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How are dual-role films shot? Use counter before its value is set I'd like to use a counter in the text which however is only set at a later point. Like so:  \newcounter{howmany} There are \thehowmany items in this list: \begin{enumerate}   \item one   \item two   \item three \setcounter{howmany}{\theenumi} \end{enumerate}   And it should say "There are 3 items in this list". But that doesn't work. Well, sure. I need to use \refstepcounter to get that save-functionality. But \refstepcounter only increments it by one, and there doesn't seem to be a \refsetcounter ;) Any suggestions? A loop after the enumerate over \refstepcounters? Redefining \item to include \refstepcounter? There gotta be a simpler way, no?  Thanks! How do you clean a seasoned cast iron skillet? I have a seasoned cast iron skillet, and I don't want to mess up the seasoning when I'm cleaning it.  What do I use and what don't I use to get it back to clean?  I've heard not to use soap and to make sure it is dry, but nothing beyond that. We know that the addition and multiplication operators are both commutative, and the exponentiation operator is not.  My question is why.  As background there are plenty of mathematical schemes that can be used to define these operators. One of these is   where $H_0(a,b) = b+1$   (successor op) $H_1(a,b) = a+b$   (addition op) $H_2(a,b) = ab $   (multiplication op) $H_3(a,b) = a^b$   (exponentiation op) $H_4(a,b) = a\uparrow \uparrow b$   (tetration op: $a^{(a^{(...a)})}$ nested $b$ times ) etc.    Here it is not obvious to me why $H_1(a,b)=H_1(b,a)$ and $H_2(a,b)=H_2(b,a)$ but not $H_3(a,b)=H_3(b,a)$  Can anyone explain why this symmetry breaks, in a reasonably intuitive fashion?  Thanks. Minimal cut edges number in connected Eulerian graph. I have to prove that Connected graph is Eulerian Graph if and only if the number of edges in minimal cut is even.  Implication from left to right. Well if $G$ is Eulerian Graph then degree of each vertex must be even. It's oblivious if i try to disconnect graph by removing all edges connected to the vertex with minimal degree. But minimal cut can be done also by dividing graph into 2 connected graphs (each graph with more then one vertex) and i have no idea how to deal with it.  Implication from right to left - completly no idea. plotting discrete signals How Do I get into the castle walls? Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$ I have the following code and I expect the resulting angle to be 135 degrees but whatevet I try, I get 90.  \documentclass{article} \usepackage{tikz} \usetikzlibrary{calc} \begin{document} \begin{tikzpicture}  \coordinate (A) at (1,0); \coordinate (B) at (-1,1);  \pgfmathanglebetweenpoints{A}{B} \edef\angleAB{\pgfmathresult} \node at (0,0) {\angleAB};  \end{tikzpicture} \end{document}   I also tried the following command without knowing what it means, it also prints 90 except one case. The only working case is when A=(1,0) and B=(-1,0), which it prints 180.  \pgfmathanglebetweenpoints{\pgfpointanchor{A}{center}}{\pgfpointanchor{B}{center}}   Why is that? Couldn't find any reference document for "pgfmathanglebetweenpoints" by the way, that's why I am asking here.  EDIT: B is corrected from (-1,-1) to (-1,1) Find the maximum value of the expression ${\frac {x}{1+x^2}} + {\frac {y}{1+y^2}}+{\frac {z}{1+z^2}}$. Find the maximum value of the expression :   $${\frac {x}{1+x^2}} + {\frac {y}{1+y^2}}+{\frac {z}{1+z^2}}$$   where $x,y,z$ are real numbers satisfying the condition that $x+y+z=1$.   Taking $x=y=z=\frac {1}{3}$, I get the expression as $\frac {3x}{1+x^2}$, which is equal to $\frac {1}{1+{\frac{1}{9}}}$ or $\frac {9}{10}$.  How can I actually solve the problem without making unnecessary assumptions ? Add a note about downvoting on Meta Some days I'm working with extremely large Excel files.  They have too many sheets that can't be shown in one sheet tab. (see image)      So, I'm wondering whether or not we can show Excel sheet on more than 1 row. Many tries with Google don't help much.    Many tries but I still can't make Excel show the sheet bar the way I want (≥ 2 rows), so I'm working with some VBA Scripts kopischke suggested.    FYI, right click on |&lt; &lt;&lt; &gt;&gt; &gt;| button on the bottom-right corner show you a list of up to 15 sheets.  For more, click on View more in the list appeared. What is the emergency phone number in different countries? If I take a screenshot, often the next action is to paint on it. Sometimes I paint a circle around something, sometimes I blank parts to anonymize them.  Below is an example of the window after the screenshot was taken:    It would be great if I could directly go to "edit image".  BTW, I use Pinta, not Gimp.  I guess this is impossible.  Off-topic but nevertheless relevant:  I know the terms "Wayland", "Xorg", "Gnome".  But my grand mother is a user, not a geek. She does not know these terms. And it would be great, if she could use ubuntu without learning these terms. How to change default viewport shading in 2.8? Is it possible to change the default mesh color/shading in 2.8 to be more like 2.79? I'm finding it hard to see finer detail in 2.8. On the left is 2.8 and the right is 2.79 Hybrids are fairly common in Star Trek:  is half Vulcan,  is half Betazoid,  is half Klingon and, just for good measure,  is ¼ Romulan.  However, in all of these cases that I can think of, the other half is always human.  Are there any non-human hybrid characters? Especially ones that are recurring or at least the focus of an episode?  If not, is there an out-of-universe explanation for their absence/rarity/scarcity? From a fandom point of view, I can’t imagine a half-Klingon half-Vulcan might not make for an interesting story, for example. How do I install Java? If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer? Supposing that a real number $c$ is given, is the following true?  "If $n^c$ is a natural number for every natural number $n$, then $c$ is a non-negative integer."  Though this seems true, I can't prove that. Can anyone help? Restore default apt repositories in sources.list from command line I am looking for the best method to restore /etc/apt/sources.list to default from the command line.  Is there no way to reference the source code of the package which generates this file or something like that? I want a trusted and version-independent way of restoring this file.  Solutions Ruled Out  Before you mark this as a duplicate, note that I have reviewed  already. It is only applicable if you have the Ubuntu GUI available. This question is specific to the command line.  I have also reviewed  where the accepted solution is someone pasted the contents of their sources.list file. This is not an appropriate way to restore the file as the intentions of the person providing the file contents cannot be verified and the file is subject to change with new releases.  I checked out the , but this is also not from Ubuntu so I do not plan to use it. Why use "need not" instead of "do not need to"? The header of  states:     High-level languages need not be slower than low-level ones.     Why use need not instead of do not need? What does it mean? Also, why no to before be?