Proving a simple claim concerning order without using LaGrange's Theorem
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
Is there any UNIX variant on which a child process dies with its parent? Show Google results along with related questions A significant number of downvotes are given to questions whose askers didn't first check Google. This seems to be closely related to downvotes from asking a question with duplicates in the "Related Questions" field. How about also showing Google's "I'm feeling lucky," or some other results, in the Related Questions to help out with that?   EDIT: to clarify, I'm not talking about questions with answers on Stack Overflow, but rather questions with easy solutions available via Google. Here's a question just like that: Continuing enumerate Counters in Beamer I'm trying to continue the numbering of examples in enumerate environments in beamer. For example, I'd like one slide to feature   Foo Bar   and the next slide   Zip Yadda   My strategy so far has been to define a counter that saves the enumerate counter at the end of the first environment and can then be queried to set the enumerate counter at the start of the second enumerate environment. (This is essentially the proposal also found at )  That works wonderfully so long as I don't try to uncover elements of the slide sequentially. The problem, of course, is that as each of the pdf-pages that make up the slide is created, the counter is advanced. Here's a MWE.  \documentclass{beamer}  \setbeamercovered{highly dynamic}  \newcounter{saveenumi} \newcommand{\seti}{\setcounter{saveenumi}{\value{enumi}}} \newcommand{\conti}{\setcounter{enumi}{\value{saveenumi}}}   \begin{document}  \begin{frame}[&lt;+-&gt;]   \begin{enumerate}   \item foo   \item bar%     \seti   \end{enumerate} \end{frame}  \begin{frame}[&lt;+-&gt;]   \begin{enumerate}     \conti   \item zip   \item yadda%     \seti   \end{enumerate} \end{frame}  \end{document}   As the second slide is progressively uncovered (pages 3 and 4 of the resulting PDF), the counter at the beginning of the enumerate environment is advanced each time. So page 3 of the PDF has the right numbering, (3) and (4) respectively, while the fully revealed page has the wrong numbering. Pictures follow:   on one of the slides    on the following one $x^{x^{x^{\dots}}}=2$, what is the value of $x$? I came up with this little simple exercise, stating:  $x^{x^{x^{\dots}}}$ infinite times is equal to $2$, find $x$.   As we're dealing with infinity, we can just separate the first $x$ and get $x^2=2 \implies x=\sqrt2$  But then I thought what if we change $2$ to $4$? Now we get $x^4=4 \implies x=\sqrt[4]4=\sqrt2$  Something went wrong, can someone explain? If A is a finite set and B is an infinite set, then B\A is an infinite set Prove: If $A$ is a finite set and $B$ is an infinite set, then $B \setminus A$ is an infinite set.   I've tried proving the contrapositive, that if $B \setminus A$ is a finite set then $A$ is infinite or $B$ is finite, but I don't think this is the way to go. If I run along the aisle of a bus traveling at (almost) the speed of light, can I travel faster than the speed of light? How to remove duplicate values from an array in PHP If the distribution of test statistic is bimodal, does p-value mean anything? I use dd in its simplest form to clone a hard drive:  dd if=INPUT of=OUTPUT   However, I read in the manpage that dd knows a blocksize parameter. Is there an optimal value for the blocksize parameter that will speed up the cloning procedure? How is effect precedence determined? I was using  and my opponent has a . I attacked Sylvanas, fearing that the Deathrattle will take control of one Hyena. I feel lucky, because it did not happen.  I want to know if there are some general rules of effect precedence.   Has Blizzard published something about this?  Are there articles teaching about precedence?   Please note, I want guidance about effect precedence in general, not just about Deathrattle. While studying rotational mechanics, I came across a section where it mentioned that angular momentum may not necessarily be parallel to angular velocity. My thoughts were as follows:  Angular momentum ($L$) has the relation $L=I\omega$ where $\omega$ is angular velocity and $I$ is the moment of inertia, so following this relation, it seems they should be in the same direction. Why are they not? Disable chat migration notification if one of the users has insufficient rep? Simple request, really.  Can we add a detection for the     Please avoid extended discussions in   comments. Would you like to   automatically move this discussion to   chat?   prompt, so that if one of the users in the "extended discussion" has under 20 rep it doesn't appear?  I think a lot of the users this apply to will have low rep and it may take some back and forth to get good info out of them.  New suggestion: how about if a sufficiently high-rep user is clicking on the link, the low-rep user gets a field promotion sufficient to chat? Low-rep users are particularly prone to post questions to lead in this direction of needing to move to chat. Update #2: Seems that it was my secondary screen the one that didn't show the color! Tried with another screen and I could see the progress clearer... perhaps a stronger color will make it easier to see across different devices?  Update: Seems to be an issue in Firefox, as I tried on Chrome and the progress is visible.    I just noticed that the badge progress on your user profile had it's style changed (don't know when but it seems that recently).  However, seems that the progress of gold badges is not working properly. If we see the Bronze and Silver badges, they are "filled with color" as you progress on the badge, however golden ones are not colored (just the border).   Here a picture illustrating what I say:    Is there a reason for this behavior? I have a problem with a virus in windows 7, I don't know what kind of virus is infected my OS, I installed kasersky antivirus, and clear all detected viruses. After that I can't open any antivirus sites, can't ping any antivirus sites. example:  C:\Windows\system32&gt;ping kaspersky.com Pinging kaspersky.com [38.117.98.231] with 32 bytes of data: General failure. General failure. General failure. General failure.  Ping statistics for 38.117.98.231:     Packets: Sent = 4, Received = 0, Lost = 4 (100% loss),   When I ping to other sites, I get reply normally: example woth pinging to google.com  C:\Windows\system32&gt;ping google.com  Pinging google.com [31.7.160.224] with 32 bytes of data: Reply from 31.7.160.224: bytes=32 time=2ms TTL=61 Reply from 31.7.160.224: bytes=32 time=2ms TTL=61 Reply from 31.7.160.224: bytes=32 time=1ms TTL=61 Reply from 31.7.160.224: bytes=32 time=1ms TTL=61  Ping statistics for 31.7.160.224:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 1ms, Maximum = 2ms, Average = 1ms   I tryed any antispyware/antimalware softwares, but null results.  Anyone else encountered this problem? How does the US federal income tax system work? General question here about US personal income federal tax rates.  Is it a cumulative effect where your income is first taxed at the lower tranches and move up, or is it one specific percent for your entire taxable income? Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$ I am looking for a short proof that $$\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$$ What do you think?  It is kind of amazing that $$\int_0^\infty \frac{\sin x}{x} \mathrm dx$$ is also $\frac{\pi}{2}.$ Many proofs of this latter one are already in this . Firefox 37.0.2 not opening (removing firefox did not help) runing ubuntu 14.04 LTS Having problems with listings and UTF-8. Can it be fixed? I'm having some problems with listings and UTF-8 in my document. Maybe someone can help me? Some characters work, like é and ó, but á and others appear at the beginning of words...  \documentclass[12pt,a4paper]{scrbook} \KOMAoptions{twoside=false,open=any,chapterprefix=on,parskip=full,fontsize=14pt}  \usepackage[portuguese]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{listingsutf8}  \usepackage{inconsolata} \lstset{     language=bash, %% Troque para PHP, C, Java, etc... bash é o padrão     basicstyle=\ttfamily\small,     numberstyle=\footnotesize,     numbers=left,     backgroundcolor=\color{gray!10},     frame=single,     tabsize=2,     rulecolor=\color{black!30},     title=\lstname,     escapeinside={\%*}{*)},     breaklines=true,     breakatwhitespace=true,     framextopmargin=2pt,     framexbottommargin=2pt,     extendedchars=false,     inputencoding=utf8 }  \begin{document} \begin{lstlisting} &lt;?php  echo 'Olá mundo!'; print 'Olá mundo!'; \end{lstlisting}  \end{document} \end{lstlisting} I have a spawn area I am hoping to make a safe haven, so I have a command block on a clock that kills each hostile mob type. This works to keep the place free of any hostile mobs, however every night I see rotten flesh, bones, arrows, and string everywhere.  I would like to add something to my command blocks so that they are killed without dropping loot. How can I accomplish this?  Note that I want mobs to drop loot generally elsewhere in the world, so /gamerule doMobLoot false will not do the trick for me. I'm hoping for a command that only applies to the mobs killed by the command block, and not anything else. When I look at the black and white photographs from professional photographers, I notice that they have a special look. Not a specific style—obviously each photographer has her own style—but a look which make them different from similar color photos, a special feeling, which makes them shine specifically as black and white and makes color irrelevant.  When I convert my own photos to black and white in Lightroom, they don't have any special look. They just look like any other of my photos, simply converted to black and white. I imagine that there are two reasons for that:   Some scenes are better for black and white. Talented and/or experienced photographers know which scenes would be beautiful in black and white, and shoot specifically those scenes. Moreover, they know how to adapt the scene itself and the lighting to black and white (for instance by not relying on the color contrast itself).  In my case, I don't think much about shooting for black and white. It comes only in post-processing, when I either think that the photo will look great in black and white (and very often, it doesn't), or I find the colors to be poor and turn the photo to black and white (which actually doesn't make the photo any better). Post-processing is much more complex than clicking on black and white button in an app. It involves not only adjusting black and white mix (i.e. raising or lowering the lightness of specific colors), but doing lots of other adjustments.  In my case, I do black and white mix, but other adjustments I do are similar to what I would do for a color photo: actually, I may even do them on a color photo, and only then turn it to black and white.   So, what should I take in account if I want to have decent black and white photographs? Are there specific techniques, tips, tricks or warnings for someone who usually shots in color and wants to start black and white photography?  Let me show some examples. Are those scenes not great for black and white photos in the first place? Or can they be salvaged through proper post-processing?  1.  First, a poorly done photo from Scotland with dubious composition and very poor colors that I was unable to correct in Lightroom.  The same image in black and white isn't much better. The difference between the trees and the grass on the hill is barely visible. Houses on the hill fade with the sky much more than in the original version.      2.  Here's a photo of a cute pet.  In black and white, the gap between the mouse's ear and the background is barely visible. There is absolutely no benefit compared to the original.      3.  Finally, an example of a much more contrasty picture. The black and white version is weird, since the lack of color makes it difficult to understand whether the soil is the actual sand or something else. I find the sky to be weird as well, and making the blue channel darker or lighter in Lightroom haven't changed that.