Suppose, that $ K $ is normal subgroup of $ N $, and $ N $ is also normal subgroup of $ G $. Prove, that $ K $ needn't be normal subgroup of $ G $. I can give only counter-example?
Let $F,G,H$ be groups such that $F\trianglelefteq G \trianglelefteq H$.  I am asked whether we necessarily have $F\trianglelefteq H$. I think the answer is no but I cannot find any counterexample with usual groups. Is there a simple case where this property is not true?
In MTG, what happens when a player loses in multiplayer? Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity? What is the difference between shell, console, and terminal? Why doesn't pressing enter return '\n' to getch()? #include &lt;stdio.h&gt; #include &lt;conio.h&gt; main() {     char ch,name[20];     int i=0;     clrscr();     printf("Enter a string:");     while((ch=getch())!='\n')     {         name[i]=ch;         i++;     }     name[i] = '\0';     printf("%s",name); }   When I give "abc" as input and if I press enter it's not working. Can anyone let me know why the condition ch=getch() != '\n' is not becoming false when I press enter? I have also observed that ch is taking \r instead of \n. Kindly let me know. Thanks Cycles Render Renders all white How to solve "Extra junk at end of file" when using apt? I'm trying to configure some proxies for a guest virtual machine and now I'm getting:  sudo apt-get update E: Syntax error /etc/apt/apt.conf.d/95proxy:4: Extra junk at end of file   The content of the file is:  cat /etc/apt/apt.conf.d/95proxy   Acquire::http::proxy  "http://10.0.0.60:3128/" Acquire::ftp::proxy "http://10.0.0.60:3128/" Acquire::https::proxy "http://10.0.0.60:3128/" I'm adding a title clock in the foot line of a beamer slide, if I compile it with pdfLaTeX it works fine; while the clock doesn't align in the middle vertically if compiling with XeLaTeX. How can I fix this.  Here is my MWE:  \documentclass[10pt]{beamer} \usepackage[font=Times,timeinterval=1]{tdclock} \usetheme{Madrid} \title{Title} \author{Authors} \institute{Institute} \date[\initclock\tddate\ \ \tdtime]{\today} \begin{document} \frame{\titlepage} \end{document} How to evaluate environment variables into a string in Python? I have a string representing a path.  Because this application is used on Windows, OSX and Linux, we've defined environment variables to properly map volumes from the different file systems.  The result is:  "$C/test/testing"   What I want to do is evaluate the environment variables in the string so that they're replaced by their respective volume names.  Is there a specific command I'm missing, or do I have to take os.environ.keys() and manually replace the strings? Python element-wise tuple operations like sum Is there anyway to get tuple operations in Python to work like this:  &gt;&gt;&gt; a = (1,2,3) &gt;&gt;&gt; b = (3,2,1) &gt;&gt;&gt; a + b (4,4,4)   instead of:  &gt;&gt;&gt; a = (1,2,3) &gt;&gt;&gt; b = (3,2,1) &gt;&gt;&gt; a + b (1,2,3,3,2,1)   I know it works like that because the __add__ and __mul__ methods are defined to work like that. So the only way would be to redefine them? The standard files/tools that report memory seem to have different formats on different Linux distributions. For example, on Arch and Ubuntu.   Arch  $ free               total        used        free      shared  buff/cache   available Mem:        8169312     3870392     2648348       97884     1650572     4110336 Swap:      16777212      389588    16387624   $ head /proc/meminfo  MemTotal:        8169312 kB MemFree:         2625668 kB MemAvailable:    4088520 kB Buffers:          239688 kB Cached:          1224520 kB SwapCached:        17452 kB Active:          4074548 kB Inactive:        1035716 kB Active(anon):    3247948 kB Inactive(anon):   497684 kB  Ubuntu  $ free              total       used       free     shared    buffers     cached Mem:      80642828   69076080   11566748    3063796     150688   58358264 -/+ buffers/cache:   10567128   70075700 Swap:     20971516    5828472   15143044   $ head /proc/meminfo  MemTotal:       80642828 kB MemFree:        11565936 kB Buffers:          150688 kB Cached:         58358264 kB SwapCached:      2173912 kB Active:         27305364 kB Inactive:       40004480 kB Active(anon):    7584320 kB Inactive(anon):  4280400 kB Active(file):   19721044 kB    So, how can I portably (across Linux distros only) and reliably get the amount of memory—excluding swap—that is available for my software to use at a particular time? Presumably that's what's shown as "available" and "MemAvailable" in the output of free and cat /proc/meminfo in Arch but how do I get the same in Ubuntu or another distribution? Custom setting Setting type not visible Let $f:\mathbb{R}\to\mathbb{R}$ be a map sending closed intervals to closed intervals. Prove that $f$ is continuous or find a counter example.  WLOG we just have to prove continuity at $0$ and we can also assume that $f(0)=0$ and $f(1)=1$ (by considering $x\mapsto (f(x)-f(0))/(f(1)-f(0))$ ).  I build up this question while thinking of the question . I met a guy on a sugar daddy dating site and we talked, I told him my situation and he said he would help.   He asked for my bank account information and I told him you can use cash app or PayPal to go through. He said his account manager deals with his finances. So I set up an account with a bank that I don’t use so that my primary account isn’t used.  Eventually he was in the process of sending me money and we had agreed on a amount that wasn't crazy. But then he asked for my address and I asked why and he said just wondering. Then said he wanted to send me a surprise for being his baby. Which I didn’t give.  Then later on he sent the money and said he sent me a bonus and that I was supposed to use that to pay his mothers caregiver, which he didn’t mention until after.  I kept questioning him and he was saying that he works in construction and he’s trusting me to carry out the errand. Then he said don’t let him down and I asked him if he was threatening me and he kept saying I need this done but didn’t really answer my question.  Am I being scammed? I’m about to change my password but is this a scam? Show that the boundary of a set equals the boundary of its complement $\newcommand{\bdy}{\operatorname{bdy}}$  I'm trying to show that $\bdy(A) = \bdy(A^c)$.  I know that $\bdy(A) = \operatorname{closure} A \setminus \operatorname{int}(A) = (\operatorname{int}(A^c))^c \setminus \operatorname{int}(A)$, but I don't know where to go from there.  Any help or hints would be very much appreciated. Aliens like giant grasshoppers invade earth, give black people power over whites How can I assign the output of a command to a shell variable? What should I do if a user posts sensitive information as part of a question or answer? Returning from a finally block in Java I was surprised recently to find that it's possible to have a return statement in a finally block in Java.  It seems like lots of people think it's a bad thing to do as described in ''. Scratching a little deeper, I also found '' which shows some pretty horrible examples of other types of flow control in finally blocks.  So, my question is, can anyone give me an example where a return statement (or other flow control) in a finally block produces better / more readable code? Find the all possible real solutions of $x^y=y^x$ Find the all possible real solutions of $$x^y=y^x$$ $x,y$ both are real numbers.  My attempt:I observed the following solutions  $x=2,y=4$  $x=4,y=2$  $y=x$  Is there any other possible solutions? What is a complete book for introductory quantum field theory? There's a fairly standard two or three-semester curriculum for introductory quantum field theory, which covers topics such as:   classical field theory background canonical quantization, path integrals the Dirac field quantum electrodynamics computing $S$-matrix elements in perturbation theory, decay rates, cross sections renormalization at one loop Yang-Mills theory spontaneous symmetry breaking the Standard Model   What is a good, complete and comprehensive book that covers topics such as these?