Null pointer exception in Java
What is a NullPointerException, and how do I fix it?
How to show that $|D_{2n}| = 2n$ via the presentation? Positive correlation and negative regressor coefficient sign Is it possible to obtain a positive correlation between a regressor and a response (+0,43) and, after that, obtain a negative coefficient in the fitted regression model for this regressor?  I'm not talking about changes in the sign of the regressor among some models. The coefficient sign always remains.  Could  the remaining variables of the fitted model influence the changing of the sign? Let $I = \langle 2\rangle$. Prove $I[x]$ is not a maximal ideal of $\mathbb Z[x]$ even though $I$ is a maximal ideal of $\mathbb Z$.   My professor mentioned that I should try adding something to it to prove that $I[x]$ is not the maximal ideal. I want to assume he meant to add $ \langle 2 \rangle$ to $I[x]$? From A Classical Introduction to Modern Number Theory by Ireland and Rosen, page 33:     Corollary 1 (Euler's Theorem). If $(a,m) = 1$, then $a^{\phi(m)} \equiv 1\,(m)$.      Proof. The units in $\mathbb{Z}/m\mathbb{Z}$ form a group of order $\phi(m)$. If $(a,m) = 1$, $\bar{a}$ is a unit. Thus $\bar{a}^{\phi(m)} = \bar{1}$ or $a^{\phi(m)} \equiv 1\,(m)$.   If I'm interpreting this correctly, this proof implicitly uses the fact(?) that if $G$ is a group and $x\in G$, then $x^{|G|}=1$, where $1$ is the identity element of $G$.  If this is indeed true, can someone explain why? (I have had no prior exposure to group theory.) NOR Gate is Working Correctly with Vcc Pin Disconnected What does "had had" mean? How does this differ from "had"? For example, what is the difference between the following two sentences:     I had a bad day      I had had a bad day Meaning of the word "axiom" Thus, axioms are propositions we assume to be true and we use them in an axiomatic theory as premises to infer conclusions, which are called "theorems" of this theory.  For example, we can use the  to prove theorems of arithmetic.  This is one meaning of the word "axiom". But I recognized that the word "axiom" is also used in quite different contexts.  For example, a group is defined to be an algebraic structure consisting of a set $G$, an operation $G\times G\to G: (a, b)\mapsto ab$, an element $1\in G$ and a mapping $G\to G: a\mapsto a^{-1}$ such that the following conditions, the so-called group axioms, are satisfied:   $\forall a, b, c\in G.\ (ab)c=a(bc)$, $\forall a\in G.\ 1a=a=a1$ and $\forall a\in G.\ aa^{-1}=1=a^{-1}a$.      Why are these conditions (that an algebraic structure has to satisfy to be called a group) called axioms? What have these conditions to do with the word "axiom" in the sense specified above? I am really asking about this modern use of the word "axiom" in mathematical jargon. It would be very interesting to see how the modern use of the word "axiom" historically developed from the original meaning.   Now, let me give more details why it appears to me that the word is being used in two different meanings:  As peter.petrov did, one can argue that group theory is about the conclusions one can draw from the group axioms just as arithmetic is about the conclusions one can draw from the Peano axioms. But in my opinion there is a big difference: while arithmetic is really about natural numbers, the successor operation, addition, multiplication and the "less than" relation, group theory is not just about group elements, the group operation, the identity element and the inverse function. Group theory is rather about models of the group axioms. Thus: The axioms of group theory are not the group axioms, the axioms of group theory are the axioms of set theory.  Theorems of arithmetic can be formalized as sentences over the signature (a. k. a. language) $\{0, s, +, \cdot\}$, while theorems of group theory cannot always be formalized as sentences over the signature $\{\cdot, 1, ^{-1}\}$. Let me give an example: A typical theorem of arithmetic is the case $n=4$ of Fermat's last theorem. It can be formalized as follows over the signature $\{0, s, +, \cdot\}$: $$\neg\exists x\exists y\exists z(x\not = 0\land y\not = 0\land z\not = 0\quad\land\quad x\cdot x\cdot x\cdot x + y\cdot y\cdot y\cdot y = z\cdot z\cdot z\cdot z).$$ A typical theorem of group theory is  which states that for any finite group G, the order of every subgroup H of G divides the order of G. I think that one cannot formalize this theorem as a sentence over the "group theoretic" signature $\{\cdot, 1, ^{-1}\}$; or can one? I have had the last Ubuntu distro (10.something) installed for a year and love it.  But I have run in to an issue when I tried to upgrade it to the latest one it did not work and there has come some serious issues now with almost everything and I want to remove Ubuntu completely and install the new one.  How can I remove the operating system (I don’t mind formatting the whole thing if that’s what’s needed). I am generating one report where I need to use background image. But I found that image always starts leaving some margin space to left side.    \documentclass{article} \usepackage{wallpaper} \usepackage{mdframed} \usepackage[top=2cm, bottom=2cm, outer=0cm, inner=0cm]{geometry} \begin{document}  Some content \ThisLRCornerWallPaper{1.0}{image.jpg} \end{document}    How can I use background image covering whole page? Can spells or spell-like abilities do non-lethal damage? I'm working on a Paladin/Warlock combination, based off of , and as part of this, I noticed Miniman's remark that Repelling Blast won't be that useful, because as a Paladin, you want people up close and personal when you're in a combat situation, not further away.  However, as a Paladin, your creed sometimes leads you to not want to engage in full-blown combat with a potential adversary -- you may want to drive them off or incapacitate/capture them instead.  With this, I wonder: can Repelling Blast, or other spells and spell-likes (such as invocations), be made to do non-lethal damage?  If so, I'm thinking that it'd be useful in exactly that sort of situation -- halting someone/pushing them away without having to wade into a melee with them or blow them to smithereens. In C/C++, are global variables as bad as my professor thinks they are? How do I install Wi-Fi drivers for Realtek RTL8723DE device in Ubuntu 16.04?  lspci -v | grep -i network 02:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device d723 Is there a way to convert an image to grayscale? Why did Dumbledore 'put on' the Resurrection Stone (Ring)? Downloading files instead of opening directly I have kept files in site assets and created hyperlinks to the files (which may be PDF or word ). When i click on the link it opens up in the browser. How do i force it to download ? Programmatically determining amount of parameters a function requires - Python why arcane legacy steps to boot from USB with GPT and UEFI? To run the live AVG rescue "disk" on USB for Windows 10, how is it made to work with a GPT and UEFI system?  (Possible solution listed below.)  I enabled the boot menu so that pressing F12 will display a list to select from.  Also, I put everything USB at the top of the boot sequence and Windows and the HDD at the bottom.  However, I hadn't realized GPT and UEFI are so different from a BIOS.  Because the USB flash drive isn't compatible with GPT it's not being picked up?  This  was suggested:   Open the notebook and press quickly F2 to enter the BIOS. Under the MAIN menu, enable the F12 Boot Menu option. Under the BOOT menu, select Legacy boot and press F10 Save &amp; Exit. While the notebook is rebooting, press F2 again to enter the BIOS. Under the BOOT menu, select as your first boot option the USB HDD stick (your USB stick). Press F10 Save &amp; Exit.    Perhaps this will work, but what is the problem that prevents UEFI boot from registering the thumb drive?  Because it's using GPT and not an MBR?  I don't want to switch to legacy, but stay with UEFI.  The laptop: Downgrading from OS X 10.9.2 to 10.9 How do I animate time? Pixel Perfect 2D tiles I'm trying to make an 64x64 tilemap using Super Tilemap Editor &amp; Unity but my tiles looks terrible. I did my research about pixel perfect 2D and all of the solutions were for pixel art, they didn't work for me.  I have the following tileset I made in Adobe Illustrator as an example    Tiles looks like this when placed in game (1x zoom)    I'm pretty sure they're not 64x64 in game, they also look pixelated probably because they're smaller than they actually are on camera.  So my question is, how can I calculate the correct camera size for 64x64 tiles and do I have to make any changes in order to make sprites look pixel perfect? I'm currently using 1080/64/2=8.4375 (vertical resolution / PPU / 2) as camera size.