Web services API design: XML elements vs. attributes
XML attribute vs XML element
When $z\neq 0$, $\arg z$ is defined to be the set $\{\theta \in \mathbb{R} : z=|z|e^{i\theta}\}$.  What if $z=0$? Usually does one leave the argument of $0$ undefined? Or is $\arg 0 = \mathbb{R}$? Show that, if $a$ and $h$ are positive numbers, $h &lt; a^2$, then $$\sqrt{a^2 + h}-a &lt; \frac{h}{2a} &lt; a - \sqrt{a^2 - h}$$  I've been working on this problem for about 2 hours now, but I've made no progress. I'm not looking for an answer, but I just need some help to get me started since we didn't practice inequalities this complex in highschool. Thanks.   All I can tell is that we're supposed to take the square root of an expression at some point since one inequality ( h &lt; a^2 ) becomes two.   Edit : Thank you guys for the replies, but I'd appreciate only hints in the future (like Robert Israel) so that I can learn. Regardless, I found a different way to do it, so it's cool :) Cursor is set to move by increments. how to reset to normal? How can I get this symbol without using bbold? Disable Screenshot Security I don't want to use the Super for that, I want to use Alt+Space instead. This question is inspired by    I see these constructs  for file in `find . -type f -name ...`; do smth with ${file}; done   and  for dir in $(find . -type d -name ...); do smth with ${dir}; done   being used here almost on a daily basis even if some people take the time to comment on those posts explaining why this kind of stuff should be avoided... Seeing the number of such posts (and the fact that sometimes those comments are simply ignored) I thought I might as well ask a question:  Why is looping over find's output bad practice and what's the proper way to run one or more commands for each file name/path returned by find ? Preventing reverse search engines from finding the origin of your image? I am planning to make a game, where I give the user an anime related image and they have to guess where its from.  However, most of the images, specially from popular anime are easy to use on Google reverse search to find and pin point the anime.  I've tried to see if I could make so it would not recognize the image but unhappily my tricks were not good enough.  Original image:    Grey-scale with horizontal flip:    Watermarking:    Puzzling the image with grey-scale:    Grey-scale with horizontal and vertical flip worked for this image but doesn't always work:    Also the above mentioned methods are rather easy for people to guess the anime.  I would like to know if there any good trick, that I could use on my images to make so it would not work on reverse search engines and yet not be so overcomplicated that I can implement on my program.  For example grey-scale, cropping, flipping are rather easy things to achieve in C#. Misplaced/Overlapping Navigation Item Text on iOS 10 The bug displayed in the attached screenshot occurs consistently for me while running the developer beta of iOS 10 using v1.5.2 of the Stack Exchange app on an iPhone 6.  I was able to recreate this by simply tapping on any question or answer in my feed with a long title. This doesn't appear to be a bug with iOS 10 itself since I haven't seen it in other apps, but I could be wrong. $\mathbb S_n$ as semidirect product In  note, I've read that $\mathbb S_n$ is a semidirect product of the alternating group $A_n$ by $\mathbb Z_2$. So I am trying to define a morphism $\rho: \mathbb Z_2 \to Aut(A_n)$ to show that $\mathbb S_n \cong A_n \rtimes Z_2$. I would appreciate suggestions on how could I define the morphism. Thanks in advance. Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds] I need to find the gcd of two polynomials: $f(x) = x^4+1$ and $g(x)=x^2-1$ using the Euclidean algorithm.  Wolfram shows that the gcd is equal to $1$, but for some reason I don't get the same answer.   First I divided $f(x)$ by $g(x)$ and got that the remainder is $2$. Then, I divided $g(x)$ by the remainder, $2$, and got a remainder of zero, hence concluding that the gcd is $2$.   What am I doing wrong? Identify duplicate lines in a file without deleting them? I have my references as a text file with a long list of entries and each has two (or more) fields.   The first column is the reference's url; the second column is the title which may vary a bit depending on how the entry was made. Same for third field which may or may not be present.  I want to identify but not remove entries that have the first field (reference url) identical. I know about sort -k1,1 -u but that will automatically (non-interactively) remove all but the first hit. Is there a way to just let me know so I can choose which to retain?  In the extract below of three lines that have the same first field (http://unix.stackexchange.com/questions/49569/), I would like to keep line 2 because it has additional tags (sort, CLI) and delete lines #1 and #3:  http://unix.stackexchange.com/questions/49569/  unique-lines-based-on-the-first-field http://unix.stackexchange.com/questions/49569/  Unique lines based on the first field   sort, CLI http://unix.stackexchange.com/questions/49569/  Unique lines based on the first field   Is there a program to help identify such "duplicates"? Then, I can manually clean up by personally deleting lines #1 and #3? If $2^p-1$ is a prime, (thus $p$ is a prime, too) then $p\mid 2^p-2=\phi(2^p-1).$  But I find $n\mid \phi(2^n-1)$ is always hold, no matter what $n$ is. Such as $4\mid \phi(2^4-1)=8.$  If we denote $a_n=\dfrac{\phi(2^n-1)}{n}$, then $a_n$ is , but how to prove it is always integer?  Thanks in advance! Why are disabled apps still running? Error message "sudo: unable to resolve host (none)" Is there any intuition or meaning regarding Cauchy-Riemann equations? Difference between StringBuilder and StringBuffer Suppose $G$ is a group and $K\lhd H\lhd G$ are normal subgroups of $G$. Is $K$ a normal subgroup of $G$, i.e. $K\lhd G$? If not, what extra conditions on $G$ or $H$ make this possible?  Applying the definitions, we know $\{ghg^{-1}\mid h\in H\}=H$ and $\{hkh^{-1}\mid k\in K\}=K$, and want $\{gkg^{-1}\mid k\in K\}=K$. Clearly, the best avenue for a counterexample is if $gkg^{-1}\not\in K$ for some $k\in K$ and $g\in G-H$.  If no such element exists, $\{gkg^{-1}\mid k\in K\}\subseteq K$ implies $\{gkg^{-1}\mid k\in K\}=K$ because if $k'\in K$, $gk'g^{-1}=k\in K\Rightarrow k'=g^{-1}kg\in\{gkg^{-1}\mid k\in K\}$. Cauchy-Product of non-absolutely convergent series While grading some basic coursework on analysis, I read an argument, that a Cauchy product of two series that converge but not absolutely can never converge i.e. if $\sum a_n$, $\sum b_n$ converge but not absolutely, the series $\sum c_n$ with $$c_n= \sum_{k=0}^n a_{n-k}b_k$$ diverges.  Although we didn't have any theorem in the course stating something like this, it made me wonder if it was true. If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$