log in cpp 14 and 17
Is floating point math broken?
Right identity and Right inverse implies a group Let $(G, *)$ be a semi-group. Suppose   $ \exists e \in G$ such that $\forall a \in G,\  ae = a$;  $\forall a \in G, \exists a^{-1} \in G$ such that $aa^{-1} = e$.    How can we prove that $(G,*)$ is a group? PythonTEX not working on current Overleaf compiler Is there a way to make PythonTEX compile as of today in Overleaf V2 ?  \documentclass[]{article} \usepackage[utf8]{inputenc} \usepackage{pythontex}  \begin{document} \begin{pyverbatim} def calc_ellipticity(theta, delta):     theta = np.deg2rad(theta)     psi = np.arcsin(np.sin(2*theta) * np.sin(delta))/2     return np.tan(psi) \end{pyverbatim} \end{document}   Compiling gives : ? PythonTEX ? Why shouldn't I use getnonfreefonts to install additional fonts? Why shouldn't I use updmap when installing or removing fonts? Why can not upgrade texlive2016 to texlive2017 on windows I have texlive 2016 installed on my windows OS, to use texlive 2017 you need to download it (over then 2.5GO), I think this is a tedious operation every time you  want to pass from an old texlive to a recent one.  My question is is there a posibility just to upgrade texlive 2016 to texlive 2017without removing, downloading, and installinig  the entire texlive? Possible Duplicate:          In a question, I see that each time I refresh the page, the answers were placed in a different order. The question has 3 answers each with zero votes. The users' reputation was something like 6, 1200, and 7300 but these numbers didn't affect the order.  What is the criteria of the sort order of the answers? How is it the Voyagers are a few seconds closer to Earth than earlier? The  of March 01, 2013 put it's distance at 14 hrs 04 mins 23 secs of light-travel time from Earth. A  (earlier today) tweet says it is 14 hrs 04 mins 22 secs of light-travel time from Earth. An  tweet put it still further out at 14 hrs 04 mins 25 secs of light-travel time.  The Voyager 2 tweets on Voyager 1's proximity to Earth too has reduced similarly to  earlier today from  reported on Feb 28 2013  It could quite simply be a typo ... If not a typo then my curiosity is piqued; I was under the impression the Voyagers are outbound from the Solar System now without any major in-system activities now.   How is it the Voyagers are closer to Earth than before? Why is an untranslated string not showing up? In my module I have some custom strings. I use these in the t() function. When I go to admin/config/regional/translate/translate and filter the untranslated strings my custom strings do not show here.  What could be going wrong? In Harry Potter and the Philosopher's Stone, Hermione is in the toilets when Harry and Ron lock in the troll. She lies and says that she went looking for the troll. Why? She could have just said that she was in there because she needed the toilet (she was allowed to be, it's a girls' bathroom) and Harry and Ron came to save her.   Is there a reason she lied? How to add a dot after the section number? I wonder is there any way to change the format of section numbering from 1.1 to 1.1. ? I know this is trivial, but I really need to add one more dot after the section number. Does anybody know how to do that?  Thanks a lot How do I install Geforce GTX 660 in 13.10 Just bought a Geforce GTX 660 and replaced my Radeon HD 5870 (it finally died after 3 years). I'm having terrible problems getting the video card to work. As I only had command line options so far I've ran:  (purged fglrx*)  then  sudo add-apt-repository ppa:xorg-edgers/ppa sudo apt-get update sudo apt-get install nvidia-331  and then I started getting low graphics mode errors. did some searching on my tablet, and I tried several things but what finally worked better was:   sudo apt-get install bumblebee bumblebee-nvidia  However now that I'm logged into my computer finally, I have no access to terminal, no access to the top bar, and hitting Super Key does nothing, alt-f2 does nothing, and I only can post because I tried running WoW and it had an error and the error report opened a link.   All I can see on my desktop is my wallpaper and desktop icons. I can CTRL+ALT+F1, and navigate to the downloaded official nvidia driver, however that won't run because of x-server, and I can't run it from my desktop.   Can anyone help me? $$\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$$  when f is continuous on $[0,1]$  I know it can be proved using bounded convergence theorem but,  I wanna know proof using only basic properties of riemann integral and fundamental theorem of calculus and MVT for integrals ...   Thank you. Body Diode of a MOSFET So for some MOSFETs, specially with Power MOSFETs, the body diode is a flyback diode that (as far as aI can tell) can be conveniently added to the MOSFET's bulk as there already PN junctions (correct me if I'm wrong).  I've looked at the datasheet of a Power P-MOSFET and it has parameters like "Internal Source Inductance" and "Internal Drain Inductance". So, is the build up of reverse voltage on the source and drain sides, when said MOSFET is suddenly turned off, a behavior intrinsic to (at least some) MOSFETs? Or are these from the rest of the circuit, say inductive loads? Why is it "come" rather than "go" ? Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$ computing the orbits for a group action Ubuntu 18 - how to ungroup apps in dock? I want to make Ubuntu dock like Windows taskbar  Ubuntu:    Windows:    (as you see Windows has three Explorer icons and Ubuntu has only one Files icon  Is it possible to uncombine/ungroup apps in Ubuntu? GCD of two numbers divided by their greatest common divisor is 1 Currently the migration path options from SO are:   Meta.SO Serverfault SuperUser Webmasters Programmers   If we are going to be limited to 5 options, shouldn't we periodically re-evaluate which sites are most appropriate?   (10k only) indicate that the top sites for the last 90 days are:   Superuser - 564 - 5% rejected ServerFault - 278 - 10% rejected Tex - 157 - 13% rejected DBA - 144 - 2% rejected Sharepoint - 127 - 1% rejected Programmers - 126 - 26% rejected CodeReview - 100 - 3% rejected Meta.SO - 81 - 18% rejected Wordpress - 75 - 14% rejected Webmasters - 58 - 8% rejected   All these migrations for sites out of the list required a flag and a moderator to process it.  This is just extra work for the mod team!  If we had the top 5 destinations by volume as the 5 options, we would have had a net savings of 160 flags to be processed.  I suspect we will actually see these numbers change quite a bit if it's easier for users to put questions in the appropriate spot without moderator intervention.  Can we have a review of the migration path list based on migration volume?  Think of the flags! If $\sum_{n=1}^{\infty} a_n^{2}$ converges, then so does $\sum_{n=1}^{\infty} \frac {a_n}{n}$ 90s (or earlier) movie with experimental, invisible, teleporting, time-traveling ship