NullPointerException when adding an object to ArrayList in Android
What is a NullPointerException, and how do I fix it?
Can someone show me a straightforward proof that  $\lim_{m\to\infty}(1+\frac{r}{m})^{mt}=e^{rt}$  Thanks! How to prove the divisibility rule for $3\, $ [casting out threes] The divisibility rule for $3$ is well-known: if you add up the digits of $n$ and the sum is divisible by $3$, then $n$ is divisible by three.  This is quite helpful for determining if really large numbers are multiples of three, because we can recursively apply this rule:  $$1212582439 \rightarrow 37 \rightarrow 10\rightarrow 1 \implies 3\not\mid 1212582439$$ $$124524 \rightarrow 18 \rightarrow 9 \implies 3\mid 124524$$  This works for as many numbers as I've tried.  However, I'm not sure how this may be proven.  Thus, my question is:     Given a positive integer $n$ and that $3\mid\text{(the sum of the digits of $n$)}$, how may we prove that $3\mid n$? Can I SSH into a specific directory? I SSH into a multitude of different servers every day and some of them have different filesystem structures for their websites. Each time I change server, I have to work out where I'm going to get to the files I really want (because it's very rarely that I want to be in ~). I use Fabric files to automate all my actions (pushing to git, automated SSH to the server to pull from git, restarting the web application, changing dependencies, etc), so I was wondering if I couldn't also tell it that I want to SSH into the right directory so I can run fab ssh and be in a normal SSH session, just in the right place and start working immediately. This is not about Fabric though; please ignore it. Fabric is just running a batch of commands. My argument is with the ssh command. That's what I'll be telling Fabric to run. So how I can get ssh to cd into a specific directory on login? Note: this cannot be a server or user-wide thing. I have multiple websites under one user on some servers so sticking something in ~/.bashrc would not work for me. Graphical glitches using Ubuntu 18.04 on Dell XPS 13 2019 laptop My laptop keeps on having weird screen glitches, sometimes for a second, and that goes away just by moving the cursor, sometimes, making me restart the whole thing.  I could still use the play/pause key and it still played/paused the video that was running even though the screen was completely teared.  Also, printscreens actually print a normal screen and do not show the problem.  Some pictures of the screen when it happens :     Do you guys know what I could do to solve the issue ? Is there a definition of  and proper explanation of it?  It is said "Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter."  How is it though that matter can get charged?  Defining charge as the property of feeling a force with other charged matter seems circular.  What is charge?  Is there a non-circular definition / explanation? How to compute rational or integer points on elliptic curves This is an attempt to get someone to write a canonical answer, as discussed in this . We often have people come to us asking for solutions to a diophantine equation which, after some clever manipulation, can be turned into finding rational or integer points on an elliptic curve. See , , , , . (This list is biased towards questions I have answered because I remember them best; other people have answered such questions as well.) I would like an answer to which, after one of us has explained the cleverness, we could direct the OP.  An ideal answer would address    How to find both rational and integer solutions Good software solutions. Ideally, it would nice to have a walkthrough for doing these things with , so that people could find solutions without even installing anything. References for how to transform some standard presentations of elliptic curves into Weierstrass form, so that we don't have to write out the algebra every time. I'm thinking of  a cubic in $\mathbb{P}^2$ with a rational point that is not a flex,  $y^2 = \mbox{degree 4 polynomial}$, a $(1,1)$ curve on $\mathbb{P}^1 \times \mathbb{P}^1$, or an intersection of two quadrics in $\mathbb{P}^3$. CKEditor buttons not showing I'm using Drupal CKEditor module 7.x-1.13 and CKEditor 4.3.2. Everything is installed and appears to work fine... except that there are some buttons that don't appear despite being configured to do so, notably "Select All" and the justify left/right/centre/justified buttons. Here are the buttons as configured:    And here are the buttons as they appear: What are tag synonyms and merged tags? How do they work? What are tag synonyms? How can tag synonyms be distinguished from "real" tags? How are new tag synonyms created? Who can create tag synonyms? How can I delete/reverse/undo bad tag synonyms? What are merged tags? Add space before and after tabular environment The tabular environment does not add any vertical space before or after it. This looks odd, in my view. What is the "correct" or "best" way to add some space? Also, why is there more space after the tabular environment than before it, as seen in the example below?  \documentclass{article} \begin{document} \noindent Here is a line with some text in it.  \begin{tabular}{*4{l}}     Worg &amp; Worg &amp; Worg &amp; Worg\\     Worg &amp; Worg &amp; Worg &amp; Worg\\ \end{tabular}  \noindent Here is another line with some text in it. \end{document} What does the function f: x ↦ y mean? I am doing , and am having a few problems with function notation. I understand the form f(x).  What does the form f: x ↦ y mean? Could you also give one or two examples?  And, if possible, state your source. Thank you. Why there are real numbers with infinite digits, but no such natural numbers (or another reason why real numbers are uncountable) This question is me trying to understand (again) why there can be no one-to-one correspondence between the sets of natural and real numbers.  The source of confusion is this: if we abstract completely from the properties and operations on numbers and just think of them as strings of digits, it appears to be possible to list all the real numbers between $0$ and $1$ and all positive integers having the same digits in the same (or reverse) order, for example:  $$0.1 \to 1$$  $$0.01 \to 10$$  $$0.0101 \to 1010$$  $$0.110101 \to 101011$$  I use binary expansion for simplicity.  Since irrational numbers have infinite expansions, we would have to consider some kind of 'infinite natural numbers', like:  $$101110001\dots$$  or  $$\dots101110001$$  I think the main (and only) reason why such numbers don't exist is this requirement:   We need the sets of real and natural numbers to be ordered. We need to be able to do arithmetics on real and natural numbers.   Obviously, if we consider any of two types of 'infinite natural numbers' and the usual absolute value, we find that it's impossible to order them, or do arithmetics with them.  The only way is to change the norm (to $p-$adic norm for example).  While with the real numbers it's still possible to order them, and do arithmetics with them when they have infinite amount of digits in their expansion (or at least in principle).     Is my reasoning correct? Are the two requirements (ordering and arithmetics) enough to explain why natural numbers with infinite amount of digits do not exist, while real numbers do?   This confusion is not restricted to me alone, see  for example Requirements for a clan war? I am currently in a clan with three members. When we tried to initiate a clan war it said we had insufficient clan requirements. Does anyone know what the full requirements are? Is there a minimum clan member requirement? I am trying to solve the following question which is Ex3 from Arthur Engel, Problem Solving strategies. Here is the question: $\sum_{k=1}^n k^3 {n \choose k}$ and asks to find the sum. I am sincerely having a hard time trying to figure out how to solve it and get $n^2 (n+3)(2)^{n-3}$. I would really appreciate if someone could show the step-by-step process. Thank you! There are many different kind of options that you can do  in order to start using LaTeX on Ubuntu. I would prefer doing that through Eclipse, but if there is a better way of doing it, feel free to write your opinion on why using this instead of something else. I'm so puzzled about this:   $$a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}.$$  Why isn't $a^{b^c}$ equal to $a^{(bc)}$? Why is $a^{b^c}$ instead equal to $a^{(b^c)}$? And how is it possible that $(a^b)^c = a^{(bc)}$?  My mind is pretty much exploding from trying to understand this. Best way to capture historical changes between levels in a dimensional hierarchy What is the cleanest way to capture changes between levels in a dimensional hierarchy?  I have the dimensional hierarchy [Area] > [Region] > [Location], where Area is the parent to Region and Region is the parent to Location. Location is lowest level of the hierarchy, and is associated with the fact table.  The business rules are: Locations are able to change the Region they are assigned to based on business need. Furthermore, Regions are able to change the Area they are assigned to.  We want to capture those changes so that when we do historical analysis, we can compare business metrics before and after a Location changed its Region, and a before and after a Region changed its Area.  What is the best way to do this?  The four ways that I have come up with all seem to have major drawbacks:   Using a bridge table between hierarchy levels requires that you use time bounds (effective start/end dates) to correctly identify which parent a child belongs to as you walk up the hierarchy. That makes queries prone to error, especially with hierarchies with many levels. Versioning a child record whenever its relationship to its parent changes (e.g., versioning Region A when it moves from Area A to Area B) and then cascading that change all the way down the hierarchy (e.g., creating new versions of Locations tied to Region A so that they are tied to the new Region A). Updating the child record's reference to the parent record, making you use time bounds to reassemble the correct history (prone to error). Always use time bounds when querying up the hierarchy to make sure Location A is associated with the correct Region (likewise, Region A is associated with the correct Area) for the moment of the fact being analyzed.   None of these seems clean to me.  Is there a better way?  Thanks a lot Why does my Nikon D3100 give the error "Lens not attached" with a Vivitar 200 telephoto lens? I have a Nikon D3100 camera, and am trying to use an "Automatic Fixed Mount Vivitar 200mm lens" with it. When I attach the lens, I get the message "Lens not attached". and nothing works. HELP!  I can't easily take it to a camera shop, as I live in the Mojave Desert, about 200 miles away from any camera shop. This is a new lens, and a new camera. Prevent mail being marked as spam How does one decide whether to use who or that? In the title example:   The correct pronoun is who. The correct pronoun is that. Either is correct. They're interchangeable. It depends on the context. How to cite sources written in a different language than English?