Why $ \infty - \infty \neq 0 ?$  Please explain
I would say $\infty - \infty=0$ because even though $\infty$ is an undetermined number, $\infty = \infty$. So $\infty-\infty=0$.
Give an example about limits: $\lim\limits_{x\to0}f(x^{2})$ exists but $\lim\limits_{x\to0}f(x)$ does not. "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? Dynamic Server Name in SQL Statements (from clause) Why is $\frac{1}{\frac{1}{0}}$ undefined? Seemingly random reputation gain of 1 I'm trying to make a systemd timer that runs every 15 minutes. Right now I have:     timer-fifteen.timer:  [Unit] Description=15min timer  [Timer] OnBootSec=0min OnCalendar=*:*:0,15,30,45 Unit=timer-fifteen.target  [Install] WantedBy=basic.target    timer-fifteen.target:  [Unit] Description=15min Timer Target StopWhenUnneeded=yes    This runs over and over again without stopping. Does it need to be *:0,15,30,45:* instead? How can I make this work? Render issue - Model doesn't appear to be on any layers and won't render Really odd on this... using Blender 2.75... I started modelling and lost the objects from the 3d view, but they were still showing in the object lists on the outlier... I was able to copy them and continued working... when I did a test render I discovered that only the original lost objects were rendering and nothing that I had modelled over the previous 2/3hrs was showing up...  I have no idea what I did but I created another 3d view and the original bits showed up along with the layer buttons which had been missing from the screen which I thought was just a new feature from  2.75...!  Picture to show the 2 screens, top one doesn't render but bottom one does    Any idea's what I've done? On what site can I ask questions related to copyright? I want to make a summary of a book and use it to earn money. However, I don't know whether it's legal or not.  Which Stack Exchange site can I ask this question on? How does sudo handle $HOME differently since 19.10? Since the  would it make sense to create a Stack Exchange site dedicated to homework help? It wouldn't have to be limited strictly to homework either, possibly including discussions of puzzles and brain teasers and possible approaches to solving them.  I have a programming background so I would be interested in helping with CS or math related homework, discussions of programming contest problems, etc. Topics don't necessarily have to be related to programming either. That's just where my interests are.  What are your thoughts? I am writing a cover letter and CV using moderncv. Everything works fine so far, but the text in the cover letter is not justified. I think it is good that it is not hyphenated, but it would look much nicer if the text was justified.  Here is a minimal example:  \documentclass{moderncv} \moderncvstyle{classic}  \usepackage{lipsum} % just for dummy text  \firstname{John} \familyname{Doe}  \begin{document} \recipient{Prof.\ Dr.\ Foo Bar}{} \opening{Dear Professor Dr.\ Bar,} \closing{Yours sincerely,} \enclosure[Attached]{curriculum vit\ae}  \makelettertitle \lipsum[1] \makeletterclosing  \clearpage  \makecvtitle  \section{Education} \cventry{2009--present}{PhD Student}{here}{and}{there}{} \end{document} Watched screen recording but it's not saved to the desktop I recently recorded a session with my dad. I stopped the recording after the session ended (with the setting set to save to Desktop), clicked the icon that appeared on the lower right corner to open the file, and played back a few minutes to make sure it worked. I then clicked Share to send it via AirDrop to my computer, which did not work; the status remained &quot;cancelled&quot; despite my efforts. I assumed I'd be able to access it through my phone by sending it through a third app, so I pressed cancel on the AirDrop pop-up window. The entire screen recording closed and (apparently) vanished forever after the action. I'm extremely frustrated because I can't seem to locate this video. Sort Order on Close Vote Queue The Close-Vote queue is large and growing. I searched for definitive information on how that queue is sorted for reviewers, and the nearest I could find is that it is randomized - but that post was some years old.  Would it be possible to sort on order of votes already received? That is, all questions with 4 votes to close are surfaced first (in random order) to reviewers? Questions with 3 votes would come up before ones with 2, etc. In that manner a given question gets out of 'will it close?' limbo faster.   This feature request would, in my opinion, be supportable if the majority of reviewer votes were going to single-vote questions. I cannot (I think) actually find these numbers. If this is the case, the majority of the work is going to an ever-increasing queue, and proportionally fewer votes are being resolved.  Note there are other distributions that could help get in this direction without being a strict ordering, like weighting the chance a given question is surfaced to a reviewer by the number of votes. However, for discussion purposes I thought I'd keep it simple.  Usual apology if this has actually been addressed. Search is sad-making. How do I properly clean up Excel interop objects? Forcing smoothness of regression coefficients It is a general and maybe basic question, but it will help me to avoid a mistake. To test the dependence of continuous variable on nominal with parametric test (t-test, ANOVA), "the data has to be normally distributed" (distribution have to be not much violated from normal).   But I don't clearly understand: I have to test the normality of the continuous data together (whole sample) or the normality of data in every single group?   And if my groups have small sizes (n=4-6), and therefore I fail to reject null, does this indicate a permission to use parametric methods?  Can anyone provide me a link to some good examples of statistical (biomedical) hypothesis testing with R (google did not helped)? I am encountering two definitions of the special orthogonal lie algebra, and I would like to know if they are equivalent, and if there are advantages to working with one over the other.  If we begin with an $n$-dimensional vector space $V$ over a field $k$ and a chosen basis, we can define a bilinear form on $V$ by a matrix $S\in M_n(k)$, ie, let $\langle v,w\rangle=v^tSw$ for all $v,w\in V$.  Now $g\in GL_n(k)$ preserves the form ($\langle g(v),g(w)\rangle=\langle v,w\rangle$) if and only if $g^tSg=S$, so all such $g$ form a linear algebraic group $G$.  The tangent space at the identity of $G$ will be contained in that of $GL_n(k)$, so $T_eG\subset T_eGL_n(k)=M_n(k)$, and in fact, $T_eG=\{B\in M_n(k)\mid B^tS+SB=0\}$.  $T_eG$ becomes a lie algebra, $Lie(G)$, if we define the bracket to be the commutator of two matrices.  Now, if $S=I_n$, it follows that $G=O_n(k)$ is the orthogonal group of matrices satisfying $g^tg=I_n$, and $Lie(G)=\mathfrak{so}_n$ is the lie algebra of antisymmetric matrices.  In Humphrey's Introduction to Lie Algebras and Representation Theory, he defines $\mathfrak{so}_n$ to be all matrices $B$ satisyfing $B^tS+SB=0$, where $$ S=\begin{pmatrix} 1&amp;0&amp;0\\ 0&amp;O&amp;I_l\\ 0&amp;I_l&amp;O \end{pmatrix} \hspace{.5in}\text{or}\hspace{.5in} S=\begin{pmatrix} O&amp;I_l\\ I_l&amp;O \end{pmatrix} $$ depending on the parity of $n$.  The matrices obtained in this way are not antisymmetric, nor is the group $G$ preserving the form defined by $S$ the orthogonal group $O_n(k)$.  Are the two groups obtained from considering different $S$ isomorphic?  Are the two lie algebras isomorphic?  If so, why would one prefer one form to the other? Which one is correct, or are both of them fine?    "It would take the average person 10 days to read this novel"    Or    "It would take an average person 10 days to read this novel" Does it mean that two threads can't change the underlying data simultaneously? Or does it mean that the given code segment will run with predictable results when multiple threads are executing that code segment? A function for which one-sided limits are zero and infinity