Prove that $S_n$ is isomorphic to a subgroup of $A_{n+2}$
Embedding $S_n$ into $A_{n+2}$
How does the ternary operator work? What's the main difference between Intel processor generations? What are the main differences between each processor generation of Intel processors/chipsets? Is there a performance difference?  I've already seen processors from first to sixth generation, however I don't know/understand the exact differences. Is the neutral wire considered safe? With java.sql.ResultSet is there a way to get a column's name as a String by using the column's index? I had a look through the API doc but I can't find anything. Turning off swapping for only one process with cgroups? I would like to turn off swapping for only one process. Swap should work as usual for the other processes.  How I can implement this with cgroups? How can I force my browser to search Google in English? I'm too bored of seeing sites like Google and such show up in my native language, I would rather like them to be in English. Yet, I have to explicitly change the URL to .com and en and that kind of parameters in order for them to show up in English. Can I somehow force this?  So, how is Google configured?  However, it is set to English on the site itself so it has to be my browser:    Then, how does my browser land up on non-english pages, like Google?  It usually shows up in non-English when I'm performing a search, which uses:  {google:baseURL}search?{google:RLZ}{google:acceptedSuggestion}{google:originalQueryForSuggestion}{google:searchFieldtrialParameter}{google:instantFieldTrialGroupParameter}sourceid=chrome&amp;ie={inputEncoding}&amp;q=%s   When performing a search, it fills these variables in with non-english values.  How can I tell my browser to fill these in with the English values?  My Google Chrome options give preference to English: Is it possible to install an old version of Mac OS on a new Mac? I know that Apple doesn't want me to run a version of Mac OS older than the one my Mac came with, but is there a way around this?  For example: if I buy a new Retina MacBook Pro, is there a way to run OS 10.6 on it without a VM? My friend Evan,is griefing me. When I went on his world to get revenge, he banned me. The screen said " HerobineYoung has banned enderpizza you will be kicked out in 5 minutes." I begged him to tell me how but he wouldn't tell me.   How can I ban people in Minecraft PE? Suppose I have some theorem in the paper  Section 1 Theorem 1.1. Let ...  And then later in the paper I want to recall the theorem by reprinting it  Section 4 We recall Theorem 1.1: Theorem 1.1. Let ...  What's the proper way to do this? I got a integrated GD, which is Intel, and another discrete GD, AMD Radeon 6490 HD I am using ubuntu 11.10  1st, when I boot into Windows, my GD is indeed AMD Radeon 6490 HD, but when I boot into Ubuntu, it shows that I have AMD Radeon 6470 instead.  2nd, I try most methods only to install driver for my AMD/ATI graphic card. First by jockey(fail, boot with unity 2D instead) and install manually (fail, boot into blank screen).   3rd, I give up using the AMD/ATI graphic card. Then I got a new problem. Both my graphic cards are powered on on startup, which causes my laptop to over heat.   I view the content of /sys/kernel/debug/vgaswitcheroo/switch  0:DIS: :Pwr:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   Then I switch off IGD using echo OFF &gt; /sys/kernel/debug/vgaswitcheroo/switch and I get  0:DIS: :Off:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   But after I reboot, the discrete graphic card is powered on again. How to solve this? A question about long exact sequence of finite dim vector spaces What's the meaning "them" here? I've confused about the word "them" in the middle of the sentence:     They know all about them   Westovers in Idaho.   Could you please tell me what the meaning of "them" here is?     Does it mean "they know about the oils which are made by Westovers in Idaho"?   The full text is here:      Dad had always said he wanted to build a room the size of a cruise ship   but I’d never thought he’d have the money. I looked to Mother for an   explanation but it was Dad who answered. The business was a roaring   success, he explained. Essential oils were popular, and Mother had the best   on the market. “Our oils are so good,” he said, “we’ve started eating into the   profits of the large corporate producers. They know all about them   Westovers in Idaho.”   Educated by Tara Westover PHP validation/regex for URL I've been looking for a simple regex for URLs, does anybody have one handy that works well?  I didn't find one with the zend framework validation classes and have seen several implementations. Are any of these verb phrases grammatical?        allows the user of modeling and resolving     allows the user to model and resolve      Which version of the following sentence is correct/better?        In particular, it allows to acquire a signal using a sample rate significantly lower than the one dictated by the Nyquist criterion.   In particular, it allows acquiring a signal using a sample rate   significantly lower than the one dictated by the Nyquist criterion.      I searched Google Scholar for "" and "", and it seems people use both more or less with the same frequency. "This box of matches is empty" There are several Japanese books teaching Japanese students how to write in English. I found this example in  (Correcting Errors in English Composition Manuals) by Michio Kawakami and J.D. Monkman.  The authors of this book claim that this sentence is incorrect:     This box of matches is empty.   They note that a “box of matches” is a box containing matches (and not a box made for keeping matches), hence the sentence should instead be:     This matchbox is empty.   Likewise, an “empty bottle of beer” should instead be an “empty beer bottle.”  Is this actually an error that I should avoid in writing English? If so, is it a grammatical error or something else? Minion Pro, TL2016 and LuaLaTeX When I compile with LuaLaTeX and TL2016 this MWE   \documentclass{article}  \usepackage[no-math]{fontspec} \usepackage{luatex85} \usepackage{shellesc}  \setmainfont{Minion Pro}  \begin{document}  \huge{huge} \textbf{\huge{huge}}  \Huge{Huge} \textbf{\Huge{Huge}}   \end{document}   I have this .pdf.     Any help? With TL2015 all is correct. Thanks Which LaTeX to install on Linux? Which LaTeX distribution would you recommend for using on Linux from command line? I am looking for one with most complete coverage of packages. Let $p$ be a prime number. Let $R$ be the subset of all rational numbers $m / n$ such that $n \neq 0$ and $n$ is not divisible by $p$. Show that $R$ is a ring. My Proof-trying. $R1$. Associativity for under addition is clear. $R2$. $\dfrac {m} {n}+0=0+\dfrac {m} {n}$, so there exist the identitiy element for under addition. $R3$. $\dfrac {m} {n} + \dfrac {-m} {n}=\dfrac {-m} {n} +  \dfrac {m} {n}$, so there exist inverse element. $R4$. $\dfrac {m} {n} + \dfrac {m'} {n'}=\dfrac {m'} {n'}+\dfrac {m} {n}$, so commutativity. So $R$ is an additive abelian group. $R5$. $\dfrac {m} {n} ( \dfrac {r} {s} + \dfrac {t} {v})=\dfrac {mr} {ns} + \dfrac {mt} {nv}$ and $( \dfrac {r} {s} + \dfrac {t} {v})\dfrac {m} {n}=\dfrac {rm} {sn}+\dfrac {r} {s}+\dfrac {tm} {vn}$ $R6.$ $R$ is associativity for under multiplication, clear. $R7.$ $1 \dfrac {m} {n}=\dfrac {m} {n} 1 = \dfrac {m} {n}$, so there exist identity element for under multiplication. Can you check my answer? If false, can you write true answer? What torque for caliper brakes onto carbon-alloy forks? I've recently got a new bike with a . This comes with deep-drop calliper brakes (Shimano R451 Dual Pivot). The first time out I bumped one of the brakes and it twisted around the single attachment bolt and rubbed on the rim.  I managed to easily twist it back by hand and carry on, however I thought the bolt probably needs tightening. The question is: How tight can it be?  As the fork is part carbon I've so far only dared to take it up to 4Nm, but it still seems possible to twist the whole calliper around with a bump of the hand. Maybe that's normal? Perhaps it's easier to bump around because of the longer deep-drop lever. Should I be aiming to get it really secure?    I'm not sure whether the brake mount in the fork is all carbon, or some of it is alloy underneath, but either way I'd like to know what a sensible torque is. As far as I can see from the  there is no such specification. How can I find this out? How accurate is the GPS on the iPhone's Find My iPhone app?  I used Find My iPhone app to track a friend. The first 3 stops were dead on but when it refreshed it showed them to be several streets over from actual location. What could cause that?