"Less" and "fewer" in English 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")?
"Less" vs. "fewer" 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?
Preventing robots from crawling specific part of a page As a webmaster in charge of a tiny site that has a forum, I regularly receive complains from users that both the internal search engine and that external searches (like when using Google) are totally polluted by my users' signatures (they're using long signatures and that's part of the forum's experience because signatures makes a lot of sense in my forum).  So basically I'm seeing two options as of now:   Rendering the signature as a picture and when a user click on the "signature picture" it gets taken to a page that contains the real signature (with the links in the signature etc.) and that page is set as being non-crawlable by search engine spiders).  This would consume some bandwidth and need some work (because I'd need an HTML renderer producing the picture etc.) but obviously it would solve the issue (there are tiny gotchas in that the signature wouldn't respect the font/color scheme of the users but my users are very creative with their signatures anyway, using custom fonts/colors/size etc. so it's not that much of an issue). Marking every part of the webpage that contains a signature as being non-crawlable.   However I'm not sure about the later: is this something that can be done?  Can you just mark specific parts of a webpage as being non-crawlable? While looking over various PHP libraries I've noticed that a lot of people choose to prefix some class methods with a single underscore, such as  public function _foo()   ...instead of...  public function foo()   I realize that ultimately this comes down to personal preference, but I was wondering if anyone had some insight into where this habit comes from.  My thought is that it's probably being carried over from PHP 4, before class methods could be marked as protected or private, as a way of implying "do not call this method from outside the class".  However, it also occurred to me that maybe it originates somewhere (a language) I'm not familiar with or that there may be good reasoning behind it that I would benefit from knowing.  Any thoughts, insights and/or opinions would be appreciated. Problem  I have various footnotes, which are hyperlinked from the text to the bottom of their respective pages. When I click on the hyperlinks (in the main text), they always take me to the first page of my document. I also have footnotebackref which puts a hyperlink at the footnote to take the reader back to the main body of text and these links for fine.   Edited MWE  After a lot of deletion, I have managed to reduce the document to the following lines. One might say that I have found the problem, since the removal of \usepackage[hang, flushmargin]{footmisc} stops the problem, but I would still like to have non-indented footnotes.  \documentclass{article}  \usepackage[usenames,dvipsnames]{color} \usepackage[colorlinks=true]{hyperref}  \usepackage[hang, flushmargin]{footmisc}         %Problem line. \usepackage{footnotebackref}  \begin{document} \tableofcontents             \newpage                 \section{Section} This is some text\footnote{This is a footnote.}. \end{document} Find the volume of rotation about the y-axis for the region bounded by $y=5x-x^2$, and $x^2-5x+8$  Here is an image:    Normally I can do this question, but this one is tricky because since we are rotating about the y-axis, and we are quadratic, when I solve for $x$ I get two answers, one positive and one negative.   What I mean is that if you look at the graph $5x-x^2$, then there are two halves, and if you look at the green line, that's one half of the curve (positive one), and the red half is the negative one.  Since we can see both the negative and positive sections in this graph, and both are being rotated, I wasn't sure how to create the equation that I can later integrate.  Usually in the problems I do, the negative doesn't exist, and so it's trivial. In this case I am not sure. Word for person always after what he does not have and not cherishing what he has Possible Duplicate:          Is there a word for a person who is always after what he does not have and does not cherish what he has? If not, any idiom or phrase? Using The Terminal Command to Shutdown, Restart and Sleep My Mac? I'm getting more interested in using Terminal as an alternative way to address solutions on my Mac. I have seen this question entitled .  I would therefore like to know:  How to shut down, restart and sleep my Mac using the Terminal command exclusively ? Why doesn't the "zig-zag" comb deformation retract onto a point, even though it's contractible? I am starting to read Hatcher's book on Algebraic Topology, and I am a little stuck with exercise 6(c) in Chapter $0$. Unfortunately a picture is involved so it doesn't quite make sense for me to repeat it here - but I'll do it anyways (maybe it helps)     Let $Z$ be the zigzag subspace of $Y$ homeomorphic to $\mathbb{R}$ indicated by the heavier line in the picture:       Show there is a deformation retraction in the weak sense of $Y$ onto $Z$, but no true deformation retraction."   Now the definition for deformation retraction and weak deformation retraction as as follows:  We say that $f: X \to X$ is a deformation retraction of a space $X$ onto a subspace $A \subset X$ if there exists a family of maps $f_t : X \to X$ with $t \in [0,1]$ such that $f_0 = \mathbb{1}$ (the identity) and $f_1 (X) = A$ and also $f_t$ restricts to the identity on $A$ for each $t$.   A weak deformation retraction is almost the same, only that we now relax the conditions $f_1(X) = A$ to $f_1 \subset A$ and, for each $t \in [0,1]$ we require that $f_t(A) \subset A$.  Hence, as far as I understand the question and the concepts involved, I need to show that basically no map can be constructed such that the bold zigzag - line stays put while the thin lines retract to the bold line over a finite time interval $0 \leq t \leq 1$. However, I should be able to show that I can pull the thin lines continously onto the thick line, provided I am allowed to move points on the zigzag line .. is that correct ?  Now, the problem is I can't see why I shouldn't be able to do the former, given that I could find a weak deformation retract. Any help would be great! How much did the Trade Federation know about their 'lord' at time of blockade? restore table from .frm and .ibd file? I have previously saved a copy of /var/lib/mysql/ddms directory ("ddms" is the schema name). Now I installed a new MySQL on a freshly installed Ubuntu 10.04.3 LTS by running apt-get install mysql-server, I believe version 5.1 was installed. After I copy the ddms directory under /var/lib/mysql, some of its tables work fine, these are the tables with an associated set of three files: a .frm file, a .MYD file and a .MYI file.  However, there are two tables with a different set of files: a .frm file and a .ibd file. These two tables didn't show up in the table list in phpMyAdmin. When I look at the error log, it says:  [ERROR] Cannot find or open table ddms/dictionary_item from the internal data dictionary of InnoDB though the .frm file for the table exists. Maybe you have deleted and recreated InnoDB data files but have forgotten to delete the corresponding .frm files of InnoDB tables, or you have moved .frm files to another database? or, the table contains indexes that this version of the engine doesn't support.   Please help with restoring these two tables. Thanks. Let be $V$ a vector space over the complex numbers with inner product. Let be $T$ and $S$ linear operators in $V$ with adjoint operators $T^*$, and $S^*$ respectively. I know that it satisfies this: $\left&lt; T(x),y \right&gt;=\left&lt; x,T^{*}(y) \right&gt;$ $\left&lt; S(x),y \right&gt;=\left&lt; x,S^{*}(y) \right&gt;$    $\forall x,y \in V$ But, How can I prove that the adjoint operator of $ST$ is $(ST)^{*}$? And how can I  prove that $(ST)^{*}=T^{*}S^{*}$? How to migrate a WordPress installation from one site to another, including all images? Extra blue line appearing in the top bar (Firefox only) Whenever we click on the Inbox or the Achievements in the top bar, an extra blue line appears near by them. This is reproducible on Stack Overflow and Anime &amp; Manga(as I use only those) but not on Meta Stack Overflow. Here is a snapshot of that.    I'm using Firefox 25.0.1 on Win7 Pro.  Edit: Just to be double sure, I restarted the FF and still I'm able to see it. Here is another snapshot, with the 2 distinct sites. Show reference label when it is undefined How to embed Stack Overflow flair in a WordPress.com (free) blog? Has anyone successfully embedded their  on a WordPress.com-hosted blog?  The free hosted version of  (not )  from all posts before publishing. So they to strip out just about anything I can add to embed my Stack Overflow flair.  Note: I'll be switching to a paid, hosted site in the future (fixing the problem), but I'm looking for a quick, short-term solution. Unique (non-repeating) random numbers in O(1)? I'd like to generate unique random numbers between 0 and 1000 that never repeat (i.e. 6 doesn't show up twice), but that doesn't resort to something like an O(N) search of previous values to do it. Is this possible? What is the most straightforward way to pad empty dates in sql results (on either mysql or perl end)? I'm building a quick csv from a mysql table with a query like:  select DATE(date),count(date) from table group by DATE(date) order by date asc;   and just dumping them to a file in perl over a:  while(my($date,$sum) = $sth-&gt;fetchrow) {     print CSV "$date,$sum\n" }   There are date gaps in the data, though:  | 2008-08-05 |           4 |  | 2008-08-07 |          23 |    I would like to pad the data to fill in the missing days with zero-count entries to end up with:  | 2008-08-05 |           4 |  | 2008-08-06 |           0 |  | 2008-08-07 |          23 |    I slapped together a really awkward (and almost certainly buggy) workaround with an array of days-per-month and some math, but there has to be something more straightforward either on the mysql or perl side.   Any genius ideas/slaps in the face for why me am being so dumb?    I ended up going with a stored procedure which generated a temp table for the date range in question for a couple of reasons:   I know the date range I'll be looking for every time The server in question unfortunately was not one that I can install perl modules on atm, and the state of it was decrepit enough that it didn't have anything remotely Date::-y installed   The perl Date/DateTime-iterating answers were also very good, I wish I could select multiple answers! Significance of the second focus in elliptical orbits Precedence of user and group owner in file permissions How can I get more of this macro photo in focus? I want to make a full focus on the body, for example: I need to have a clear focus on the each balls in the photo. I used just single point focus.    In this picture I used:   shutter speed: 8 aperture: F/4 ISO: 200 2 flashes, one in the right and one on the top of project camera: nikon d300s lens : 105mm micro 2.8   Thanks How do tag merge requests work? I had raised a  to merge pre-build-event, and pre-buildevent; and postbuild-event and post-build-event. That was about 11 months ago, and I still see these two tags even now.  How are tag merge requests handled? Is there a better way for tag merge requests other than posting on Meta?