This is the line C-3PO speaks when he meets BB-8 in The Force Awakens (2015):  C-3PO: Come along, BB-8, quickly. Yes, I must get my proper arm reinstalled.  That means they know each other even before.
A lot of people will probably gloss over this fact, but it looks like C-3PO meets BB-8 for the first time in this scene 0:20:                                But how does C-3PO know BB-8's name? Is there a time where C-3PO meets BB-8 before this and knows his name?
The achievements drop-down menu in the new top bar shows me when a question/answer earns me reputation and how much, and that's great, but I don't know what caused that to happen. I'd like to know why I received reputation: was it an upvote? An accepted answer? An accepted edit? If I have the list of reputation values in my head I can figure it out, but it would help me to see it somewhere in the drop-down, even as title text on hover.    Edit:  It sounds like the items in the menu can roll up multiple events, and that's why it doesn't show the event there. How about adding a link to my reputation tab to the menu so I can quickly get to a breakdown? Suppose that $ f $ is entire and that for each $ z $, either $ |f(z)| \leq 1 $ or $ |f^\prime (z) |\leq 1 $. Prove that $ f $ is a linear polynomial. My question is in the title. I'm a little lost in how to solve this problem. There is a hint associated with the problem that states the following:   Use a line integral to show that $ |f(z)| \leq A + |z| $ where A = $\max\{1, |f(0)|\}$  Thanks for the help. MongoDB could not connect local server I had mongdb installed and evrything was working fine. I wanted to delete the mongodb lock. By mistake the directory /var/lib/mongodb/ got deleted.  So, I uninstalled mongo db and installed again. But now i always keep getting this error:  Error: couldn't connect to server 127.0.0.1:27017 at src/mongo/shell/mongo.js:145 exception: connect fail   The error remains same even if I try to login from terminal or rockmongo or my application. I am using ubuntu12.04 and have latest version of mongo. Best way to save a ordered List to the Database while keeping the ordering I was wondering if anyone has a good solution to a problem I've encountered numerous times during the last years.  I have a shopping cart and my customer explicitly requests that it's order is significant. So I need to persist the order to the DB.  The obvious way would be to simply insert some OrderField where I would assign the number 0 to N and sort it that way.  But doing so would make reordering harder and I somehow feel that this solution is kinda fragile and will come back at me some day.  (I use C# 3,5 with NHibernate and SQL Server 2005)  Thank you Irreducibility of $X^n - 2$ over $\mathbf Z[i]$. I was “playing” with Eisenstein's criterion and the polynomials $X^n-p$ ($p$ being a prime number).  Over $\mathbf Z$, the classical Eisenstein's criterion directly applies and shows that $X^n - p$ is an irreducible element of $\mathbf Z[X]$. The question was “what happens over $\mathbf Z[i]$?”  We know that in this new ring, a prime number $p$ has one of three different fates:   if $p \equiv -1\ (\mathrm{mod}\, 4)$, $p$ still is an irreducible element of $\mathbf Z[i]$, or equivalently $(p) \subset \mathbf Z[i]$ still is prime. (Unless I'm mistaken, number theorists say that $p$ is inert). Eisenstein's criterion still applies and the polynomial is irreducible over $\mathbf Z[i]$. if $p \equiv 1\ (\mathrm{mod}\, 4)$, $p$ can be written as a sum of two squares: $p = n^2 + m^2$ and is therefore reducible on $\mathbf Z[i]$: $p = (n+im)(n-im)$. These two factors aren't associated (the units in $\mathbf Z[i]$ being $\pm 1$ and $\pm i$) so $(p)$ splits: $(p) = (n+im)(n-im)$ is the product of two different prime ideals. One can still use Eisenstein's criterion with either of these prime ideals, and $X^n - p$ is irreducible over $\mathbf Z[i]$. if $p = 2$, the oddest of all primes, one still has a factorisation $p = (1+i)(1-i)$ but this time, $1+i$ and $1-i$ are associated. In NT slang, $(2)$ is ramified: $(2) = (1+i)(1-i) = (1+i)^2$ and one cannot directly use Eisenstein's criterion.   So here's my question: how do we prove (or disprove) the irreducibility of $X^n - 2$ over $\mathbf Z[i]$? Quoting within $(command substitution) in Bash What is the smallest positive integer $n$, such that there exist positive integers $a$ and $b$, with $b$ obtained from $a$ by a rearrangement of its digits, so that   $a – b = 11\dots 1$ (The number of '$1$'s equal to $n$)?   Is there any example that can satisfy the equation? Is there a rational number between any two irrationals? Suppose $i_1$ and $i_2$ are distinct irrational numbers with $i_1 &lt; i_2$.  Is it necessarily the case that there is a rational number $r$ in the interval $[i_1, i_2]$?  How would you construct such a rational number?  [I posted this only so that the useful answers at  could be merged here before that question was deleted.] Which rationals can be written as the sum of two rational squares? Which rational numbers can be written as the sum of two rational squares?  That is, for which rational numbers $a$, are there rational numbers $x$ and $y$ such that $a = x^2 + y^2$.  It is a famous theorem that if an integer can be written as the sum of two rational squares then it can be written as the sum of two integral squares, and then the solution is the famous one by Fermat, but I didn't find anything about the general case. If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$ I am working on some past prelim problems and one of them is the following: If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$   Update: Following Jackie Chong's advice, I am attempting this problem with the dominated convergence theorem. Since $f\in L^1(\mathbb{R})$, $f$ can be approximated from below by a sequence of continuous functions $f_n$. Then, I believe I can say that, for all $n$ sufficiently large, $|f_n(x+\frac{1}{n})-f_n(x)|\le 2|f(x)|$. (I'm not sure of this part thought). Then $2|f(x)|$ is integrable and hence a dominating function for $|f_n(x+\frac{1}{n})-f_n(x)|$. So by the dominated convergence theorem we can take the limit inside $\lim_{n\rightarrow \infty}\int|f_n(x+\frac{1}{n})-f(x)|dx=\int \lim_{n\rightarrow \infty}|f_n(x+\frac{1}{n})-f(x)|dx=0$ Is this on the right track?  Another approach that I thought may work, but which I'm less certain of is the following: If $f$ can be approximated by $C^1$ functions (I have no real justification for this, so please correct me if its wrong), then for each $n$ and each $x$ there is some $y(x,n)\in B_{1/n}(x)$ such that $|f(x+\frac{1}{n}-f(x)|=\frac{1}{n}|f'(y(x,n)|$ but from here I don't see how to proceed, because just because $|f|$ is integrable, I can't justify $|f'|$ being integrable, but if there is some way to fix this approach, hints would be appreciated.   Another thing I was thinking was to first approximate $f$ from below by continuous functions $f_n$ then to define $g_{m,n}=|f_n(x+\frac{1}{m})-f_n(x)| \chi_{[-m,m]}$. Then, for each $n$, the function $g_{m,n}$ is continuous on its support, and since it support is compact, it is uniformly continuous there. Can this be used to justify bringing the limit $\lim_{n\rightarrow \infty}$ inside the integral? Then apply the monotone convergence theorem? I know this idea is probably even more sketchy than my previous one, but if it can be fixed please let me know :)  Thanks! Use a baseline including all observations in lm() Bump right-aligned text to next line iff no room Phone : nexus 5 version 2013 Android version : 6.0 Kernel version : 3.4.0-g2aa165e Build number : MRA58N   For the last few days, 10118 has been draining my phone's battery. It drains battery by using GPS. I typed 'ps' in a terminal emulator, and there was no application with PID 10118. I don't know what exactly 10118 is. My guess is that it's one of recently installed weather apps.  How can I fix this?    Screenshots (click images for larger variants) I'm having trouble with \includegraphics I'm using MacTeX Firstly and fore-mostly I am a complete new comer to the world of LaTeX and so please do bear with me. I will try to be as accurate as I can but if you need any more info please let me know.  All I want is to figure out how to import a graphic into LaTeX (MacTeX).  I am using the following in my code:  \documentclass[10pt,a4paper,draft]{report} \usepackage{graphicx}   Then in my document section I'm using   \begin{figure} \includegraphics[width = 50mm]{Name.jpg} \caption{Label} \end{figure}   Once I compile the document, the area for the picture has been allocated but there is no image, I have tried .png and .pdf files also.  I know that this is a very simple question and I hope there is a simple solution but I cannot find anything on the net about this (which may mean I'm being dim).  Also I'm using Latexian but I have tried 4 different editors and it doesn't work in any. If $A=AB-BA$, is $A$ nilpotent? If $T^n$ is $q$-contractive, $T$ exactly has one fixed point Consider a complete metric space $(X,d)$ and $T\colon X\to X$. Suppose there exists $n\in\mathbb{N}$ such that the n-th power of $T$ is $q$-contractive. Show that then $T$ has exactly one fixed point $\overline{x}\in X$.      The n-th power is defined inductively: $$ T^{n+1}(x):=T(T^{n}(x)), n\in\mathbb{N}. $$ And for a function $T\colon X\to X$, $q$-contractive means  $$ \exists 0\leq q&lt;1~\forall~x,y\in X: d(T(x),T(y))\leq q d(x,y). $$    Now to the proof.  I think I have to show, that $T$ is q-contractive, because then it follows with Banach, that $T$ does have exactly one fixed point. So I have to show, that there exists a $0\leq q&lt;1$ so that for all $x,y\in X$ it is $$ d(T(x),T(y))\leq q\cdot d(x,y). $$ And most likely I have to use the q-contractivity of $T^n$, i.e. that there exists a $0\leq q &lt;1$ so that for all $x,y\in X$ it is $$ d(T^n(x),T^n(y))\leq q\cdot d(x,y). $$  Can you help me? Imaging new hard drive in Windows 7 laptop? I'm upgrading my Windows 7 laptop to a new hard drive.  How can I clone or image the old hard drive over to the new hard drive, so that it looks like nothing has changed (other than the new hard drive) to my operating system and applications?  Can I use what is built into Windows 7 Backup or should I use something else? Changing footnote symbols Windows 8 upgrade Recovery Disk I have upgraded to Windows 8 from Win 7. I want to create a recovery disk for Windows 8, just in case something goes wrong. I didn't find the option of creating it from the control panel.  How do I create a Recovery CD/DVD? Subsurf Modifier artifacts So I was messing with Subsurf modifier to create a certain sword and then some weird artifacts began to appear (cape-like). I've tried adjusting the Crease, but couldn't achive what I wanted. Basicly, what I whant is the as on the screens, but wo any artifacts :)   Also, here's the .blend file, cause I assume I didn't make myselt 100% clear.