How to fix NullPointerException on Android Studio?
What is a NullPointerException, and how do I fix it?
Say $R$ is a commutative ring and $I\in R$ is an ideal. Let us consider the quotient $R/I$. It is created by taking every element $a\in R$, and adding all the elements of $I$ to it. The elements of $R/I$ are of the form $a+I$ and $b+I$, $\forall a,b\in R$.   Now $$(a+I).(b+I)=(a+i_{1}).(b+i_{2}),\forall (i_{1},i_{2})\in I \times I$$  $$(a+i_{1}).(b+i_{2})=ab+a.i_{2}+b.i_{1}+i_{1}i_{2}=ab+I$$  We know that $a.i_{2}+b.i_{1}+i_{1}i_{2}\in I$.   If $(a+I).(b+I)=ab+I$, then taking suitable $(i_{1},i_{2})\in I\times I$, we should be able to prove $(a+i_{1}).(b+i_{2})=ab+i_{3},\forall i_{3}\in I$. However, can every element in $I$ be generated by taking suitable $i_{1},i_{2}\in I$? And if not, is that the reason why $(a+I).(b+I)$ has to be defined as equal to $ab+I$ in violation of the distributive property of ring elements? This has confused me for a long time.   EDIT: I figured addition does not have to be defined as such because $(a+i_{1})+(b+i_{2})=a+b+i_{1}+i_{2}$, where $i_{1}+i_{2}\in I$. In fact, every element $i\in I$ can be constructed by taking $i_{1}=0$ and $i_{2}=i$. Hence, $(a+I) + (b+I)=a+b+I$ naturally. This is the logic I followed to determine that $(a+I).(b+I)$ doesn't quite work as nicey. I'm not sure if this logic is flawed or not as I haven't had the opportunity to ask anybody.   Thanks for your help in advance! Evaluation of Differentiation and Integration I was having some thought about what would be the syntax to make the end point evaluation of derivatives or integrals. Such as making the | with the two end points of evaluation on the top an bottom of the line. Any suggestions would be wonderful. Sudoers blacklist How do you show a hidden folder (whose name starts with .) in File Manager a.k.a. Nautilus on Ubuntu?  I am somewhat new to Ubuntu and can't seem to find the "view" menu. Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal Let $x$ be a non zeo (column) vector in $\mathbb{R}^n$. What is the necessary and sufficient condition for the matrix $A = I-2xx^t$ to be orthogonal? Invisible software updates list in Software Updater Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$ I am stuck with the following problem.     Prove that $$\limsup_{n \to \infty} (a_n+b_n) \le \limsup_{n \to \infty} a_n + \limsup_{n \to \infty} b_n$$   I was thinking of using the triangle inequality saying $$|a_n + b_n| \le |a_n| + |b_n|$$ but the problem is not about absolute values of the sequence.  Intuitively it's clear that this is true because $a_n$ and $b_n$ can "reduce each others magnitude" if they have opposite signs, but I cannot express that algebraically...  Can someone help me out ? How to create and animate the water reflection (Caustics) on an object? What is the best method to create this kind of reflection and how to animate it? Selecting all objects that have been specified in Modifiers Could anyone help in making a script for selecting all objects that are specified in the different modifiers that an object has stacked? For example if my object has a Boolean modifier and an Array modifier, which both refer to an empty or another object (in the Array modifier there is for example an Object offset you can specify). Would it be possible to select all those object with one click? Thanks. What methods can I use to create balance and consistency between a group of differing logos? A regular challenge that I face is balancing two (or more) logos. Whether they need to be equal or one needs to be given priority. Some logos however might be squares, others rectangles, circles, etc...   As a quick sample I snagged a nice high resolution photo from  and pretend its going to be an advertisement that needs to show some footwear brand logos on it. In this case I used Adidas and Saucony.  This is certainly not balanced even though they're height is the same:    Likewise this is not balanced even though they're width is the same:    So then the question becomes when are they in balance, is this balance:    Maybe a little more adjustment, is this balance:    And in these examples I'm only working with two Black Logos. Factor in color and it can get even more difficult to balance. Another issue being when there's tiny text as part of the logo.  So the question is, other than estimating / eye-balling it, what tips, methods or even tools are there to balance different sized logos? \pause in tikzpicture breaks footline I've discovered that you can \pause within a tikzpicture, which works well until I switched the theme to one with a footline.  I've created a "test case" that illustrates the problem.  \documentclass{beamer} \providecommand\thispdfpagelabel[1]{} % Not sure what this does but our installation requires it. \usepackage{tikz} \usetheme{Madrid} % Has a footline.  \begin{document}   \begin{frame}     \frametitle{test}     \begin{tikzpicture}       \node at (0, 1) {Hello};       \pause       \node at (0, 0) {World};     \end{tikzpicture}   \end{frame} \end{document}   This creates two slides, but the footline is only drawn on the second (the headline/title appears on both). Is there anything I can do about this? How to find out the reason, why my PC can't run Windows 11? Windows 11 requires this features:  Processor 1 GHz or faster with 2 or more cores on a compatible 64-bit processor or System on a Chip (SoC) Memory 4 GB RAM Storage 64 GB or larger storage device System firmware UEFI, Secure Boot capable TPM Trusted Platform Module (TPM) version 2.0 Graphics card DirectX 12 compatible graphics / WDDM 2.x Display &gt;9” with HD Resolution (720p) Internet connection Microsoft account and internet connectivity required for setup for Windows 11 Home  I have a 15-ay108nh laptop. As far as I know, it supports all the required features. It has 8GB ram, 256GB storage, UEFI support, TPM 2.0 ( I enabled it in the BIOS ), DirectX 12 compatible graphics / WDDM 2.x, and 1080p screen. I installed the , but for some reason, I get this result:  How is it possible to find out exactly, why it fails? E: Problem executing scripts APT Update::Post-Invoke-Success error during apt-get update I cannot install any package. It seems the command apt-get update must be run but it throws some errors:  $ sudo apt-get update Get:1 http://security.ubuntu.com/ubuntu xenial-security InRelease [102 kB]      Hit:2 http://ve.archive.ubuntu.com/ubuntu xenial InRelease                      Hit:3 http://ve.archive.ubuntu.com/ubuntu xenial-updates InRelease              Hit:4 http://ve.archive.ubuntu.com/ubuntu xenial-backports InRelease            Fetched 102 kB in 23s (4337 B/s)                                                *** Error in `appstreamcli': double free or corruption (fasttop): 0x000000000210f4b0 *** ======= Backtrace: ========= /lib/x86_64-linux-gnu/libc.so.6(+0x777e5)[0x7fac8d8317e5] [...] Aborted (core dumped) Reading package lists... Done E: Problem executing scripts APT::Update::Post-Invoke-Success   'if /usr/bin/test -w /var/cache/app-info -a -e /usr/bin/appstreamcli;   then appstreamcli refresh &gt; /dev/null; fi' E: Sub-process returned an error code Is it possible to raise stats? I found a lot of dialogue choices requiring high Perception and I started the game with just 10 plus 1 for being an elf. With a magical helm and tower rest bonus I can temporarily boost it to 13, but is it possible to raise it permanently? How are "needs to be washed," "needs washing," and the regional variant "needs washed" to be distinguished"? I'm from Central Pennsylvania, and apparently, we have a strange language construct in this area. I was recently talking about how "my car needs washed" to a friend from NJ, and she told me that my sentence was grammatically incorrect.   I realize she's right, and I realize my options are "my car needs to be washed" or "my car needs washing". But I'm not clear on the precise rule being invoked. Why is the determinant the volume of a parallelepiped in any dimensions? For $n = 2$, I can visualize that the determinant $n \times n$ matrix is the area of the parallelograms by actually calculating the area by coordinates.  But how can one easily realize that it is true for any dimensions? "Neither Michael nor Albert is correct" or "Neither Michael nor Albert are correct"? What is the correct sentence?  Neither Michael nor Albert is correct.   Neither Michael nor Albert are correct. Badge Notification Repeats Is it purely a 'gotta-have-them-all' mindset, or do they actually serve some purpose?  I notice that you are able to sell them on a community market. For a test I listed one, and someone bought it for 50p. Not exactly a huge amount, but I don't understand why someone would spend real money on them.  Am I missing something?   Are they redeemable for games or money off vouchers or something 'tangible' that I'm missing? Can I set max_retries for requests.request?