English uses two lexemes to denote that something is smaller in number or size/amount: "Less" and "fewer". "Less" is used for uncountable nouns ("I needed less time to mow the lawn today"), while "fewer" is used for countable ones ("I needed fewer attempts to get the lawnmower going today").  However, sometimes "less" is used with countable nouns (famously the "X items or less" register in supermarkets). When can countable nouns be used with "less"? Consider these examples:    I'll only need five minutes or less to mow the lawn. A lawnmower may only go 5 mph or less. You may only use my lawnmower if you weigh 75 kg or less.   These sentences sound correct to me, while the use of "fewer" in these contexts seems incorrect or at least odd to me (as a non-native speaker of English):    ? I'll only need five minutes or fewer to mow the lawn. ? A lawnmower may only go 5 mph or fewer. ? You may only use my lawnmower if you weigh 75 kg or fewer.   Which of these do native speakers prefer?  Could it be that "less" is acceptable, when the countable noun refers to an uncountable entity (such as time, speed or weight)? If so, is this restricted to units (minutes, mph, kg)? Also: Would this explain the use of "less" in "X items or less", as "items" as a countable noun refers to an abstract, uncountable entity (i.e. "shopping")?
I've just received a memo which says (effectively)      As more people leave, there will be less people available.   I want that word to be fewer. Are there guidelines for which word ought to be used when?
What are FML and BWSS? I see this ad sometimes and I would like to know what the acronyms are. Find out which process is locking a file or folder in Windows Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$ I am looking for the combinatorial argument for the identity:  \begin{equation} k\binom{n}{k} = n\binom{n-1}{k-1} \end{equation}  This is easy to show algebraically as:  \begin{equation} \binom{n}{k} = \dfrac{n(n-1)(n-2)(n-k+1)}{k(k-1)!} \end{equation}   What is the combinatorial argument? What are some general ideas to get started?   Here is a clarification of 2. From what I have seen so far, proving (combinatorially) an identity with an addition sign usually implies that we need to partition a set (this makes sense because of the addition rule and provides a nice visual). On the contrary, the previous observation leads me to believe that multiplication in identities can be resolved with the multiplication principle, but what is the "visual/interpretation" for this? Could someone provide such an interpretation for the example identity given above? I have this problem as part of a school assignment:  NOTE: In case it's hard to read in the image above, here's the directory tree: $ tree . `-- sample_dir1     `-- sample_dir         |-- admin         |-- cambridge         |   |-- cafeteria         |   |-- library         |   `-- security         |       |-- annex         |       |-- building         |       `-- parking         |-- faculty         |-- history.exe         |-- markham         |   |-- annex         |   |-- building1         |   `-- parking         |-- oxford         |   |-- outline.doc         |   |-- programming         |   |   `-- report.pdf         |   `-- security         `-- stenton             |-- gen_ed             `-- lib_arts                 |-- english.txt                 `-- match.doc  15 directories, 11 files  I tried doing the command: $ cp ../cambridge/security/parking ./parking2  ...but it isn't working. The question in the image above states that the current directory is stenton, and that we need to make a copy of the file named parking (from the security directory), and to name the new file parking2, and place it in the current directory, stenton, using relative pathnames. What am I doing wrong? My cp command seems to be correct. How can I change GNOME Shell theme? I've installed the GNOME Shell in Ubuntu 12.04 and I want to change the "Shell Theme", But it doesn't allow me to do that.  The alert says something like: "The GNOME-Shell extension is not activated", and I want to install it with the console, But it returns me an error.  How can I solve this problem? In the example  $\cup^{i=1}_{\infty}F_i$   How do you get the i=1 directly below the union symbol and the infinity directly above? How do you test that a Python function throws an exception? How does one write a unittest that fails only if a function doesn't throw an expected exception? How to send variable to an inline shell-script? Is JavaScript's "new" keyword considered harmful? In another , a user pointed out that the new keyword was dangerous to use and proposed a solution to object creation that did not use new. I didn't believe that was true, mostly because I've used Prototype, Scriptaculous and other excellent JavaScript libraries, and everyone of them used the new keyword.  In spite of that, yesterday I was watching Douglas Crockford's talk at YUI theater and he said the exactly same thing, that he didn't use the new keyword anymore in his code ().  Is it 'bad' to use the new keyword? What are the advantages and disadvantages of using it? Proving an entire, complex function with below bounded modulus is constant. How would I show that an entire function $f$ with the property $|f(z)| \geq 1$ must be constant?    I'm aware of Liouville's theorem, just not sure how to apply it here. Writing a string array to text file separated by new line character Embedding a link (or other html) in a JSF message Finite Abelian groups with the same number of elements for all orders are isomorphic Let $A$ and $B$ be finite abelian groups. Suppose that for every natural number $m$, the number of elements of order $m$ in $A$ is equal to the number of elements of order $m$ in $B$. Prove that $A$ and $B$ are isomorphic.  Idea Given that these groups are finite, I think you have to use the primary decomposition theorem somehow. Why don’t I have the Get Windows 10 icon? I want to get Windows 10, but I do not see this icon in the notification area (tray):    How do I get the icon to get Windows 10? Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only I have found a proof using complex analysis techniques (contour integral, residue theorem, etc.) that shows $$\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$$ for $n\in \mathbb{N}^+\setminus\{1\}$   I wonder if it is possible by using only real analysis to demonstrate this "innocent" result?  Edit A more general result showing that  $$\int\limits_{0}^{\infty} \frac{x^{a-1}}{1+x^{b}} \ \text{dx} = \frac{\pi}{b \sin(\pi{a}/b)}, \qquad 0 &lt; a &lt;b$$ can be found in How can I reduce the ever-increasing time to push a subtree? The question is about the encryption equation in asymmetric encryption.  For $c\equiv m^e\bmod n$, prove that for every unique $m$ there is a unique $c$.  Here $n=pq$ where $p$ and $q$ are primes larger than $m$ and the exponent $e$, is $\geq3$ and coprime with $p-1$ and $q-1$.  Thanks! Show that conguence $\bmod m\,$ is an equivalence relation is a psychological phenomenon wherein an individual is convinced that they do not deserve the success that they have achieved despite (perhaps extensive) empirical evidence to the contrary.  Some people with imposter syndrome doubt their own ability level. For me, this usually manifests in the thought:  I've somehow convinced everyone into believing that I'm actually good at this.  followed by the horrifying notion that eventually I'll be found out and my world will collapse. I believe that the imposter syndrome is not uncommon in academia. I'm interested to know how other people here have experienced and dealt with it.  In particular, I'm looking for actual tactics that someone might use to combat imposter syndrome.   Why I asked this question: Beyond the obvious reason that this is something I have struggled with for many years and only recently gotten a handle on myself, there's also some evidence that merely realizing that other people experience imposter syndrome helps fellow imposters. As a grad student, I've managed to meet a fair number of people who are in their own struggles with imposter syndrome; however, the tactics and self-trickery that have helped me don't always speak to them and perhaps someone else's methods might. I would like to have multiple bibliographies (reference lists) as described in   ().   However, I'd like to use with a single .tex file, which would contain the bibliography database embedded, as in  ...   Now, I want to use letter documentclass, for which the bibliography needs to be defined ()   So what I end up is with this example (code below, compiled with just pdflatex, no bibtex(which I'd like to avoid in this case)):     ... obviously, something works (multibib recognized primary and secondary cites, assigning them number "1" as start) -- however I don't get two, separate primary and secondary list of references; would that be possible in this context? (doesn't have to be with multibib, but I'd like to avoid a separate .bib file and a bibtex call)  EDIT: I'd also like separate cite keys (i.e. rendered as [a1] and [b1]; not yet sure if multibib can do that; edit: no it cant,  says "You can also edit the .bbl files created by BibTEX and add 'a', 'b',. . . to the labels, but your changes will be overwritten by subsequent BibTEX runs." and recommends \cite[a]{key}) - how possible would that be?  &nbsp;  The code is this:   \documentclass{letter}  % Environment thebibliography undefined when using letter: http://www.latex-community.org/forum/viewtopic.php?f=4&amp;t=3359 \makeatletter \setlength \labelsep {.5em} \newcommand\newblock{\hskip   .11em\@plus.33em\@minus.07em} \let\@openbib@code\@empty \newcommand\refname{References} \newcommand\section{\@startsection   {section}{1}{\z@}%   {-3.5ex \@plus -1ex \@minus -.2ex}%   {2.3ex \@plus.2ex}%   {\normalfont\Large\bfseries}} \newenvironment{thebibliography}[1] {\section*{\refname}%   \@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}%   \list{\@biblabel{\@arabic\c@enumiv}}%   {\settowidth\labelwidth{\@biblabel{#1}}%     \leftmargin\labelwidth \advance\leftmargin\labelsep \@openbib@code     \usecounter{enumiv}%     \let\p@enumiv\@empty \renewcommand\theenumiv{\@arabic\c@enumiv}}%   \sloppy \clubpenalty4000 \@clubpenalty \clubpenalty   \widowpenalty4000%   \sfcode`\.\@m} {\def\@noitemerr {\@latex@warning{Empty       `thebibliography' environment}}%       \endlist} \makeatother  \usepackage{multibib} \newcites{pri}{Primary sources} \newcites{sec}{Secondary sources}  \begin{document}   \begin{letter}{Addressee} Blah, blah - content...  Primary cite: \citepri{lamport94} ...  Secondary cite: \citesec{lamport94} ...   \begin{thebibliography}{9}  \bibitem{lamport94}   Leslie Lamport,   \emph{\LaTeX: A Document Preparation System}.   Addison Wesley, Massachusetts,   2nd Edition,   1994.  \bibitem{lamport95}   Leslie Lamport,   \emph{\LaTeX: A Document Preparation System}.   Addison Wesley, Massachusetts,   2nd Edition,   1995.  \end{thebibliography}  \end{letter}   \end{document}