How do taxes work if I don't live in any country
With constant travel, is it possible to not have a tax residence?
With CSS, use "..." for overflowed block of multi-lines Rigorous proof that $dx dy=r\ dr\ d\theta$ I get the graphic explanation, i.e. that the area $dA$ of the sector's increment can be looked upon as a polar "rectangle" as $dr$ and $d\theta$ are infinitesimal, but how do you prove this rigorously?    1. Geometrically, the exact area would be $$\frac{(r+dr)^2d\theta}{2} - \frac{r^2d\theta}{2}$$$$= (r + \frac{dr}{2}) dr d\theta  $$$$= r dr d\theta + \frac{dr^2 d\theta}{2}.$$  How do we get rid of $\frac{dr^2 d\theta}{2}$? Is it too insignificant in value compared to $r dr d\theta$ so that it vanishes? If so, is it the reason it gets ignored? And what's more, geometrically speaking, why would the two areas - $dx dy$ and $r dr d\theta$, be equal?  2. Approaching it algebraically, setting $$x = r\sin\theta$$$$y = r \cos\theta$$  gives $$\frac{dx}{d\theta} = r\cos\theta,  dx = r\cos{\theta} d\theta$$$$ \frac{dy}{dr} = \cos\theta,  dy = \cos\theta dr. $$  Multiplying both equations, side by side, gives $$dxdy = r\cos^2\theta dr d\theta.$$  Again I get an extra term, which is $\cos^2 \theta$. In both cases I am unable to derive that $dxdy = rdrd\theta$.  What do I do wrong in my reasoning? It all makes me think that I'm getting something essential terribly wrong. Removable singularities and an entire function Function $f(z)$ is an entire function such that $$|f(z)| \le |z^{n}|$$ for $z \in \mathbb{C}$ and some $n \in \mathbb{N}$.  Show that the singularities of the function $$\frac {f(z)}{z^{n}}$$ are removable. What can be implied about the function $f(z)$ if moreover $f(1) = i$? Draw a far-reaching conclusion.  My attempt: If the singularities of $\frac {f(z)}{z^{n}}$ are removable, it is entire (not sure, need help with the justification) and bounded, so constant from Liouville's theorem, the constant value of the funcion is $i$, hence $f(z)=iz^{n}$.   But what about the $n$ here, is it arbitrary? Could somebody help me prove the removability of the singularities and suggest if my attempt is going the right way? Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$? I dont get it, if I look at $$\lim \limits_{n \to \infty}\left(1 + \frac{1}{n}\right)^n = e$$    It seems like it should be $1$ because $1 \over n$ is almost zero and $1^\infty$ is still $1$ You know, some of us read right to left...  Certain sites like  and  have an obvious need for this, as Arabic and Hebrew are Right To Left (RTL) languages. Many answers on those sites cite the Torah and the Quran respectively. Directly quoting these sources properly requires RTL text. Green is the most common circuit-board color because it has become an industry standard.  What I'm interested in is How the traditional "PCB Green" become a standard in the first place?   Were there any interesting historical reasons for the initial choice, or was it just a product of what one particularly successful company was doing that became the de-facto standard? Enumeration within self defined environment My self defined environment having a symbol at the beginning and at the end works fine for text without enumeration. When including enumerate the symbols are not there where desired. Is it possible to have the first symbol directly in front of &quot;1.&quot; i. e. in the same line and the ending symbol in the same line as the last line of the enumeration? With \ignorespacesafterend and \unskip I did not succeed. \documentclass{article} \usepackage{amssymb} \newenvironment{myenv}{$\blacktriangleright$}{\hfill$\blacktriangleleft$}  \begin{document} There is a text.  \begin{myenv} And an example \end{myenv}  Here is another text.  \begin{myenv} \begin{enumerate} \item A \item B \end{enumerate} \end{myenv}  \end{document} Calculate bounding box coordinates of a selected polygon with QGIS I just manually (and somewhat inaccurately I'm sure) retrieved the bounding box coordinates for a county polygon, which is a selection from a larger layer of county shapes. I'd like to be able to use a QGIS plugin or other function to calculate this quickly and not-by-hand. This is almost certainly possible but I couldn't find anything with a Google search How does one prove that the Klein bottle cannot be embedded in $R^3$? I'm talking about smooth embeddings. Increasing post view count automatically Should we write “allow” or ”allows” in “require that the class allow[s]”? Can you explain to me whether I should or should not use ‑s at the end of the  verb allow in this sentence?     This function requires that the container class allow[s] random access   The sentence in the book I read wrote allow without ‑s. However, the container class is a third-person singular, so the ‑s must be required. Is that right? I have a few questions regarding Named Credentials. I need to perform a SOAP based call out to an external system from Sales Force. I used the wsdl2apex function to generate the class for the call out. When I started integrating this class into my process I got to thinking about securely storing the username and password for the call out, which led me to discover Named Credentials. Question is, can Named Credentials be used in the auto-generated apex class? If so, could you please provide an example?  Thanks in advance How to Understand the Relationships Among Random Variables, Samples, and Populations? I created a bitmap with transparent background but in the Windows Picture Viewer I see the white background and even if I reopen it in Photoshop CS3. how do I make sure the white colour in bitmap is really transparent or see if contain any transparent colour? The question is to calculate the radius of convergence of $\sum\limits_{n=0}^\infty n!x^{n^2}$.  I dont know how to calculate R.O.C for such type of questions involving $n^2$ as power of x. How do we do this? Any help appreciated. Am I allowed to make a Stack Overflow clone? SO is not Open-Source, but I like the whole idea of Stack Overflow :   Giving bounties for Questions Up/Downvoting Questions The Badges The intelligent use of Ajax-Technologies Highly Rated users have administrative powers Reputation system Editing posts like a wiki   So I would like to program a (what is it called) Q&amp;A site / board / wiki system. Am I allowed to? Circular References Cause Memory Leak? I'm trying to run down a memory leak in a windows forms application.  I'm looking now at a form which contains several embedded forms.  What worries me is that the child forms, in their constructor, take a reference to the parent form, and keep it in a private member field.  So it seems to me that come garbage-collection time:  Parent has a reference to the child form, via the controls collection (child form is embedded there).  Child form is not GC'd.  Child form has a reference to the parent form, via the private member field.  Parent form is not GC'd.   Is this an accurate understanding of how the garbage collector will evaluate the situation?  Any way to 'prove' it for testing purposes? Automating the scanning of graphics files for corruption Does anyone know of a way to check graphics files (particularly JPEG, GIF, and PNG) for corruption (preferably in an automated way)?    Explanation:  A few days ago, a command worked incorrectly and ended up deleting thousands of graphics files from a FAT32 volume that was practically out of space. I’ve used several different file/photo-recovery programs, but naturally, they are limited in how much they can recover (though fortunately the volume has 8KB clusters, which helps somewhat).  Anyway, some of the larger files, that were fragmented, are now corrupt. Some of them are not even real files at all (the recovery software merely dumped the clusters that were pointed to by now-overwritten directory entries), while others are broken because of fragmentation.  Moreover, because some picture formats embed a smaller version of the picture as a thumbnail, scanning the thumbnails for corruption is not reliable because it may be intact while the actual file (i.e., the picture when viewed full-size), could be corrupt.    Here are a couple of examples:      Here’s the second one. It’s so damaged that it doesn’t display anything.    (A third one wouldn’t even upload because it doesn’t even have the correct header!) ‘ld: warning: directory not found for option’ Is there a function whose inverse is exactly the reciprocal of the function, that is $f^{-1} = \frac{1}{f}$? Is there a function whose inverse is exactly the reciprocal of the function? That is $f^{-1} = \frac{1}{f}$.  We know that the inverse of a function is not necessarily equal to its reciprocal in general.