Reading an  I came across the following C# syntax in method name.  private class sortYearAscendingHelper : IComparer {    int IComparer.Compare(object a, object b)    {        ...    } }   I understand Compare method is method of IComparer interface, but coming from C++ I am not certain what this syntax means. If Compare is part of interface, I would expect to mention that only like int Compare(...). Why we have to specify class?
What are the differences in implementing interfaces implicitly and explicitly in C#?  When should you use implicit and when should you use explicit?  Are there any pros and/or cons to one or the other?    Microsoft's official guidelines (from first edition ) states that using explicit implementations are not recommended, since it gives the code unexpected behaviour.  I think this guideline is very valid in a pre-IoC-time, when you don't pass things around as interfaces.  Could anyone touch on that aspect as well?
If a function has a finite limit at infinity, does that imply its derivative goes to zero? I've been thinking about this problem: Let $f: (a, +\infty) \to \mathbb{R}$ be a differentiable function such that $\lim\limits_{x \to +\infty} f(x) = L &lt; \infty$. Then must it be the case that $\lim\limits_{x\to +\infty}f'(x) = 0$?  It looks like it's true, but I haven't managed to work out a proof. I came up with this, but it's pretty sketchy:  $$ \begin{align} \lim_{x \to +\infty} f'(x) &amp;= \lim_{x \to +\infty} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \lim_{x \to +\infty} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \frac1{h} \lim_{x \to +\infty}[f(x+h)-f(x)] \\ &amp;= \lim_{h \to 0} \frac1{h}(L-L) \\ &amp;= \lim_{h \to 0} \frac{0}{h} \\ &amp;= 0 \end{align} $$  In particular, I don't think I can swap the order of the limits just like that. Is this correct, and if it isn't, how can we prove the statement? I know there is  already, but I think this is different in two aspects. First, that question assumes that $\lim\limits_{x \to +\infty}f'(x)$ exists, which I don't. Second, I also wanted to know if interchanging limits is a valid operation in this case. When I compile the Python code below, I get      IndentationError: unindent does not match any outer indentation level     import sys  def Factorial(n): # Return factorial     result = 1     for i in range (1,n):         result = result * i     print "factorial is ",result     return result   Why? Complex zeros of the polynomials $\sum_{k=0}^{n} z^k/k!$, inside balls this is a question from a Temple prelim exam, and i'm trapped in it! We have $p_n(z)=\sum_{k=0}^n\frac{z^k}{k!}$ and we have to prove that $\forall r&gt;0 \quad \exists N\in\mathbb{N}$ s.t. $p_n(z)$ has no zeros in $B_r(0)$ for $n&gt;N$.  I tried to use Rouche's theorem observing that $1+\frac{z^n}{n!}$ has the nth roots of $n!$ as complex zeros, which are outside a fixed ball for n sufficiently large, but i'm having trouble proving that $|1+\frac{z^n}{n!}|&gt;|z+\cdots+\frac{z^{n-1}}{(n-1)!}|$ in $|z|=r$ (if this is true). If anyone could help.. I have a problem with energy conservation in case of interfering waves.  Imagine two harmonic waves with amplitudes $A$. They both carry energy that is proportional to $A^2$, so the total energy is proportional to $2A^2$. When they interfere, the amplitude raises to $2A$, so energy is now proportional to $4A^2$ and bigger than before.  The equivalent question is what happens to the energy with the superposition of two waves that interfere destructively.  Also, if someone could comment on the statement about this problem in my physics book (Bykow, Butikow, Kondratiew):      The sources of the waves work with increased power during the interference because they feel the wave from the other source. Since when did kidnapping come to include adults too? As per , the word 'kidnap' originated to denote nabbing away of a child. When and how did kidnap come to denote nabbing of adults?  Update: Just found a link to a  that mentions kidnapping of souls. Now not sure how correct the above link is. Show that $F\subset Y$ is closed in $Y$ iff $F=Y\;\cap\;H$ where $H\subset X$ is closed in $X$. I have the following problem:      Let $(X,\tau)$ be a topological space and $(Y,\tau_y)$ be its    subspace, that is $Y\subset X$ and $\tau_y=\{\;A\;\cap\;Y\mid  A\in\tau\;\}$. Let also $F\subset Y$ and $H\subset X$, where $H$ is    closed in $X$. Show that $F=Y\;\cap\;H$ if and only if $F$ is closed   in $Y$.   I solved this problem by assuming that if $F$ is closed then $F=Y\;\cap\;H$, where $H$ is closed in $X$, but I got stuck proving this in the other direction, that is showing that if $F=Y\;\cap\;H$ then $F$ is closed in $Y$.  I tried to do something like this:   Assumption: $F=Y\;\cap\;H$, where $H$ is closed in $X$. If $H$ is closed in $X$ then $X\;\setminus\;H$ is open in $X$ and then $X\;\setminus\;H \in \tau$ which means that $B = (X\;\setminus\;H)\;\cap\;Y\in \tau_y$.  How should I proceed now? Should I investigate the set $B$ now more or what? Our admins deployed a new version of Notepad++ (version 6.3) on our machines, and this version is highlighting all changes done in a file by default. It does so by setting the background color of every modified line to a bright orange, which I find very distracting.  We  have dozens of plugins installed, but I double checked and we do not have the "Change Markers" plugin (which could be the culprit).  Any idea where I can disable this feature? Changing the highlight color could also be an option. If $F_n$ is the $n$-th fibonacci number, then prove that, $$F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$$  I tried the idea of using Pascal's triangle, but it seems to need some adjustment, so I am stuck, please help.    Any combinatorial argument would be of greater help than rigorous proof.  Thank you. I found an asnwered question concerning this topic already here:  Copying \captionsetup[subfigure]{justification=centering} doesn't help me thought for I am using different packages.  I would like my Captions and Subcaptions to be justified as the text below. Just under my pictures. Any suggestions?  Thanks a lot  \documentclass{article} \usepackage{subfig} \usepackage[labelfont=bf, justification=justified]{caption} \usepackage[demo]{graphicx}% Remove demo option in real document  \begin{document}     \begin{figure} %   \captionsetup[subfigure]{justification=centering}     \centering       \subfloat[Subcaption one \newline including a linebreak ]   {     \includegraphics[width=0.2\textwidth]{image1}     }     \hspace{1cm}     \subfloat[Subcaption two \newline including a linebreak]     {     \includegraphics[width=0.2\textwidth]{image2}     }        \caption{Figure caption \newline with additional text right here} \end{figure}  \begin{center} This is correctly justified Text \\ including a longer linebreak than blabla. \end{center} \end{document} How do I set a static IP address in Windows? Is there an easy way to disable this laptop's touchpad? Specifically, I'm on a . I'd like to disable the  so that I can re-enable if my mouse were to run out of batteries (so physically breaking the connection to the motherboard or uninstalling the driver will not be the best options). In the Control Panel, when I go to "Mouse" and find the touch pad, there is no disable option. Any ideas?  Edit: I am on Windows 7. There is a driver on the Dell site that might allow an option to disable it, but I cannot install it on Windows 7. scp copy over ssh doesn't work - permission denied error, please? Why is the Night's Watch so depleted at the start of ASOIAF? At the start of AGOT, the total number of the Night's Watch is said to be less than a thousand. During Aegon's conquest, the Watch numbered ten thousand men. Out of the nineteen castles on the wall, only three are manned today. Castle black itself is once said to have housed 5000.   This rapid deterioration doesn't make sense to me from a world-building perspective. The NW have continued to maintain themselves pretty well for nigh on 8000 years (if the tales can be believed that is, Sam Tarly finds no written evidence of Lord Commanders earlier than #673, which suggests that 8000 years may be an inflated 'legendary' number).   Whereas in the real world, one of the oldest and most venerable institutions, the Catholic Church, has been around for less than 2000 years and has been administered by ~200 popes. The Night's Watch has had a few rocky years, sure, but for it to maintain itself so well for so long and then deteriorate only in the last 300 years seems strange to me.   The NW has two purposes. The ostensible one of defending against the Others, and the (arguably much more real, at least at the start of AGOT) purpose of serving as a dumping ground for the 'losers' of Westeros. By 'losers', I mean the people on the losing side of various wars and political battles, as well as criminals and n-th sons of noble houses with nothing to inherit.  I am currently reading through Fire and Blood, and was struck by one chapter, where an armed revolt of members of the Faith were defeated by Maegor, and 2000 brothers were forced to take the black. Those sorts of numbers don't exist in the recent histories it seems.   One would expect that after Robert's Rebellion, there would be a surfeit of defeated Targaryen loyalists who were forced to take the black, but apart from a smattering of named characters (including Ser Alliser Thorne), there seem to be hardly any Night's watch recruits from recent wars.  Given the way the Night's watch is continually bolstered by the losers of wars and by criminals and other people who elsewise have nothing going for them, why, at the start of AGOT, is the force so depleted? I have this value    How to read that in English? translating from my native language, I would say     Ten base of nine.   but is that really correct? How to remove film from stainless steel pan I have an unsightly film around my stainless pan as shown here:    What is causing this to happen?  And how can I remove the film? I have soaked it in soapy water, scraped it with a plastic scraper, and run it in the dishwasher several times, but I can't seem to get rid of the film.   UPDATE: the pan is an All-Clad stainless, fully-clad frypan: Usually \label does not create any white spaces. However, It creates an white space when \label is used after \phantomsubcaption from subcaption package.   Why? How can I get rid of this white space?   Here is a MWE:  \documentclass{article} \usepackage{subcaption}  \begin{document}  \section{a} a\label{sec:a}b% no white space between `a' and `b'  \begin{figure}   \centering   {a\phantomsubcaption\label{fig:a}}%   {b\phantomsubcaption\label{fig:b}}   \caption{With label}% undesired white space between `a' and `b' \end{figure}  \begin{figure}   \centering   {a\phantomsubcaption}%   {b\phantomsubcaption}   \caption{Without label}% no white space between `a' and `b' \end{figure}  \end{document} Are the memories still there? What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$? What is the function represented by the power series $$ \sum_{k=2}^\infty\frac{x^k}{k(k-1)}\quad? $$  It looks like $\dfrac1{1-x}$ but I don't know. Vertical line for the the right margin in Notepad++ When to use an offset in a Poisson regression?