that flag when in fact, I can't do anything about it?  Images, with free-hand circles:  A flag exists in the notification bar:    I have already done my part of the flag handling:    And yet the flag remains in the notification bar.