Triangle Inequality for quotients
To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$
How do I limit the number of rows returned by an Oracle query after ordering? Is there a way to make an Oracle query behave like it contains a MySQL limit clause? In MySQL, I can do this: select *  from sometable order by name limit 20,10  to get the 21st to the 30th rows (skip the first 20, give the next 10). The rows are selected after the order by, so it really starts on the 20th name alphabetically. In Oracle, the only thing people mention is the rownum pseudo-column, but it is evaluated before order by, which means this: select *  from sometable where rownum &lt;= 10 order by name  will return a random set of ten rows ordered by name, which is not usually what I want. It also doesn't allow for specifying an offset. The given differential equation $$\lvert{dy\over{dx}}\rvert\,+\mid{y}\mid+1=0 $$  I don't know how to deal with modulus sign in order to prove the statement  Reference-Different Equations by Shipley L Ross Ch1 Exercise 7(a) Where can I access OS X keyboard shortcuts, say for Dropbox sync? filling area between 2 functions, with shading If $[\cdot]$ denotes greatest integer function, then what is the value of natural number $n$ satisfying the equation $$[\log_21]+[\log_22]+[\log_23]+\dots[\log_2n]=1538 ?$$   My try:  Note that  $$0+1\times2+2\times2^2+3\times2^3+4\times2^4+5\times2^5+6\times2^6+7\times2^7=1538$$  But the answer is $$n=\sum_{i=0}^72^i=255.$$  How is it derived? Looking at the questions and answer to these two questions.  &amp;  and neither mentions the longevity of magic. I recall several instances of magic failing to last; the money that was spread at the  and the broken  on.  If I recall correctly when Voldemort died, the curses on several people were lifted.  I don't recall if any other spells fell apart with his death.  Is there any canon evidence on the the length of time a spell will live? combine 2 fields in 1 to use it in the "group by" section of the reports is it possible to combine two fields in one and use that field to group by in reports? for example, i would like to combine ee id and ee name fields in 1 and show as 1 field in the "group by" section on reports. When posting an HTTPS url like https://stackoverflow.com/..., it does not onebox in chat. For example: Does C# have anything comparable to Python's list comprehensions? Cross-thread operation not valid: Control accessed from a thread other than the thread it was created on Here's an example of a short conversation between me and a native speaker via text messages:  A: I'm so exited for this app B: Yeah, me too A: We start tomorrow B: OK   Shouldn't it be "We are starting tomorrow"?! Is it safe to disable System Integrity Protection? While using OS X El Capitan 10.11.x, is it safe to disable System Integrity Protection? There are all these additional apps that modify folders and the dock that I want to install but you have to disable rootless first.  Good idea or bad idea? What causes a java.lang.ArrayIndexOutOfBoundsException and how do I prevent it? What is the problem with nested environments using \BODY (environ package)? This question led to a new package:      I want to define some environments, which place their content into multiple different other environments. To access the contents I used the environ package, which introduces the \BODY command. However at some point pdflatex seemed to be stuck in an infinite loop.  I reduced it to a minimal example:  \documentclass{article} \usepackage{environ}  \NewEnviron{assertion}{Assertion: \BODY} \NewEnviron{outerassertion}{\begin{assertion}\BODY\end{assertion}}  \begin{document}  \begin{assertion} test \end{assertion}  \begin{outerassertion} test2 \end{outerassertion} \end{document}   Any ideas how to work around this problem? I guess, the problem is with the \BODY command since everything works fine as long as I use it in only one of the new environments. Here, we suppose that $x,y\in\mathbb{R}$ and that $x^n=y^n$, where $n$ is odd. I want to prove that $x=y$.  Maybe we can use that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+...+xy^{n-2}+y^{n-1})$  So, it suffices to show that if $x^n=y^n$ then $x^{n-1}+x^{n-2}y+...+xy^{n-2}+y^{n-1}\neq 0$  Any hint? The first and (the) second chapter(s) are difficult - which is correct? How can I create an executable JAR with dependencies using Maven? Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question Merge two data frames while keeping the original row order Using getopts to process long and short command line options I wish to have long and short forms of command line options invoked using my shell script.  I know that getopts can be used, but like in Perl, I have not been able to do the same with shell.  Any ideas on how this can be done, so that I can use options like:  ./shell.sh --copyfile abc.pl /tmp/ ./shell.sh -c abc.pl /tmp/   In the above, both the commands mean the same thing to my shell, but using getopts, I have not been able to implement these?