I used to think we should say "keep your hands off the wall", but one of the lines in Money, from Pink Floyd, they say "keep your hands off of my stash". That made me confuse.   Do we always say keep your hands off of  something? How does it work for "keep your hands off (of) the wall"?   Thank you
What is the difference when you say "get off of something" and "get off something"?
What's the thing with $\sqrt{-1} = i$? Do they really teach this in the US? It makes very little sense, because $-i$ is also a square root of $-1$, and the choice of which root to label as $i$ is arbitrary. So saying $\sqrt{-1} = i$ is plainly false!  So why do people say $\sqrt{-1} = i$? Is this how it's taught in the US? Using a Java library with Scala reserved words how to calculate $\int_C \frac{2xy^2dx-2yx^2dy}{x^2+y^2}$ using green theorm or directly Calculate $$\int_C \frac{2xy^2dx-2yx^2dy}{x^2+y^2},$$ where $C$ is the ellipse $3x^2 +5y^2 = 1$ taken in the positive direction.   I tried to calculate the integral using green theorm.  now i need to build enclosier that doesn't enclose $(0,0)$ i am having hard time guessing what to build.  a circle and ellipse might be perfect but then the domain is not easy to write. can i have hint please ? Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$. Let $B$ be a compact subset of a metric space $X$. Let $x \in X \setminus B$. Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.   Is this an existence proof? If yes, do I get to define $U,V$? Array with labeling columns Is there an intelligent way to label (or name) columns in a matrix? I would like to have something like  \[M=\left[\begin{array}{c|cc} 1 &amp; 2 &amp; 3\\ 4 &amp; 5 &amp; 6 \end{array}\right],N=\left[\begin{array}{c|cc} 7 &amp; 8 &amp; 9\\ 10 &amp; 11 &amp; 12 \end{array}\right]\] \[A \ B \ C \ D \ E \ F\]   where A, B,..., F are the labels (or rather names) of the first, second, ..., sixth columns, respectively. What I want is to label A be exactly below the first column, label B be below the second column, etc., of course, nicely aligned. So far I have forced some extra spaces before the labels manually, and also experimented with the \phantom command. How should a user's death be handled? It is a bit of a morbid concept, but having recently had a friend die unexpectedly and having to deal with the online repercussions of this event has gotten me to thinking about what should happen to my accounts when I kick the bucket.  I haven't had any great insights yet, but here are some things I think are worth thinking about:   an entry in the FAQ telling the person's loved ones what to do with respect to the account would be extremely helpful, specifically who to contact, how to contact them, and what proof is necessary some form of optional date of death on the user account screen some way to mark the user as no longer being able to generate content and blocking any attempt to login as the user.   The danger I see in implementing such features is the possibility of someone faking another person's death and thereby locking a user out of his or her account or worrying his or her friends. How to install Ubuntu 18.04 alongside Windows 10 How to install Ubuntu 18.04 alongside Windows 10?  I have tried different process to install Ubuntu 18.04 in my PC in dual boot mode alongside Windows 10. But it turned out that most of the process didn't worked for my PC. My PC's configuration is 500 HDD, 3.5GHz Intel processor, 4GB RAM, 1GB Intel graphics &amp; supports both BIOS &amp; UEFI. How to count the node a user has created in a View? I have installed an Ubuntu server on a VMWare workstation with a space of 20GB storage as seen below;    After the installation I've attached another 40GB worth storage to the existing Ubuntu server installation (seen below);    Now I want to add this 40GB to my / (root) directory or to /var/ directory but my df -h result shows;  root@Userver:~# df -h Filesystem      Size  Used Avail Use% Mounted on /dev/sda1        18G  900M   16G   6% / udev            990M  4.0K  990M   1% /dev tmpfs           400M  308K  399M   1% /run none            5.0M     0  5.0M   0% /run/lock none            999M     0  999M   0% /run/shm none            100M     0  100M   0% /run/user root@Userver:~#   What should I do now? Further, I have only ssh access to the server. I am using NCR18650 batteries with the tp4056 charging module.  When I connect the charger at 2.8&nbsp;V (fully discharged), the tp4056 IC is getting hot at a 1&nbsp;A charge current. Is it OK to reduce this charge current by changing the charge current selecting resistor? So the tp4056 IC heat would be reduced, wouldn't it?  For my application I don't need a quick charge. With a low current, charging time will be increased, but it does not matter for my application.  Will reducing the charge current affect the battery's lifetime? Or will it damage the battery?  I am trying to reduce the heat of the tp4056 IC by reducing the charging current, maybe from 1&nbsp;A to 500&nbsp;mA or less. The 18650 battery never heats for a 1&nbsp;A charge current. This is one thing that keeps bugging me, and maybe there's a direct answer. Grammatically, which one is more correct of these two?  Does it make a difference?  I tried not to do that. I tried to not do that. If I run along the aisle of a bus traveling at (almost) the speed of light, can I travel faster than the speed of light? Android and setting width and height programmatically in dp units How to set scale across all blender objects and keyframes? Uses of the 3D Cursor Will Winterbash promote mass spamming due to its short time frame? Is there any concern that , due to their time-limited nature, will encourage mass spamming of posts? Cosmopolitan, for example, can only be achieved by posting to Meta. There are over one million users on Stack Overflow who may want this hat, and have only until January 4th to get it, and their only means of doing so is to invent some reason to post to Meta. How do I "Show total up and down vote counts" since I'm at 1K rep? Dynamic Paint not showing in rendered image Is it possible to prevent an NSURLRequest from caching data or remove cached data following a request? On iPhone, I perform a HTTP request using NSURLRequest for a chunk of data. Object allocation spikes and I assign the data accordingly. When I finish with the data, I free it up accordingly - however instruments doesn't show any data to have been freed!  My theory is that by default HTTP requests are cached, however - I don't want my iPhone app to cache this data.   Is there a way to clear this cache after a request or prevent any data from being cached in the first place?  I've tried using all the cache policies documented a little like below:  NSMutableURLRequest *theRequest = [NSMutableURLRequest requestWithURL:[NSURL URLWithString:url]]; theRequest.cachePolicy = NSURLRequestReloadIgnoringLocalCacheData;   but nothing seems to free up the memory! $P(\limsup A_n)=1 $ if $\forall A \in \mathfrak{F}$ s.t. $\sum_{n=1}^{\infty} P(A \cap A_n) = \infty$ Let $\mathfrak{F} = (A_n)_{n \in \mathbb{N}}$. Prove that $P(\limsup A_n)=1$ if $\forall A \in \mathfrak{F}$ s.t. $P(A) &gt; 0, \sum_{n=1}^{\infty} P(A \cap A_n) = \infty$. (Side question 1 Is second Borel-Cantelli out because we don't know if the $A_n$'s are independent?)  Suppose $\forall A \in \mathfrak{F}$ s.t. $P(A) &gt; 0, \sum_{n=1}^{\infty} P(A \cap A_n) = \infty$, but $P(\limsup A_n)&lt;1$. My prof gave us this convenient hint: Show $\exists M &gt; 0$ s.t. $P(\bigcap_{j=M}^{\infty} A_j^{c}) &gt; 0$.  $1 &gt; P(\limsup A_n)$  $1 - P(\limsup A_n) &gt; 0$  $P(\liminf A_n^{c}) &gt; 0$  By definition of $\liminf A_n^{c}$, $\exists M &gt; 0 $ s.t. $P(\bigcap_{j=M}^{\infty} A_j^{c}) &gt; 0$. (Side questions 2 and 3 Isn't this =1? ...Wait, is that what we're trying to prove? Haha)  $\to 1 - P(\bigcup_{j=M}^{\infty} A_j) &gt; 0$  $\to 1 &gt; P(\bigcup_{j=M}^{\infty} A_j)$  Main question: Now I guess we have to come up with some A s.t.  $\to 1 &gt; P(\bigcup_{j=M}^{\infty} A_j) \geq \sum_{n=1}^{\infty} P(A \cap A_n)$, or is there something else to do?