How would it be if the SE network kept a "donate" button for their own, for site improvement?
Why not introduce a donate button in Stack Exchange sites?
Using past tense when referencing a still-true fact In the sentence: "I didn't know she had a son,"   Can I say "I didn't know she has a son" instead, because he is a teenager now?  Or are both correct? A few days ago I was recalling some facts about the $p$-adic numbers, for example the fact that the $p$-adic metric is an ultrametric implies very strongly that there is no order on $\mathbb{Q}_p$, as any number in the interior of an open ball is in fact its center.  I know that if you take the completion of the algebraic closure of the $p$-adic completion you get something which is isomorphic to $\mathbb{C}$ (this result was very surprising until I studied model theory, then it became obvious).  Furthermore, if the algebraic closure is of an extension of dimension $2$ then the field is orderable, or even real closed. Either way, it implies that the $p$-adic numbers don't have this property.  So I was thinking, is there a $p$-adic number whose square equals $2$? $3$? $2011$? For which prime numbers $p$? How far down the rabbit hole of algebraic numbers can you go inside the $p$-adic numbers? Are there general results connecting the choice (or rather properties) of $p$ to the "amount" of algebraic closure it gives? Lets assume my classes are loaded from a compressed .war file or loaded elsewhere,  how can I discover all the resources in a given package?  Enumerating files will not really work, since this is a war file.  Most likely this will involve using the current classloader?  Is there a library out there that does something like that? Googling revealed only some hacks with listing files. I know that the finite sum of Bernoulli i.i.d. random variables is a binomial distribution, but what is the distribution of $$\lim_{n \to \infty}\sum_{k=1}^{n} \frac{x_k}{2^k}$$ where $x_k$ is a Bernoulli random variable with parameter $\frac12$? Looking for a scifi novel with advanced pheromone technology How can I open a text file with TextWrangler from the Terminal (command line)? Is returning a pointer to a static local variable safe? I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); $P(x) = 0$ is a polynomial equation having at least one integer root, where $P(x)$ is a polynomial of degree five and having integer coefficients.  If $P(2) = 3$ and $P(10)= 11$, then prove that the equation $P(x) = 0$ has exactly one integer root.  I tried by assuming a fifth degree polynomial but got stuck after that.  The question was asked by my friend. In Dark Souls 2 there is a 'Shrine of Winter' near Sinners Rise. When you approach the shrine it will not let you open the door and a message pops up that says      Seek Mightier Souls   What does this mean and how do you open this shrine? I am looking for a injective cochain map $\psi: C^*\rightarrow D^*$ such that the map $\Psi^i$ from $C^i$ to $D^i$ is injective, but the map $\psi^*$ from  $H^i(C^*)$ to $H^i(D^*)$ is not injective for any $i\geq0$. How to add a node in the middle of the line with tikz? Excuse me if the question is naïve. I am not a physicist.  Let's imagine formation of a black hole from a homogeneous collapsing star. At certain moment when enough of matter is inside of a small enough spherical area the event horizon starts to exist. When does the singularity start to exist and why?  The matter below the event horizon still continues to collapse towards the centre (e.g. in the reference frame of the falling matter). What are the necessary conditions for the singularity to appear?  I have found two similar questions but the answers did not really explain this problem to me: How can I customize different nodepart with different textures? My question is how can I customize hatch patterns(grid, vertical line, etc.) for different nodepart in a node?  The following is a failed try.  \documentclass[border=2mm,convert]{standalone} \usepackage{tikz} \usetikzlibrary{shapes.multipart,patterns}  \begin{document} \begin{tikzpicture} \node[rectangle split,rectangle split parts =2,rectangle split part fill={red!30,red!10}, rectangle split part pattern={grid,},draw]{one \nodepart{second}two}; \end{tikzpicture} \end{document} package makeidx: print first letter for each group of keys I've created index with makeidx package. It works. What really need is to print the first letter above every group of keys (i.e. referring to the image I want to print the red letter, that I have manually inserted). Integral around unit sphere of inner product For arbitrary $n\times n$ matrices M, I am trying to solve the integral  $$\int_{\|v\| = 1} v^T M v.$$  Solving this integral in a few low dimensions (by passing to spherical coordinates) suggests the answer in general to be  $$\frac{A\,\mathrm{tr}(M)}{n}$$ where $A$ is the surface area of the $(n-1)$-dimensional sphere. Is there a nice, coordinate-free approach to proving this formula? I've got a qml file and I just want to ssh to the phone and do  qmlscene myfile.qml   Is it possible without doing all that stuff with SDK and packages? Just vim and some simple commands that can fit into person's memory. Is it possible now to use microtype with opentype fonts? What is crop factor and how does it relate to focal length? I'm reading that a 50mm lens is recommended as a first prime lens for DSLR owners as it's supposed to give a 'natural' perspective, but when used on (most) DSLRs, the view is cropped, as if you were zoomed in by 1.5-1.6x, so it's more of a telephoto lens when used on a DSLR. I've also read however that the 50mm lens gives the same perspective on a DSLR and a 35mm, and shouldn't really be considered to be 'equivalent' to an 80mm lens as the crop factor isn't really a magic focal length changer.  Can someone explain how the image is different from (for example) a 50mm lens on a DSLR and an 80mm lens (assuming 1.6x crop factor) on a 35mm camera? I'm starting out in Visual C++ and I'd like to know how to keep the console window.  For instance this would be a typical "hello world" application:   int _tmain(int argc, _TCHAR* argv[]) {     cout &lt;&lt; "Hello World";     return 0; }   What's the line I'm missing? Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$ I had an example in the book given as follows:        Find the minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$ .       Solution:  $~~~~~$$(\sqrt{2}+\sqrt{3})^2=5+2 \sqrt6$      $(\sqrt{2}+\sqrt{3})^4=49+20 \sqrt6$       Then $(\sqrt{2}+\sqrt{3})^4-10(\sqrt{2}+\sqrt{3})^2+1=0.$       Thus $a=\sqrt{2}+\sqrt{3}$ satisfies $f(x)=x^4-10x^2+1$ over $\mathbb Q$.       Let $p(x)$ be the minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$.Then $(\sqrt{2}-\sqrt{3}),(-\sqrt{2}+\sqrt{3}),(-\sqrt{2}-\sqrt{3})$ are also roots of $p(x).$   So degree of $p(x)$ is atleast $4$.      But $f(a)=0 $ and $f(x) \in \mathbb Q[x] \implies p(x)$ divides $f(x)$ .      So $f(x)$ is minimal polynomial of $\sqrt{2}+\sqrt{3}.$   But I can't get the step  how are $(\sqrt{2}-\sqrt{3}),(-\sqrt{2}+\sqrt{3}),(-\sqrt{2}-\sqrt{3})$ also roots of $p(x).$   Kindly help with this.