For example,  120 cats are rescued.  is not usually considered as good style. :  If you need to begin a sentence with a number, spell it out. It is better, however, to reword the sentence, if possible.  Thirty-two workstations were provided by the university. \ The university provided 32 workstations.   :  Spell out a number—or the word number—when it occurs at the beginning of a sentence, as well as any related numbers that closely follow it:  :   Spell Out Numbers at the Start of a Sentence. Avoid Opening a Sentence with a Large Number. Consult Your Style Guide before Starting a Sentence with a Number.  Our four primary style guides (i.e., The Chicago Manual of Style, The Associated Press Stylebook, the Publication Manual of the American Psychological Association, and the MLA Handbook from the Modern Language Association) all agree that numbers should normally be spelled out at the start of sentences.
3 more votes from other users are needed to close this question.   This is the message I got hovering the mouse over close voting tab.   I wonder can we begin any sentence with a numeric value? Is it good practice?
Cannot install R-forge package using install.packages Need clarification on the Draw 4 rule. - Player 1 lays down a Draw 4 Card and says the color is Red. - Player 2 does not have a Red card but has a Draw 4 Card. Can Player 2 lay down his Draw 4 Card and have Player 3 draw 8 cards? Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$ I have my CIFS setup in fstab and they are working as they are supposed to on boot. They mount as they should and work for a while. Out of nowhere it seems (could be after unlocking machine etc) I get "Host is down" error trying to access it. I have multiple and they are all down. They are also shared from the same server. At this time i check on a windows computer and an outdated 14.04 machine and they are up and functioning as they are supposed to. After clicking around on the shares in nautilus and getting repeat errors they will just start working again. To access a share that is "down" takes about 2-3min of randomly clicking different mounts and going back to the first one when automagically it shows the data in the mount point.  I do not have this problem on 14.04 machines that have not been updated in a while. All of those machines are fully functional and the CIFS never go "down". On 16.04 they were not a problem until more recently.  I have made sure to update every other day and have cleaned old linux headers (in hind sight i probably should have reverted). I do this because im begging for a fix to just appear but its been weeks of battling CIFS mounts without any solution. Why don't the Ubuntu repositories have the latest versions of software? Why are packages in the official Ubuntu repositories older than the latest (upstream) versions from Debian Sid, PPAs, the authors, etc.? drawing different parts of a line in different colours How to draw different parts of a line in different colours. In the following code can each part of the line be drawn in different colour      \documentclass{beamer} \beamertemplatenavigationsymbolsempty \usepackage{tikz} \usepackage{pgfplots} \begin{document} \begin{frame}[fragile,t] \frametitle{} { \begin{tikzpicture} \draw [thick, green] (2.3,1.4) +(-27:2.2cm)-- +(153:2.2cm) +(42:1.88cm) -- +(-138:1.88cm); \end{tikzpicture} } \end{frame} \end{document} Auto-inserting Stack Overflow affiliate into all Amazon links We have officially discontinued the Amazon book affiliate remnant ads, since despite our best efforts they don't perform well for our audience and cannot be made to perform well.  We've often wondered,   I'm thinking this isn't a problem; it has gotten lots of support historically. So we're going to go ahead and do it, so the company Amazon account is still getting some use, and we benefit a little.   To be clear: from this point on, all Amazon links posted on all sites will automatically be rewritten to add our affiliate link. We have a clever affiliate redirect that geolocates the IP address and redirects to the appropriate regional Amazon store (amazon.uk, amazon.ca, et cetera).  If you have any feedback on this, or suggestions, as they say &hellip; speak now or forever hold your peace! How do you find all $n$ such that $\phi(n)|n$ Java Command line arguments Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$. Let $G$ be  a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.   $a,b\notin H\implies aH,bH\neq H\implies $ $aH=bH$  since $H$ has only two distinct left cosets in $G$.  $\implies a^{-1}b\in H$  How to show that $ab\in H$ from here? Travelling as unmarried couple in Dubai I'd wish to visit Dubai with my girlfriend, but after reading  and  I started to get a little worried about it. How should I book an hotel? Must I book two singles? Could it be a problem if we walk together in the city and go together to restaurants and malls without being married? Can “whose” refer to an inanimate object? We lit a fire whose fuel was old timber wood.   Is the word whose referring to fire, an inanimate object, correct in this sentence? Or is there a more appropriate word? Try Ubuntu - Where does it store my files? I am wondering, when you select the option of just "Try Ubuntu" instead of installing, where does Ubuntu store the files that you download / copy / save?  I right click in the Home folder, and it specified I had 4GB free space. Where did it get this 4GB space from, and if I transition to another OS system, how can I access or delete all the previous data from the session of "Try Ubuntu"?  Thank you! New Beamer Version: Transparent Title Page Boxes Is being good at mathematic contests necessary to pursue a career in mathematics or physics? I am extremely poor in solving a problem quickly, which leaves me doing badly in olympiads and other contests. But, if I just don’t give up on a problem, no matter how much time it takes, I usually end up solving it. To have a future in mathematics or physics, is it necessary for me to excel at contests, because these days children excelling at contests have an advantage over those who don’t (not complete advantage, but advantage nonetheless)? Bring a "human factor" into review audit composition/selection My linear algebra professor proved that      Diagonalizable matrices with complex values are dense in set of $n \times n$ complex matrices.   He defined a metric (I believe) that was somehow related to the usual metric on $\mathbb{R}^{n^2}$.  Then somehow proved that diagonalizable matrices were dense because for any matrix $A$ if $\det(A - \lambda I) = 0$ on an open subset, then $\det(A - \lambda I)$ was the zero polynomial.  I Googled around a bit and found some stuff talking about the Zariski topology, and I am not sure this is what I want. Most of what I have found on this topology is much more general than what he was doing.  Does anyone know any resources that would explain how to go about proving this statement?  Edit: I found out how to prove this the way my professor did.  We define the norm of a matrix by $$ |A| = \max\{|Ax| : |x| = 1 \}.$$ Now we have a distance $d(A, B) &lt; \epsilon$. You can prove that if $(A - B)_{ij} &lt; \epsilon/n$, then $|A - B| &lt; \epsilon$.  Let $p(x)$ be the characteristic polynomial of $A$, an $n \times n$ matrix.  $$p(x) = \prod_1^n (x - x_i) = x^n + (-1)\sigma_1 x^{n - 1} + \cdots + (-1)^n\sigma_n$$ where $\sigma_1, \ldots, \sigma_n$ are the elementary symmetric polynomials of $x_1, \ldots, x_n$ which are the eigenvalues.  The discriminant of the characteristic polynomial is a symmetric polynomial, therefore it can be written in terms of the elementary symmetric polynomials, which in turn can be written in terms of the entries of the matrix.  But since the discriminant is a polynomial, it only has finitely many roots. Therefore for $\epsilon &gt; 0$, by changing the entries of the matrix less than $\epsilon / n$ we can find a new matrix $B$ such that $|B - A| &lt; \epsilon$ and the discriminant is not zero.   The discriminant being not zero means $B$ has distinct eigenvalues, thus has a basis of eigenvectors. Therefore, it is diagonalizable.  Thus the set of diagonalizable matrices is dense in the set of matrices with respect to that metric. Why my sql query run faster than my stored procedure? I am trying to write a script in MYSQL Workbench to update my database every day using stored procedure but I find it too slow compared normal query or temporary tables. If i use temporary table the time of execution : 6 second but my stored procedure 370 second.  I really need help.        CREATE DEFINER=`datasll`@`...` PROCEDURE `product`()       BEGIN       EXPLAIN SELECT                cs.id,              cs.fk_c,              cs.so,               cs.pr,              cs.date,              cs.o_p,              cs.sh_c,              cs.x,              LEFT(cs.x,2),              cs.doc,              cs.fk_op,              cc.id_c_c,              cc.name,              cc.descrip,              left(cc.n_o,3) as bon,              cc.fk_c_br,              cc.de,              cc.m_mat,              cc.color,               cc.fk_c_s       FROM             data_pro.catas cs        LEFT OUTER JOIN             data_pro.c_co cc ON  data_pro.cs.fk_c_c = data_pro.cc._id_cc       WHERE             data_pro.cc.pap = 1       AND   data_pro.cc.stati = 'b';       END   When i use EXPLAIN this's the result :   Many Thanks for any help. Restore All Databases Script I am migrating SQL Server DBs to a new instance.  I have been told that it is possible to dynamically build a RESTORE script from available backups in the system catalog.  Does anyone know of a sample script to do this?  Thanks! Step to reproduce  Answer a question; Answer gets accepted or upvoted; Receive notification in the app; Change the title of the question; Notification is duplicated with updated title.  Expected behavior When going into notifcations you should see only one entry for that reputation event. Actual behavior You get two notification entries. In the screen notice the two entries for the same question, the one related to EF. After answering I have changed the name to make it more searchable for future questions and i've noticed it.      App Version: 1.6.1.2 Device: iPhone 6s OS Version: Version 10.1.1 (Build 14B100)