Only do 1 SphereCastAll in Unity3D?
Difference between 'max distance' and 'radius' in Physics.SphereCastAll
How do I remove an OpenID or login? How do I remove login credentials (emails or OpenIDs) from my account?     For more information, see "" in the . When I include a  \usepackage{forest} all colored text title, section headings disappears with IEEE Access journal template How can I tackle this problem? MySQL: SELECT from another server I'm afraid that I already know the answer to my question, but I'll ask it anyway:  When there are two MySQL DB servers, can I access data that is stored on the other server?   In other words: Can I somehow do this:  INSERT INTO table (x, y, z)    SELECT x, y, x+y       FROM [otherserver].[database].[table]   Is the answer really as short as "No"? Difference between [NSMutableArray array] vs [[NSMutableArray alloc] init] I installed Ubuntu 14.04.1 on one of my laptops and now I want distribute that exact installation to a few of my friends. I tried making an iso with Gparted on a live session but it makes a 500 GB file (I've only used around 8 GB) .   Thanks in Advance ! Help with proving that $\pi$ is irrational I was trying to prove that $\pi$ is irrational, just to see if I could do it. So far, I've tried to do this by using the fact that the sum   $$S=\sum\limits_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}$$ and arguing that $S$ is irrational instead, and thus implying that $\pi$ is also irrational.  To do this, I thought I could use partial sums $S_n$ of $S$:  $$S_n=\sum\limits_{k=1}^n \frac{1}{k^2}=\frac{A_n}{B_n}$$ where the fraction $A_n/B_n$ is written in lowest terms. We can note that the sequence $\lbrace S_n \rbrace$ is a strictly increasing sequence, with $\pi^2/6$ as its lowest upper bound, so I thought that maybe the sequences $\lbrace A_n \rbrace$ and $\lbrace B_n \rbrace$ both have no upper bound, and the sequences would tend to infinity, and if I were able to prove this, I thought I could use it to argue that $S$ is an irrational number, using the fact that every rational number can be written as the quotient between two finite integers.  We note that $A_n\geq B_n$ for all natural $n$, as $S_n\geq 1$, so all we would really need to prove in that case is that $\lbrace B_n \rbrace \rightarrow \infty$(if this assertion is even correct).  At first I thought that both $\lbrace A_n \rbrace$ and $\lbrace B_n \rbrace$ would be increasing sequences, but after checking with Maple I noticed that they weren't, sadly enough($S_9=\frac{9778141}{6350400}$ and $S_{10}=\frac{1968329}{1270080}$). However, they do indeed seem to get very large very quickly, so I'm thinking that my hypothesis about $\lbrace A_n \rbrace$ and $\lbrace B_n \rbrace$ is correct.  But I have trouble proving my hypothesis, and I'm kind of stuck, no knowing what to do. Is there a way to prove that $\lbrace B_n \rbrace \rightarrow \infty$? And of course, is this approach to prove that $\pi$ is irrational logically sound, or is it fundamentally flawed in some important aspect? In the latter case, what idea should I try next? A gateway to a new world/future where things can be improved with use This book is about an explorer (with robot companion) who walks through a "gateway" into the future/parallel world. In this world, things that are created do not fall into disrepair, instead things get better.  The main character is kidnapped early on in the story and forced to labor by beating the outside of a castle with a spear. It is explained to him that this makes the wall better and able to resist attacks by these weapons. In his cell, he meets a man wearing an extravagant shirt and asks about it and the man explains to him that the shirt has been in his family for several generations, which is why it looks so nice.   To escape from the jail cell, the man tears one of his zippers from his jump suit and uses it like a saw to cut a hole in the wall. He escapes with the man in the fancy shirt and a woman.   The woman, is something special in this world. (She can focus on the change that is happening to an item and somehow enhance or speed up the process)  The man makes a wheeled cart for them to escape in. While the wheels are at first rough and wobbly, they soon "become better" and spin better. How is Dru-Zod/General Zod still alive after this character died? Do I need Intel Smart Response when installing Ubuntu? tasks package: items are in two line with 4 columns and 4 items I write some choice questions into beamer frame, after some research, here is my code:  \documentclass[aspectratio=169]{beamer} \usetheme{Berkeley} \usepackage{tasks,CJK} \begin{document} \begin{CJK*}{utf8}{bsmi} \begin{frame} \transwipe 1.Which one you want to choose? \begin{tasks}[counter-format=tsk[A].,debug=true](4) \task A \task B \task C \task D \end{tasks} \end{frame} \end{CJK*} \end{document}   output with pdflatex:  But I don't want the D choice goto the second line, I want them stay in one line, what should I do? launch app, capture stdout and stderr in c++ Can infinitely many primes lie over a prime? Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence? $$ \sum_{n=1}^\infty \frac{n!e^n}{n^n} $$ Where $e$ is Euler's number.  Recently on calculus class we were covering convergence tests and my group got stuck with this infinite series. Our calculus teacher told us that it diverges but he doesn't see any elementary way or simple test to prove it. He told us something about Euler's Gamma function and said that he knows it diverges because of Stirling's formula but this is not quite our level yet.  I tried to think about it myself but I established only that this  is some kind of an edge case. We could generalize the problem to series of $\frac{n!a^n}{n^n}$. Then, from the ratio test we know that it converges for $a &lt;e$ and diverges for $a&gt;e$. For $a=e$ the test is inconclusive. I've also tried to compare it with various divergent series, but nothing worked...  Does anybody have any idea for a simple solution? I have my A* pathfinding algorithm right now working such that given a graph it can find the route from one starting node to one goal node.   This works well for many problems, but sometimes I find that multiple goal nodes are valid.  For example, in a game, an NPC might have to go to a switch to shut a door. If there are multiple switches that shut the door in question, it doesn't matter which switch it goes to - it just needs to go to one of them.  How can I augment my pathfinding algorithm to find the path to the best goal (the shortest path)? As in, the algorithm searches for multiple goals and when it finds just one, it returns the path to that one.  One solution would be to run the algorithm as many times as there are valid goals, but you can guess why that might be inefficient. How can I keep multiple live/bootable ISO images on a single USB drive? I am looking to create a USB flash drive that I can put multiple  ISO images on and select which boots from startup. The ideal candidate supports Linux and Windows-based ISO images, and is relatively simple. It also must have some reasonable process for adding and removing an ISO image from the drive/list.    Things that I'm not looking for in this specific question:    or other swiss-army knife live CDs. The point is to boot any one of multiple CDs, not to boot a (certainly useful) utility CD. Installing a single live CD to a USB drive. I'd like to have multiple ISO images, selectable at startup.   I don't have a specific purpose in mind, possibilties include a single drive with a  variant, Ubuntu desktop, UBCD4Win for DOS, the Offline NT Password Cracker, etc.  Flexible and easy to use are the name of the game! Real Analysis - Prove a set is countable I am asked to prove the following question:  For each finite set of real numbers, $F$, define $\sum F$ to be the sum of all the numbers in $F$.  For each set $P$ of positive real numbers, define $\sum P=\sup\{\sum F: F\text{ is a finite subset of } P\}$.  Suppose $P$ is a set of positive real numbers such that $\sum P &lt; \infty$. Prove that $P$ is a countable set.  My attempt (just a sketch proof):  Suppose $P$ is uncountable, $\exists \epsilon_1 &gt; 0$, s.t. $$ P_1 = [\inf P + \epsilon_1, \sup P]\cap P $$ is uncountable. Pick $a_1 \in [\inf P, \inf P + \epsilon_1] \cap P \in P$, such a $P$ must exists due to greatest lower bound property.  Now $P_1$ is uncountable, $\exists \epsilon_2 &gt; 0$, s.t. $$ P_2 = [\inf P_1 + \epsilon_2, \sup P_1]\cap P_1  $$  is uncountable. Pick $a_2 \in [\inf P_1, \inf P_1 + \epsilon_2]\cap P_1 \in P$. Carry on this process (this should be formalized using induction), we can find  $$ a_1 \leq a_2 \leq a_3 \leq ... $$ with $a_n &gt; 0$ and $a_n \in P$ for all $n$.  Now $\sup\{\sum F_n: F_n = \{a_1,...,a_n\}, n \in \mathbb{N}^+\} = \lim_{n \to \infty}\sum_{i = 1}^n a_i &gt; \lim_{n \to \infty}na_1 = \infty$. This means that $\sum P = \infty$ since $\{\sum F_n: F_n = \{a_1,...,a_n\}, n \in \mathbb{N}^+\} \subset \{\sum F: F\text{ is a finite subset of } P\}$.  I think my proof is a bit clumsy but is it correct? My machine can't play encrypted DVDs on a fresh install.  How do I add this capability?  Another useful bit of information would be what programs are best for playing DVDs, once I'm able to do so.  See the .  Will I be able to play DVD movies from ? How to disable all Vim-LaTeX mappings? I like some of the features provided by the Vim-LaTeX suite, but not all of them.  In particular, I dislike all of the mappings like [[ = \left[ \right] and the automatic placeholder stuff with &lt;++&gt;. I am a very fast typist but with that comes more typing mistakes, which I correct almost instantly by pressing backspace. Unfortunately, if something has automatically added a bunch of place-holders or expanded some expression, I then have to move around the document and remove more characters than necessary. For example, if I accidentally press [ twice, instead of only having to delete one character, I have to delete 10.  Having already looked through the documentation, and some of the source, I have managed to disable some of these "features", but not all of them:  In particular:  let g:Tex_SmartKeyBS = 0 let g:Tex_SmartKeyQuote = 0 let g:Tex_SmartKeyDot = 0   (Turn off maps for backspace, double quote and triple dot.)  let g:Imap_UsePlaceHolders = 0   (Turn off &lt;++&gt; placeholder insertion.)  But I can't seem to find a way of turning off the other stuff. Anyone have any suggestions?  Edit: I was able to "disable" some more things by setting:  let g:Tex_Leader = '`tex' let g:Tex_Leader2 = ',tex'   (Which stops some expansions but still not all. It's not really disabling it but just making it less likely that you're going to type in `texa as opposed to the potentially more common `a, for example.)  PS: Personally, I think it is very poor practice to make an optional package that, when installed, greatly changes the default handling of your system. I don't mind some intelligent source highlighting etc, or some new commands (that don't clobber any old ones), but it seems unhelpful to enable this drastic kind of key remapping by default. How can I reverse (flip horizontal) a table? How to get a JavaScript object's class?