Is there any difference with/without @override java
When do you use Java's @Override annotation and why?
Is every metric space a subspace of some connected metric space? Is every metric space a subspace of some connected metric space? If the space itself is connected then we're done, but if not then I think we can extend our metric space to make it connected.  I'm not sure whether this will work or not, but intuitively I think the answer is yes. During the end credit scene of Spider-Man: Far from Home, we see that,      Nick Fury and Maria Hill are two Skrulls, Talos and (presumably) his wife.   And we also see that,      Nick Fury is in a spaceship like structure, presumably away from Earth.   So that begs the question,      How long has Talos been impersonating Nick Fury? Is it since the events of Captain Marvel or since Avengers: Endgame or sometime in between? Finding how multiplication and addition behave on $\mathbb{F}_4$ without any result I'm currently tutor in an undergraduate course and the students are asked to find how addition and multiplication behave on the field with 4 elements: $\{0,1,x,y\}$. In the solution the teacher gave me, he uses the fact that $(\mathbb{F}_4^*, \cdot )$ is cyclic with order 3 to find that $x$ and $y$ are both generators and that $(\mathbb{F}_4,+)$ is a group of order 4 to deduce that $0=1+1+1+1=(1+1)(1+1)$ and hence, $(1+1)=0$ since a field is integral.   However, I'm not satisfied with this reasoning because this question is asked to student in first year and they juste have been introduced to fields (and this was part of an analysis course so they won't see any result soon). So I tried to find how it behaves by myself, using as few results as possible.  Multiplication is the easy part, $0\cdot a$ and $1 \cdot a$ is trivial for all $a\in \mathbb{F}_4$. Then, $x\cdot y\not = 0$ because it is invertible, and it can't be equal to $x$ or $y$ because that would imply the other element to be equal to $1$. Hence, $x\cdot y=1$. We are left to find what is $x^2$ (and similarly, $y^2$). $x^2$ cannot be $0$, nor $x$. If $x^2=1$, then $y=(x^2)y=x(xy)=x\cdot 1=x$. Contradiction. Hence $x^2=y$ and by the same reasoning, we have $y^2=x$.  It was easy with the multiplication, but I can't figure out any non-trivial result concerning addition. My intuition tells me that distributivity should be used here but I'm feeling like it's just converting a problem into another one because we don't know anything about addition.  Does anyone here have an idea of how addition can be "found" without using any advanced result (or as few results as possible)?  Thanks in advance. What is the simplest way to convert char[] to/from tchar[] in C/C++(ms)? This seems like a pretty softball question, but I always have a hard time looking up this function because there seem there are so many variations regarding the referencing of char and tchar. Omission of definite article with musical instruments What is the rule for omitting/including the definite article in the following sentences:     I used to play piano.   I used to play the piano.   I would pick the first sentence, but I've heard people say the second sentence even when they are not referring to a specific piano. Which one is correct? How do I create an Excel (.XLS and .XLSX) file in C# without installing Microsoft Office? How can I create an Excel spreadsheet with C# without requiring Excel to be installed on the machine that's running the code? What is the maximum or minimum tire width I can fit on my bicycle We often get questions on bicycles.stackexchange about fitting wider or narrower tires to bicycles. We have a large number of these with answers suiting the specific bike or style of bicycle in question, but I have been unable to find one that provides a generic answer covering off all things that need to be considered. For most bicycles, the answer is the same regardless of the specific style and sizes of tires in question.   This is intended as a canonical question that we can point closed questions to. Google analytics: Tracking Not Installed A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$ How do I fix this "E: Type '*' is not known on line * in source list ..." update error? Installing Guest Additions causing problems I am trying to install Guest Additions in VirtualBox with Windows XP host and Ubuntu 12.04 guest. I followed the above steps:  Devices-&gt; Insert Guest Additions CD Image. After that I locate the folder /media/VBoxAdditions4.3.4_91027/ and run sudo ./VBoxLinuxAdditions.run   I want to be able to create shared folders and adjust the resolution of the screen. I achieved to do the first issue, but I couldn't do the second one. I didn't get any message, however it is not possible to change the resolution of the screen and I cannot switch to fullscreen. What am I doing wrong?  I found in the instal log the following message: unknown version of the X Window System. I've tried the solution of the proposed link but I got the following message:  Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies: virtualbox-guest-x11 : Depends: xorg-video-abi-11                     Depends: xserver-xorg-core (&gt;= 2:1.10.99.901) E: Unable to correct problems, you have held broken packages.   I tried also to install with the command sudo apt-get install virtualbox-guest-dkms but nothing is changing. During the installation of dkms I got the message: Error! Bad return status for module build on kernel 3.13.0-32-generic(i686). Different and opposing voltage sources? &ndash; Schematic created using   The diagram above, the voltage sources are equal and wired parallel, they would increase the current(2x) flow to the load(R), but what about this case:          Are the two voltage sources in series now? How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups? I am working through Paolo Aluffi's new GSM text on my own (self-study). On page 63, he asks the reader to     Prove that $\Bbb{Q}$ is not the direct product of two nontrivial groups.   For some context, this is an exercise following a section entitled "The category Grp".  I am assuming that he means "is not isomorphic to the direct product of two nontrivial groups", and I can see two possible ways to proceed with this proof, but have been unsuccessful with either approach.    Approach 1:  Show that the additive group of rationals has a property that is preserved by isomorphism that the direct product of two nontrivial groups does not have or vice-versa.  This seems challenging unless I can significantly narrow down the properties that a direct product of two nontrivial groups that was isomorphic to $\Bbb{Q}$ would necessarily have.  Approach 2:  Considering the section in which this question occurs, show that if $G$ and $H$ are nontrivial groups and $\Bbb{Q} \cong G \times H$, then there are homomorphisms $\varphi_{G}:\Bbb{Q} \rightarrow G$ and $\varphi_{H}:\Bbb{Q} \rightarrow H$ which do not factor or do not factor uniquely through the product $G \times H$.  This would be a contradiction, as $G \times H$ is a final object in the category Grp.  I would greatly appreciate suggestions on how to proceed further with either of these approaches or with alternate approaches. Is it possible to annotate equations (i.e. arrow signs/curly braces) to define each variable? I have quite a simple question. I was wondering if it was possible to do something like this in LaTeX:    But formatted a little more nicely.  It doesn't need to be arrows necessarily. Just some form of annotation marker. Discrepency in unanswered questions counts On , I notice that if I use the lower &quot;unanswered&quot; tab (the one in line with &quot;All Questions&quot;), the count is 1,432 questions. If I use the upper &quot;Unanswered&quot; tab (in line with the site title), I get 1,383 &quot;questions with no upvoted or accepted answers&quot;.  This changes the options in the lower tab, one of which is &quot;no answers&quot;.  Clicking here, I now get 1,083 &quot;questions with no answers&quot;. If I run select Id from Posts where PostTypeId=1 and AnswerCount=0;  in the , I get 1158 rows back. Which of these is correct, and why is the first one (1,432) so much higher than the others?  I understand that the numbers may only be updated periodically, but that difference in particular seems much too great for this to be the reason. To clarify:  1,432 is the number of &quot;unanswered questions&quot;. 1,383 is the number of &quot;questions with no upvoted or accepted answers&quot;. 1,083 is the number of &quot;questions with no answer&quot; 1,158 is the number of questions with no answer in the data explorer.  This is not live data, but that means it should be smaller, not larger, than 1,083.  I promise we did not offset this with answers to the tune of 80 questions this week.  The first three are obviously live because they fluctuate. The difference between the first two is ~50, implying they actually don't refer to the same thing, and the difference between the last two seems too great (and in the wrong direction) to be explained by the a live vs. data explorer source. Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$ How should different sized RAM be added to iMac? I have a mid-2011 iMac which came with 4GB RAM (2x2GB). I just bought 8 GB (2x4GB) and added it to get a total of 12GB. The current configuration is as follows:    Given that the RAM is a different size, do I have the optimal locations for the different RAM chips? At the moment what I did was to simply add the 2 new sticks of RAM in the two empty slots. What is a meta for? A guest at my house over the weekend stood puzzled next to my driveway. &quot;What is that for?&quot; she asked, pointing to a framework of 2x4s and hardware cloth perched on an old tire amid piles of sand. &quot;Sifter.&quot; I said. &quot;For what?&quot; &quot;For sifting gravel.&quot; &quot;Why?&quot; &quot;To line walking paths, such as the one you're standing on...&quot; Spend enough time working with something, and it's easy to forget how strange and unnatural your makeshift tooling can appear to those unfamiliar with it.  Such is the nature of these meta sites. For 5 years, we've been directing folks to them for discussion and feedback, to commune with their community, hash out misunderstandings, propose changes and document the current state of things. And... We haven't always been good about helping them get past the initial shock and confusion of dealing with this system. This has manifested in several unfortunate behaviors:  Downvoting of legitimate support questions - those that are not duplicates and reflect an actual bug or honest misunderstanding of how the system operates. Folks who are acting in good faith should be treated as such - , not shutting them down.  Closing questions that seek input and discussion from the community - in hindsight, adding &quot;primarily opinion based&quot; as a close reason on meta sites was... a terrible idea. The old &quot;not constructive&quot; close reason made some sense for rants and so on, but for a discussion site closing down questions that solicit opinions is just silly. Here on MSE, we prefer the following off-topic reason instead:  This question does not appear to seek input and discussion from the community. If you have encountered a problem on one of our sites, please describe it in detail. See also:    The perception that Stack Exchange is disrupting the normal operation of the site by talking about future plans - even when those plans involve the community. I talked about this a bit more on , but seeing this kind of backlash toward folks at the company who were trying to be open and receptive to discussion about what they were doing was kinda disheartening - we need to be doing more of that, not less.  A reluctance to ask questions about asking questions - which is about as meta as you can get, and yet we probably get more of these via email than we see on meta, while being the least-qualified to answer them well.   After an increasing number of complaints from both core users and moderators on a number of sites, we're taking a hard look at how we can improve this situation... Starting with a change to :  Meta is for...  ...$SiteName users to communicate with each other about $SiteName (asking questions about how the websites work, or about policies and community decisions) ...$SiteName  users to communicate with Stack Exchange the company (posting bugs, suggesting improvements, or proposing new features), and ...Stack Exchange to communicate with the community (soliciting feedback on new ideas or features, or discussing policies that affect the whole network)  Lots of topics are fair game, as long as they are about the Stack Exchange family of Q&amp;A sites in some way. Any issue that concerns the core Stack Exchange engine that runs all Stack Exchange websites is welcome here.  This replaces the previous bullet list of specific topics, and aims to outline broad purposes with examples for clarification rather than constraining the scope to those examples. So... that's a start. But a documentation change isn't going to change misconceptions that've already built up among newer users. So I'm asking y'all for help: What do you think meta should be used for, and how can we better communicate this intent to new users? I have been running Ubuntu 12.04 for the past few weeks. I recently tried to download and install some files through the Update Manager. It located a few files, downloaded them, but then failed to install them. It gave the error:  installArchives() failed: (Reading database ...  (Reading database ... 80% dpkg: unrecoverable fatal error, aborting:  reading files list for package 'libasn1-8-heimdal': Input/output error   I tried using apt-get upgrade but a similar error was produced:  Reading package lists... Done Building dependency tree        Reading state information... Done The following packages will be upgraded:   icedtea-6-jre-cacao icedtea-6-jre-jamvm openjdk-6-jre openjdk-6-jre-headless   openjdk-6-jre-lib 5 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. Need to get 0 B/34.6 MB of archives. After this operation, 1,024 B of additional disk space will be used. Do you want to continue [Y/n]? y (Reading database ... 80% dpkg: unrecoverable fatal error, aborting:  reading files list for package 'libasn1-8-heimdal': Input/output error E: Sub-process /usr/bin/dpkg returned an error code (2)   Any help would be greatly appreciated. Thanks in advance.  Edit: Here's some extra information that may be useful. My original problem was that the Ubuntu Software Centre would not open. I found that the Update Manager and Synaptic Package Manager also failed to open. They all gave an error along the lines of:   "installArchives() failed: dpkg: error: reading package info file '/var/lib/dpkg/available': Input/output errorError in function:"   After much googling I seemed to fix that problem as the package managers would open again. When I then tried to download and install any updates from the Update Manager I got the error at the beginning of this post. Rotate a point on a circle with known radius and position Having a circle $\circ A(x_a, y_a)$ of radius $R$ and a point on the circle $B(x_b, y_b)$, how can we rotate the point with a known angle $\alpha$ (radians or degrees, it doesn't really matter) on the circle so we will obtain a new point on the circle $C(x_c, y_c)$, like in the image below? How to calculate the $C$ coordinates?   Here the rotation angle is $90 ^ {\circ}$. In this example, $x_b = x_a$, $y_b = R$, $\alpha = 90 ^ \circ$. From the image we see that $x_c = R$ and $y_c = y_a$.  However, I want a general solution for any $A, B, R$ and $\alpha$.