How to use `\end{frame}` in a command?
Difficulty in creating macro '\newcommand' for the beginning and end of frames in Beamer
How do I reference the only element in a singleton set? You can turn any element $n$ into a singleton set by adding braces, $\{n\}$. Is there an inverse to this operation, such that if I know the set is a singleton set I can easily reference its element?  For example, say I have the set $A = \{5,6,7,8\}$, and then some process that iteratively eliminates all but one element of $A$, and then I want to see what 10 plus the resulting element is, how could I write that?  The only way I can think of is by referencing the first element by its index, e.g., $10 + A_1$. Is there another way to do it though? In my case the elements of $A$ are already indices, so I would have to index an index, like $10 + x_{A_1}$. Which is not the worst thing in the world, I was just wondering if there is a better way. Benefits of Toad houses I have a few red Toads and a Toad is just hanging out in town. I see an option to buy a red Toad house, ostensibly for him. Are there any added benefits of purchasing this or are the colored Toad houses just cosmetic? Why is it possible to conclude everything from a false statement? Possible Duplicates:             I heard a professor of mathematics explaining that the following conslusions are true.   $\textrm{False}\Rightarrow \textrm{True}$ $\textrm{False}\Rightarrow \textrm{False}$   Could someone please explain to me why both conclusions are true? I am especially interested in the first case. I'd like to hear two explanations if possible: One for mathematicians and one for non-mathematicians. :-) Multiple vs single field capture for phone number form input Working on a form dealing with phone numbers, I've seen two methods to capture user input .   In past practices example 2 (image below) has proved effective in controlling phone number lengths on forms.   However with responsive in mind it would seem example 1 is considered a more popular pattern on forms. I've researched both patterns with the findings below.     Example 1  Pros   1 input = less taps on mobile device 1 input = less coding   Cons   could be difficult to control phone number format (1-555-555-5555, +22444455555, and etc)   Example 2  Pros   easier to control phone format reduced user error   Cons   3 inputs = more taps on mobile device more inputs = more coding   Both inputs have pros and cons and I'm not such which method would provide the best user experience for responsive environments. Can anyone share some insight or provide a better way to use phone number inputs? crisscross, dillydally, riffraff, etc Some English words only differ in their vowels: crisscross, dillydally, riffraff, etc. Is there a name for them? We now that Fermat's last theorem is true so there are not positive integer solutions to $$x^n+y^n=z^n$$ for $n\in\mathbb{N}$ and $n&gt;2$.  But what about if $n\in\mathbb{R}$ or $n\in\mathbb{R}^+$? I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file? I had one batch class in which i am passing some data required for creating object record.But when i call that batch class from parent class variables are initialized but start method are not called as there is no record to query i also tried with iterable object but not able to do that.My code is as below  global class testBatchClass implements Database.Batchable&lt;SObject&gt;,Database.Stateful{     public List&lt;sObject&gt; sObjectList;     public string objectName;     public String dataList;      public testBatchClass(String objectName,String inputdata){          String listType = 'List&lt;'+objectName+'&gt;';         system.debug('list type value is'+listType);         List&lt;SObject&gt; castRecords = (List&lt;SObject&gt;)Type.forName(listType).newInstance();         this.sObjectList = castRecords;         this.objectName = objectName;         this.dataList = inputdata;      }     global Iterable&lt;SObject&gt; start(Database.BatchableContext batchableContext) {         return new sObjectList{};     }     global void execute(Database.BatchableContext batchableContext, List&lt;sobject&gt; scope){          List&lt;OpportunityRenewal__mdt&gt; mdtList = new List&lt;OpportunityRenewal__mdt&gt;([Select id,Api_Name_of_Fields__c,Sobject_Name__c from TestFileUploadCustomSetting1__mdt where Sobject_Name__c=:objectName]);         List&lt;String&gt; fieldName = new List&lt;String&gt;();         for(OpportunityRenewal__mdt md : mdtList){             if(md.Sobject_Name__c == objectName){                 fieldName = md.Api_Name_of_Fields__c.Split(',');                 break;             }         }         List&lt;String&gt; dataRowsSplit= dataList.split(',');         dataRowsSplit.remove(0);         for(String eachRow: dataRowsSplit){             List&lt;String&gt; splitString = eachRow.Split(',');             sObject sobj = Schema.getGlobalDescribe().get(objectName).newSObject();             for(Integer i=0; i &lt;= splitString.Size(); i++){                 sobj.put(fieldName[i],splitString[i]);             }             scope.add(sobj);         }         if(scope != Null &amp;&amp; scope.Size() &gt; 0){             upsert scope;         }     }      global void finish(Database.BatchableContext batchableContext) {} }   Thanks Understanding reference counting with Cocoa and Objective-C I'm just beginning to have a look at Objective-C and Cocoa with a view to playing with the iPhone SDK. I'm reasonably comfortable with C's malloc and free concept, but Cocoa's references counting scheme has me rather confused. I'm told it's very elegant once you understand it, but I'm just not over the hump yet.  How do release, retain and autorelease work and what are the conventions about their use?  (Or failing that, what did you read which helped you get it?) Efficient online linear regression How come Dropbox gets an icon in Finder sidebar? How come Dropbox gets a non-generic icon in Finder's sidebar, when other directories like Google Drive and Sites (native in OS X before Lion) all have the same generic one?    How can I customise the icons used by the folders in the sidebar? OS X used to show individual icons of all folders there — not any longer. I was wondering if it's possible to run an Ubuntu virtual machine using VirtualBox in background, I mean, without any window open.  The idea is to connect via SSH to the Linux host, that would be running in background.  Has anyone ever done something like this? Is it possible? Windows OS on external hard drive Is it possible to install Windows OS to plug and play storage devices such as external hard drives, HDD enclosures (with SATA hard drives), USB flashdrives and the likes? What OS's? And if it's possible, can I boot on it after the installation/formatting?  I've read someone has tried this already using Windows XP but failed since XP reinitializes all attached USB devices before loading OS, thus disabling the External HDD that is attached via USB port.  What about other Windows OS: on Windows 7 or 8.... or Windows 10?  I'm asking this because I'm planning to create a portable OS. When I'm at my house, when I go to my grandmother's, or to a friend's place: I just simple plug that portable storage device, change the boot priority, and turn on the system and ta-da! I will only see one environment every time. Quantum information references In Volo's Guide it is suggested that a curse could transform someone into a race of 'monstrous origin' (p. 118). Does this apply to the Bestow Curse spell specifically? Note: this is a  (my apologies).  In film / lore, such magic does , ,   - or even  transformative curses.  Points &amp; Concerns:   this is within guidelines for a 'reasonable' curse, i.e. less harm than the listed set Bestow Curse writeup encourages DM-homebrewing &amp;/or interpretation. Great role-play possibility / RAI (hence most myths, fairy tales, cartoons, legends, etc) this could be subject to abuse, temptation to bestow a 'curse' as a blessing / boon one could also change: age, size, weight &amp;/or gender (all great curse ideas... but RAW-legal?)   Summation:  What are the limits of the 3rd lvl / Necromatic Bestow Curse spell for transformation? A question on $p$-groups, and order of its commutator subgroup. $\textbf{QUESTION-}$ Let $P$ be a p-group with $|P:Z(P)|\leq p^n$. Show that $|P'| \leq p^{n(n-1)/2}$.  If $P=Z(P)$ it is true. Now let $n &gt; 1$, then  If I see $P$ as a nilpotent group and construct its upper central series, it will end , so let it be,  $e=Z_0&lt;Z_1&lt;Z_2&lt;......&lt;Z_r=P$   Now as $Z_{i+1}/Z_i=Z(P/Z_i)$, so if if I take some $x\in Z_2$\ $Z_1$ then $N$={$[x,y]|y\in P$} $\leq Z_1(P)$ and $N \triangleleft P $, so $P/N$ is a group with order $\leq p^{n-1}$.  Now if I let $H=P/N$ then obviously |$H/Z(H)$|$\leq p^{n-1}$.  Now $H'\cong P'N/N \cong P'/(P' \cap N)$ so from here I could finally bring $P'$ atleast into the picture, now |$P'$|=$|H'|.|P'\cap N|$ so $|P'|\leq |H'||N|$.   This is where I am $\textbf{STUCK}$  Now , from here how can I calculate or find some power $p$ bounds on $|H'|$ and $|N|$ so i could get my result. Proving that $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ is compact using the open cover definition Let $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ be a subset of $\mathbb{R}$. I have to prove using the open cover definition that this is compact. Could you help me, please? Mathematics Ph.D program foreign language requirement I will soon be attending a Ph.D program in mathematics. I do not know how common this practice is, but the department has a requirement that graduate students must learn a foreign language and be able to read and write mathematics in that language. The three choices are French, German, or Russian. I personally have no preference on which to learn, but I was wondering if there were other reasons that would make one language more advantageous over the others in terms of a general mathematical career. Thanks in advance in any response. How does the Schengen 90/180 rule work? "Can not setup lock file:/tmp/g2ipmsg.lock errno : -11 (Resource temporarily unavailable)" I installed IP Messenger (GNOME 2) from Ubuntu software center but its not working. It's always showing an error message on Ubuntu 12.04.  FileName:ipmsg.c Function:create_lock_file Line:157 Can not setup lock file:/tmp/g2ipmsg.lock errno : -11 (Resource temporarily unavailable)