Prove that any group of order $15$ is cyclic.  I know that if order of group is a prime then the group is cyclic, but how to approach such questions?
How can i show with quite simple methods that a group of order 15 is cyclic?
How can I produce the text Word_one_two in LaTeX?  I tried:  Samp\_Dist\_Corr   But, it doesn't quite look right. Also, I want it in the typewriter font, so actually, I'm doing:  \texttt{Samp\_Dist\_Corr}   I find it looks a bit like the underscore is merging in to the bottom of the "D", but maybe it's just because of the typewriter D? With the Superman lore, we know that light from a yellow star gives him his powers, light from blue stars makes him stronger, and light from red stars weakens him.  However, what happens if he is near a white dwarf, or a neutron star?  Has there been any evidence of Superman visiting a star system that wasn't red/yellow/blue? How to use Launchctl for schedule application I try to work with Launchctl and have a question:  How can I set up an application to run in a few minutes using Launchctl? (for example, open the program MyApp.app with arguments "hello" "world" Every 10 minutes)  I know that it can easily be done by creating Launch Agent, I looking for a way to do it using Launchctl directly to programmatically. I have created this with cycles:  But the edge between the glowing and non glowing materials is very sharp. The material was manually applied to faces in edit mode. Is there any way I can smooth the edge between them in cycles? My server is still vulnerable to heartbleed even after I update OpenSSL I have an Ubuntu 12.04 server. I have updated the OpenSSL package in order to fix the heartbleed vulnerability. But I am still vulnerable even, even though I have restarted the web server, and even the whole server.  To check my vulnerability I used:       dpkg gives:  dpkg -l |grep openssl ii  openssl  1.0.1-4ubuntu5.12   Secure Socket Layer (SSL) binary and related cryptographic tools   (launchpad.net/ubuntu/+source/openssl/1.0.1-4ubuntu5.12) Calculate relative time in C# Given a specific DateTime value, how do I display relative time, like:   2 hours ago 3 days ago a month ago equality of two operators... Please help me with the following problem( give some hints or references):  Let $X$ be a Banach space and $B(X)$ be the algebra of bounded linear operators on $X$. Suppose that $A$ and $B$ are two operators in $B(X)$ such that for every $T \in B(X)$ we have $\sigma(AT)=\sigma(BT)$. Show that $A=B$.  Here $\sigma(A)$ denotes the spectrum of $A$, i.e., the the set of all complex numbers $\lambda$ such that $\lambda I − A$ has no inverse in $B(X)$.  Thanks in advance. How do I survive in the Nether? Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$ Why is a conservative force defined as the negative gradient of a potential? I'm learning about work in my dynamics class right now. We have defined the work on a particle due to the force field from point A to point B as the curve Integral over the force field from point A to B. From math I know that if a vector field has a potential, we only need to evaluate the potential at point B minus the potential at point A to get the result of the curve Integral. In the text that I'm reading, it's explained that if the integral over a force-field is path-independent, then the force field $F = -{\rm grad}(V)$, where $V$ is the potential. Why is it defined as the negative gradient? Doesn't one determine the potential from $F$ mathematically. Why do we impose the sign on the potential? How to hide quoted text in Lion Mail? In Mail's conversation view, by default, quoted text is hidden and can be shown by clicking "See More from XXX" in the bottom of each message. After clicking that, how can quoted text be hidden again? This question is regarding the minecraft Beta 1.8 prerelease -- I have a beautiful house in single player survival which I'd like to record while flying.  I want to be able to change the game mode of my survival map to creative to be able to fly through it without installing a mod. I know it is possible if you run the map on a multiplayer server via the command /gamemode &lt;user&gt; 0|1 but I want to achieve this in single player :)  I think this would be possible through editing your level.dat file as I think that's where the game mode for the map is stored. Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically? proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$ I am currently working through Velleman's book How To Prove It and was asked to prove the following  $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$  This is my work thus far  $(P \to Q) \wedge (Q \to P)$  $(\neg P \vee Q) \wedge (\neg Q \vee P)$ (since $(P \to Q) \equiv (\neg P \vee Q)$)  $\neg[\neg(\neg P \vee Q) \vee \neg (\neg Q \vee P)]$ (Demorgan's Law)  $\neg [(P \wedge \neg Q) \vee (Q \wedge \neg P)]$ (Demorgan's Law)  At this point I am little unsure how to proceed.   Here are a few things I've tried or considered thus far:  I thought that I could perhaps switch some of the terms in step 3 using the law of associativity however the $\neg$ on the outside of the two terms prevents me from doing so (constructing a truth table for $\neg (\neg P \vee Q) \vee (\neg Q \vee P)$ and $\neg (\neg P \vee \neg Q) \vee \neg (P \vee Q)$ for sanity purposes)  I can't seem to apply the law of distribution since the corresponding terms are negated.  Applying demorgans law to one of the terms individually on step 2 or 3 doesnt seem to get me very far either.  Did I perhaps skip something? Am I even on the right track? Any help is appreciated var self = this? Using instance methods as callbacks for event handlers changes the scope of this from "My instance" to "Whatever just called the callback". So my code looks like this  function MyObject() {   this.doSomething = function() {     ...   }    var self = this   $('#foobar').bind('click', function(){     self.doSomethng()     // this.doSomething() would not work here   }) }   It works, but is that the best way to do it? It looks strange to me. I would like to update VirtualBox on my 32 bit Ubuntu 15.04 machine from 4.3.26 to 4.3.28, using a Debian package I manually downloaded from . But simply double-clicking the package opens up the Software Centre which gives an error that installing it would break an existing package (the exact message was:   Breaks existing package 'virtualbox' conflict: virtualbox-4.3 ()   and it does not appear to have an option to ignore this and proceed with the installation anyway. Is there a command-line work-around this problem, perhaps? I have installed the Citrix Receiver 13.0.0.256735 as described for Ubuntu 13.10 here:   The installation has succeded under Ubuntu 14.04 64 bit. But if I start the Citrix Receiver nothing happens.  Is there someone who has it running with Ubuntu 14.04? Area enclosed between the curves $y=x^2$ and $y=60-7x$ Find the area enclosed between the curves $y=x^2$ and $y=60-7x$.  I am completely new at this but I have tried and I believe that it should be between the numbers $0$ and $60$ is this right? I'm working on a web application that needs to prints silently -- that is without user involvement.  What's the best way to accomplish this?  It doesn't like it can be done with strictly with Javascript, nor Flash and/or AIR.  The closest I've seen involves a Java applet.  I can understand why it would a Bad Idea for just any website to be able to do this.  This specific instance is for an internal application, and it's perfectly acceptable if the user needs to add the URL to a trusted site list, install an addon, etc. Answer textbox's content starts overlapping when adding new lines in middle on Android app When typing/editing an answer, sometimes if I scroll the editor textbox, go upwards and add lines, the text will start overlapping each other. The behaviour is that when you add a newline, the text below it does not move downwards.  Minimizing soft keyboard fixes this.  This does not affect the Ask Question box in my test.    I am using Android 4.1.2