Is there a notation to refer to all the n element subsets of a set? I know the power set denotes all of the subsets.
How would one denote the set of all subsets of $A$ which have size $2$?  Would  $$\binom{A}{2}$$  be a good idea?
New 16GB of RAM installed yet I see 15.3 on my system. Why? Just switched 4GBs to 16GBs of RAM. However, when I look at how much memory I have, it says 15.3. I'm just wondering why did my memory drop down when I just installed 16 GBs of RAM. Connect iPhone to Mac Without Charging I am developing iOS apps and I hate, that always when I connect my iPhone to my Mac to install and test an app, the iPhone gets charged. Is there any possibility to connect my iPhone to my Mac without charging the phone?    My Environment: -  iPhone 4S (No Jailbreak) -  MacBook Air3,2 (Late 2010) How do I get back my suspend option in Gnome Shell? With the new version of Gnome Shell in Ubuntu 12.10 they turned  around by just displaying the shutdown option which becomes suspend on pressing Alt.  How do I get back my beloved suspend option? Beamer to HTML using make4ht \documentclass{beamer} \usetheme{Madrid} \begin{document} \begin{frame} aaa \end{frame} \begin{frame} bbb \end{frame} \end{document}   The above tex file is to be converted into html. I am using the following command   make4ht filename.tex   However it throws error. The basic question is "Is it possible to convert beamer presentation to html using make4ht?" In Star Wars: "The Force Awakens," how could this lightsaber have turned up where it did? In The Force Awakens:      Maz Kanata tells Rey that the lightsaber she just picked up and had visions from belonged to Anakin and Luke and now it's hers.   The lightsaber that Luke got from Obi-Wan Kenobi in A New Hope was lost/destroyed when Luke fought Darth Vader in Star Wars: The Empire Strikes Back.  In Return of the Jedi Darth Vader compliments Luke on building a new lightsaber and tells Luke that his skills are now complete.   How could that possibly be the lightsaber that Anakin used originally, and that was then passed on to Luke, when that lightsaber no longer exists?  Writers notes, director's notes, interviews, cast interviews, etc. are welcome. Thanks. Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $ $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $ = -$  2.887270... $  The function has no antiderivate and there's no symmetry here to help, if you solve this I would be thankful if you would for a highschooler ^^ Error while running Quickly Rules for Profiles Are there any rules concerning what I can put in my profile? How do I find out which process is eating up my bandwidth? I think I'm being the victim of a bug here. Sometimes while I'm working (I still don't know why), my network traffic goes up to 200 KB/s and stays that way, even tough I'm not doing anything internet-related.   This sometimes happens to me with the CPU usage. When it does, I just run a top command to find out which process is responsible and then kill it. Problem is: I have no way of knowing which process is responsible for my high network usage. Both the resource monitor and the top command only tell me my total network usage, neither of them tells me process specific network info.  I've found questions here about monitoring total bandwidth usage, but, as I mentioned, that's not what I need. Is there another command I can use to find out which process is getting out of hand?  The command iftop gives results that disagree entirely with the information reported by System Monitor. While the latter claims there's high network traffic, the former claims there's barely 1 KB/s.  I've already tried killing all the obvious ones (Firefox, update-manager, Pidgin, etc) with no luck. So far, restarting the machine is the only way I found of getting rid of the issue. Why an R-module is an R/I-module precisely when it is annihilated by I? Let $I$ be an ideal of $R$ and let $M$ be an $R$-module. Prove that the formula $(r + I) \cdot m = r \cdot m$ for $r + I \in R/I$, and $m \in M$ makes $M$ into an $R/I$-module if and only if $i \cdot m = 0$ for all $i \in I, m \in M$.   I don't quite understand why we must have $i \cdot m = 0$ instead of $I \cdot m \in M$. This is for proving the only if part. OSVR has a right-handed system: x is right, y is up, z is near.  I need to convert orientation data from a sensor in OSVR to a different right-handed system in which x is forward, y is left, and z is up.  I need to calculate the transformation that will convert a quaternion from one system to the other.  I naively tried:  void osvrPoseCallback(const geometry_msgs::PoseStampedConstPtr &amp;msg) { // osvr to ros     geometry_msgs::PoseStamped outputMsg;      outputMsg.header = msg-&gt;header;     outputMsg.pose.orientation.x = msg-&gt;pose.orientation.y;     outputMsg.pose.orientation.y = msg-&gt;pose.orientation.z;     outputMsg.pose.orientation.z = msg-&gt;pose.orientation.x;     outputMsg.pose.orientation.w = msg-&gt;pose.orientation.w;      osvrPosePub.publish(outputMsg);     ros::spinOnce(); }   But that made things really weird. Facing north pitch is pitch, facing west, pitch is yaw, facing south, pitch is negative pitch...  How can I convert my OSVR quaternion to the a corresponding quaternion in the new coordinate system? Ok, after seeing , I have decided to skip to the end and go with .  So what I need is a beginner's practical guide to Git.  "Beginner" being defined as someone who knows how to handle their compiler, understands to some level what a  is, and has touched source control without understanding it very well.  "Practical" being defined as this person doesn't want to get into great detail regarding what Git is doing in the background, and doesn't even care (or know) that it's distributed.  Your answers might hint at the possibilities, but try to aim for the beginner that wants to keep a 'main' repository on a 'server' which is backed up and secure, and treat their local repository as merely a 'client' resource.  So:  Installation/Setup    How do you set up Git?  Try to cover Linux, Windows, Mac, think 'client/server' mindset.         Working with the code          How do you handle binary files (visio docs, for instance, or compiler environments)? How do you merge files changed at the "same time"?    Tagging, branching, releases, baselines    How do you pull a particular 'release'?   How do you resolve conflicts and complete the merge? How do you merge parts of one branch into another branch?        Other   Describe and link to a good GUI, IDE plugin, etc. that makes Git a non-command line resource, but please list its limitations as well as its good.    - Cross platform, included with Git  - Cross platform history viewer, included with Git  - Mac OS X  - Mac OS X history viewer  - Cross platform, commercial, beta  - console GUI for Linux  - GUI for Windows, Linux  - package for Windows, includes friendly GUI  Any other common tasks a beginner should know?     How do I work effectively with a subversion repository set as my source control source?   Other Git beginner's references                 Delving into Git     (and )    I will go through the entries from time to time and 'tidy' them up so they have a consistent look/feel and it's easy to scan the list - feel free to follow a simple "header - brief explanation - list of instructions - gotchas and extra info" template.  I'll also link to the entries from the bullet list above so it's easy to find them later. Where to put the periods when using a parenthetical sentence? I have two complete sentences; the second is in parentheses, essentially a comment on the first.  Where do I place the periods?  I would use this:     They played opera. (I covered my ears.)   Is this punctuation correct? WAMP Server not working Okay so a continuation from , where you experts intro'd me to , which can basically execute PHP within a Windows XP environment.  So now I've got it installed, but the tray icon forever shows YELLOW, and when I visit any PHP page in my browser, it just shows me the PHP source!  Also, when I visit "" in IE7 it gives me a 404 Not Found, FF3 just shows a blank page.    BTW I've tried "Restart All Services" and restarting my machine, but it still won't work.  Any ideas? Any of you had this problem and solved it? Please help me here, I'm desperate to execute PHP client-side and I'm just reverting to testing on-server for now! How can I mute the YouTube app while playing music on another player? Where can I find legendary crafting materials? How to write “ä” and other umlauts and accented letters in bibliography? How to write in bibliography (package natbib) letter "a" with two dots above? Specially, I mean the word Birkhäuser.  Is there a general rule or way how to write such umlauts or other accented letters in bibliographies? I want to add a check constraint on a column if entered value for column is greater than 3 than it should be saved as 1 else entered value. For that scenario I am using below query but on insertion of data it shows an error message.  create table tblTestCheckConstraint  ( id int, NewColumn int )   alter table tblTestCheckConstraint add constraint chk_tblTestCheckConstraint_NewColumn1 CHECK   (     CASE         WHEN NewColumn &gt;4 THEN 1         ELSE NewColumn     END = 1 )   Insert Statement:   insert into tblTestCheckConstraint values ( 1,5) insert into tblTestCheckConstraint values ( 1,2)   Error Message:   Msg 547, Level 16, State 0, Line 1 The INSERT statement conflicted with the CHECK constraint "chk_tblTestCheckConstraint_NewColumn1". The conflict occurred in database "DBName" , table "dbo.tblTestCheckConstraint", column 'NewColumn'. The statement has been terminated. Do megapixels matter with modern sensor technology? Explicitly finding the sum of $\arctan(1/(n^2+n+1))$