Is it good English to say "They have just left", when talking about a single person (perhaps someone you don't know the gender of)?  (I am a native English speaker, I'm looking for the view held by lexicographers).
Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end.
How do I install and manage GNOME Shell extensions? How to zip a whole folder using PHP PHP preg_match (.*) not matching past line breaks There is (there's) vs.There are What are the roots of the creeping usage of "there's" for both singular and plural predicates? (This seems to be more common in spoken English.) I have 2 theories.  Perhaps it is because spoken communication our society is becoming less formal by the day. Or perhaps it is a reflection of speakers of other languages having increasing contact with native English speakers.  I am aware of German  "es gibt" and Spanish  "hay" constructions. Please comment.  3/06/14 I ran a couple of Google Ngrams and was surprised to find a greater rise in the use of "there's" in English fiction than in general English language books, since the turn of the century.  This would seem to support my contention that informality is behind the shift. I often see tutorials on the web or posts on this site which make heavy use of the following characters at the command line. Often it seems that they are used for pretty similar purposes. What are the differences between them when used on the command line or for shell programming? For what purpose do I use which of them?  " " double quotes  ' ' single quotes  ` ` backticks I am trying to capitalize Western Canada or western Canada properly and am wanting a definition for when the "ern" is added as a suffix to a locational distinction of a proper noun.  I believe the capitalization is related to the suffix and am grouping two questions.  After researching on the internet I have found a trend that areas of discrete area become capitalized along with their proper noun   East New York West Hollywood East London (Britain) East Los Angeles   Some locations have "ern" added to their locational modifier.    Web Examples (from government sites):   eastern Canada ( Western Canada ()   All the examples listed contain discrete areas.  The "ern" suffix is used for larger areas, but I am unable to determine when an area becomes large enough. Can I use mirroring to make a copy of my Database? error: file '/grub/i386-pc/normal.mod' not found. grub rescue&gt;   What can I do? I just sit and stare at it.   I found my old netbook (Dell Inspiron 1010) which I have not used for about four years. I replaced Windows XP with Ubuntu 12.10. I used my bootable USB drive. I installed and rebooted. I got the message that normal.mod is not found.   What should I do? Type exit, reboot, or quit? Should I re-install? Linear Algebra: If $A^3 = I$, does $A$ have to be $I$? How to make a LAMP server accessible from the internet? Hi I want to make my own SNS (Social Networking Site), so I installed LAMP on my Ubuntu 14.04. But its not accessible from the internet! I can run the server only on my computer by typing "https:\localhost" on my browser.  I don't want any domains; I just want that whosoever from any part of the world wants to use my SNS he/she just have to type the ip-address and my SNS opens i.e. I want my server accessible from the internet.  My router is Binatone DT 850W. Can you please tell me what should I do? Where did the ~/Library folder go in Lion? Can I see my active diplomatic deals in Civ 6? When making deals with AI I'm having a hard time assessing if I'm already trading for the resource or not. Is there a way I can see my currently active deals or deal history?  If not, is there a way I can see which resources I am currently importing? When are infinities okay? I'm a little confused about how to handle infinities in physics. On the one hand, I always here things like infinities are not physically tenable answers. GR can't answer anything about the origin of the universe because of singularities. Throw away the radial solution that gives an infinite potential when solving the Laplace equation in spherical coordinates. But then there are other times that the infinities are okay. For instance, it is usually okay to set the reference point for your potential at infinity. There are certain times in David Tong's quantum field theory lecture notes where he seems to almost to hand wave away infinities. So, philosophically, physically, and mathematically when are infinities okay, and when are they not okay? I'm trying to understand at a deeper level the ubiquity of log-likelihood (and perhaps more generally log-probability) in statistics and probability theory.  Log-probabilities show up all over the place: we usually work with the log-likelihood for analysis (e.g. for maximization), the Fisher information is defined in terms of the second derivative of the log-likelihood, entropy is an expected log-probability, Kullback-Liebler divergence involves log-probabilities, the expected diviance is an expected log-likelihood, etc.    Now I appreciate the many practical and convenient reasons.  Many common and useful pdfs are from exponential families, which leads to elegantly simplified terms when log-transformed.  Sums are easier to work with than products (esp for differentiating).  Log-probs have a great floating point advantage over straight probs.  Log-transforming a pdf often converts a non-concave function into a concave function.  But what is the theoretical reason/justification/motivation for log-probs?  As an example of my perplexity, consider the Fisher information (FI).  The usual explanation for intuiting the FI is that the second derivative of the log-likelihood tells us how "peaked" the log-likehood is:  a highly peaked log-likelihood means the MLE is well-specified and we are relatively sure of its value, while a nearly flat log-likehood (low curvature) means many different parameter values are nearly as good (in terms of the log-likelihood) as the MLE, so our MLE is more uncertain.   This is all well-and-good, but isn't it more natural to just find the curvature of the likelihood function itself (NOT log-transformed)?  At first glance the emphasis on the log-transform seems arbitrary and wrong.  Surely we are more interested in the curvature of the actual likelihood function.  What was Fisher's motivation for working with the score function and the Hessian of the log-likelihood instead?  Is the answer simply that, in the end, we have nice results from the log-likelihood asymptotically? E.g., Cramer-Rao and normality of the MLE/posterior.  Or is there a deeper reason? Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$ I'm having a hard time truly understanding the meaning of $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$ where $V$ is the domain of a linear transformation $T:V\to W$. I've used this equation several times in many problems, and I've gone over the proof and I believe that I fully understand it, but I don't understand the intuitive reasoning behind it. I'd appreciate an intuitive explanation of it.  Just to be clear, I do understand the equation itself, I am able to use it, and I know how to prove it; my question is what is the meaning of this equation from a linear algebra perspective. How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$? A question on my math homework asks us to show that if $0 &lt; p &lt; 1$ and $a, b &gt; 0$, then $a^p + b^p &gt; (a + b)^p$. I have no idea how to do this, any pointers? Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Let's say you have the ability to shine some light into a perfectly round sphere and the sphere's interior surface was perfectly smooth and reflective and there was no way for the light to escape.  If you could observe the inside of the sphere, what would you observe? A glow? And would temperature affect the outcome?  Seems silly, it's just something I've always thought about but never spent enough time (until now) to actually find an answer. Find $\lim_{n \to \infty} \sqrt[n]{n!}$. I am playing around with the root/ratio test to practice with series. I just showed that $\sum \frac{1}{n!}$ converges by using the ratio test. I decided to see how things would go with the root test and I got stuck at something that I can't find on google. Right away while running the root test I encountered $\lim_{x \to +\infty}\left(\frac{1}{n!}\right)^\frac{1}{n}$. I have made the claim that $\left(n!\right)^\frac{1}{n}\geq 1 \hspace{3mm}\forall n\in \mathbb{N}.$ I have begun the proof and I think it is on the right track but some verification would be nice.  Proof: We can see that for n=1, this obviously holds, $\left(1!\right)^1\geq 1.$ Now suppose that this is the case for some $n=k$, then we have $\left((k+1)!\right)^{\frac{1}{k+1}}= \left((k+1)k!\right)^\frac{1}{k+1}$. It is at this point that I start to have a little trouble. Can somebody give me a push in the right direction? Thanks! Do fluorescent lighting and shutter speed create a problem with color cast? I took a bunch of photos at my son's martial arts club using a D90 with a 50mm F1.8.  The club is lit with overhead fluorescent lighting, and I was getting some weird results where some shots are "white", others have an "orange cast", and still others are partly white and partly orange in the same shot.  I suspect it has to do with the combination of the frequency of the light flicker and with the camera shutter speed. Here is a sequence of 3 shots that show the problem.  The shots were taken with 1/500s at F2 and ISO-800 and with Auto-WB.  First shot ("white/normal"):    Second shot ("orange cast" at top):   Third shot ("orange cast" at bottom):   These were taken in burst mode within a second of each other.  Can anybody tell me what is going on?  And, how I can avoid this?