How can I reproduce the same mesh many times 9000 (seriously)
What techniques have been used to repeat geometry or other detail to the infinite horizon?
Where are icons stored? I want to change an icon of a specific theme. Where do themes save their icons? Ramsey Number Inequality: $R(\underbrace{3,3,...,3,3}_{k+1}) \le (k+1)(R(\underbrace{3,3,...3}_k)-1)+2$ I want to prove that:  $$R(\underbrace{3,3,...,3,3}_{k+1}) \le (k+1)(R(\underbrace{3,3,...3}_k)-1)+2$$  where R is a Ramsey number. In the LHS, there are $k+1$ $3$'s, and in the RHS, there are $k$ $3's$. I really have no clue how to start this proof. Any help is appreciated! Is there a way to target the arrow from an OP bow via command block? I am trying to make an effect trail for a specific weapon in MC, a bow with power 120.  I want to use a command block to target any arrow with the damage it should be doing (63) and summon a trail of splash potions.  I also want to kill any arrow entities that have inGround=True  Is there any way to do this or do I have to come up with something else?  Attempt:  /execute @e[type=Arrow,damage=63,inGround=0] ~ ~ ~ summon ThrownPotion ~ ~ ~ {Potion:{id:potion,Damage:8197}} /kill @e[type=Arrow,inGround=True]   Each unfortunately just affects all arrows.  Is this even possible? I followed the beginner steps for creating a .  The child theme was created and it appears as an option on my Themes page. But unlike the other Themes on the page (including its parent), there is no preview.  The other themes ("Twenty Twelve," "Twenty Thirteen," and "Twenty Fourteen") are all listed with an image preview.  My child theme ("Twenty Fourteen Child") does not have any image. The child theme can be applied without issue.  This issue arises when I create child themes from other themes as well. Any ideas why this is happening and if I can resolve? How to implement custom icons for my script/addon? Is it possible to use different icons other than the default set and how? So this homework question is in the context of $\mathbb{R}$ only, and we are using Lebesgue measure.  The sum $A+B$ is defined to be $A+B=\{a+b|a\in A,b\in B\}$. The question is: If $m(A),m(B)&gt;0$, is it necessarily the case that $A+B$ contains an open interval?  This question is quite annoying, since it is quite difficult to calculate the sum even after you construct an example. However, it seems like no matter how I constructed a set of positive measure, there is a region that have a lot of point in it (yet this region is not necessarily dense). This suggest that when summed up, the holes should be covered up somehow and thus there would be an open interval, and so the answer is yes. Sorry for a rather vague idea, but I'm just not sure what to do with this problem. I have a feeling that somehow topology would have a way to capture precisely the idea above about a region with a lot of point.  (also, I think my middle school teacher mentioned this once, and I remembered the answer to be yes; but that is quite a while ago though)  Thank you. Any help will be appreciated.  EDIT2: So Camilo's answer is gone. I am looking at the convolution method right now. Because the convolution is continuous, if it is nonzero I am done. But then there is no guarantee that the convolution is nonzero even if $x\in A+B$. I still need help with this direction. Can someone give me some hints?  EDIT: Camilo's answer below essentially suggest the method of getting 2 open interval from regularity theorem, one cover a subset of A and one cover a subset of B such that the sum of the measure of these two subset is bigger than the measure of the larger interval. user99680's answer point to a wiki which show a method that essentially simply acquire an open set. After some thinking, I believe that these method simply can't be made to work. I constructed this example in the hope that it would convince you that it is the case:  Let $I_{0},I_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is nonzero and $m(I_{n})=9^{-n}$ and all of them are inside $[0,2]$. Let $J_{0},J_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is at least $3$ and $m(J_{3n})=m(J_{3n+1})=m(J_{3n+2})=\frac{m(I_{n})}{3}$. Let $O=\bigcup I_{n}$ and $H=\bigcup J_{n}$. Construct $A\subset O$ such that $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$. Construct $B\subset H$ such that $m(B\bigcap J_{n})=\frac{3m(J_{n})}{4}$. Now if you apply Camilo's method, it is possible that your $I$ would be one of the $I_{n}$ above, and your $J$ is one of the $J_{m}$ above. No matter which $I_{n},J_{m}$ you have, the argument does not work. Rewrite $m=3q+r$ where $0\leq r\leq 2$. If $q&lt;n$ then $m(J_{m})&gt;m(I_{n})$ so the longer interval have length $\frac{m(I_{q})}{3}$; $m(A\bigcap I_{n})$ is at most $\frac{3m(I_{q+1})}{4}=\frac{m(I_{q})}{12}$ and $m(B\bigcap J_{m})=\frac{3m(J_{m})}{4}=\frac{m(I_{q})}{4}$. Thus $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. If $n\geq q$ then $m(I_{n})&gt;m(J_{m})$ so the larger interval is of length $m(I_{n})$; $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$ and $m(B\bigcap J_{m})$ is at most $\frac{3m(J_{3n})}{4}=\frac{m(I_{n})}{4}$. Once again $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. Hence the Camilo's argument does not work. user99680's method does not work either, since you get $O$ and $H$ which is even bigger than any interval. I've installed emacsformacosx on my OSX box.  I'd like to shove my macmini in a data center and run it headless.  I've gotten x-windows working.  If I run xeyes, it displays on my Windows 7 client.  Emacs works from the command line on the osx box.  However, if I start up emacs from the windows client, it pops it up on the server instead of the client.  What am I doing wrong? The link to the recommended job in the app brings you to a page with the text: Not Found    Looking at the link it seems like after changing the URL structure in Stack Overflow Jobs they have not been updated in the apps.  For the job in the screenshot this is the used URL in the app:    The correct URL is: The external Flash is not showing up in the configuration Menu when using Pixel TF-321 hot shoe. Is this the wrong adapter for that camera, as there is no X connection? I want to trigger a studio flash via sync connection. Can you recommend me a working hot shoe? Thanks! Is it safe to delete from C:\Windows\Installer? it seems my bash-completion got corrupted. Every time I try to use command substitution, for example when I type  ls $(ls Deskto&lt;Tab&gt;   ..result is..  ls $(ls Desktobash unexpected eof while looking for matching ")".   I tried removing my .bashrc file and cp /etc/skel/bashrc ~/ to get a new one. That works until I add something into my new bashrc. Even when I do echo '#" &gt;&gt; ./.bashrc it breaks again. Removing my bash_aliases did not help either.  Also sudo apt-get install --reinstall bash-completion did not do the trick.  However there are some threads about similar problem, nothing works.  ANY hint will be greatly appreciated! :) Why did my windshield freeze instantaneously? Which arena do free and crown chests use when determining the cards you will get? If I am in arena X when I collect my tenth crown for the crown chest, or a free chest becomes unlocked, then proceed to climb to arena X+1 before opening the chests, which arena will be used to determine the cards I get? Will it use the arena I was in when I unlocked the chests in, or the arena I opened them in? When using Alt+Tab, I can't seem to get back to Skyrim. When clicking its icon or Alt+Tab to get back, I just see an empty window. Windowed mode doesn't allow me to use it in a Windowed (Fullscreen) manner as seen with other games, so that doesn't seem to be an option either. Is there any way to fix this behavior? How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards? I'm a computer science student who is a maths hobbyist. I'm convinced that I've proven a major conjecture. The problem lies in that I've never published anything before and am not a mathematician by profession. Knowing full well that my proof may be fallacious, erroneous, or simply lacking mathematical formality, what advice would you give me? On the Goblet of Fire Barty Crouch exactly got Mad-Eye's voice when he transformed into him, but on the Deathly Hallows, they were all able to have their own voices instead of Harry's. Why is the effect of the polyjuice potion inconsistent? Pointer to class data member "::*" I came across this strange code snippet which compiles fine:  class Car {     public:     int speed; };  int main() {     int Car::*pSpeed = &amp;Car::speed;     return 0; }   Why does C++ have this pointer to a non-static data member of a class? What is the use of this strange pointer in real code? Prove the definitions of $e$ to be equivalent How to prove that the following definitions of $e^x$ are equivalent, with as simple tools as possible and without any knowledge of $e$ or logarithms ?  $$\sum_{n=0}^{\infty} \frac{x^n}{n!}=\lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n$$  Also preferably, prove that this is $a^x$ for some real number $a&gt;0$. How to Toggle Selected Objects Visibility with H shortcut as in Maya Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$ Let $z_1$ and $z_2$ be two complex numbers. Show that there exists $C &gt; 0$ with   $$  |z_1 + z_2|^2 &lt; (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2. $$   I tried to simplify the L.H.S and R.H.S, SNF I was finally left to compare between a real number and a complex number  I really couldn't think of anything else. Please help.