I want to add numbering to each equation below:  \documentclass[fleqn,12pt]{article}  \usepackage[top=0.75in, bottom=1in, left=1in, right=1in]{geometry} \geometry{a4paper}  \usepackage{tikz} \usepackage{amsmath} \usepackage{systeme}  \begin{document}  $$ \Sigma F=ma: \begin{cases}  for(M): M\ddot x_1&amp;=-kx_1+T-2k(x_1-x_3-r\theta)+F_1 \\ for(3m): 3m\ddot x_2&amp;=F_2-T\\ for(m): m\ddot x_3&amp;=-c\dot x-3-3kx_3+2k(x_1-x_3-r\theta)+F_3 \end{cases} $$  \end{document}   I want the numbers to be 1,2 and 3 not 1.a,1.b and 1.c
As much as I have tried, it doesn't seem possible to use separate labels when using a casesconstruction (from the amsmath package).  Ideally, I would like to be able to write something like  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x)=\begin{cases}   1&amp;x\geq0\label{positive}\\   0&amp;x&lt;0\label{negative} \end{cases} \end{equation} \end{document}   and later refer to both cases at different places. What would be the best way to achieve this result?
'this is' or 'these are'? I have the following sentences.        This is our first arrival in the UK.   These are our first arrival in the UK.      I am not sure, which sentence is correct? A man wonders why perforations don't work. He decides nothing is the strongest thing in the universe. He exploits his finding. What would you consider to be the best exception type to throw when an extension method is called on a null instance (where the extension method does not allow it)? Since extension methods are nothing but static methods you could argue that it should be ArgumentNullException, but on the other hand they're used like instance methods so it might be more natural to use the NullReferenceException. Let's take the following example:  public static string ToInvariantString(this IFormattable value, string format) {     return value.ToString(format, CultureInfo.InvariantCulture); }   This way a NullReferenceException will be thrown if the value parameter is null.   The other example would be:  public static string ToInvariantString(this IFormattable value, string format) {     if (value == null) throw new ArgumentNullException("value");     return value.ToString(format, CultureInfo.InvariantCulture); }   EDIT: In some of the answers you have pointed out that an extension methods can be called like a static method and in those cases a null reference exception would be wrong, which is a great point, and actually one of my concerns, not sure why I forgot to mention that in the question in the first place.   Someone also pointed out that it's wrong to throw a NullReferenceException, and yes, it is. That's why I don't throw it, I just let it happen (let the CLR throw it) by not guarding the method.  I think I favor the ArgumentNullException (that's what I've use so far) but I still think there is at least room to argue for an against the NullReferenceException since it seems more natural in most places where the method is going to be used. On Windows 7 can one make UAC on an admin account prompt for the password, just like a limited account? I am one of the very few who likes the security of UAC and so I have the UAC set to "Always Notify" on my Admin account. But I would be even happier if the system would prompt me for a password, when notifying me.  I can get what I want by adding a second non-admin user and using that account.  But somehow it seems wasteful to have two accounts set up when I will always use the non-admin account day-to-day.  So I am wondering if there is any setting that would cause an Admin account to behave password-prompting-wise as a standard account? @future method: Unsupported parameter type I am trying to copy records from one org to other via web services. I am calling a class which has logic written into a trigger. But @ future method is not taking sObject  list as a parameter. Can someone suggest me an alternative?  The Code:  public class webServicesTriggerClass   {     @future public static void webServicesMethod(list&lt;MyFriend__c&gt; mfList)     {         partnerSoapSforceCom.Soap sp = new partnerSoapSforceCom.Soap();       partnerSoapSforceCom.LoginResult lr = sp.login('hitesh.kumar.singh@accenture.com.varun','4Rajyavardhan');      soapSforceComSchemasClassNiralaapp.SessionHeader_element ses = new soapSforceComSchemasClassNiralaapp.SessionHeader_element();      ses.sessionId = lr.sessionId;       soapSforceComSchemasClassNiralaapp.MyFriendsDetailSoapApi vNapp=new soapSforceComSchemasClassNiralaapp.MyFriendsDetailSoapApi();      for(MyFriend__c mf:mfList)       {        string  s1= mf.myEmail__c;        string  s2=mf.friendName__c;         string  s3=mf.friendEmail__c;        string  s4=mf.aboutFriend__c;        integer i1=Integer.ValueOf(mf.age__c);        boolean result=vNapp.addFriendDetails(s1,s2,s3,s4,i1);        system.debug('################' +result);           }     }    }     Trigger-->  trigger webServicesTrigger on MyFriend__c (after insert)     {      webServicesTriggerClass.webServicesMethod(trigger.new);    }     Error--    Error: Compile Error: Unsupported parameter type LIST at line 3 column 30 This week I've read two news stories about two different camera lenses that can magnify things that are very far away.  The first is the , which is a point-and-shoot camera that costs $600, has an 83x optical superzoom lens ("the same field of view as a 2,000mm lens on a full-frame camera"), and lets you see the craters of the moon.  The second is the , which weighs 36 pounds, costs $180,000, and can take portraits of people a half mile away.  A non-photographer might ask, "Why would somebody spend their life savings on a gigantic telescope of a lens when you could take far away pictures with a handheld camera for 1/300th the price?"  Well, I am basically a non-photographer, and I would like to ask that question. What does the big one give you that the little one doesn't provide? I understand that small changes in lenses can make a big difference in size and price, but this seems to be of a different scale entirely.   What is going on with the optics of the lenses that makes the small one able to be so small and the big one have to be so...big?   I'm trying to get a basic intuition for what makes lenses different, and I realize I don't understand enough about how lenses work to even know how to compare these apples and watermelons. prove that if two real valued  functions are uniformly continuous on some interval $I$  and each is bounded on $I$ then their product $f\cdot g=f(x)\cdot g(x)$ is also uniformly continuous on $I$ . Is boundedness of each function  on $I$ is  necessary for the product Is there an international taxonomy of academic titles/ranks? Looking at the  on Wikipedia shows that the same academic rank/title can mean quite different things in different countries. For instant, a "research assistant" in the US can stand for an undergrad student doing an internship, while in the UK it can stand for a postdoc. Similarly, the term "lecturer" might stand for a permanent position (e.g. in the UK) or for a teaching assistant position, open to graduate students.   However, when thinking about it, there are not so many kind of possible positions (permanent or not, with teaching or not, with research or not, with PhD supervision or not, with team responsibility or not, etc), and having a clear title could help a lot (for instance, in my case, I've been working in four different countries, with a different job title each time!).    Is there some kind of official taxonomy that one could refer to?  If not, who could be in charge to create it? (the EU, if only for intra-Europe mobility?) I was improving some of my old posts on Stack&nbsp;Overflow when I ended up encountering this:     You have already edited 5 of your own post today; futher edits are not   allowed until tomorrow   I know this it is not a major deal, but what's the logic underneath to this restriction? Error: could not start the command in Texmaker when I run makeindex I'm trying to create a nomenclature but I'm getting the following error when I run makeindex:     Error: Could not start the command   This error appears even with this basic example:  \documentclass{article} \usepackage[refpage]{nomencl}  \makenomenclature  \begin{document} Example of nomenclature \nomenclature{A}{Area}  \printnomenclature \end{document}   In the Configure Texmaker editor I wrote: makeindex %.nlo -s nomencl.ist -o %.nls in the makeindex slot. Then I run:   PdfLaTeX MakeIndex   And the error appears... I also tried all suggestions , but nothing seems to work.  I have installed MacTex 2012 distribution, Mac OS X 10.7.5 Why does resistivity increase with temperature?  The explanations I have heard so far are that increasing temperature increases vibrations in the lattice structure resulting in the number of collisions increasing.  But the vibrations from thermal energy are random, so around half of the vibrations would result in the atoms moving out of the electrons way and half would result in atoms moving into the way of the electrons.  And since half of the vibrations result in increasing the drift speed and half reduce it, shouldn't the average drift speed remain the same? XmlInclude : List and array How to change permissions of multiple files found with find command? Why do variable names often start with the letter 'm'? How do I prevent and/or handle a StackOverflowException? I would like to either prevent or handle a StackOverflowException that I am getting from a call to the XslCompiledTransform.Transform method within an Xsl Editor I am writing. The problem seems to be that the user can write an Xsl script that is infinitely recursive, and it just blows up on the call to the Transform method.  (That is, the problem is not just the typical programmatic error, which is usually the cause of such an exception.)  Is there a way to detect and/or limit how many recursions are allowed?  Or any other ideas to keep this code from just blowing up on me? Where to place 'only' relative to prepositions? I know that questions about the placement of 'only', are often asked here; accordingly, I searched for an answer to my question before posting it.  Question  Where are focusing adverbs placed relative to prepositions?  For example,   For his presentation, he needed to talk only about tomatoes. For his presentation, he needed to talk about only tomatoes.   My Attempt to Answer the Question  In both examples, it seems to me that 'only' is placed close enough to what it is intended to modify (the topic of the subject's discourse: tomatoes) that I cannot see any justifiable misinterpretations.  One of the examples sounds better to me, but at this point in my studies, I am more interested in what the traditional rules of grammar require, than in how the wordings sound. Installing Elementary OS - will it automatically be added to the Grub menu? I currently have Windows 7 and Linux Mint installed.  When my PC starts up, it shows me the Grub menu, it shows an entry for Mint Linux and the Windows boot menu.  I am wondering, if I was to install Elementary OS, would it be automatically added to grub or do I have to put some command in the terminal?  I also want to ask, when I boot from my Elementary OS cd, and install it, just before it finishes, it shows some kind of error saying some error about cannot install to grub or something, I've tried installing to a separate partition and alongside "Them", but had no luck.  I'm really new to Linux, and want to keep my Mint Linux and Windows 7 because I have files on them. Sneak Attack has the same type , this is easy, unless there are multiple damage types.  A Flame Tongue does slashing (or piercing) damage, and fire. Can I chose the Sneak Attack damage in this case to be fire too? What is the difference between Non-preemptive, Preemptive and Selective Preemptive Kernel? In Knuth's book "The Art Of Computer Programming Vol.1" there is a description about Euclid's algorithm to find the greatest common divisor of m and n.   And there is a phrase.     $m = qn+r$.  If $r = 0$, then $m$ is a multiple of $n$, and clearly in such a case $n$ is the greatest common divisor of $m$ and $n$. If $r \neq 0$, note that any number which divides both $m$ and $n$ must divide $m -qn =r$ , and any number which divides both $n$ and $r$ must divide $qn+r =m$.   I don't understand why any divisor of $m$ and $n$ must divide $m-qn =r$.