The value of a limit
Calculate Limit 0f nested square roots
Is it ok to ask to explain a certain piece of code on SO? Is it OK to ask on SO for help in explaining someone else's working piece of code, from Open Source projects or library examples etc.? Or does this belong somewhere else? I've seen the word static used in different places in C code; is this like a static function/class in C# (where the implementation is shared across objects)? Placing finger twice on Finger Scanner on iPhone 6 plus changes view Remove appx package for all users Fresh Windows 10 install. Somehow the MSN Weather app became corrupted. (Unable to launch) I removed the app with the following Powershell command:     Remove-AppxPackage -Package Microsoft.BingWeather_4.7.118.0_x86__8wekyb3d8bbwe   However, when running     Get-Appxpackage –Allusers   the package is still present. When I attempt to reinstall the app via the Windows Store, the download is skipped and the same corrupted package is installed.  I've tried restarting (many times) and using WSReset to no avail.  What can I do? Thank you! dpkg error: "trying to overwrite file, which is also in..." For example:  $ sudo apt-get install curl Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies: bsh : Depends: libjline-java but it is not going to be installed groovy : Depends: libjline-java but it is not going to be installed rhino : Depends: libjline-java but it is not going to be installed E: Unmet dependencies.   Try 'apt-get -f install' with no packages (or specify a solution).   I get the same or similar errors when I attempt to install clojure1.3, leiningen, and several other packages.   When I try the suggestion made in the error message, this is what happens:  $ sudo apt-get -f install  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages were automatically installed and are no longer required:   diffstat linux-headers-3.2.0-26-generic linux-headers-3.2.0-26 dh-apparmor dkms html2text libmail-sendmail-perl libsys-hostname-long-perl Use 'apt-get autoremove' to remove them. The following extra packages will be installed:   libjline-java Suggested packages:   libjline-java-doc The following NEW packages will be installed:   libjline-java 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. 23 not fully installed or removed. Need to get 0 B/72.0 kB of archives. After this operation, 129 kB of additional disk space will be used. Do you want to continue [Y/n]? Y (Reading database ... 226243 files and directories currently installed.) Unpacking libjline-java (from .../libjline-java_1.0-1_all.deb) ... dpkg: error processing /var/cache/apt/archives/libjline-java_1.0-1_all.deb (--unpack):  trying to overwrite '/usr/share/java/jline.jar', which is also in package scala 2.9.2-400 Errors were encountered while processing:  /var/cache/apt/archives/libjline-java_1.0-1_all.deb E: Sub-process /usr/bin/dpkg returned an error code (1)  $ sudo apt-get upgrade Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt-get -f install' to correct these. The following packages have unmet dependencies:  bsh : Depends: libjline-java but it is not installed  groovy : Depends: libjline-java but it is not installed  rhino : Depends: libjline-java but it is not installed E: Unmet dependencies. Try using -f. Extracting only the BibTex records relevant to the paper My colleague asked me to write a page for a paper he writes. I wrote the page in LyX, compiled it to LaTeX, and sent him the TeX files. Then he reminded me that I forgot to send the .bib file with all the references.  But, my .bib file is huge - it contains over 1000 references (I have a global BiBTeX file for all my papers). The page I wrote uses only about 20 of them.  Is there an automatic way to extract from the bib file, only the records relevant to the current paper? Why is it that if I go to install an add-on from User Preferences > Add-ons > Install from File... and choose a *.ZIP, some add-ons will install, while others will return me to the User Preferences with nothing having happened (as far as I can tell)?  Is there a specific file structure required in the .ZIP? I get many add-ons from GitHub, using the Download Zip button, and even there installation of the actual Zip file only works some of the time. Why can templates only be implemented in the header file? Currently, the only way to link to a revision (clicking "link"), you just get  which shows what the post looked like at that revision:        Personally, I rarely use this and haven't ever found myself in a scenario (as far as I remember) where I would prefer the way it currently works to what I'm suggesting here.  Could we:   Add another link, or Change the current link   Such that it:   Displays the diff on a separate page (I'd prefer this, since the highlight and scroll thing doesn't always work properly - although perhaps it has something to do with loading images, so it might not apply here, or, if it doesn't, we could fix that instead), or          Highlights and scrolls to a diff, like what is done when you link to an answer () How do I change my Minecraft username during the 30-day restriction? Do newer laptop batteries still need to be drained before recharging? 10 years ago when I was doing hardware support it was best practice to fully drain a laptop battery prior to recharging in order to maximize its life.  Is this still the case or can a battery now be recharged at any point without worrying about shortening the lifespan? What is the closed form of $\int e^{x^2} \, dx$? How can I do a closed form expansion of $\int e^{x^2} \, dx$? Please be specific as to which method I must use. Why KL divergence is non-negative? Why is KL divergence non-negative?  From the perspective of information theory, I have such an intuitive understanding:  Say there are two ensembles $A$ and $B$ which are composed of the same set of elements labeled by $x$. $p(x)$ and $q(x)$ are different probability distributions over ensemble $A$ and $B$ respectively.   From the perspective of information theory, $\log_{2}(P(x))$ is the least amount of bits that required for recording an element $x$ for ensemble $A$. So that the expectation $$\sum_{x \in  ensemble}-p(x)\ln(p(x))$$ can be interpreted as at least how many bits that we need for recording an element in $A$ on average.   Since this formula puts a lower bound on the bits that we need on average, so that for a different ensemble $B$ which brings about a different probability distribution $q(x)$, the bound that it gives for each element $x$ will surely not bit that is given by $p(x)$, which means taking the expectation, $$\sum_{x\in ensemble}-p(x)\ln(q(x))$$ this average length will surely be greater than the former one, which leads to $$\sum_{x\in ensemble }p(x)\frac{\ln(p(x))}{\ln(q(x))} &gt; 0$$  I don't put $\ge$ here since $p(x)$ and $q(x)$ are different.  This is my intuitive understanding, is there a purely mathematical way of proving KL divergence is non-negative? The problem can be stated as:  Given $p(x)$ and $q(x)$ are both positive over real line, and $\int_{-\infty}^{+\infty}p(x)dx = 1$, $\int_{-\infty}^{+\infty}q(x)dx = 1$.  Prove $$\int_{-\infty}^{+\infty}p(x)\ln\frac{p(x)}{q(x)}$$ is non-negative.  How can this be proved? Or can this be proved without extra conditions? Is 'efficate' a word in English? I routinely hear the word "efficate" being used.  For example, "The most powerful way to efficate a change in the system is to participate."  I do not find entries for this word in common English dictionaries, but I do not have an unabridged dictionary.  I have checked the OED (I'm not sure if it is considered unabridged), and it has no entry for "efficate".  It does have an entry for "efficiate", which is used in the same way.  Wordnik has an  for "efficate" with over 1800 hits, thus providing some evidence for the frequency of use.  I personally like the word and find the meaning very clear and obvious when others use it.  If it's not currently an "officially documented" word, perhaps its continued use will result in it being better documented. Is it possible to transform an armature into a curve? I have a tunnel that I want a camera to go through, and want to replace the armature with a curve so it moves exactly on that path. I'd like the camera to also rotate to follow the bends of the tunnel. Using cycles.   Appreciate it, the problem I'm having now is that the camera follows the path, but after each turn, kind of snaps back or bumps, like a recoil of sorts. I reduced the size of the turns, but it still happens. And within the graph editor I can't change the interpolation mode, it's all greyed out. The only reason it looks kind of decent is because the camera is set to 15mm. Any ideas? Possible bug in sidebar "question asked:" date I use 'Helvetica' as my font and build my document using Texmaker. But the PDF generated has jagged edges while using this font and when I use a different font (say Times or even Helvetica sans-serif) it builds just fine.     Please suggest if there is anyway I can get over this. The problem with these jagged edges is that it appears very dull and unreadable at 100% resolution.  OK guys, now here is the MWE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% HEADER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[a4paper,twoside,12pt]{book}  %% Language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} %\usepackage[utf8]{inputenc} \usepackage{graphicx,color,subfigure}  %% Line Spacing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{setspace} %\singlespacing        %% 1-spacing (default) %\onehalfspacing       %% 1,5-spacing \doublespacing        %% 2-spacing  %% Other Packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[left=1.5in, right=1.5in, top=1in, bottom=1in, includefoot, headheight=13.6pt]{geometry} \usepackage[pagebackref=true,breaklinks=true,letterpaper=true,colorlinks,bookmarks=false]{hyperref} \usepackage{helvet} \usepackage[square,numbers]{natbib} \usepackage{hyphenat} \usepackage{fancyhdr}   \begin{document}  \pagestyle{empty} %No headings for the first pages.  \cleardoublepage %The first chapter should start on an odd page.  \pagestyle{plain} %Now display headings: headings / fancy / ...  \pagebreak  %------------------------------------------------------------------------ \chapter{Divorce}   A major change that has occurred in the Western family is an increased incidence in divorce. Whereas in the past, divorce was a relatively rare occurrence, in recent times it has become quite commonplace. This change is borne out clearly in census figures. For example thirty years ago in Australia, only one marriage in ten ended in divorce; nowadays the figure is more than one in three (Australian Bureau of Statistics, 1996: p.45). A consequence of this change has been a substantial increase in the number of single parent families and the attendant problems that this brings (Kilmartin, 1997).   \end{document} Can a ring without a unit element have a subring with a unit element? A girl who transcends time I remember quite a bit, but can't seem to find the title or (female) author.   A girl accompanies her father as he captains a mission to travel at near-light speed in order to experience the effects of time dilation and return to Earth 100 years into its future. She leaves behind her boyfriend (Tal or Tel or something), who promises he'll find a way to stay with her despite the time travel that will render him, well, dead before her return. She's accompanied by a close friend who is deaf but lip-reads and speaks so well as to occasionally fool others into believing she is hearing. They spend a lot of time in the ship's garden. I believe he ends up either getting on a different ship to survive into the future via time dilation, or else having himself frozen. Either way, if I recall correctly, Earth isn't doing well at all by the time the mission with the girl returns. There's been a war or some other disaster. There's an extended period of vague, ambiguous, existential crap in which the girl (now a woman) eventually ends up transferring her consciousness into her own daughter, presumably in order to go on living. Everything wraps up somehow and the girl and her boyfriend walk together hand in hand on a desolate planet into the sunset near the end of time.   It was all really rather trashy and silly, I remember, and took itself entirely way too seriously, but I'd like to at least know what it was so I could read it again. Either it'll be worth a laugh, or it'll turn out to be surprisingly good. Why singularity in a black hole, and not just "very dense"? Why does there have to be a singularity in a black hole, and not just a very dense lump of matter of finite size? If there's any such thing as granularity of space, couldn't the "singularity" be just the smallest possible size?