Are there any real examples of Infinite, or possible infinite, in our universe?
Does infinity exist in physical systems?
How to move an element into another element? I am an Indian living in Italy and I am going to the UK for a leisurely family vacation for about 10 days. Please note, this application is not very straight forward. There are four applicants, one applicant is applying from India another two are applying from Singapore and I am applying from Italy. The checklist at the top has the statement  all documents must be in English translated documents must be certified  I got the proof of accommodation from my commune, but it is in Italian. Getting it translated, isn't such a big deal as the commune itself provides multi-lingual certificates. For the rest of the documents, this is an issue. Such as for &quot;Evidence of being in education&quot;, my university provides an online certificate for this purpose which is in Italian. Multiple acquaintances said that they provided their Italian house contract (in Italian) as proof of residency and no requirement came up for translation. Can anyone comment on how strict are they while enforcing the translational requirements of documents in respect to a short term visitor visa? Is it possible to test apex that relies on field history tracking? The  gives the recoil force, $\mathbf{F_{rad}}$, back on a charged particle $q$ when it emits electromagnetic radiation. It is given by:  $$\mathbf{F_{rad}} = \frac{q^2}{6\pi \epsilon_0 c^3}\mathbf{\dot{a}},$$  where $\mathbf{\dot{a}}$ is the rate of change of acceleration.  If a particle has a constant acceleration, $\mathbf{\dot{a}}=0$, then there is no reaction force acting on it. Therefore the particle does not lose energy.   Does this mean that a constantly accelerating charged particle does not emit electromagnetic radiation? /usr/sbin/grub never finishes I did apt-get upgrade it never finishes at this point:  Searching for GRUB installation directory ... found: /boot/grub Searching for default file ... found: /boot/grub/default Testing for an existing GRUB menu.lst file ... found: /boot/grub/menu.lst Searching for splash image ... none found, skipping ... Found kernel: /boot/vmlinuz-3.2.0-24-virtual Updating /boot/grub/menu.lst ... done  You already have a NoLOADER configuration in /etc/grub.conf Running boot loader as requested Running /usr/sbin/grub  ...    The system does not freeze (Ctrl-Z works, I get my console back) just that that /usr/sbin/grub seems to never complete.  What should I do? How much time is too much time playing educational computer games? I recently bought an iPad primarily for my 3-year-old daughter. I put nothing on it but educational apps and children's books. No YouTube, no Internet, no (non-educational) games. I've decided to let her use it as much as she wants, for now, and see how it goes. That was a few weeks ago.  So far she's been using the iPad maybe 2 to 5 hours each day. She still enjoys other activities -- playing outside, playing with dolls and blocks, interacting with friends, being read to, etc. And I think she might be learning a thing or two from the apps. Still, several hours a day seems like a lot. How do I know if it's too much?  I've searched the web, and there's lots of info on limiting TV time and video games, but I can't find any recommendations on limiting use if it's only educational games.  Relevant: Multi armed bandit for general reward distribution unable to change php version on cli What is the correct way to show tiered possession? When there are multiple places where possession is shown, how are the words structured?  A few examples:   Greg's son's laptop is on fire. Mary's friends' boat is sinking. Thomas's neighbor's cat ate a mouse. Apple's Stock App's stats are useful. Microsoft's Xbox 360's games are fun.   Are these the correct ways to express possession? Why is $5^{n+1}+2\cdot 3^n+1$ a multiple of $8$ for every natural number $n$? I have to show by induction that this function is a multiple of 8. I have tried everything but I can only show that is multiple of 4, some hints? The function is $$5^{n+1}+2\cdot 3^n+1 \hspace{1cm}\forall n\ge 0$$, because it is a multiple of 8, you can say that$$5^{n+1}+2\cdot 3^n+1=8\cdot m \hspace{1cm}\forall m\in\mathbb{N}$$. Security importance of Key Schedule in Block Cipher Are $(x^3)^{1/3} $ and $\sqrt{x^2}$ monomials?    In mathematics, a  is, roughly speaking, a polynomial which has only one term. Two different definitions of a monomial may be encountered:  For the first definition, a monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions.   For the second definition, a monomial is a monomial in the first sense multiplied by a nonzero constant, called the coefficient of the monomial. The full prophecy by Trelawney, the part my question is about in bold:     "The one with the power to vanquish the Dark Lord approaches ... born to those who  have thrice defied him, born as the seventh month dies ... and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not ... and either must die at the hand of the other for neither can live while the other survives ... the one with the power to vanquish the Dark Lord will be born as the seventh month dies ..."    – Sybill Trelawney (to Dumbledore)    I am interpreting      for neither can live while the other survives   as: Harry can't live while Voldemort survives and vice versa. But why? It clearly worked until the end of book 7. One could argue with Dumbledore's thery of the self-fulfilling prophecy. But clearly Voldemort was smart enough to see that there was no mechanism that would kill him just because Harry stayed alive.    and either must die at the hand of the other    Again: Why? If somebody else destroyed all Horcruxes and then killed Harry, Voldemort would be just as vulnerable and could be killed by anyone. On the other hand, Harry could have been killed by anyone - his mum's protection transferred to Voldemort by Harry's blood was only helping against Voldemort.  I guess that I am interpreting this part of the prophecy in the wrong way or maybe there is an alternate, less obvious and more tricky one. So my question is: What exactly does the highlighted part of Trelawney's prophecy state? Good text on Clinical Trials? I'm an undergraduate statistics student looking for a good treatment of clinical trials analysis. The text should cover the fundamentals of experimental design, blocking, power analysis, latin squares design, and cluster randomization designs, among other topics.   I have an undergraduate knowledge of mathematical statistics and real analysis, but if there's a fantastic text that requires a bit higher level of statistics or analysis, I can work up to it. What is the best way to clean the sensor on a interchangeable lens camera (mirrorless or digital SLR)? I'm running 12.04 - I installed kubuntu to try it out and realized that with all the bloatware applications that I didn't want it anymore - I was able to uninstall the kubuntu-desktop but there are still packages left over... How can I make sure I get rid of EVERYTHING Kubuntu installed - even the kde leftovers?  Here's some of what's left when I ran sudo apt-get autoremove kde then "tab" it displayed this:     kdeaccessibility              kdepim-runtime kdeadmin   kde-runtime kde-baseapps                  kde-runtime-data   kde-baseapps-bin              kdesdk-dolphin-plugins kde-baseapps-data   kde-style-oxygen kde-config-cron               kdesudo kde-config-gtk    kdeutils kde-config-touchpad           kde-wallpapers   kdegames-card-data            kde-wallpapers-default   kdegames-card-data-extra      kde-window-manager kde-icons-mono   kde-window-manager-common kdelibs5-data                 kde-workspace   kdelibs5-plugins              kde-workspace-bin kdelibs-bin   kde-workspace-data kdemultimedia-kio-plugins   kde-workspace-data-extras kdenetwork   kde-workspace-kgreet-plugins kdenetwork-filesharing   kde-zeroconf kdepasswd                     kdf kdepim-kresources   kdm kdepimlibs-kio-plugins        kdoctools   Those are all installed by kubuntu... correct?  I just want to go back to my Ubuntu 12.04LTS with Gnome2-classic and without all the kubuntu extras.  I started it off by just removing unnecessary apps that came with kubuntu-full - then realized I didnt want the whole thing at all and uninstalled kubuntu-full but it still says I have these as well:     alex@griever:~$ sudo apt-get --purge remove kubuntu-   kubuntu-debug-installer           kubuntu-netbook-default-settings   kubuntu-default-settings          kubuntu-notification-helper   kubuntu-firefox-installer         kubuntu-web-shortcuts PCA on correlation or covariance? I have been using LaTeX for a long time now, and I find myself often going to this website to solve my problems. This often includes copy pasting codes which include \newcommand, \newenvironment and \def. I think it is time I start to learn how to use them so I can solve my problems myself! It is always better if you actually know what is going on inside your code.  I am wondering if there is any turtorial or book out there that handles how to use those commands. Or is the best way to learn to just mess with a random file?   Thanks in advance!  (Also this is my first time I post here after using this website for so long, I really appreciate everyone who posts and tries to help other people here!) I'm sure its a simple question and I suppose it was asked many times, but I just can't figure it out from other answers, sorry.  I use recent versions of PostgreSQL and MySQL. I have 2 tables:  CREATE TABLE authors (     id INT,     name VARCHAR )  CREATE TABLE posts (     id INT,     author_id INT,     text VARCHAR,     date DATE )   I need to select one most recent post for each author. Thanks!  UPDATE  Thanks, both links provide answers to my question with some exception. All the following queries give the same result (which one is the most efficient btw?) The issue is when there is more than one post from the same author with the same date. Then the returned result set contains all such posts. How should I modify these queries to return exactly one post per author?  SELECT p1.* FROM posts p1 LEFT JOIN posts p2 ON p1.author_id = p2.author_id AND p1.date &lt; p2.date WHERE p2.author_id IS NULL ORDER BY p1.author_id;  SELECT p1.*  FROM posts p1 INNER JOIN (   SELECT author_id, MAX(date) AS max_date   FROM posts   GROUP BY author_id) p2   ON p1.author_id = p2.author_id AND p1.date = p2.max_date ORDER BY p1.author_id;  SELECT * FROM posts p1 WHERE date = (SELECT MAX(p2.date)               FROM posts p2               WHERE p1.author_id = p2.author_id) ORDER BY author_id;  SELECT * FROM (     SELECT author_id, MAX(date) date     FROM posts GROUP BY author_id ) p1 INNER JOIN posts p2 USING (author_id, date) ORDER BY author_id; Collinearity diagnostics problematic only when the interaction term is included