Let $R$ be a finite ring such that $x^2=x$ for all $x$ in $R$. Prove that $R$   has unity.   I was able to show that it was commutative.  Proof:  $x^2=x$ $x^2-x = 0$ $x (x-1) =0 $  thus $x = 0$  or $x = 1$. Since   $x\cdot 1 = x$. 1 is the unity of $R$. Thus $R$ has unity.   I feel like there is something wrong with my solution.
Question: If $R$ is a finite boolean ring, then show $R \cong \mathbb Z_2 \times \mathbb Z_2 \times \cdots\times \mathbb Z_2$.   I know that   $\mathrm{char}(R) =2$  $R$ has $2^k$ elements for some $k$  (this is because, if $p\neq 2$ is a prime with $p\mid|R|$, then there exists a non-zero $x \in R$ s.t. $px=0$ and $p $ is odd $\implies x=0$, contradiction).   Does this suffice to answer my question?
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable? Can the definite article be omitted when referring to a person qualified by a noun? Polynomial in $n$ variables What is the fastest way to parse & split XML content with huge file size (800MB UP) into several xml files in Java Do I need a transit vsa in Kuwait; what about checked baggage? Convert a number to a string with specified length in C++ Unzip File: Permission Denied I am trying to unzip a file (Facebook download-your-info zip file), but here's what I got:   Is there a way I can force-unzip it?  Update: I tried sudo unzip file.zip -d destination_folder in terminal, and it unzipped the file, but what came out, all the files have size 0 bytes:   Update 2: I do have permission to the directory and the file.    (I'm really sorry if my question is asked badly. Let me know down in the comments :) ) One of the products being shown a CES is a  intended to let you charge a tablet from a laptop USB port that normally wouldn't work because it didn't provide enough power.  The CNET writeup implies that it's actually boosting the power output from the port beyond the normally available amount.  This seems improbable to me because the ports should have current protection to protect themselves from shorts.  Also, if it was possible to bypass the current limit externally, I'd've expected at least some tablet vendors to have included the ability to do so directly in their cables.  One possibility that occurs to me is that the dongle is just spoofing responses to the tablet when it queries the laptop about the maximum power it can deliver while only providing a trickle charge that the tablet would otherwise reject as too slow to bother with. Easiest way to solve $y''+y=\frac{1}{\cos x}$ Why did I receive a message saying I have been granted a privilege, yet I don't have enough reputation? The site shown a message saying I have been granted a privilege, but the reputation required for that privilege is higher than the one I actually have. What happened? 'AND' vs '&&' as operator Careers ad asking if I want to work where I already work? What do you call somebody who asks a question and somebody who answers a question? What do you call somebody who asks a question and somebody who answers a question?  I have exhausted the thesaurus with no real luck... any ideas?  EDIT: It is in reference to this - or any other StackExchange - site in which the question is posed by X and answer is submitted by Y.    EDIT 2: In the context of StackExchange, and the fact I need plurality (something I neglected to mention oooops), I have decided upon "Posters" and "Respondents"... 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I understand that the question has been asked before () but the situation has changed and I believe it warrants asking again. How to play blu ray .mkv files on ubuntu 20.04 LTS? How to play blu ray .mkv files on Linux? e.g:1080p.BluRay.DD5.1.x264-NTb.mkv Install ffmpeg in Ubuntu 12.04 LTS Background :  I used ffmpeg to merge two videos side by side. First I install ffmpeg by following command as it suggest by Ubuntu itself.  sudo apt-get install libav-tools   or   sudo apt-get install ffmpeg   But then I realize it is not the correct version since it doesn't support for -filter_complex and few other functions.   After a few hours researcher I found  and I succeed with video conversion as well. As per that article, it is suggesting we need to build it our own.        Question :  What is easiest way to install that ffmpeg version (which is support for -filter_complex ) without following all those steps ? Do Chinese citizens require a visa to go to Hong Kong for less than 7 days? What makes scaling pixel art different than other images? Recently I was coaching a developer who's new to making pixel art games, and realized there's some "conventional wisdom" around scaling pixel art that's not obvious to a newcomer, and might not be well documented. So, here's an attempt to fix that....     I've heard I should only scale pixel art by 200%, 300% etc. not in-between sizes like 120%   Why is that? Shouldn't scaling "just work" the way it does with other images? What if I really need to make my character just a fraction larger or smaller to get the right gameplay or look? How do I fix this?  I'm told it's "bad" to use pixel art at different scales in one game - why?    For example, if I scaled up my character so each sprite texel is 4x4 screen pixels, while my background art is scaled up so each sprite texel is 6x6 screen pixels. Isn't a pixel a pixel at the end of the day? Find the Unit Vector of a Three Dimensional Vector