Prove that $4$ divides $n$
Prove that n is divisible by 4 in a cylic sum with variables which have only two possible values
Parsing JSON from URL I installed Ubuntu 15.04 on the VM and I have downloaded Eclipse Luna. When I try to install it, this error occurs:      An error has occurred.   See the log file   /home/master/.eclipse/1473617060_linux_gtk_x86_64/configuration/1442224462970.log   Can you help me to fix  it? Thanks How to show also the name of the parent counter with cleveref? Consider the following piece of code:  \documentclass{book} \usepackage{cleveref} \usepackage{lipsum}  \begin{document}   \chapter{Chapter One}   \section{Section One.One}   \label{mysection}   \lipsum    \section{Section One.Two}   Please ignore \cref{mysection}.    \chapter{Chapter Two}   \section{Section Two.One}    As you may have noticed, \cref{mysection} is useless. \end{document}   By default, in both uses of \cref I get Section 1.1 as expected.   Is it possible to change the way the reference is shown in such a way that the second use of \cref above will print Section 1 of Chapter 1? i.e., naming the parent counter as well.   However, this should be done only outside the own chapter, so the first use of \cref in the above example should print Section 1.  This comes from a use case of a normative text where the document is divided in "articles" and "commas", and it is good to have references like "Comma 1 of Article 2" or "Article 2, Comma 1". Problem recreating BCD on Windows 7 64bit - The requested system device cannot be found Clicking on a notification on Android app opens an empty feed When I receive a message on an SE post, I get a notification like this:    If I double tap this notification, the SE application opens, but my feed is empty approximately half the time. It looks like this:    If I refresh the feed (slide from the top), the feed does refresh and shows the new notification.   The notification, above, leads to  comment.  I haven't figured out the pattern yet, but this occurs roughly half the time I open a notification. It's occurred for chat messages, comments and answers - but not consistently. I have received notifications for the same post (for example, the two comments after the one linked above) that do not show an empty feed. But, a chat message barely 10 minutes later will show the empty feed again.  I am utilizing the beta app - version 1.0.72 on Android 5.0.1. Let, $X$ be a countable set. Which of the following are true?   There exists metric $d$ on $X$ so that $(X,d)$ is complete. There exists metric $d$ on $X$ so that $(X,d)$ is not complete. There exists metric $d$ on $X$ so that $(X,d)$ is compact. There exists metric $d$ on $X$ so that $(X,d)$ is not compact.   4 is true as we can take discrete metric. Then $\{\{x\}:x \in X\}$ is an open cover containing no finite subcover.  If there exists a compact metric then it would automatically become complete also. Hence if 3 is true, so is 1.  What about 2? Any other comment? I'm trying to fill out the skills section on my first character, but when I look at the character sheets in the Starter Set as examples of how to make a character, the skills that are circled have higher modifiers than their Dexterity or Strength or whatever should make them.  I've filled out all skills but those. What do I add to the ability modifier to get those numbers?   My abilities are Strength 13, Dexterity 14, Constitution 11, Intelligence 15, Wisdom 8, and Charisma 8. Proficiencies are Arcana, Athletics, History, Investigation and Stealth. My saving throws are Strength and Dexterity.   I just started D&amp;D and have the Player's Handbook, DM's Guide, Monster Manual, and the Starter Set. Will inverse functions, and functions always meet at the line $y=x$? If I have a function, the inverse function, by definition will be a reflection of the original function in the line $y=x$, so if I wanted to find the point of intersection, instead of solving it with equating both of the functions to equaling each other, could I assume that the point of intersection, between the two functions, will always be at the point $y=x$? This would enable me to solve problems much easier, instead of having to solve quartic equations, for example. I came across this example on WordWeb while going through the meaning of the word ''.     the program brought an avalanche of mail (Just like "a group of man men").   I'm quite sure it should be mails. Kindly confirm. Which is faster in Python: x**.5 or math.sqrt(x)? I've been wondering this for some time. As the title say, which is faster, the actual function or simply raising to the half power?  UPDATE  This is not a matter of premature optimization. This is simply a question of how the underlying code actually works. What is the theory of how Python code works?  I sent Guido van Rossum an email cause I really wanted to know the differences in these methods.  My email:     There are at least 3 ways to do a square root in Python: math.sqrt, the   '**' operator and pow(x,.5).  I'm just curious as to the differences in   the implementation of each of these.  When it comes to efficiency which   is better?   His response:     pow and ** are equivalent; math.sqrt doesn't work for complex numbers,   and links to the C  sqrt() function. As to which one is   faster, I have no idea... Nautilus bookmarks are missing since upgrade to 13.04 My bookmarks are not shown anymore after upgrading to 13.04 Raring ringtails and I can't add any new bookmarks. The function is not shown and the shortcut Ctrl+D isn't working either. Is this functionality just gone for some reason (as the split screen with F3) or is there something wrong with my upgrade?  Thanks for any hints. What is involved in converting a PC video card to have boot screen on the Mac? Help me identify this insect from Bangladesh I have seen this insect flying literally everywhere in Dhaka city (Bangladesh) over the last two months. It's small -- around 1-1.5 inches long. It's not an agile flyer and can be easily grabbed by hand during flight. Finite group with isomorphic normal subgroups and non-isomorphic quotients? I know it is possible for a group $G$ to have normal subgroups $H, K$, such that $H\cong K$ but $G/H\not\cong G/K$, but I couldn't think of any examples with $G$ finite. What is an illustrative example? Have you used any of the C++ interpreters (not compilers)? I am curious if anyone have used UnderC, Cint, Cling, Ch, or any other C++ interpreter and could share their experience. How to batch import Wavefront OBJ files? Is it possible to batch import Wavefront .obj to blender? I'm working on 2.69. If I select multiple .obj files, only one gets imported. Also if I hit A on file selection window to select all files (.obj and .mtl) I get an error, nothing gets imported. I have to import several hundreds of .obj into the blender file, is this possible? I have some cites in my captions. But I do not want to appear them in the table of figures or listings. With figures I managed to display an different caption like this:  \begin{figure}   \centering   \includegraphics[width=0.55\linewidth]{images/FIPA_Message-Transport-Reference-Model}   \caption[FIPA Message Transport Reference Model]{FIPA Message Transport Reference Model (\cite{FIPA2000}).}   \label{fig:FIPA_Message-Transport-Reference-Model} \end{figure}    But with lstlisting I have some troubles because the caption is an option of the listings and that seems not to have an optional caption label.  \begin{lstlisting}[ language=Scala, label={lst:Publisher}, caption={Publisher notify\cite{Zenger2013}}]    protected def publish(event: Evt) {     filters.keys.foreach(sub =&gt;       if (!suspended.contains(sub) &amp;&amp; filters.entryExists(sub, p =&gt; p(event)))         sub.notify(self, event)     )   } \end{lstlisting}   Any Ideas how to solve this? Thanks in advance! I was reading a blogpost here:  () One thing that threw me off was that after the first four large displayed equations, there is the statement &quot;it is sufficient to prove that if the theorem holds for $n=m+1$, then it holds for $n=m$.&quot; How is this type of induction valid? I browsed around for things like backward induction, reverse induction, and Cauchy induction, but couldn't find a justification for how this is valid. With the usual forward induction of verifying a base case and proving $P(n)\implies P(n+1)$, it's easy to intuitively understand how induction will show a property holds for all natural numbers (or at least starting at the base case). But with this reverse induction, it seems to me that if you prove $P(m+1)\implies P(m)$, then if you were able to verify a specific case like $P(15)$, then you would only know it's true for numbers up to $15$. How does it actually prove the property for all naturals? I know classical physics, quantum mechanics, special relativity, and basic nuclear physics. I would like to get into some particle physics.   Where can I find a good introduction? It might be useful to segment books by whether they require quantum field theory or not. Every partially defined isometry can be extended to a isometry I know that the following theorem holds true:  Let $S$ be a subset of $\mathbb R^n$, and let $f:S\to \mathbb R^n$ a map such that $d(p,q)=d(f(p),f(q))$ for every $p,q \in S$ (here $d$ is the usual euclidean distance). Suppose that $0 \in S$ and $f(0)=0$. Then $f$ can be extended to an orthogonal transformation of $\mathbb R^n$.  I have two questions:   Can someone give me a reference of a proof of this theorem? I believe that the previous theorem holds true also if we change $\mathbb R^n$ with $\mathbb C^n$ and "orthogonal" with "unitary", with nearly the same proof. Does it holds true also in the $ \ell^2$ space? With the same proof?