Guessing game not working coded wrong?
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$\\$   A normal subgroup $N$ is a subgroup where the left cosets are the same as the right cosets. $N$ is normal $\iff $ $xnx^{-1} \in N,  \forall x\in G$.   5.) Why is it that if $[G:H]=2 \implies $ $H$ is normal subgroup?  6.) Can we say that a factor group is just a group that has left cosets of $N$ (being a normal subgroup) as its elements? So if $N$ is a normal subgroup, then the left cosets of $N$ forms a group under coset multiplication given by $aNbN = abN$.   7.) The group of left cosets of $N$ in $G$ is called the factor group, why do we denote this by $G/N$? These are the same things as the integers modulo $n$ groups? How can I relate those exactly? When I'm about to install a program in the terminal it wants the password:  [sudo] password for xxx:   But when I start to type my password nothing happens. What should I do? Is returning a pointer to a static local variable safe? I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); How can I display the current branch and folder path in terminal? *.xhtml url-pattern causes java.lang.NullPointerException at com.sun.faces.context.flash.ELFlash.loggingGetPhaseMapForReading Is there any "official" guidance to upgrading from Lubuntu 18.04 LTS (LXDE) to Lubuntu 18.10 (LXQt) What happens if my ESTA expires on the day of arrival? I'm French and will travel the 14th of June to the US. My ESTA expires the 14th of  June 2013 and I'm wondering if my ESTA will be valid when I'll land in the US on the 14th of June 2013.  Does someone know anything about that? How to remove the Mail icon indicator applet? Change Legend Right to Left Reading in QGIS I am a new QGIS user and i have a challenge to convert legend from right to left reading in QGIS like ArcGIS. This is a  about DNS (Domain Name Service).   If my understanding of the DNS system is correct, the .com registry holds a table that maps domains (www.example.com) to DNS servers.   What is the advantage? Why not map directly to an IP address? If the only record that needs to change when I am configuring a DNS server to point to a different IP address, is located at the DNS server, why isn't the process instant? If the only reason for the delay are DNS caches, is it possible to bypass them, so I can see what is happening in real time? Strange noise when moving files When I move files, a small 'noise' noise comes through my headphones or speakers.  It only happens when moving files.  Is there a reason why moving files causes this slight static?  It only lasts for as long as the files are moving.  I'm not as much as annoyed as I am curious.  It is a Gigabyte board with a integrated sound card.  I'm running Windows 7.  I don't think it used to do this but I'm not quite sure. Getting MTP enabled devices to work with Ubuntu? he or she vs their when using 'one' as a pronoun Mindfulness allows one to cope with their daily challenges.   Is "one" correct with "their" here?  I want to know if it is okay to user their (instead of he or she) when using 'one' as a pronoun. Windows INSERT key anti-functionality accidentally triggers; how to stop it permanently? It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here? Prove that $G$ is abelian iff $\varphi(g) = g^2$ is a homomorphism I'm working on the following problem:     Let $G$ be a group. Prove that $G$ is abelian if and only if   $\varphi(g) = g^2$ is a homomorphism.   My solution: First assume that $G$ is an abelian group and let $g, h \in G$. Observe that $\varphi(gh) = (gh)^2 = (gh)(gh) = g^2h^2 = \varphi(g)\varphi(h)$. Thus, $\varphi$ is a homomorphism.  I'm having trouble completing the proof in the reverse direction. Assume that $\varphi$ is a homomorphism. We then know that $\varphi(gh) = \varphi(g)\varphi(h)$ and $\varphi(hg) = \varphi(h)\varphi(g)$. However, I don't see a way to use this to show that $gh = hg$.  Could anyone lend a helping hand? Lewis Carroll's Pillow Problem via Bayes' Theorem In Pillow Problems and a Tangled Tale Lewis Carroll presents the following problem:     A bag contains a counter, known to be either white or black. A white counter is put in, the bag is shaken, and a counter is drawn out, which proves to be white. What is now the chance of drawing a white counter?   One can easily reason that in the end, the bag must be in one of three states:   Black remains, new white taken New white remains, original white taken Original white remains, new white taken   In two of those states, a white counter remains to be drawn. Therefore, the chance is 2/3.  How can one arrive to this answer using Bayes' theorem? List or IList Can anyone explain to me why I would want to use IList over List in C#?  Related question: It was nice to discover the option for a room owner to add any user to a room, even if their rep is too low.     ...so I notified the user in question, and as instructed on the next screen, I had them got to chat.stackoverflow.com so that I'd be able to add them.    ...but when they did their part, and I did my part, I got the message:    Obviously both frustrated, the user's next logical question was:  "So I just have ask a couple questions and get someone to upvote them, right?"    Needless to say, we don't want to encourage new users to post questions for the sole purpose of bypassing a frustrating, misdocumented rule.  I realize this will likely quickly get closed since it has at least one  - which hasn't been touched in 5½ years.  However it would be nice if the issue was revisited:  Ideally, it would be cool if RO's did have the option of deciding who had access to the room they "own", but short of that, is it possible to remove the 6 "misleading" words from that page? Maximum log level exceeded in Developer Console Recently I have regularly been getting the error message below when opening the Developer Console:     The Developer Console didn't set the DEVELOPER_LOG trace flag on your   user. Having an active trace flag triggers debug logging. You have 316   MB of the maximum 250 MB of debug logs. Before you can edit trace   flags, delete some debug logs.   It happens in sandbox and scratch orgs. Haven't tried in production.  This only started happening recently. It goes away after clearing the logs but comes back after a few test runs.  Also: the Debug->Clear->Log Panel action is not working for me -- the logs stay put. I can remove them using the Query Editor as described , but it's pretty tedious.  Two questions:   Does anyone know a way to prevent the logs from exceeding the max level? Perhaps by having old logs cleared out automatically? Is there a known issue with the Clear Log Panel action? I am using Chrome btw.   Thanks!