Who is the person that says "Rey"?
In Rey's vision, whose voice says "These are your first steps"?
Proof of $\pi$ not being a quadratic irrational number. Does someone know a proof (books, articles) that $\pi$ is not a quadratic irrational?   The proof should not use that $\pi$ is transcendental.  Any hints would be appreciated. The 'ok' on the 'Your Answer' dialog on unregistered sites is a bit too high The 'ok' on the 'Your Answer' dialog on unregistered sites is a bit too high:     You can see the top of the k is outside the actual box, increasing the margin-top by 10px in the containing div fixes it. How to prove that this set is closed? Suppose $Y$ be an ordered set in the order topology. Let $f, g: X \to Y$ be continuous. How to show that the set $\{x| f(x) \leq g(x)\}$ is closed?  This is a excercise from munkres. Maybe trying to show that the set $f(\{x| f(x) &gt; g(x)\})$ is open is suffice. But I could not figure out the connection between this set and the continuity of the two functions.Could you give a hint?  Thanks. Switching between windows with scroll wheel on Ubuntu Dock I would like to switch between windows using the scroll wheel of the mouse over each app icon in Ubuntu dock, as we could do in Unity, but apparently this doesn't work in Ubuntu 17.10. Is there a way to enable it?   Related: Can I get US sales taxes refunded for electronics purchased while on vacation? How to Backup and Restore Android OS without Rooting Find $f(x)$ for $f(f(x))=\sin x$ Find all (if that's possible) functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f(f(x))=\sin x.$$  This is a problem a friend gave me. He said he saw it on a book a long time ago, but he couldn't remember what book. I literally have no idea how to solve this so I can't post my attempt here. As mentioned in the , Ubuntu 18.04 LTS will not have a 32 bit Desktop Image Installer. But in the  it has  32bit Desktop Images.  This is little off topic, but I'm confused. How to compute the  formula $\sum  \limits_{r=1}^d r \cdot 2^r$? How can I install Windows software or games? modulo version of the quadratic formula and Euler's criterion Use the modulo version of the quadratic formula and Euler's criterion to decide if the following has a solution or not.  $2x^2+5x+8 \equiv 0\pmod{37}$  I'm not sure how I would use what was being asked of me to decide if this has a solution or not, but I have came to the conclusion that it does not, because I plugged in every possible answer $0-36$, and none of them were congruent to zero.  The way people have answered the question, isn't exactly the way I need.  I have made some progress, but I'm not exactly sure how to finish:  $2x^2+5x+8 \equiv 0\pmod{37}$  $x^2+21x+4\equiv0\pmod{37}$  $x^2+58x+841\equiv837\pmod{37}$  $(x+29)^2\equiv23\pmod{37}$  I know that if $p$ is an odd prime and $p$ doesn't divide $a$, then $x^2\equiv a\pmod{p}$ has a solution or no solution depending on whether $a^\frac{p-1}{2}\equiv 1  \space\space \text{or}\space -1\pmod{p}$.  This is where I get stuck.  Can someone help me from here?  I have a feeling this problem has no solutions, so could someone also explain to me what to do if a problem like this did have solutions. Limits involving factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$ I am trying to calculate the following limit  $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$$ where $k$ can be any number between $0$ and $N$.  I thought of the following:  If I take the logarithm of the expression then I get:  $$\lim_{N\to\infty} \left(\log(N!)-\log((N-k)!)-k\log N\right)$$    Using the Stirling formula this can be approximated as:  $$\lim_{N\to\infty} \left(N\log(N)-(N-k)\log(N-k)-k\log N\right)$$  Now there are two cases: If $k$ is $N$, then the second term vanishes and the remaining terms cancel. If $k$ is smaller than $N$, then I can drop the $k$ inside the second logarithm and all the terms cancel. So the limit $$\lim_{N\to\infty} \log\left(\frac{N!}{(N-k)!N^{k}}\right)=0$$ Which means that: $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}=1$$ I don't know if this is mathematically rigorous. Would like some help. Thanks When and how did "pretty" enter English as an intensifying adverb? Finder windows just show screen artefacts On our Macbook Air (Mid-2011 11", OS X 10.9.5 Mavericks), starting a few days ago, every time we open Finder windows, the right side just shows screen artifacts/cheese. File Open dialogs in MS Word work fine - it is just the Finder windows with the problem.  Can someone help?  I have tried rebooting, and Verify Disk in Disk Utility. Neither helped. Maybe I should upgrade to El Capitan? But why would this start happening all of a sudden? Change color of links created with \in, \at, etc Can I reduce the MAC size in TLS? The MAC size is reduced to 80 bits in  , which says "forging of MAC values cannot be done off-line: in TLS, a single failed MAC guess will cause the immediate termination of the TLS session."  Question 1 (main question): So can I reduce MAC size to something even smaller, say 32 bits?  Question 2: The truncated_hmac extension does not effect AEAD. Can I reduce the tag's size in AEAD, e.g. GCM or CHACHA-POLY? Avoiding if statement inside a for loop? In a Silverlight application I'm trying to find out when a property on a usercontrol has changed. I'm interested in one particular DependencyProperty, but unfortunately the control itself doesn't implement INotifyPropertyChanged.  Is there any other way of determining if the value has changed? What is the difference between “within” and “inside”? Here is the definition of the word within from Oxford Dictionary:     inside (something)   So does that mean the two words have no difference, and can be used exchangingly? Is there any connotation that one word can be used but not the other? What is dependency injection?