why there is no non cyclic group other than $D_{61}$.
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
Since multiple inheritance is bad (it makes the source more complicated) C# does not provide such a pattern directly. But sometimes it would be helpful to have this ability. For instance I'm able to implement the missing multiple inheritance pattern using interfaces and three classes like that: public interface IFirst { void FirstMethod(); } public interface ISecond { void SecondMethod(); }  public class First:IFirst  {      public void FirstMethod() { Console.WriteLine(&quot;First&quot;); }  }  public class Second:ISecond  {      public void SecondMethod() { Console.WriteLine(&quot;Second&quot;); }  }  public class FirstAndSecond: IFirst, ISecond {     First first = new First();     Second second = new Second();     public void FirstMethod() { first.FirstMethod(); }     public void SecondMethod() { second.SecondMethod(); } }  Every time I add a method to one of the interfaces I need to change the class FirstAndSecond as well. Is there a way to inject multiple existing classes into one new class like it is possible in C++? Maybe there is a solution using some kind of code generation? Or it may look like this (imaginary c# syntax): public class FirstAndSecond: IFirst from First, ISecond from Second { }  So that there won't be a need to update the class FirstAndSecond when I modify one of the interfaces.  EDIT Maybe it would be better to consider a practical example: You have an existing class (e.g. a text based TCP client based on ITextTcpClient) which you do already use at different locations inside your project.  Now you feel the need to create a component of your class to be easy accessible for windows forms developers. As far as I know you currently have two ways to do this:  Write a new class that is inherited from components and implements the interface of the TextTcpClient class using an instance of the class itself as shown with FirstAndSecond.  Write a new class that inherits from TextTcpClient and somehow implements IComponent (haven't actually tried this yet).   In both cases you need to do work per method and not per class. Since you know that we will need all the methods of TextTcpClient and Component it would be the easiest solution to just combine those two into one class. To avoid conflicts this may be done by code generation where the result could be altered afterwards but typing this by hand is a pure pain in the ass. Finder sidebar flashing text and high CPU load since El Capitan After update to OS X 10.11 I started having these bugs:   Finder sidebar text flashing  Very high CPU load:      I have Macbook Pro Retina 13" Mid 2014  I reset NVRAM.  I deleted com.apple.finder.plist, it didn't help.  Also I did this: , no longer flashes. How to add a dot after the section number? I wonder is there any way to change the format of section numbering from 1.1 to 1.1. ? I know this is trivial, but I really need to add one more dot after the section number. Does anybody know how to do that?  Thanks a lot Change Proxy Settings In Ubuntu I want to use the Ubuntu Software Center to install software, but I cannot download them.  How can I give my proxy settings in Ubuntu terminal (just like we use cmd in Windows to choose IE proxy settings)? I came to Netherlands from Dubai on a business visa. Now I wish to travel to Paris by train and after two days wish to leave to Dubai direct from Paris. Am I allowed to exit Paris to Dubai when the entry stamp in my passport is Amsterdam? Complex roots of $z^3 + \bar{z} = 0$ Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$ The group $\left(\Bbb{ Q}\setminus\{-1\},\star\right)$ has as its underlying set the rational numbers different from $-1$ and the operation $\star$ is defined as $a \star b=a \cdot b+a+b$ where multiplication/addition are the usual operations with rational numbers.Show that this is a binary operation.  What I did (Please help verify):  identity element has to be 0 since $a\star 0 = a+0+a(0)$ so for $a\star b=0$ we have  $ab+a+b=0$ $$ab+a=-b \\ a(b+1)=-b \\ a=\frac{-b}{b+1}$$ so $b$ cant be $-1$ since that solution is not in $\Bbb{Q}$. Similar question might have been answered here. Is this operation true for all groups? I think so.  Thanks for the tips and help. Password protect files/folders using cli I have some important documents that I need to protect from anyone else having access to my machine.   The problem being the other persons have access to my machine via root account so changing the file permissions is not a option for me. I have seen apps like cryptkeeper but I was wondering can I password protect my files/folder by command line mode in ubuntu. I've seen papers (e.g., in Science) where the first two authors are listed in non-alphabetical order, and yet there are asterisks behind their names to say that they contributed equally.   It seems strange to me, because if the two authors are in alphabetical order, then it could be that the first author contributed more or the two contributed equally, and this can be made clear with asterisks in the paper if it's the latter case. When they're in non-alphabetical order, however, if someone only sees the author list without seeing the paper, he/she will likely assume that the first author contributed most.  So my question is: Are there particular reasons why people do that? (This  is related, but I don't think the answers there get to my question.) Volumetric Lighting is not working I have a simple setup to try out Volumetric Lighting. I have a spot lamp and Volume Scatter set for the World. The cube has a window for the light of the spot lamp.     But no Volumetric Lighting. I have read most questions on this subject. But I have no idea where I am going wrong. How to understand linux versioning I need to understand the Linux versioning system and distribution concepts. what are public, stable or final terms for versions? 1970s scifi/horror novel where protagonist is used by a crablike creature to feed its larvae, goes mad, and is defeated by retraumatising him $\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$ Give a convincing argument that $\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers $x$ and $y$. Could someone please explain how to prove this? I attempted to say that the largest values that could be added to $x$ and $y$ is $0.99$ and that doing so still made $\lfloor x\rfloor + \lfloor y\rfloor &lt; \lfloor x+y\rfloor$. However, my answer was not accepted. Removing Ubuntu from UEFI Bios Menu I've been writing checks this way for the last ~15 years or so:    Namely, the amount field is written using numbers like     1,500 and 00/100    rather than the tedious, painful spelling out of      One Thousand Five Hundred and 00/100   99 times out of 100, this works fine. But occasionally you'll get certain rare human tellers who simply refuse to believe this is a valid check and you have to fight over it. I still figure the time I've saved by not writing out all those ridiculous numbers-as-words is still worth it, overall, but it's definitely irritating.  So: who's right? Is a check with the amount written in numbers valid ... or not? Do WALLS matter if I'm building the 6-inch brick defense from Corruption/Crimson for my city? Does borrowing from my 401(k) make sense in my specific circumstance? "Economic" vs. "economical" What are the best practices for battery longevity? how to get the string-lengths stored in array (C)