Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?
Is there a c# equivalent of Java ConcurrentHashMap Splitting string into pair of characters in Ruby How to get the last argument to a /bin/sh function What's a better way to implement print_last_arg?  #!/bin/sh  print_last_arg () {     eval "echo \${$#}"  # this hurts }  print_last_arg foo bar baz # baz   (If this were, say, #!/usr/bin/zsh instead of #!/bin/sh I'd know what to do.  My problem is finding a reasonable way to implement this for #!/bin/sh.)  EDIT: The above is only a silly example.  My goal is not to print the last argument, but rather to have a way to refer to the last argument within a shell function.    EDIT2: I apologize for such an unclearly worded question.  I hope to get it right this time.  If this were /bin/zsh instead of /bin/sh, I could write something like this  #!/bin/zsh  print_last_arg () {     local last_arg=$argv[$#]     echo $last_arg }   The expression $argv[$#] is an example of what I described in my first EDIT as a way to refer to the last argument within a shell function.  Therefore, I really should have written my original example like this:  print_last_arg () {     local last_arg=$(eval "echo \${$#}")   # but this hurts even more     echo $last_arg }   ...to make it clear that what I'm after is a less awful thing to put to the right of the assignment.  Note, however, that in all the examples, the last argument is accessed non-destructively.  IOW, the accessing of the last argument leaves the positional arguments as a whole unaffected. I am pretty sure it shouldn't, but want to make sure that I am doing this correctly in a proposal that I am working on.  Should job titles like "Project Manager" ever be capitalized, and if so when?  In particular I am concerned about capitalization in sentences like this where the title refers to a specific person, not the role in general.     "The Project Manager will   evaluate the alternatives and offer a   solution."   I'm a lot more certain that it should NOT be capitalized in sentences like this.     "A project manager is the person who   manages the budget and deliverable for   a project." nth fibonacci number in sublinear time Is there something like python's interactive REPL mode, but for Java? How do I remove a directory and all its contents? In bash all I know is that   rmdir directoryname   will remove the directory but only if it's empty. Is there a way to force remove subdirectories? The following will cause infinite recursion on the == operator overload method      Foo foo1 = null;     Foo foo2 = new Foo();     Assert.IsFalse(foo1 == foo2);      public static bool operator ==(Foo foo1, Foo foo2) {         if (foo1 == null) return foo2 == null;         return foo1.Equals(foo2);     }   How do I check for nulls? Can git be integrated with Xcode? Addressing a former office-holder by that office's title When is it appropriate to use an "expired" honorific to address or refer to a person?   In the U.S., former state governors are occasionally referred to as "Governor So-and-so", although they have not held that office for several years. I see this happening most often when the former governor is actively campaigning for a new office (usually U.S. President), and my impression is that it's done only by someone with an interest in the campaign (for or against) rather than a (relatively) neutral party like a newspaper.  Certainly this could be used as a jab: in a political campaign for high office, addressing one's opponent by a former title — lower than one's own — could imply that the opponent is not qualified for the new job. It could also be used the other way around, to remind listeners that a candidate one supports used to hold an important title.  I'm curious whether there are formal rules for this in the U.S., or at least style or journalist guidelines, for various offices. Are ambassadors, for example, entitled to some sort of emeritus honorific? Is there a "null coalescing" operator in JavaScript? Is it correct to sometimes capitalize words mid-sentence in computer user interfaces? Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG? If $F$ a PRF, and we construct $G$ using $F$ in the following way:  $$G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$$ where $|s|= n$.   Is $G$ then a PRG? If so how can I prove this? If not how can $G(s)$ be distinguished from a random $r$? And what if $n+1 &lt;$ range of $F_s$? or it could be for any $n &gt; |s|$. In discussing , I noted that while the statement:     Any vector space has a basis   is equivalent to the axiom of choice, I wondered if the statement that:     Any vector space either has a finite basis or an infinite set of linear independent vectors   was weaker than the axiom of choice. It feels weaker - it feels like you can inductively define a countably infinite set of linearly independent vectors without full choice, but I'm not sure if that is possible with ZF alone, or requires all of the Axiom of Choice, or is weaker but requires some form of choice. Android finding missing numbers Does a GFCI receptacle provide overcurrent protection? Does a GFCI receptacle provide over-current protection? (note that I'm not referring to GFCI circuit breakers as may be found in a service panel, nor to specialty devices such as an inline plug-in GFCI that may offer over-current protection)  I've checked some GFCI  (note, this link opens a PDF) but haven't found any that mention overcurrent protection, or provide trip curves as would be expected in a circuit breaker datasheet.  So, does a GFCI receptacle provide any inherent over-current protection or must it always be used with a circuit breaker for over-current protection?  This question was prompted by  where the answer suggests using a GFCI outlet as a circuit breaker. This seems like very big misconception of the protection offered by a GFCI, and is potentially dangerous if it leads someone to think that GFCI outlets are the same as circuit breakers. undefined control sequence when using \addchap When I compile my thesis.tex file which is compiled fine including the \addchap, I noticed that I have used \usepackage{unnumberedtotoc}. When I want to use my thesis.tex file on another computer it says tex capacity exceeded, sorry [input stack size=5000]. When I uncomment \usepackage{unnumberedtotoc}, it says ! undefined control sequence  \addchap.  Here I have pasted all the beginning of the packages that I have used in my thesis but I still get some problems in compilation, I don't know why, but I think if I can compile this code, then I can solve the problem  :   \immediate\write18{makeindex \jobname.nlo -s nomencl.ist -o \jobname.nls} \documentclass[12pt]{report} \DeclareMathSizes{12}{30}{16}{12} \usepackage[utf8]{inputenc} \usepackage{graphicx} \usepackage{lineno} \usepackage{amsmath}  \usepackage{array, nccmath}  \usepackage[nottoc]{tocbibind} \newcolumntype{L}{&gt;{$}l&lt;{$}} \newcolumntype{m}{&gt;{\displaystyle}l} \usepackage{framed} \usepackage{cclicenses} \usepackage{makecell} \usepackage[french]{babel} \usepackage{setspace} \usepackage{mathptmx}  \usepackage{multirow}  \usepackage{gensymb}  \usepackage{empheq}   \usepackage{mathtools}   \usepackage{array}   \renewcommand{\arraystretch}{1.9}   \newcolumntype{P}{&gt;{\centering\arraybackslash$}p{1.6em}&lt;{$}}   \newcolumntype{C}{&gt;{\centering\arraybackslash$}c&lt;{$}}   \usepackage{makecell}   \usepackage{booktabs}   \usepackage{subcaption}   \usepackage[intoc]{nomencl}   \makenomenclature   \setcounter{secnumdepth}{4}   \setcounter{tocdepth}{4}   \usepackage[justification=centering]{caption}    \usepackage{etoolbox}     \usepackage{unnumberedtotoc} %https://github.com/johannesbottcher/unnumberedtotoc/     \usepackage[automark,     plainheadsepline,     headsepline,     plainfootsepline,      footsepline,     markcase=ignoreupper]{scrlayer-scrpage}    \clearpairofpagestyles    \ihead*{\leftmark}    \cfoot*{\pagemark}    \setkomafont{pageheadfoot}{\scshape}    \usepackage{titlesec}    \graphicspath{{imagesthesis/}}    \def\frenchlistfigurename{Liste des figures}    \usepackage[a4paper,right=20mm,left=25mm,top=26mm, bottom=26mm]{geometry}    \makeatletter    \titleformat{\chapter}[display]    {\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}    % this alters "before" spacing (the second length argument) to 0    \titlespacing*{\chapter}{0pt}{0pt}{20pt}    %\patchcmd{\@makechapterhead}{\vspace*{20\p@}}{}{}{}% Removes space above \chapter head    %\patchcmd{\@makeschapterhead}{\vspace*{20\p@}}{}{}{}% Removes space above \chapter* head    \makeatother    \title {itle of the thesis}    \titleformat{\paragraph}    {\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}    \titlespacing*{\paragraph}     {0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}     \usepackage[thin, , thinc]{esdiff}  \usepackage{subcaption}  \usepackage{caption}  \usepackage{framed}    \usepackage{nomencl}   \setlength{\nomitemsep}{-\parskip}\usepackage{booktabs,multirow}  \renewcommand{\cellset}{\renewcommand{\arraystretch}{0.5}}   \begin{document}  \renewcommand\arraystretch{0.8} %\noindent  \doublespacing  \maketitle  \tableofcontents %\listoffigures  \addchap{Publications et communications}   \section*{$\:$  a. Publications:}  \section*{$\:$  b. Communications:}  \addchap{Remerciements}  \end{document} Fourier series of Log sine and Log cos Why I cannot unpin some directories from file explorer in windows 10 I need to define a new command to create a squiggle arrow with some text on it. Something similar to what \xrightarrow command produces but with wiggly arrows as in \rightsquigarrow. The length of the arrow should automatically be adjusted to fit the text above it and I do not know how to handle this part in TikZ. Any ideas would be much appreciated.