Apparating within Hogwarts in the Half-blood Prince
How did Montague Apparate into the Hogwarts bathroom?
Commenting out large sections To &quot;comment out&quot; a line, I need to insert a % at the beginning of the line (so that the line will not be compiled). Is there a way to comment out a large section without having to manually place % in front of each line? "This one is" OR "This is" I have seen people using "This one is Daddy's" with the word "one" before a form of the verb be. I am confused about which is more accurate, to use:     This is Daddy's.   or     This one is Daddy's.   Hope you can address my concerns, thank you. Do people sometimes get blocked by a webservice for things someone else has done with their dynamic IP-Address It is common practice for operators of web services (e.g. web sites) to block IP addresses when there was malicious traffic originating from that address.  It is also common practice that internet users don't have a static IP address but get one assigned by their ISP via DHCP.  Now I would expect that it sometimes happens that a specific IP address gets banned from a service and later that address gets assigned to another user, leaving the new user (temporarily) banned from the service for no apparent reason. However, I never had this problem or heard of someone having that problem.  Does this sometimes happen? If not, what prevents this from happening? Why doesn't the percentage of oxygen in Earth's atmosphere diminish significantly with altitude? According to numerous sources online, the percentage of oxygen is approximately the same at sea level and 10,000 meters. Since oxygen is heavier than nitrogen, shouldn't the percentage of oxygen decrease with altitude? I'm running the following script on Ubuntu 14.04:  #!/bin/bash  apt-get purge -y nginx apt-get install -y nginx  date   When I run it like cat /tmp/script | bash, apt-get starts installing, then "date" is printed (not the actual date, but the command name), then the remaining apt-get output is printed.  If however I run the script like /tmp/script, it works as expected: printing the date after apt-get finished.  Why does this happen and how can I force bash to work when being piped to the same way it does when invoked directly? If an ideal contains the multiplicative identity, then it is the whole ring I have to prove that if $I\subseteq R$ is an ideal, and $1\in I$, then $I=R\,$. So I know $I\subseteq R$ is an ideal if $a,b\in I$ implies $a+b\in I$, and if $a\in I$, $r\in R$, then $ra\in I$. I'm finding it hard to put this into words. Since $1\in I$ and $I\subseteq R$ is an ideal, then let $a=1$ and $r=1$ so $1\cdot 1\in R\,?$ How to see if SkyDrive is still syncing in windows 8.1? Windows 8 displayed overlay icons on my SkyDrive files, so I could see which files are current and which are in sync.  After I upgraded to Windows 8.1 the files still sync, but I can't see if the files are current or not. The only way is to load a file, check for myself if the latest changes are there (if I remember them) and refresh until the file is synced. Which is a pain! The sync overlay does only show for files which modified locally and are waiting to upload, it does not show up for files which had been changed on the server (other computer) and are waiting to download!!  So how do I get the file sync Status on Windows 8.1? Uxie and Azelf Are Not Appearing in Nameless Cavern The Quotation Mark character in TeXworks editor has vanished Now, my version of TeXworks is 0.4.5r.1280 and I can't have the " character on the keyboard.    I have ``  or '' instead. Why?  And It's the same with Alt+034. I'm very disappointed with that. How do servlets work? Instantiation, sessions, shared variables and multithreading Elementary proof for $\lim\limits_{n \to\infty}\frac{n!e^n}{n^n} = +\infty$ As seen in  question, the series $\sum\limits_{n=1}^{\infty} \dfrac{n!e^n}{n^n}$ diverges. (One way to see this is by noting that the terms of the sum are greater than $1$ and, therefore, don't converge to zero.)  However, more is true: not only are the terms greater than $1$, they blow up to $+\infty$! To see this, one can apply Stirling's approximation and get $\dfrac{n!e^n}{n^n} \sim \sqrt{2\pi n}$.  My question is: is there an elementary proof for $\lim_{n \to\infty}\dfrac{n!e^n}{n^n} = +\infty$?  The reason I'm asking this is that I'm taking a Calculus course and I was assigned the exercise of proving the divergence of the series above and I would feel more satisfied if I could prove that its terms go to $+\infty$ (as opposed to merely proving the terms are greater than $1$.) Obviously, things like Stirling's approximation are outside the scope of the course, so I can't really use them.  (To be clear, you can use anything one learns in $4$ semesters of standard Calculus courses. I hope this restriction is not too obscure.) Why is $\sqrt{-x}*\sqrt{-x}=-x?$ I think it's well established that for the basic premise in the Back to the Future Trilogy to work, we have a system of alternate timelines.  If this is the case though, then why would Marty in Back to the Future (the original) begin to fade?  Logically, there would simply be no Marty in the alternate timeline created when Marty travels back to 1955 for the first time; why should this affect the original Marty from the original timeline? What does "ain't" mean? What does the contraction ain't mean? Is it appropriate to use it in formal settings? How many days a year is a U.S. citizen allowed to stay in Morocco? I arrived in Morocco in October of 2014 and renewed my visa by traveling to Spain by ship for a day and getting my passport stamped again in January of 2015. My question is, am I allowed to leave the country and repeat this process this year by traveling again to another country, other than my own in order to return to Morocco for another 90 days? And if so, how many times a year is this allowed? I have read 180 days on some websites but there is not any clear answers anywhere about this that I can find. Setting ArcGIS Desktop license to lower level for testing whether Python script still runs? I have a Python script that will need to be given to a client.   We are currently evaluating what license level the client will need in order to run the script for their software acquisition purposes.   We all have ArcGIS 10.1 Advanced license in our company.   I checked all the tools and extensions used in the script against the web help and found that they should work on the Standard license level.   Is there a way I can test the script against the Standard license level, when we have no Standard license level in or company (only the higher Advanced level)? Assume $x \in \mathbb{R}$ and $(x + \frac{1}{x}) \in \mathbb{Z}$.   Use Induction to prove that for all $n \in \mathbb{N},~ (x^n + \frac{1}{x^n}) \in \mathbb{Z}$.  I'm not sure how to use the information given to prove the induction step. What I have so far is.  $P(n) : (x^n + \frac{1}{x^n}) \in \mathbb{Z}$  Base Case Then $(x^0 + \frac{1}{x^0}) = 2 \in \mathbb{Z}$  Induction Hypothesis: $x^k + \frac{1}{x^k}\in \mathbb{Z}$  Want to prove: $x^{k+1} + \frac{1}{x^{k+1}} \in \mathbb{Z}$  My first step was  $x^{k+1} + \frac{1}{x^{k+1}} = x \cdot x^k + \frac{1}{x} \cdot \frac{1}{x^k}$ Difference between  and  in Java Why did my windshield freeze instantaneously? It was very cold outside, this morning, when I took the car that slept in the snow, with a simple cloth on the windshield. I entered the vehicle, drove a kilometer or so. The air inside was so cold I could see my breath (or maybe I forgot to brush my teeth). Warm air was blowing on the windshield from the inside and suddenly…  The glass in front of my became opaque, starting from the bottom (the place where the hot air was blowing) and freezing up, up, up until the whole screen was filled in about 5 seconds. It reminded my a little bit of how some baterias spread.  When I tried to remove the mist, I realised it was ice in the car. My windshield instant froze.  I know the theory behind supercooling: a very cold and still liquid can freeze when moved. I'm not sure what happened here, but there were some pretty big turns in the road before it froze. It really looked like the hot air froze the place and not the movement.  Any idea about what happened ? How much energy does lowering an object into a black hole generate? An object of mass m is slowly lowered into a black hole of mass 1000 m. Is the amount of braking energy larger than $0.6 mc^2$?   Now what if, after lowering the mass close to the event horizon, we wait the black hole to shrink to mass 100 m, by emitting Hawking radiation, and then we lower the mass some more? Is the braking energy of the second lowering process larger than $0.5 mc^2$?   I wonder can we extract more than $E=mc^2$ energy from mass m?  (In this thought experiment we use a wire and a winch, or anything that works)