How to rectify NullPointerException in v4.DrawerLayout?
What is a NullPointerException, and how do I fix it?
Let $(x_n)_{n\in \mathbb{N}}$ be a sequence of real numbers. A well known result is:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ converges to $a\in \mathbb{R}$.   Now, I'm working on an exercise which essentialy asks to prove the following:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if for every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ there is a (sub)subsequence $(x_{n_{k_j}})_{j\in \mathbb{N}}$ which converges to $a$.   Now, one direction is trivial. If in fact $(x_n)_{n\in \mathbb{N}}$ converges to $a$, then by the result I've mentioned, every subsequence of $(x_{n})_{n\in \mathbb{N}}$ converges to $a$. Let then $(x_{n_k})_{k\in \mathbb{N}}$ be an arbitrary subsequence. In that case, we know that it is a subsequence of itself, and hence we've found a (sub)subsequence which converges to $a$.  The other way around seems quite complicated for me. The reason is as follows: I must assume that every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ has a (sub)subsequence which converges to $a$ and the proof that the original one converges to $a$.  My problem is exactly that "a". If it had all (sub)subsequences converging to $a$, then by the result i've mentionted, the subsequence $(x_{n_k})_{k\in \mathbb{N}}$ would converge to $a$. In that case, we would have every subsequence converging to $a$ and the result would follow.  My idea to prove the claim was then:  First remember that a subsequence is the restriction of the original one $x: \mathbb{N}\to \mathbb{R}$ to an infinite subset $\mathbb{N}'\subset \mathbb{N}$. In that case a (sub)subsequence is the restriction of $\tilde{x} = x|\mathbb{N}'$ to an infinite subset $\mathbb{N}''\subset \mathbb{N}$. But since $\tilde{x}$ is the restriction of $x$ to $\mathbb{N}'$ and since $\mathbb{N}''\subset \mathbb{N}'$, the restriction of $\tilde{x}$ to $\mathbb{N}''$ is itself the restriction of $x$ to $\mathbb{N}''$.  In other words, every (sub)subsequence can be viewed as a subsequence of the original one. Considering this, by hypothesis every subsequence has a (sub)subsequence which converges to $a$. But by this argument, this means that we can replace every subsequence with a convergent one. And then we can use the result I stated.  Is my idea correct? Is this really the way to prove the claim? My only doubt is that I need every subsequence converging to $a$ to use the result. In this case I can't see how I can argue that this implies every subsequence converges to $a$.  How can I finish this proof? When should a Test Case be marked as "No Apply"? With CSS, use "..." for overflowed block of multi-lines On Windows 10 Professional, with the November update (Build 10586, Version 1511) , is there any possibility to completely remove Windows Defender ?  I don't want to just disable Windows Defender.  I want to completely uninstall from my system. What's the starting wealth for higher levels? The PHB only gives starting wealth for Level 1 PCs. Based on my experience in other games, specifically Pathfinder, I would expect to get more at higher levels. Where can I find an appropriate table or calculation? How do I disable System Integrity Protection (SIP) AKA "rootless" on macOs [OS X] Apple has introduced , also known as "rootless", with OS X 10.11, El Capitan. I understand this is a step for general protection against malware but as a developer I need write access to some of the files it locks away.  How do I disable this protection? Can I have a common account across the Stack Exchange family of sites? One who has potential, but never gives the effort to show it.   What would be the best word or words that match this description? How can I define a 3D version of the built-in VoronoiDiagram (VoronoiMesh in V10) function? The international Stack Overflow sites in Spanish, Portuguese, Russian, and Japanese seem to have a bug in their quick site descriptions (under their titles), for they all start with the word  For...  in English, instead of their respective languages As an example, the Spanish Stack Overflow site description is:  For programadores y profesionales de la informática  Obviously, this isn't something too big of a deal, but since they offer those sites in their respective languages, it would be nice if this issue were fixed. You can see this under &quot;More communities&quot; in the top bar.    You can also see this on the  page, where the descriptions begin with  Q&amp;A for... Make an Ubuntu bootable USB drive for a PC using Mac? brute force password guessing on SSH server isn't going to work? I'm running an SSH server on my personal computer. The log had many people(or bots?) repeatedly trying to log in to my server (that is before I changed the default port), which made me a little freaked out. I was worried about their dictionary attacks or brute force password guessing.  But then if you type wrong password (or wrong username), the server waits for about 2 seconds before it asks for password again. So an attacker can try one password per 2 seconds. So I concluded that these attacks aren't that great a threat (as long as your password does not consist of dictionary words.) Am I correct? Do mankind and manmade activities/constructions have any effect on the rotation of the Earth? Just curious whether the process takes a while, and whether it scrapes through history to determine if it was once valid or not. Currently, I have 6 0-vote accepted answers and 20 1+-vote answers (), and that makes it > 5 and > 20% but not for long if voting goes up or down from here. ;-P  Update:  Special thanks to Grace Note for pointing out the  to follow. I upgraded this to a bug because it's been 48 hours during which the criteria supposedly were met. 6 0-votes, 20-23 1+ votes during the whole period. The criteria only last so long, so it may go out of scope soon. If it only checks every 3 days, I'm not sure if that's intentional or a bug. Why don't planets have Circular orbits? This might be a completely wrong question, but this is bothering me since many days ago. Given the mass (Sun) curves the space around it, gravitation is the result of such curved space (Correct me if I am wrong, source: A Documentary film). Given any point on a circle with center same as center of the mass, curvature in the space should be equal (Intuition).   Planets rotate around the Sun because of the curve in the space they should follow a circular path and the distance between planet and Sun should be at a distance.  Given the fact that earth has a elliptical orbit around the sun, and the distance between Earth and Sun varies according to position of the earth. Why do we have a elliptical orbit not a circular orbit. What is the exact $SU(2)$ representation to which these Hermitian generators belong? \begin{equation} t_a=\{t_1,t_2,t_3\}=\left\{\frac{1}{\sqrt{2}}\begin{pmatrix}  0 &amp; 1 &amp; 0 \\ 1 &amp; 0 &amp; 1 \\ 0 &amp; 1 &amp; 0 \end{pmatrix},\,\frac{1}{\sqrt{2}}\begin{pmatrix}  0 &amp; -i &amp; 0 \\ i &amp; 0  &amp; -i \\ 0 &amp; i &amp; 0 \end{pmatrix},\,\begin{pmatrix}  1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; -1  \end{pmatrix} \right\} \end{equation}  I'm a bit puzzled with this, these are not the generators of the triplet representation of $SU(2)$ (the triplet in $SU(2)$ is the adjoint rep which is real and constructed with the structure constants), nevertheless they are used as if they were in much literature. What are really these generators? They seem like the extension to 3 dimensions of the Pauli matrices. The 3 dimensional fundamental rep (this does not make sense to me)? some kind of non-irreducible representation? I haven't filed 2020 taxes yet. On my last return (2019) my adult daughter was on my return as a dependent. When I file 2020, I will not put her on my return as a dependent, because she finished college in 2019. I had her file her 2020 return early this year so she would be sure to get a stimulus check in case they did another one (I assumed they would exclude adult dependents as they had with previous stimulus payments). Today, she got the $1,400 deposited to her account by the Treasury. However, I was surprised to see $4,200 deposited to my account, when I expected only $2,800 (for me and my wife). They paid for my daughter twice, $1,400 to her (based on her 2020 return) and $1,400 to me (based on my 2019 return that showed her as a dependent). They have the social security numbers, so I assumed the IRS and Treasury would have figured this out. I have searched and searched, but am unsure whether this overpayment will be clawed back or not. I can't even find a mechanism for returning it (and getting credit for doing that if they later do say I owe it to them). I've read if your 2019 income made you eligible, but your 2020 income (if you file after the stimulus) would have made you ineligible, they won't claw back the stimulus they sent. Stimulus money for people that died between the tax return and the stimulus disbursement does have to be returned to the treasury. I can't find guidance for our situation. There must be a fair number of people with college kids that have the same scenario. This question  seems at first to ask the same thing, but it doesn't include the key point of overpayment by the Treasury. Contracting with Levi-Civita (totally antisymmetric) tensor How to open Nautilus (File Manager) preferences? What part of a multi-type damage roll is reduced by a non-type-specific effect? Effects like  (PHB, p. 54) and Spirit Shield (XGtE, p.  10) reduce damage by a roll, irrespective of damage  (PHB 196). However, single damage rolls can have multiple damage types, as confirmed (for wording) by Jeremy Crawford in .   How do you know which part of the damage is reduced?   This could actually make a difference to the amount of damage taken if, for example, the creature taking damage is resistant to one or more of the damage types involved.       Cutting Words: ... When a creature that you can see within 60 feet of you makes an attack roll, an ability check, or a damage roll, you can use your reaction to expend one of your uses of Bardic Inspiration, rolling a Bardic Inspiration die and subtracting the number rolled from the creature's roll.   Using this ability to expand upon the examples found in  and :     Barny, an Ice Devil (MM, p.  75) hits Bobby, rolling 9 slashing damage and 11 cold damage.      Bobby's ally, Vera, is a level 10 bard of the college of Lore, and uses her Cutting Words ability on the attack's damage roll. She rolls a 9, which is subtracted from the Barny's damage roll.      Bobby is wearing his Boots of the Winterlands (DMG, p.  156), giving him resistance to cold.   We know that "resistance and then vulnerability are applied after all other modifiers to damage" (PHB, p.  197) and both slashing damage and cold damage are treated as "one big damage roll" (see the JC tweet), so is all the 9 slashing damage removed by cutting words, and then the cold damage halved for 5 total damage, or is 9 of the cold damage removed by cutting words, leaving 2 to be halved for a total of 1 + 9 = 10 damage taken by Bobby?   Who makes this decision?  When an effect (like cutting words) reduces damage without specifying type from a source containing multiple damage types, what part of the damage is reduced?