Those are from   Here is an interface :  public interface ISupportSampling {     double? SamplingPercentage { get; set; } }   And here is what I can see from VS a class that is supposed to implement the interface.  #region Assembly Microsoft.ApplicationInsights, Version=2.6.4.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35 // nsame namespace as the above interface public sealed class EventTelemetry : ITelemetry, ISupportProperties, ISupportSampling, ISupportMetrics {     public EventTelemetry();     public EventTelemetry(string name);      public DateTimeOffset Timestamp { get; set; }     public string Sequence { get; set; }     public TelemetryContext Context { get; }     public string Name { get; set; }     public IDictionary&lt;string, double&gt; Metrics { get; }     public IDictionary&lt;string, string&gt; Properties { get; }      public ITelemetry DeepClone(); }   You can see that the only property from the interface is not in the list of public properties.    So, it means that, when coding, 2 things happen that are not desirable :  1)   This code  EventTelemetry eventTelemetry; // ... eventTelemetry.SamplingPercentage = 100;   Causes the following compilation error :     'EventTelemetry' does not contain a definition for   'SamplingPercentage' and no accessible extension method   'SamplingPercentage' accepting a first argument of type   'EventTelemetry' could be found (are you missing a using directive or   an assembly reference?`   2)   Also, the SamplingPercentage property will not show up in autocomplete.    Why ? Am I being lied to by VS on what I see from the class ? (that SamplingPercentage is indeed present and public, but for some reasons not shown to me ?)  My current workaround (and also given in the last snippet in  ) is to cast as this :  ((ISupportSampling) eventTelemetry).SamplingPercentage = 100;   Is there a more "developper friendly" way, without using explicit cast ? (using Visual Studio 2017)
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?
How to factor polynomials in $\mathbb{Z}_n$? How to factor a certain polynomial over $Zn$.  for example factor the following polynomial into irreducible polynomials in $Z5$:  $X^3+X^2+X-1$  or factor the following polynomial into irreducible polynomials in $Z2$:  $X^4+X+1$   is there a certain method (algorithm) I can follow?  Please help I'm stuck and i really need the help!  thank you in advance!! How to distinguish between gold, silver, and bronze tag badges on SEDE? I have to prove that if $E$ is a connected space, then so is $\overline{E}$ (the closure of $E$) a connected space. I tried to prove the contrapositive. So suppose that $\overline{E}$ is not connected in a metric space $X$. This implies there are $A\subset X$ and $B\subset X$ such that $A\cap B=\emptyset$, $A\cap \overline{E}\neq \emptyset$, $B\cap \overline{E}\neq \emptyset$ and $\overline{E}\subset A\cup B$. I will try to prove that this $A$ and $B$ will also work for $E$. Suppose that $A\cap E=\emptyset$ and $B\cap E=\emptyset$, this implies that $A\cup B$ is a subset of the limit points of $E$, because $A\cap \overline{E}\neq \emptyset$ and $B\cap \overline{E}\neq \emptyset$. This contradicts the fact that $\overline{E}\subset A\cup B$, so we have to conclude that $A\cap E\neq \emptyset\neq B\cap E$. Since $E\subset\overline{E}\subset A\cup B$, we have that $E$ is also not connected.  My question is whether my proof is correct, because I have a little bit doubt. If it's not correct, what is the best I can do? Thanks in advance!   Edit1: The definition we use for a connected space $E$ in a metric space $X$ is that if $E$ is connected, then there are no open $A,B\subset X$ such that $A\cap B=\emptyset$, $A\cap E\neq \emptyset\neq B\cap E$ and $E\subset A\cup B$.  Edit2: $A$ and $B$ must be open. Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact? How to edit geometry of multiple layers simultaneously in QGIS 3? I have several line layers (route, pipes, cables) that share the same geometry and would like to edit them simultaneously.   Is there a way to easily snap the geometry of the pipes and cables layers to the route layer so that I can simply change the geometry of the route layer and don't have to repeat all changes on the other two layers as well?  To clarify, I plan a fibreglass route and have three layers. The first one describes the route that I have to take to pass all homes that have to be connected. The second one contains the pipes in which the cables lie and the third layer is the cable layer. So all features on those layers have to have the same geometry. Once I change the pathway of the route layer, I have to apply the same changes to the other two layers to ensure that they are still aligned with the route layer. I'm not sure whether I understand your comments correctly, but I use the basic editing tools in QGIS 3. An idiom to describe someone who thinks he/she is wiser than others Using url package without hyperref makes link hit boxes erratic I've currently got a url link in a footnote in my document. With the hyperref package, everything works correctly. Because the IEEE PDF Express tool doesn't like having the hyperref package, I've removed it and only left in the url package.  However, some strange behavior occurs as a result of this. Instead of just the link being clickable, entire paragraphs of text before/after end up being clickable and going to the same link. This occurs for both Skim and Preview in Mac OSX.  Does anyone have an inkling of what might be causing this? Select all contents of textbox when it receives focus (Vanilla JS or jQuery) What is a Vanilla JS or jQuery solution that will select all of the contents of a textbox when the textbox receives focus? Bottom of tool shelf grayed out bibtex and genitive / possessive 's: the proper way to obtain "Kuran's (1989) model" Prove that the range of the entire function $z^2+\cos(z)$ is all of $\mathbb{C}$. Prove that the range of the entire function $z^2+\cos(z)$ is all of $\mathbb{C}$.   I'm aware this question has been  already, but the explanations were a little shakey and referenced a google sample preview of a text of whose terminology I wasn't very familiar with, so I would like some more input if possible.  Here's my attempt:  Let $f(z)=z^2+\cos(z)$. Through the power series of the cosine function $$ f(z)=z^2+1-\frac{z^2}{2!}+\frac{z^4}{4!}-\cdots=1+\frac{z^2}{2!}+\frac{z^4}{4!}-\cdots, $$ so $$ g(z):=\frac{f(z)-1}{z} $$ has a removable singularity at $z=0$ and is effectively an entire odd function. Picard's little theorem asserts that the range of $g$ is all of $\mathbb{C} $: if there exists some $z_0$ such that $g(z)\neq z_0$ for all $z\in\mathbb{C}$, then $-z_0$ is also missed by oddness of $g$, which is a contradiction (since $g(0)=0$ we rule the possibility that $z_0=0$). (I'm not sure about the following step) It follows that $zg(z)$ and so $zg(z)+1=f(z)$ is surjective.  Is this method valid? Would I need further justification to show that $z\mapsto z$ and $z\mapsto g(z)$ surjective imply its product -- $z\mapsto zg(z)$ -- is also surjective (if this is even true). Any input is greatly appreciated.  Edit: After thinking about this for a moment longer, I realize this logic would also show that the range of any entire even function is all of $\mathbb{C}$, which seems like quite a strong conclusion. This makes feel like there are holes in my logic. I've just upgraded to Ubuntu 13.10 and I'm seeing a strange behaviour. All windows I open have a black, boxy border, including popups, as you can see in the provided image. (The black box in the bottom right is a terminal, which fails to display any text. However, I can enter commands and they execute.) I followed the steps in this post:  to reset Unity using the unity-tweak-tool. Although helpful, that did not fix the issue. I'm thinking this may be a graphics card driver issue.  Any help is much appreciated. What are the antonyms of "append" and "prepend"? Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$ Seeking Methods to solve the following two definite integrals:  \begin{equation} I_(n) = \int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt \qquad J(n) = \int_0^\infty \frac{\ln^2(t)}{t^n + 1}\:dt \end{equation}  For $n \in \mathbb{R},\:n \gt 1$  The method I took was to take the following integral:  \begin{equation}  \int_0^\infty \frac{t^k}{\left(t^n + 1\right)^m}\:dt = \frac{1}{n}B\left(m - \frac{k + 1}{n}, \frac{k + 1}{n} \right) \end{equation}  Where: $0 \leq k \lt n$. Here let $m = 1$.   with respect to $k$ and taking the limit as $k \rightarrow 0^+$ (via the ), i.e.   \begin{align} \lim_{k \rightarrow 0+} \frac{d}{dk} \left[ \int_0^\infty \frac{t^k}{t^n + 1}\:dt \right] &amp;= \lim_{k \rightarrow 0+} \frac{d}{dk} \left[\frac{1}{n}B\left(1 - \frac{k + 1}{n}, \frac{k + 1}{n} \right) \right] \\ \lim_{k \rightarrow 0+}  \int_0^\infty \frac{t^k \ln(t)}{t^n + 1}\:dt  &amp;= \lim_{k \rightarrow 0+}  \left[\frac{1}{n^2} B\left(1 - \frac{k + 1}{n}, \frac{k + 1}{n}\right)\left[\psi^{(0)}\left(\frac{k + 1}{n} \right) - \psi^{(0)}\left(1 - \frac{k + 1}{n} \right)\right] \right] \\ \int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt&amp;= \frac{1}{n^2} B\left(1 - \frac{1}{n}, \frac{1}{n}\right)\left[\psi^{(0)}\left(\frac{1}{n} \right) - \psi^{(0)}\left(1 - \frac{1}{n} \right)\right] \\ &amp;=- \frac{\pi^2}{n^2}\operatorname{cosec}\left(\frac{\pi}{n}\right)\cot\left(\frac{\pi}{n} \right) \end{align}  Which is our expression for $I_n$. Taking the same approach but differentiating twice with respect to $k$ we arrive at our expression for $J_n$:  \begin{equation}  J(n) = \int_0^\infty \frac{\ln^2(t)}{t^n + 1}\:dt = \frac{\pi^3}{n^3}\operatorname{cosec}\left(\frac{\pi}{n} \right)\left[\operatorname{cosec}^2\left(\frac{\pi}{n}\right) + \cot^2\left(\frac{\pi}{n}\right) \right] \end{equation}  And in fact we may generalise:  \begin{equation}     \int_0^\infty \frac{\ln^p(t)}{\left(t^n + 1\right)^m}\:dt = \lim_{k\rightarrow 0}\frac{d^p}{dk^p}\left[\frac{1}{n} B\left(m - \frac{k + 1}{n}, \frac{k + 1}{n}\right)\right] \end{equation}  Where $p \in \mathbb{N}$  This method however was just an extension of another integral. I'm curious, if I had just started with $I_n, J_n$ what alternative methods could be used? How can I make a bash script executable by double clicking just like .exe files in Windows? I tried , but there are two consequences:   the terminal twinkles, disappears, and nothing is done. you must specify to run in terminal in order to work.   I have a script that installs tomcat on an offline PC, including all dependencies of tomcat in the script. I need to make the script work on double clicking like windows since most who use the script will not be familiar with Ubuntu.  Forget the above explanation. I want to make a script that can be run by double-clicking on it, without using the terminal. Anybody knows how? Spacing before and after section titles How do I fix inconsistent Textarea bottom margin in Firefox and Chrome? Japan is a volcanically active country which means it has a plethora of onsen (hot springs) all around the country.  Visiting these onsen is supposed to be a popular vacation destination for the work-weary Japanese.    I've been told that, as with other things in Japan, there is a rather strict etiquette surrounding the use of the onsen.  In particular, the two things I've read about so far are   Swimming Suits are not allowed. It is very important that one bathe immediately before entering the onsen.   Are these true?  Are there any other taboos that a naive American should be aware of? A finite sum involving the binomial coefficients and the harmonic numbers I can do an eval("something()"); to execute the code dynamically in JavaScript. Is there a way for me to do the same thing in C#?  An example of what I am trying to do is: I have an integer variable (say i) and I have multiple properties by the names: "Property1", "Property2", "Property3", etc. Now, I want to perform some operations on the " Propertyi " property depending on the value of i.   This is really simple with Javascript. Is there any way to do this with C#?