How can I restore the VirtualBox graphical user interface to show the snapshot menu?
VirtualBox Toolbar is hidden! How to show it?
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$ What are the subcategories of ordered sets / groups? How to enable numlock at boot time for login screen? I am trying to force numlock to be on upon initial boot at the login screen on Ubuntu 12.04. The only solutions I have found so far switch numlock on only after initial login.  I'm looking to force numlock to be on when the login screen is displayed, and before the user has logged in. Can anyone assist? How do I reboot a Ubuntu Server from the command line? sudo reboot now never seems to work for me. Because its a server, I don't have a window manager installed, so I can't do it from a GUI (which always seems to work).    I've had the problem for years on different versions of the operating system. It happens in virtual machines and on real metal. The same problem exists with sudo shutdown now, too.  I've lived with it in the past. The difference now is I don't want to just hit the power button because I might lose data. Modular exponentiation by hand ($a^b\bmod c$) How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and . How many ways can the average of n dice be a? Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$ Alright, scratch everything below the line. Let me present one cohesive question not marred by repeated edits.  The limit $\lim_{x\to a}f(x)=L$ exists iff for every $\epsilon&gt;0$ there is a $\delta&gt;0$ such that $|f(x)-L|&lt;\epsilon$ when $0&lt;|x-a|&lt;\delta$.  Thus, $\lim_{x\to0}\sin\left(\frac1x\right)$ does not exist because, being that it oscillates infinitely near $0$, there is no $\epsilon,\delta$.  On the other hand, with the limit$$\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}\\\lim_{x\to0}x\sin\left(\frac1x\right)=0\\y=x\sin\left(\frac1x\right)\\\lim_{y\to0}\frac{\sin y}{y}=1\\\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}=1$$  this proof can be shown. However, since $\sin\left(\frac1x\right)$ oscillates infinitely, by the same definition of limit we used to show the above, the limit does not exist. How do I resolve this discrepancy? Can every even integer be expressed as the difference of two primes? If so, is there any elementary proof? What is the best way to convert seconds into (Hour:Minutes:Seconds:Milliseconds) time? What makes you lose the Field Upgrade Score? When playing in a squad, you can get "Field Upgrades". However, sometimes when I die, it tells me that I have lost the "Field Upgrade Score".   Where can I see this score and what are the events that make me lose it? Let $q \in \mathbb C$, $\|q\|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n: n \in \mathbb N\}$ is dense in $S^1$ Let $q \in \mathbb C$, $|q|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n:  n \in \mathbb N\}$ is dense in $S^1$.  My attempt: As $(q^n)$ is limited, there is subsequence $(q^{n_j})$ convergent. So given $\epsilon &gt; 0, \exists j_0 \in \mathbb N, \quad |q^{n_j} - q^{n_k}| &lt; \epsilon, \quad \forall j,k \geq j_0$. Supose that $n_j &gt; n_k$, then  $|q^{n_j} - q^{n_k}| = |q^{n_k}||q^{n_j - n_k} - 1| = |q^{n_j - n_k} - 1| &lt; \epsilon, \quad \forall j, k \geq j_0$. So, there is a subsequence of $(q^n)$ that converges to $1$.  Using this fact, how can I ensure that for all $w \in S^1$ there is a subsequence of $(q^n)$ that converges to  $w$? Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods? I have seen the Fresnel integral  $$\int_0^\infty \sin x^2\, dx = \sqrt{\frac{\pi}{8}}$$  evaluated by contour integration and other complex analysis methods, and I have found these methods to be the standard way to evaluate this integral.  I was wondering, however, does anyone know a real analysis method to evaluate this integral? Should I use exit() or just return statements in main()? Personally I favor the return statements because I feel it's like reading any other function and the flow control when I'm reading the code is smooth (in my opinion). And even if I want to refactor the main() function, having return seems like a better choice than exit().  Does exit() do anything special that return doesn't? \documentclass{article} \usepackage{algorithm}  \begin{document} \setcounter{section}{54} \section{A section with no label} \begin{algorithm} \label{myalg} \caption{An algorithm with the label `myalg'.} \end{algorithm} Reference to myalg: \ref{myalg}. \end{document}   With this code, the reference givens 55 (the section number); if I move the label after the caption command, I get the correct reference (1).  Why should this be the case? I find it confusing: when thinking about an algorithm as an environment, you expect to be able to label it right after you began it. At the very least I would expect some kind of error or "??" to appear, rather than the previous environment or reference-able entity being used. Every time I open a folder from the desktop, a prompt is shown that the said folder is opened. How do I stop that? If I utilize the two columns of multicols for my Kurdish sequence of numbers, it arranges the items in column like the following figure:   But I want to arrange the items in rows splitted by some columns (two columns in this case) alike the following figure:   And for the case of "three columns", the output would be alike the following figure:   How may I achieve the functionality? And I don't want to use the sequence of the following commands:  \begin{multicols}{2}‎ \begin{enumerate}[$1)$,noitemsep] \item ‎ Yek \item ‎ Du \end{enumerate} \end{multicols}‎   Instead, I want to specify the split count of the columns and then have the items arranged in the desired arrangement automatically. For the record, I've check  post, but it's too generalized. Is there an easy way to calculate the residue at one of the poles of a rational expression of the form $\frac{1}{1+z^n}$?  I end up having to add a bunch of polar-form complex numbers in the denominator which I have no idea how to do except to convert them to rectangular coordinates, which becomes really messy.  I feel like there ought to be simple pattern/rule for such a canonical expression. As linguistics student, I have to put more than one thing on a character every now and then. For example, I need to type ā̆. I thought I could simply do that by typing \={\u{a}}, but then the macron is placed above an empty space in front of the character.  How can I solve this? Thanks  P.S. I'm using MiKTeX 2.9, running on Windows 8; in case it might be of use. As a new user without much rep, what should I do if someone else has already asked a question I have, but it has no answers? Quickest way to rename files, without retyping directory path