Environment definitions with arguments in \enddef
Why can't the end code of an environment contain an argument?
Creating random numbers with no duplicates The class will be over in 10 minutes. The class will be over after 10 minutes.  I know the first is correct but why? Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous ?  Why $v(a)  \leq v(ab)$ is not needed?  How we can deduce from the first one? The verbs dare and need do not require auxiliaries when used in the interrogative; for example, “need I?” is as acceptable as “do I need?”  Excluding the auxiliaries themselves (like be, do, have), are there any other such verbs that work that way? 9 rows is just way too small by default. Is this a text-editor for ants? Subgroup of $\mathbb{Q}$ with finite index counting number of specific string in each row Protagonist becomes the avatar of an alien deity and has to cope with adversary god I read this at least 20 years ago, and I believe it was originally published in the '60s.   The main character is a human, but somehow "inherits godhood" from an alien, whose species is very long lived. IIRC this is one of the old-style god thingies, i.e. "god of thunder" not "omniscient omnipotent omnipresent transcendent being".  The plot somehow revolved around identifying and fighting some enemy which, I believe, was in turn a member of the alien species who acted as the avatar of the opposite god in the alien pantheon.  The only thing I remember for sure is that the enemy was identified as "green green" or "gringrin" (sadly, I read this in translation so I am not sure what the original meant) What is integration by parts, really? Integration by parts comes up a lot - for instance, it appears in the definition of a weak derivative / distributional derivative, or as a tool that one can use to turn information about higher derivatives of a function into information about an integral of that function. Concrete examples of this latter category include: proving that $f \in C^2(S^1)$ implies that the Fourier series of $f$ converges absolutely and uniformly, and the Taylor series expansion with the integral formula for remainder.  However, I don't feel like I really understand what integration by parts is really doing. To me, it is just an algebraic trick that follows from the fundamental theorem of calculus and the product rule. Is there some more conceptual way to think about it?  How do you think about this useful idea? Terminal command 'login' fails with error message Coming from Mac OS X, there is a possibility for every ordinary user to open Terminal and type in 'login' to change to a different user account.  When I do this with Ubuntu, it provides the following error message:  login: Cannot possibly work without effective root   Is there any way to remedy this?  Which file do I need to edit and with what to enable the use of this command (even for a standard user)? I tried installing VLC Player yesterday, and I got the Requires installation of untrusted packages error.  I searched for hours for a solution to this problem, and finally came upon a suggestion that said to change servers for downloading updates from.  I did this, and it gave me a 404 error when I clicked on "Check" in the Update Manager.  I tried switching my server back to the main one (and after that, several other ones), but I am now still getting a 404 error:   And the other error I get when downloading or updating:   Edit: Output of cat /etc/apt/sources.list:  deb-src http://us.archive.ubuntu.com/ubuntu/ precise main restricted #Added by software-properties  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to # newer versions of the distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise multiverse universe #Added by software-properties  ## Major bug fix updates produced after the final release of the ## distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise-updates main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-updates restricted main multiverse universe #Added by software-properties  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise universe deb http://us.archive.ubuntu.com/ubuntu/ precise-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team.  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse #Added by software-properties  deb http://us.archive.ubuntu.com/ubuntu/ precise-security main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-security restricted main multiverse universe #Added by software-properties deb http://us.archive.ubuntu.com/ubuntu/ precise-security universe  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. deb http://archive.canonical.com/ubuntu precise partner deb-src http://archive.canonical.com/ubuntu precise partner  ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software. How to code an automated bot that can browse and do operations on a webpage Story about a trip to a Valley of Sound I read a short story, can’t remember if it was part of a larger narrative or just on its own.  It was about a crew that was taking a bunch of space tourists to a planet that had plants with seeds in glass-like structures that make certain sounds. The main character in this story feels connected to this planet because there’s a Valley of Sound, where there’s a large number of these glass plants that make all sounds imaginable.  People can almost pick out a loved one’s voice for instance. I absolutely love this concept but can’t for the life of me remember what the story/book was called! The model used to open the store is incompatible with the one used to create the store Google isn't surfacing Events rich snippets in SERP when JSON-LD Structured Data is valid Google confirms our site has thousands of valid MusicEvent structured data objects presented using JSON-LD, as indicated in the Structured Data section of Webmaster Tools. However, rich snippets for the events do not show up in any search result pages. The Rich Cards tab in Webmaster Tools says:     We did not find any structured data for rich cards on your website.   The structured data is valid with no errors in the Structured Data Testing Tool. We do generate some warnings occasionally for missing endDate and price fields. Comparing our code to a survey of other sites whose rich snippets do appear, we are not doing anything unique in terms of our markup.  The data has been there for months, in fact over the months we've tried also using Microdata format. The Structured Data section indicates that many pages were crawled this week.  Besides SDTT validation, what else can I check to troubleshoot this issue? Send values from one form to another form Separability over intersection of intermediate fields Let $E\mathop{/}F$ be a finite-degree normal extension of fields. Let $K$ and $L$ be intermediate fields (that is, $F\subseteq K\subseteq E$ and $F\subseteq L\subseteq E$) such that $E$ is separable over both $K$ and $L$. Show that $E$ is separable over $K\cap L$.   So I was thinking that if $f=\min_{K\cap L}(\alpha)$. Then $\min_{K}(\alpha)$ divides $f$. But if $f$ has repeated roots then I don't see what goes wrong.   Thanks! Why do high resolution cameras shoot stills at high resolutions, but only typically shoot video at 1080p which is about 2 megapixels?  For example I have a Sony-NEX 6 which can shoot stills at 16 megapixels but only 1080p by 1920p video.  Also how do digital cameras separate the frames in video if the lens shutter never closes?  And if you can shoot video at 30 fps or 60 fps then why can't cameras have a continuous drives at 30 to 60 fps? I am using MikTex 2.9 and TeXstudio for my TeX preparation. I would like to set the path to my figures folder, which contains all the figures, plots etc. required for my work.   I used \graphicspath to set the directory, but it gives me an error message:  \documentclass[12pt]{article}  \usepackage{graphicx}  \graphicspath{D:/LATEX/Reports@IIT/figures}  \begin{document} \includegraphics[width=4.5cm,height=4cm,angle=0]{logo.jpg}  \end{document}      Error: Package pdftex.def Error: File `logo.jpg' not found   However, when I prepend the filenames of the images with the same path in the \includegraphics command, it works just fine:  \documentclass[12pt]{article}  \usepackage{graphicx}  \begin{document}  \includegraphics[width=4.5cm,height=4cm,angle=0]{D:/LATEX/Reports@IIT/figures/logo.jpg}  \end{document}   Why is \graphicspath not setting the path? How did the house elves start serving wizards? How/Why/When did the house elves start serving wizards? I tried on my own to find the answer but I couldn't find anything relevant to my subject but I am bad at searching.