When extending an abstract class I understand why you would have to over ride some methods. But when it comes to interfaces I do not understand why it must be done. If all methods of an interface must be implemented, what is the use of overriding them?.  Im talking about the @Override annotation.
What are the best practices for using Java's @Override annotation and why?     It seems like it would be overkill to mark every single overridden method with the @Override annotation.   Are there certain programming situations that call for using the @Override and others that should never use the @Override?
How can I prove that the set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?  Edit:  This answer came to mind.  Is it correct?  This answer just came to mind.  By contradiction suppose the set is $\{f_n\}_{n \in \mathbb{N}}$.  Define the function $f: \mathbb{N} \to \{0,1\}$ by $f(n) \ne f_n(n)$.  Then $f \notin\{f_n\}_{n \in \mathbb{N}}$. How to include python script inside a bash script Simple question, but one that I've been curious about...is there a functional difference between the following two commands?  String::class String.class   They both do what I expect -- that is to say they return Class -- but what is the difference between using the :: and the .?  I notice that on those classes that have constants defined, IRB's auto-completion will return the constants as available options when you press tab after :: but not after ., but I don't know what the reason for this is... How best to determine if an argument is not sent to the JavaScript function Setting a custom RGB background color in beamer I believe I've correctly followed the manual in defining a custom background color in the example below.     But as the example shows, the background color is black rather than an extremely pale beige.    Could anybody advise what I'm doing wrong please?  \documentclass{beamer} \definecolor{MyBackground}{RGB}{1.0000    0.9451    0.6549} \setbeamercolor{background canvas}{bg=MyBackground} \begin{document} \begin{frame} Hullo world \end{frame} \end{document} Can't flag or close questions on all sites Whenever I try to flag or close a question here, when clicking the submit button the button gets disabled, three dots animating and nothing really happens.  JS console show a single error:  Flagging:     Uncaught TypeError: Cannot read property 'flagSubmitting' of undefined    Closing:     Uncaught TypeError: Cannot read property 'closeSubmitting' of undefined   Please fix, programming questions and spam are beginning to pile up. :(  Update: appears to work fine from within the review system, but otherwise it's the same on Stack Overflow as well Variance of a bounded random variable Suppose that a random variable has a lower and an upper bound [0,1]. How to compute the variance of such a variable? Force ssh to not print "Remote host identification has changed" warning Is there a way to avoid ssh printing warning messages like this?   @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @    WARNING: REMOTE HOST IDENTIFICATION HAS CHANGED!     @ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@   Although the remote host identity has changed but I know it is fine and  just want to get rid of this warning. How best to sum up lots of floating point numbers? BSOD: Driver State Power Failure For the past two weeks, I've been getting this BSOD error on my Lenovo laptop. I have even reset my laptop ("rest this PC"), but it's still happening.  My laptop details:     I have the latest Nvidia driver for my Nvidia Geforce MX150: 431.60 released on 23 Jul 2019.  I have the latest BIOS for my laptop: 8TCN53WW15  released on 15 Jul 2019.     I have run WhoCrashed, it says it says the problem was caused by some driver which could not be identified. If I get to know the problematic driver I will update/uninstall it.  How can I analyze my dump files, so that I can find the problematic driver?  Edit 1: If you get "Oops there was a problem with the network" on google drive page while accessing dump files, just click on download. They will be downloaded. I don't know what's causing this. Cannot Add, Remove, Move, or Drag icons from Dock I'm using OS X Yosemite (10.10.2) and recently I have been unable to drag or move any items on the dock. Right clicking them gives no option for "remove from dock", and the icons cannot be rearranged. New icons cannot be added, old icons cannot be deleted.  I have tried restarting, and resetting dock preferences to default, and killall Dock, as suggested by earlier askers. None of it works.  I heard about problems with PushBullet - but I do not have PushBullet. Just in case, I deleted a lot of random applications. Still nothing works.  I've tried various commands from lots of answerers on other questions. I've consulted the Mac Help pages. Nothing.  Does anyone know how I can resolve this? After resetting my Dock in an attempt to fix it, it is now filled with the default icons too. This is really limiting my productivity. Are the hoses in toilets in Asia something I should know about? I have noticed random bits of hose without proper fittings before I think for example in India and just assumed they are for use by the cleaners or for filling the water jug in .  But Now I'm travelling in Malaysia and Singapore and there are more western toilets than squat toilets in the places I've been yet proper hoses with proper fittings are very common in toilets:  (Hose next to a Western style toilet in my hostel in Chinatown, Kuala Lumpur.)  At one place in Singapore there were even signs on each cubicle door stating whether it contained a western or squat toilet, but also whether there was a hose! (I didn't take a photo of the sign, unfortunately)  This makes me think there is a use for the hose for clients, not just cleaners. But for what purpose? Should I know how to use it as a tourist? Please tell me it's not a kind of alternative to a bidet!  Possibly related is the fact that many toilet floors are awash with water. This can be a big problem if you're not wearing waterproof shoes or have to lower your trousers and keep them dry. Other than this toilets are pretty clean and I've seen both the hoses and the wetness in what I would regard as somewhat "fancy" places. What's the word for the when you suck snot back up your nose? My mom and I say 'soup' like: "Why are you souping the snot back up your nose?" But I realise that this is not accurate. So what's the word? Question: Let $F_n$ the sequence of Fibonacci numbers, given by $F_0 = 0, F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 2$. Show for $n, m \in \mathbb{N}$: $$F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$$   My (very limited) attempt so far: after creating a small list of the values $F_0=0, F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21, F_9=34, F_{10}=55$ i can see that yes it does seem to work for instance $F_{6+3}=F_5 F_3 +F_6 F_4 = 10 +24 = 34 = F_9$. However, I really don't know where to begin as showing that this must hold in general terms. Should I be looking to use limits? Or perhaps induction? What is the best way to solve this? Center of mass in n dimension, possible? Is it possible to calculate the center of mass for some 20-dimension ($x_i, i=1,\ldots,20$) particles? If it is possible, how can I do that? Composition of 2 involutions How can we prove that any bijection on any set is  a composition of 2 involutions ?  Since involutions are bijections mapping elements of a set to elements of the same set, I find it weird that this applies to any bijection.  Thanks for your help ! What is the difference between private and protected members of C++ classes? What is the difference between private and protected members in C++ classes? I understand from best practice conventions that variables and functions which are not called outside the class should be made private—but looking at my MFC project, MFC seems to favor protected. What's the difference and which should I use? How do you keep parents of floated elements from collapsing? Where can I get Blender test builds? I know that  provides downloads for official releases. I see on forums that people use newer versions of Blender. Where can I get newer version of Blender (nightly builds, alpha versions... etc). Range of A and null space of the transpose of A So I'm complete stuck with something. I know it the following statements are true (or at least the seem to be from the results that I got from messing around with it a bit on MATLAB), but I don't understand why they are true or how to show so. Let $A$ be and $m$X$n$ matrix. Show that:  a) if $x \in N(A^TA)$ then $Ax$ is in both $R(A)$ and $N(A^T)$.   For this one I messed around with it with my own examples and I got $Ax=0$, therefore satisfing the statement, but I don't understand what's actually going on.   b) $N(A^TA)=N(A)$  again, makes sense when I see the results in MATLAB, but don't undestand why it works.  c) $A$ and $A^TA$ have the same rank  d) If $A$ has linearly independent columns, the $A^TA$ is nonsingular.  For the last two I have no idea on how to even start showing the relationship. I feel like I'm missing some crucial relationship between $A$ and $A^TA$, but I'm just not seeing it.   I would greatly appreciate any help of sugestions on how to show that these statements are true.   Thank you very much.