Why isn't chmod doing what I want it to?
Strange behaviour of 'sudo chmod -rwx': Does not remove group write permissions
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$ I'm learning calculus, specifically derivatives and applications of MVT, and need help with the following exercice:      Show that, for all $n &gt; 1$ $$\frac{1}{n + 1} &lt; \log(1 + \frac1n) &lt; \frac1n.$$    I tried to follow the below steps in order to prove the RHS inequality:   Proving that $f &lt; g$ on $I$ from $a$ to $b$:  Step $1$. Prove that $f' &lt; g'$ on $\operatorname{Int}(I)$.  Step $2$. Show that $f(a) \leq g(a)$ or that $f(a^+) \leq g(a^+)$  Following the above steps, let $f(x) = \log(1 + \frac1x)$ and $g(x) = \frac1x$, for all $x &gt; 1$. One has  $$f'(x) =  -\frac{1}{x^2 + x} \quad \text{and} \quad g'(x) = -\frac{1}{x^2}.$$  We note that, for every $x &gt; 1$, $f'(x) &gt; g'(x)$. Moreover, $f(1^+) = \log(2) &lt; 1 = g(1^+).$   My problem is that I got the wrong inequality sign in Step $1$.    Looking at the solution in my textbook, the author suggests using the MVT but I don't know how to apply it in this case. Periodic function implies periodic primitive? If $f$ is a periodic function with $T = \pi$, does that mean that $F$ (a primitive of $f$) has the same period ? What about the inverse implication (periodic primitive implies periodic function) ? "Where will you go" vs. "Where you will go" Which sentence is correct between these?      Where will you go?     Where you will go? Isekai manga where the mc is reincarnated through his own magic How does the British-Irish Visa Scheme (BIVS) work? I am an Indian citizen and have applied for the Standard Visitor visa to the UK, and wish to travel to Ireland by using the BIVS scheme.    Do I need to fill up a separate application for BIVS endorsement or is it handed out automatically?  Also, If I enter the UK, and then travel to Ireland, can I re-enter the UK again? How can I share a directory with an another user? ContentVersion Content-Type I need to stream a file from Salesforce in our webapplication. To make sure the file is properly opened, I have to set Content-Type header.  How to retrieve the Content-Type (MIME) of a file?  I expect values like: image/png, application/pdf, text/html etc.  How to get these values? I am using the Java and a SOAP client to retrieve the data. Our iPad is locked and we're not sure of the Apple ID / iCloud password How do file permissions work? How do I use F3 to get my coordinates when my laptop makes F3 a special key? I can't get the coordinates on my computer because it keeps changing the brightness.  I have a windows 8 Samsung, and I'm playing Minecraft version 1.6.4. I have been trying for a long time to change Blender's icon, but no matter what I do, I am not allowed to edit anything in /snap/blender-tpaw/3/.  Here's what I tried:   Editing the files from nautilus without sudo. Editing the files from nautilus with sudo (sudo nautilus in terminal ). Using terminal commands such as cp or rm without sudo. Using terminal commands with sudo (such as sudo cp &lt;source&gt; /snap/blender-tpaw/3/ or sudo rm /snap/blender-tpaw/3/&lt;filename.ext&gt;) Doing everything above in a root terminal (using sudo -i)   In every case I get the following error:  cannot remove/copy '/snap/blender-tpaw/3/filename.ext': Read-only file system   where filename is the file and .ext is its extension.  This also applies to other snaps' files, not only Blender.  Am I doing something wrong here? Or is it just impossible to change those files? Although I don't think it is impossible because everything here from Ubuntu to Blender is open-source, so they have no reason to block us from modifying those files.  EDIT:  I used Main Menu (alacarte) to change the icon, but I still want to know why I cannot modify any snap file. Listing, zebra effect and broken lines In , I've found one solution to produce a zebra effect for listing. Unfortunately, this only works if the lines are not broken. Is there a way to fix this?  Here is a code with an example showing the problem:  \documentclass[10pt,a4paper]{article}     \usepackage[utf8x]{inputenc}     \usepackage{ucs}     \usepackage[T1]{fontenc}     \usepackage{lmodern}     \usepackage[frenchb]{babel}     \usepackage[x11names, svgnames]{xcolor}     \usepackage{graphicx}     \usepackage{listings}     \usepackage{amsfonts}     \usepackage{amssymb}      \makeatletter         % Patch line number key to call line background macro         \lst@Key{numbers}{none}{%             \def\lst@PlaceNumber{\lst@linebgrd}%             \lstKV@SwitchCases{#1}%             {none&amp;\\%              left&amp;\def\lst@PlaceNumber{\llap{\normalfont                         \lst@numberstyle{\thelstnumber}\kern\lst@numbersep}\lst@linebgrd}\\%              right&amp;\def\lst@PlaceNumber{\rlap{\normalfont                         \kern\linewidth \kern\lst@numbersep                         \lst@numberstyle{\thelstnumber}}\lst@linebgrd}%             }{\PackageError{Listings}{Numbers #1 unknown}\@ehc}}          % New keys         \lst@Key{linebackgroundcolor}{}{%             \def\lst@linebgrdcolor{#1}%         }         \lst@Key{linebackgroundsep}{0pt}{%             \def\lst@linebgrdsep{#1}%         }         \lst@Key{linebackgroundwidth}{\linewidth}{%             \def\lst@linebgrdwidth{#1}%         }         \lst@Key{linebackgroundheight}{\ht\strutbox}{%             \def\lst@linebgrdheight{#1}%         }         \lst@Key{linebackgrounddepth}{\dp\strutbox}{%             \def\lst@linebgrddepth{#1}%         }         \lst@Key{linebackgroundcmd}{\color@block}{%             \def\lst@linebgrdcmd{#1}%         }           % Line Background macro         \newcommand{\lst@linebgrd}{%             \ifx\lst@linebgrdcolor\empty\else             \rlap{%                 \lst@basicstyle                 \color{-.}% By default use the opposite (`-`) of the current color (`.`) as background                 \lst@linebgrdcolor{%                 \kern-\dimexpr\lst@linebgrdsep\relax%                 \lst@linebgrdcmd{\lst@linebgrdwidth}{\lst@linebgrdheight}{\lst@linebgrddepth}%                 }%             }%             \fi         }     \makeatother      \lstset{ %    * Number for lines         numbers=left,                   % Where to put the line-numbers         numberstyle=\footnotesize,      % Size of the fonts used for the line-numbers         stepnumber=1,                   % Step between two numbers         numbersep=5pt,                  % How far the line-numbers are from the code % %    * Back returns for long lines         breaklines=true,                % Sets automatic line breaking         breakatwhitespace=false,        % Automatic breaks only happen at whitespace ?         breakindent=0pt,                % Space before the text of a break         postbreak=\mbox{                % Character used at the begining of a break             \rotatebox[y=0.9ex]{180}{\color{Red} $\Lsh$}%         },     }  \begin{document}  \begin{lstlisting}[language=Python,linebackgroundcolor={\ifodd\value{lstnumber}\color{gray}\fi}] for i in range(5): for i in range(5): for i in range(5): for i in range(5): for i in range(5): for i in range(5):     sum += i**3 print sum  print('Fin de la boucle...') \end{lstlisting}  \end{document} It's taken me almost 10 years of Linux usage to ask this question. It was all trial and error and random late-night internet surfing.  But people shouldn't need 10 years for this. If I were just starting out with Linux, I'd want to know: When to alias, when to script, and when to write a function?  Where aliases are concerned, I use aliases for very simple operations that don't take arguments.   alias houston='cd /home/username/.scripts/'   That seems obvious. But some people do this:  alias command="bash bashscriptname"   (and add it to the .bashrc file)   Is there a good reason to do that? I'm trying really hard, but I genuinely can't think of any circumstances in which I'd want to do that. So, if there is an edge case where that would make a difference, please answer below.  Because that's where I would just put something in my PATH and chmod +x it, which is another thing that came after years of Linux trial-and-error.  Which brings me to the next topic. For instance, I added a hidden folder (.scripts/) in the home directory to my PATH by just adding a line to my .bashrc (PATH=$PATH:/home/username/.scripts/), so anything executable in there automagically autocompletes.  If I needed to.  I don't really need that, though, do I? I would only use that for languages that are not the shell, like Python.  If it's the shell, I can just write a function inside the very same .bashrc:  funcname () {   somecommand -someARGS "$@" }   As I stated, I found a lot of this out through trial and error. And I only truly saw the beauty of functions when my computer died and I was forced to use the computers of the people around me when they weren't using them.   Instead of moving a whole directory of scripts from computer to computer, I ended up just replacing everyone else's .bashrc with my own, since they had never even made a single modification.  But did I miss anything?   So, what would you tell a beginning Linux user about when to alias, when to script, and when to write a function?   If it's not obvious, I'm assuming the people who answer this will make use of all three options. If you only use aliases, or only use scripts, or only use functions—or if you only use aliases and scripts or aliases and functions or scripts and functions—this question isn't really aimed at you. inequality on the unit disk $n$ points $z_1,z_2,\cdots,z_n$ in the unit open disk are given. Prove or disprove that there exists $z$ in the unit circle such that $\prod_{i=1}^n |z-z_i|^i \ge 1$.  I think it can be solved by elementary analytic methods but no idea. 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? Update statement with inner join on Oracle If I select a feature and run self.iface.actionIdentify().trigger() it will open the identify window but won't open the selected feature's data, how can I make it open the data of the selected feature? How do I deal with 'sudoers.so must be only be writable by owner'? Whenever I try to install or remove something using terminal it gives the following error message:  bluebird@bluebird:~$ sudo apt-get update sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins bluebird@bluebird:~$ sudo apt-get remove vlc sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins bluebird@bluebird:~$ sudo apt-get install apt-file sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins POST JSON data denormalization error My problem is that I have only one reference. So I would like the head of this part to appear "Reference" instead of commonly "References". More generally, could we change the title "References" to an arbitrary name?  Thank you very much for your help!