I am stuck on trying to find an element in $G/H = \{g + H | g \in G\}$ that will generate the whole set. My intuition tells me it is true since $G$ and $H$ are cyclic. I have a feeling that this direct approach of definition of a cyclic group is not the effective way to tackle this problem. Any advice appreciated, thank you.
If $G$ is cyclic, then $G/H$ is cyclic?   The proof I got goes like this: $G$ is cyclic, so $G=&lt;g&gt;$ for some $g\in G$. So any coset in $G/H$ would be of the form $Hg'=Hg^n$ for some $n$. So $Hg$ is an generator of $G/H$. Thus, $G/H$ is cyclic.  I might just be confusing myself, but we have only shown that $Hg'$ is in form of $(Hg)^n$. But what if we are missing some $n\in\mathbb{N}$? That is, there is no quotient group of the form $Hg^2$, for example.  To make myself a little bit clearer, I think what the above proof has done was showing that $\forall Hg'\in G/H, Hg'\in &lt;Hg&gt;$, thus $G/H \subset &lt;Hg&gt;$. I feel that this is not a complete proof.
Has Marvel commented on the extra Infinity Gauntlet? Ubuntu Server VM: copy paste? I've installed Ubuntu Server under Virtualbox just to get a nice little shell. I've also installed the VirtualBox "Guest Additions" and set "Shared Clipboard: Bidirectional".  I still can't seem to get any copy-paste working. Am I missing something here?    I've installed  which gives mouse support in server mode (no X), and allows copy-paste using the mouse, but still the VirtualBox integration doesn't work. Difference between the use of "a" and "any" in these examples? I didn't have an idea.      I did not have any idea.   I am much more familiar with the second one. The first one sounds a bit odd to me, but sounds fine if I say:     I did not have even an idea.   But, the first one is also one of the widely used sentences by natives. What is the difference between the two? How can I add mp3 files as podcasts to my iPhone using iTunes? I am using iTunes 12.5 on Windows 10 with an iPhone 5s.  Sometimes I download hour-long .mp3 files that I want to put onto my iPhone as podcasts, so that it automatically remembers where I am in my listening if I have to stop in the middle.  I know how to transfer .mp3 files to my iPhone, where they show up as Music.  I also know that I can right click on any song, choose 'Get Info' and under Options change the media kind to 'Podcast.'  But when I change the file to a podcast, it disappears from iTunes, though it does show up on my device when I open the Podcasts app.  How can I transfer an .mp3 file to my iPhone as a podcast, and still have that podcast show up in iTunes when I look there to see what podcasts are on my device? I just installed Ubuntu 14.04 Server and cannot get wifi configured correctly to work with WPA2 personal and could use some help.    There was a simple wizard during install where I selected my SSID from a list and entered my passphrase and that worked great.  Now that the install is done I am having trouble configuring wifi.  My Access Point is setup to WPA2 Personal TKIP or AES. Any advice would be greatly appreciated.  I have been messing around with WPA supplicant ant my /etc/network/interfaces file with no luck.  Thanks Interface naming in Java Most OO languages prefix their interface names with a capital I, why does Java not do this?  What was the rationale for not following this convention?  To demonstrate what I mean, if I wanted to have a User interface and a User implementation I'd have two choices in Java:        Class = User, Interface = UserInterface   Class = UserImpl, Interface = User      Where in most languages:     Class = User, Interface = IUser   Now, you might argue that you could always pick a most descriptive name for the user implementation and the problem goes away, but Java's pushing a POJO approach to things and   most IOC containers use DynamicProxies extensively.  These two things together mean that you'll have lots of interfaces with a single POJO implementation.  So, I guess my question boils down to: "Is it worth following the broader Interface naming convention especially in light of where Java Frameworks seem to be heading?" How to convert decimal to hexadecimal in JavaScript What is a NumberFormatException and how can I fix it? Extend a filesystem when adding HDD without using LVM? Are there any method to extend a filesystem when i adding more hdd to it without using LVM? What are those ? Does registering [name]overflow.com violate Stack Overflow's trademark? What is the name of the horizontal division line? What is the name of the horizontal division line? Is there a name for it other than "division line? Search across Stack Exchange sites in Android app Is it possible to search for a question across all Stack Exchange sites in the Android app?   Right now I can search in only one specific site at a time.   If not, can you add that feature? Passing list to viewparams variables in GeoServer SQL views? Content replacement from external website Where did they go?   Where do they went?   Can you please advise which of above forms is correct?  I'm pretty sure that first one is fine but wondering about second one.   Can I use a second form as well or it's incorrect? I've been wondering why I've never seen any official specifications of the maximum allowed torque that can be exerted upon lens mounts. It seems to me like a very useful specification, but I can't seem to find it from any manufacturer.  indicates that there might be no specifications for Nikon mounts. Are there really no manufacturer that publish these specification of their mounts? Using pgfplots, why do I get "undefined control sequence" when trying to use a foreach variable as a parameter to addplot? Since I have multiple plots with error bars, I would like to shift the error bars slightly to make the overall plot more readable. However, when I try to do this using the variable of a \foreach as the amount to shift, I get an "undefined control sequence" error.  \documentclass{article}  \usepackage{tikz} \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture} \begin{axis} \foreach \x/\y in {a/-1cm, b/0cm, c/1cm} {     \addplot+ [         %every error bar/.append style={xshift=\y},         %every node/.style={xshift=\y},         error bars/y dir=both,         error bars/y explicit,     ] coordinates {         (0, 0) +- (0, 1)         (1, 0) +- (0, 1)         (2, 0) +- (0, 1)     }; } \end{axis} \end{tikzpicture}  \end{document}   (The document does not compile when I uncomment either one of the two comments.)  What's wrong here?  EDIT: Added another variable to the \foreach. In my actual use-case it would contain the filename to plot data from or the label to use for the curve. QGIS Processing - Additional Creation Parameter for GdalWarp I am having a hard time getting the "Additional Creation Parameters" to work when using GdalWarp through the processing toolbox.  I am trying to set the nodata value to 0 for the output raster.  processing.runalg("gdalogr:warpreproject","InRaster.tif","EPSG:32736","EPSG:32736",10,0,"-dstnodata 0","OutRaster.tif")   Has anyone used this functionality and managed to get it to work? A word that says a person is both female and your friend It's often confusing for me to talk about my friends, especially my female friends. This is because in Dutch there are words for both male ("vriend") and female ("vriendin") friends. In English however, there's as far as I know only the word friend, which can mean both a male or a female friend.  For this reason I was wondering if there is a word to say a person is both female and a friend. Why is a black hole black? In  (ignoring Hawking radiation), why is a  black? Why nothing, not even light, can escape from inside a black hole? To make the question simpler, say, why is a  black hole black?