How can I space the lines in the whole document? How can I space the lines in the whole  document ?
Double line spacing I would like to typeset a draft of my document with double linespacing so that my collaborators have space to write in their edits (with a pen).  How do I do it?
I just asked my first question on stackoverflow and I'm really impressed that my question seems to be answered sufficiently already! See:    The issue I have is that the last two answers combined would provide the most complete answer. What's the proper way to go about combining them, marking the question answered, and giving credit where credit is due?  Thanks big time guys for saving us all from experts exchange hell!  Edit: Wow, 5 responses in 5 minutes. I think what makes the most sense is that I create my own answer out of the two. I don't think the second part of my question was answered though.  What is the proper way to give credit to the 2 answers that I'm combining? Is an upvote for each sufficient? How do I insert a nice tilde that is centered in the middle in a lstlisting? I found another thread about  but I can't apply it because the method described there only works outside of lstlisting as lstlisting displays all the text literally. Any ideas?  Here is how the tilde looks in my document at the moment - it's at the very top of the font and I would like it to be in the middle (like ~ this).    Here is the LaTeX for this fragment:  \section{Remove duplicate, consecutive lines (emulate "uniq")}  \begin{lstlisting} awk 'a !~ $0; { a = $0 }' \end{lstlisting}  Variables in Awk don't need to be initialized or declared before they are being used. Evaluate $\mathop {\lim }\limits_{x \to 0} \left( {{1 \over {{{\sin }^2}x}} - {1 \over {{x^2}}}} \right)$ I tried l'Hospital but that will require a lot (and I mean A LOT!!!) of differentiating  Is there a shortcut? $$\mathop {\lim }\limits_{x \to 0} \left( {{1 \over {{{\sin }^2}x}} - {1 \over {{x^2}}}} \right)$$  Thanks in advance Minecraft crashes on launch with EXCEPTION_ACCESS_VIOLATION, Problematic frame: ig4dev32.dll or ig4dev64.dll or ig4icd32.dll or ig4icd64.dll $\sum \cos$ when angles are in arithmetic progression Possible Duplicate:          Prove $$\cos(\alpha) + \cos(\alpha + \beta) + \cos(\alpha + 2\beta) + \dots + \cos[\alpha + (n-1)\beta] = \frac{\cos(\alpha + \frac{n-1}{2}\beta) \cdot \sin\frac{n\beta}{2}}{\sin\frac{\beta}{2}} $$ What is the command line way of sending files to the recycle bin? Is there a command line program that can send files to the recycle bin? This is on XP and Vista. Is it possible to skip Skyrim's new game introduction cinematic? I don't want to watch the prisoner cart ride to the execution: is it possible to skip this?   If so, how? Can I replace the intro movie file by some empty video? My server is constantly being attacked I am fairly new to the system administration world. I've been working on an application recently and when I check my application server logs, I constantly get various IP addresses trying to ssh into my server by brute force. Here is an example of my server log:   Feb 14 04:07:20 foodwiz3 sshd[1264]: error: Could not load host key: /etc/ssh/ssh_host_ed25519_key Feb 14 04:07:21 foodwiz3 sshd[1264]: reverse mapping checking getaddrinfo for coenamor.columbiansabbatical.com [23.249.167.223] failed - POSSIBLE BREAK-IN ATTEMPT! Feb 14 04:07:21 foodwiz3 sshd[1264]: pam_unix(sshd:auth): authentication failure; logname= uid=0 euid=0 tty=ssh ruser= rhost=23.249.167.223  user=root Feb 14 04:07:23 foodwiz3 sshd[1264]: Failed password for root from 23.249.167.223 port 32997 ssh2 Feb 14 04:07:23 foodwiz3 sshd[1264]: Received disconnect from 23.249.167.223: 11: Bye Bye [preauth] Feb 14 04:13:04 foodwiz3 sshd[1289]: error: Could not load host key: /etc/ssh/ssh_host_ed25519_key Feb 14 04:13:05 foodwiz3 sshd[1289]: reverse mapping checking getaddrinfo for coenamor.columbiansabbatical.com [23.249.167.223] failed - POSSIBLE BREAK-IN ATTEMPT! Feb 14 04:13:05 foodwiz3 sshd[1289]: pam_unix(sshd:auth): authentication failure; logname= uid=0 euid=0 tty=ssh ruser= rhost=23.249.167.223  user=root Feb 14 04:13:07 foodwiz3 sshd[1289]: Failed password for root from 23.249.167.223 port 41562 ssh2   Is this something that is fairly normal, or should I be worried/doing something about it? Why the value of $PATH is different for root and normal user? for normal user I get :     /usr/lib/lightdm/lightdm:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/home/monty/google_appengine   which is actually the content of /etc/environment  For root I get:     /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin   what's the reason behind this and which file contains this line? How can I use a variable in the replacement side of the Perl substitution operator? I want to model this gun:  So I started to cut out the rough shapes from a cube (using the boolean modifier) Then I tried to clean up the geometry to be able to round the edges of the handguard.  But it does not work. When I try to bevel it like in the last pic top right it just gets really messy.  I think I took the wrong approach. How would you go about adding clean and workable geometry to such a piece and would you use the Bevel tool to create the round shapes? A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$ I am not sure whether this is right. Can anyone verify, whether this proof is valid? Thanks!        Define a sequence $\{a_n\}_{n\ge0}$ as follows:   $$a_0=1,\qquad,a_1=3,\qquad,a_2=9,\qquad,a_n=a_{n-1}+a_{n-2}+a_{n-3}\text{ for }n\ge3.$$   Prove that for any positive integer $n$, $a_n\le3^n$.        Proof. Let $P(n)$: $a_n\le 3^n$, $n$ is a non-negative integer.      (i) Base case:         Consider when $n=0$. LHS$=a_0=1$, RHS=$3^0=1$ $\therefore$ LHS$\le$RHS, then $P(0)$ holds.   Consider when $n=1$. LHS$=a_1=3$, RHS=$3^1=3$ $\therefore$ LHS$\le$RHS, then $P(1)$ holds.   Consider when $n=1$. LHS$=a_2=9$, RHS=$3^2=9$ $\therefore$ LHS$\le$RHS, then $P(2)$ holds.         (ii) Inductive case:   Assume $P(i)$ is true for $0 \le i \le k$, $k\ge2$.      (iii) Inductive conclusion: Consider $n=k+1$.   $$ \begin{align*} \mathrm{LHS}=a_{k+1}&amp;=a_k+a_{k-1}+a_{k-2} \qquad\text{(by definition, since $k\ge 2$)}\\                     &amp;\le 3^k+3^{k-1}+3^{k-2} \qquad\text{(by Induction Hypothesis)}\\                     &amp;=3^k(3^{-1}+3^{-2}+3^{-3})\\                     &amp;=3^k\left(\frac13+\frac19+\frac1{27}\right)\\                     &amp;=\frac{13}{27} 3^k\\                     &amp;\le 3^{k+1} = \mathrm{RHS} \end{align*} $$   Therefore, by the Principle of Strong Induction, $P(n)$ is true for all non-negative positive integers $n$. Is there a reliable way to determine the OS upgrade history leading to Windows 10 or if it was a fresh install? Why does the sum of the reciprocals of factorials converge to $e$? I've been asked by some schoolmates why we have $$ \sum_{n=0}^\infty \frac{1}{n!}=e.$$ I couldn't say much besides that the $\Gamma$ function, analytic continuation of the factorial, is defined with an integral involving $e$. Then I also know that actually $$ \sum_{n=0}^\infty \frac{x^n}{n!}=e^x.$$ Is there a reason for these facts?  P.S. I added the tag "intuition", please remove it if you think it is not pertinent. Explain how (or if) a box full of photons would weigh more due to massless photons I understand that mass-energy equivalence is often misinterpreted as saying that mass can be converted into energy and vice versa.  The reality is that energy is always manifested as mass in some form, but I struggle with some cases:  Understood Nuclear Decay Example  In the case of a simple nuclear reaction, for instance, the total system mass remains the same since the mass deficit (in rest masses) is accounted for in the greater relativistic masses of the products per $E=\Delta m c^2$.  When a neutron decays and you are left with a fast proton and a relativistic electron.  If you could weigh those two without slowing them down, you would find it weighed as much as the original neutron.  Light in a Box  This becomes more difficult for me when moving to massless particles like photons.  Photons can transmit energy from one heavy particle to another.  When a photon is absorbed the relativistic mass (not the rest mass) of the (previously stationary) particle that absorbs it increases.  But if my understanding is correct, the energy must still be manifested as mass somehow while the photon is in-flight, in spite of the fact that the photon does not have mass.  So let's consider a box with the interior entirely lined with perfect mirrors.  I have the tare weight of the box with no photons in it.  When photons are present the box has an additional quantifiable amount of energy (quantified below) due to the in-flight photons.  Say there are $N$ photons... obviously assume $N$ is large.  $$\Delta m = \frac{ E }{ c^2 } = \frac{ N h }{ \lambda c}$$  Interactions are limited to reflections with the wall, which manifest as a constant pressure on the walls.  If I hold this box in a constant gravitational field (like the surface of Earth) then there will be a gradient in the pressure that pushes down slightly.  Is this correct?  Wouldn't there still technically be mass as the photons are in-flight, which would cause its own gravitational field just as all matter does?  How is this all consistent with the assertion that photons are massless?  Is it really correct to say that photons don't have mass?  It seems to be a big stretch.  Please offer a more complete and physically accurate account of this mirror-box. A worryingly high number of bad suggested edits get accepted. For example:             (These are just examples of a few common patterns. The  exists too.)  What can we do to educate reviewers to do a better job?  This is an open question, not a feature request, because I don't have a good answer. Some possibilities:   Provide a way to notify the reviewers (“hey, check that proposed tag wikis aren't plagiarised”). Make the workflow for approval as long as the workflow for rejection, so that people don't blindly approve just because it's less work. (I don't know if some reviewers tend to do that.) How can I use Web.debug.config in the built-in visual studio debugger server? I have a list of dictionaries and want each item to be sorted by a specific value. Take into consideration the list: [{'name':'Homer', 'age':39}, {'name':'Bart', 'age':10}]  When sorted by name, it should become: [{'name':'Bart', 'age':10}, {'name':'Homer', 'age':39}] When is the graph of the divisor relation on $[n]$ planar? A recently-deleted question asked to show that if $G(n)$ is the graph on $[n]=\{1,\dots,n\}$ where $x$ and $y$ are adjacent if $x|y$ or $y|x$, then $G(n)$ is planar.  This is false if $n\geq150$, for the subgraph induced by $\{2,3,5,90,120,150\}$ is isomorphic to $K_{3,3}$.  My question is, what is the largest value of $n$ such that $G(n)$ is planar?  Of course, various software packages would make short work of this, but I'd be interested in a verbal argument, if someone can give one. Having just  from any of the queues, it was reviewing close votes; however, this audit was flawed in that I didn't even cast a close vote.  Often I press the Close button to preview greater detail and sentiment of the closure, spawning the Why should this question be closed dialog box:    Especially for duplicates, where functionality is solely dependent on spawning this dialog.  From Closing > Duplicate, I can search or view selected duplicates:    Although, I realize general closure reasons are summarized on the page:    This question had 6-upvotes, but seemed very localized referencing subjective query is "taking too long" and even had a sqlfiddle link.  Maybe overly broad regarding performance tuning, the OP was posting like a forum with two answer posts to his own question  and  with one of those answers asking follow-up questions.    Wanting to gauge community response, current closure totals struck my curiosity.  So, I pressed the Close button and boom - oh, the humanity!  I failed, and didn't even cast a close vote.    Votes are not cast until a reason for closure is selected and Vote to Close is pressed.  Taking any review very seriously on this site, it only seems fair that my review quality is tested through actionable steps instead of clicking for more detailed information, leveraging the functional design of the close vote user interface.  Sure, it's complex to seed fake vote totals, and then there's controversy of mindless voting in the majority or people who simply cherry pick 4-vote questions.  Still though, it seems unfair I should hesitate to review further information of vote totals and duplicates before skipping due to the implementation of this audit.