Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
Consider a set $A$ of $10$ integers, $A = \{a_1,a_2, \ldots ,a_{10}\}$. Prove that there is at least one subset of $A$ whose sum is divisible by $10$.
Saving memoization to disk Why are some applications so hard to find in the Ubuntu Software Centre? Some applications don't pop up in the search even when you type in their name. Take for instance Sushi. When you type in "sushi" into the search box, it fails to throw up the application. Only when you type in "gnome-sushi" does it appear. This is despite the fact that the application has "sushi" by itself in the application description. There are other applications which don't spring to mind right now, but I've discovered before. How to append something to an array? Is the notorious $n^2 + n + 41$ prime generator the last of its type? How to delete column/field in PyQGIS? I am taking a course in Mathematical Methods for physicsPhysics (Junior Level).   We are working from   > Mathematical Methods for physicists, George B.Arfken .    I just need online resources covering ( Matrices, Determinants, Vector Analysis, Tensors and differential forms and Vector spaces...etc) to study and understand from. Convert month name to month number in SQL Server Show that the locus formed by z in the equation $z^3 + iz = 1$  never crosses the co-ordinate axes in the Argand plane. Further show that $$|z| = \sqrt{\dfrac{-\Im(z)}{2\Re(z)\Im(z) +1}}$$  Concept: $z=x+iy$ $z^3=(x+iy)^3=x^3-3xy^2+i(3x^2y-y^3)$ $iz=-y+ix$ Combined equation is $x^3-3xy^2-y-1+i(3x^2y-y^3+x)=0$ How do we proceed from here onward? How are Dementors created/born? This is inspired by some discussions in .  In the Harry Potter universe, how are Dementors born?  Or are they artificially created by some magical means? I don't understand the fact that let's say hypothetically I was pushing a block on a frictionless surface, and I kept applying the same force on the object how it would keep accelerating! Wouldn't there have to be a certain velocity where it would stop getting faster? If not then what is actually acting on the object to cause it to accelerate infinitely? Apex PMD: Problem: Validate CRUD permission before SOQL/DML operation Background   I am using the Apex PMD plugin for VS Code and it's giving me this problem:     Validate CRUD permission before SOQL/DML operation   For this line of code:  insert contentVersion;   Which is part of this method:  private void attachReport(Id recordId) {      ContentVersion contentVersion = new ContentVersion(         versionData = Blob.valueOf(buffer.toStr()),         title = 'Import Report',         pathOnClient =  StringUtils.format('/Import-Report-{0}.txt', DateTime.now().getTime()),         FirstPublishLocationId = recordId);      insert contentVersion; }   Questions    Why am I getting the problem? What should I do to not get the problem?     Reference Don't let the association bonus be given away as bounties When a user with at least 200 rep on any Stack Exchange site registers a new account on another SE site, they immediately receive 100 rep on that site as an .  This is a deliberate feature to give users who are already familiar with how the SE platform and community works a bit of an extra boost (e.g. letting them upvote and comment immediately), and it's pretty much working as intended. What's probably not intended is that, currently, this bonus rep can be given away as . In fact, because awarding bounties currently requires only 75 rep, any user with 200+ rep on at least one site can join another site, receive the 100 rep bonus, and immediately award it all as a bounty to another user, without having to earn any actual rep on the site at all.  Not only does this seem contrary to the design intent of bounties (and of the association bonus), but it also seems ripe for potential abuse. (In fact, the only thing stopping a sockpuppet ring from gaining unlimited rep this way is the fact that the bounties would likely be sooner or later noticed by mods.) It's also possible for experienced users to (more or less) accidentally bounty their reputation so low that that they lose access to basic site features that they'd normally have due to the bonus.  Arguably, of course, this is entirely the user's own fault, but it can still be .  Also, this behavior , which currently require 110 rep to answer for users with the association bonus. The fix I'd like to suggest is simple:  If a user has been awarded the association bonus, don't let them award a bounty that would take their rep below 100.  Of course, it would still be possible for users with the bonus to drop below 100 rep via other means, e.g. by having their posts downvoted.  But they wouldn't be able to just give away this baseline rep to other users any more. Photons travel at the fastest speed in our universe, the speed of light.  Do photons have acceleration? Given two sets$$A=\{1,3,5\}\quad,\quad B=\{1,3,8\}.$$ Then I compute the $A\setminus B=\{5\}.$   But my book$^\dagger$said: ... . Also, observe that $x\notin A\setminus B$ does not mean that $x\notin A\lor x\in B$. Why?  I don't know how to explain the Why, please give me some example.    $^\dagger$, second edition, page $4$.  EDIT: My intuition tells me that it does mean that. I guess there is some special case about null-set or about the restriction of the universal set. How can I render an edge only mesh as solid lines? How do i know which wheels will fit my bike? Background reflected in glossy glass, but I didn't set it I've made a roughness 0 glass pane, when I'm in lookdev mode it's reflecting a background that I didn't put there. I know I could just ignore it, but I'd rather be able to see what it'll mostly look like when I'm in the later stages. I also just want to know how on Earth I managed to set this background without realising it  Reflection completely ignores any objects I put in front of it. If I placed this glass inside my house, it would still just reflect trees (This is the point where I felt I couldn't ignore it - reflections are going to play a big part in my project and I don't want to be in render mode all the time)  The nodes are the default glass BSDF, except I set roughness to 0  The glass is set to 20mm thick, if that makes a difference  The background moves with my perspective and moves when I relocate the glass  I have a few HDRI's on my PC, but none look remotely like this   Also, I'm using cycles as I find Evee buggy as hell Seeking English term for relationship between two members of extended family? Here at the Genealogy and Family History Stack Exchange we see many questions about relationship mapping which is also known as:   relationship calculation kinship terminology etc   If you are just trying to understand how to calculate "cousins and removes" then  provides an excellent guide.  However, if you are seeking an English term for a more complicated relationship between two members of an extended family, rather than asking a question like:          site users are encouraged to first review the answers below.    Note: This Q&amp;A arises from  and is set to  to help make it canonical. First post review queue: answers are questions, questions are answers I believe there is a typo in the  review queue. When reviewing a question, the information message asks the user to review the answer. Take a look at the image below.    Similarly, when an answer is posted in the queue, the description box calls it a question instead. Has anyone else noticed this? When i put the code $(f_{\mathcal{X}},f_{\mathcal{X}}^{\partial})$ I get the following:  But I want the subscripts to be aligned. How can I do this?