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Compared to, for example, completing 5 bounties in each of 5 different games. C++ Redefinition Header Files (winsock2.h) How to prove that $A_5$ has no subgroup of order 30? How do I resolve these unmet dependencies? How do you performance test JavaScript code? CPU Cycles, Memory Usage, Execution Time, etc.?  Added: Is there a quantitative way of testing performance in JavaScript besides just perception of how fast the code runs? How do I disable network manager permanently? I'm using Ubuntu 18.04.1 LTS. I want to disable network manager on an Ubuntu machine, because (1) I don't need it, (2) I prefer having hardcoded configuration, and (3) network manager regularly causes issues by changing the DHCP configuration. I tried to follow :  Stop network manager sudo systemctl stop NetworkManager.service  Disable network manager (permanently) to avoid it restarting after a reboot sudo systemctl disable NetworkManager.service   Despite this, the network manager is back again every time I reboot the machine. How can I make it go away? So basically this proof centers around proving that (S,*) is a group, as it's quite easy to see that it's abelian as both addition and multiplication are commutative. My issue is finding an identity element, other than 0. Because if 0 is the identity element, then this group won't have inverses.  The set explicitly excludes -1, which I found to be its identity element, which makes going about proving that this is a group mighty difficult. Elegant proofs that similar matrices have the same characteristic polynomial? What's the meaning of this present perfect sentence? Books for general relativity What are some good books for learning general relativity? For the following block of code:  For I = 0 To listOfStrings.Count - 1     If myString.Contains(lstOfStrings.Item(I)) Then         Return True     End If Next Return False   The output is:  Case 1:  myString: C:\Files\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: True   Case 2:  myString: C:\Files3\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: False   The list (listOfStrings) may contain several items (minimum 20) and it has to be checked against a thousands of strings (like myString).  Is there a better (more efficient) way to write this code? How I can automatically add a page if the total number of pages is odd? I need automatically add a blank page (also without document header, numbering and footer) at the end of the document, if the total numbers of pages is odd. How I can do that? And preferably without using any additional package. :) I know plants are green due to chlorophyll.  Surely it would be more beneficial for plants to be red than green as by being green they reflect green light and do not absorb it even though green light has more energy than red light.  Is there no alternative to chlorophyll? Or is it something else? Regarding the recalc in question rep increase what happens due to the cap? I am having trouble getting a basic example of a matrix of notes to show up in my beamer presentation. I am using the code copied from the pgf manual. Here is a complete working example. The error I get upon compilation is:  "Package pgfbasematrix Error: Single ampersand used with wrong catcode."  \documentclass{beamer} \usepackage{tikz} \usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,fit,petri,positioning,matrix}  \begin{document}  \begin{frame}  \begin{tikzpicture} \matrix (magic) [matrix of nodes] { 8 &amp; 1 &amp; 6 \\ 3 &amp; 5 &amp; 7 \\ 4 &amp; 9 &amp; 2 \\ }; \draw[thick,red,-&gt;] (magic-1-1) |- (magic-2-3); \end{tikzpicture}  \end{frame} \end{document} Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$. There seems to be something wrong with the sorting of Stack Exchange sites by name:    elementary OS and Русский язык appear in the wrong place at the end of the list. Interior product (contraction) symbol See the above excerpt from John Lee's Introduction to Smooth Manifolds. In differential topology and linear algebra, there's an operator called the interior product or contraction operator, denoted $\iota_X(\omega)$ or alternatively with some other "half box" like operator $X_|\omega$. Does anyone know how to markup that operator in LaTeX?   Google has turned up nothing except for this thread:   That thread did receive an accepted answer, which was \invneg from the MnSymbol package, but the suggestion given there does not seem correct to me. Or at least, it does not match what I'm familiar with. That answer results in an inverted negation symbol, whereas the contraction operator should have a stroke down at the floor of the line, and a long stroke going up almost the full height of the line. It can be found in many texts, but why can I not find the correct LaTeX markup? I want to prove that if we have a commutative integral domain $D$ with field of fractions $F\neq D$ then $F$ is not finitely generated as a $D$-module. (In this question it may be the case that $1\not\in D$.)    My original plan was to localize at a maximal ideal and then use Nakayama's lemma but as we don't have a $1$ our localization may not be local (in fact we need not have maximal ideals).  So I'm a bit lost as to where to go?  Thanks for any help. How can I get the Ubuntu shell on Windows 10 to recognize a connected android device? I'm trying to connect adb to my Android device in the Windows 10 Ubuntu shell, but it doesn't seem to be working:    adb does work normally on Windows, so it's not a problem with the phone or the connection.  Do I have to do something like mount the port in the Ubuntu shell?  How?  (The goal is to pass logcat to grep, which would obviously work better in Ubuntu.)