Conditional: More than 1 The stoplight turns green if there (is/are) more than 1 car(s) waiting   I'm having a bit of trouble figuring out the above statement. Which configuration is correct?  This is odd, as I'm a native English speaker in my mid-twenties, and I like to think my vocabulary and understanding of the English language is pretty good...but I'm always willing to learn!
"There is/are more than one". What's the difference? While adding to an Answer to  question, I needed to use the above phrase, and I suddenly realised I was unsure whether to write "is" or "are".   There is more than one way to skin a cat. If there are more than one species of cat, we will flay each species differently.   I don't think that second example above sounds quite right to me (disregarding the meaning - sorry!), but in my original Answer I felt "is" would have been even worse.  Is "are" always wrong here? If so, what exactly is the rationale? If not, is there a case where it's unquestionably preferred – and why is that?    Note that in both the problematic Answer and my example attempting to mimic the same context more briefly, the writer doesn't know how many there are. There may be one, more, or even none.  Getting even more specific, the writer might have an opinion on how many there might be, and wish to convey his leanings by choice of verb form if language allows this to be done succinctly.
I was reading this article about S&amp;P 500 short ETFs:     and I was confused when it said: "investors should note that such products are suitable only for short-term traders as these are rebalanced on a daily basis". What is ETF rebalancing exactly? and why does it make these ETFs unsuitable for long-term short trading? When it comes to getting a tenure-track position where one has both a lot of resources and academic freedom to do what one wants to do (so having a tenure-track position in a top university might be more useful because one may get more resources at a top university).   Or in short, when one wants to maximize one's chances of becoming a "top scientist".  There are obviously numerous factors, and "rank/prestige" should not be considered as a factor in itself. That said, the period after one gets a PhD is an extremely important time for building up connections, and those are easier to get at a top university. Does Google use the Meta Description Tag for Description of Page? Why does reputation start at 1, and have a lower bound of 1? If a user is the type of person to consecutively get downvoted to potential negative reputation, so be it. What's the reasoning to maintain a minimum of one?  One reason that may justify this is of trying to not deter new users from the site who haven't read the FAQ and unknowingly and wrongly ask or answer a question. But most of us acknowledge this and not downvote in such a scenario.  So what's the reasoning behind this lower bound of 1? For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$ For $n \geq 2$ prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$  We need to use induction.   The Principle of Mathematical Induction, Theorem 4.2.1, states that $n_0 \in \mathbb{Z}$. For each integer $n \geq n_o$, let $P(n)$ be a statement about $n$. Suppose that the following two statements are true:   $P(n_o)$ $( \forall n \geq n_o)[P(n) \rightarrow P(n+1)]$   Then, for all integers $n \geq n_o$, that statement $P(n)$ is true.  Suppose,  $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$, the equation, is true for some natural number $k$.  $\frac{1}{2^2})*...*(1- \frac{1}{k^2}) = \frac{k+1}{2k}$  The induction hypothesis $P(k) \rightarrow P(k+1)$ must hold for any natural number $k, P(k),$ from the basis and inductive step.  $(\frac{1}{2^2})*...*(1- \frac{1}{k^2})*(1- \frac{1}{(k+1)^2}) = \frac{k+1}{2k}(1- \frac{1}{(k+1)^2})$  $\leftrightarrow$ $\frac{k+1}{2k}(\frac{(k+1)^2}{(k+1)^2}- \frac{1}{(k+1)^2})$  $\leftrightarrow$ $(\frac{(k+1)}{2k})( \frac{(k+1)^2-1}{(k+1)^2})$  $\leftrightarrow$ $( \frac{(k^2+2k+1-1}{(2k)(k+1)})$  $\leftrightarrow$ $( \frac{(k^2+2k}{(2k)(k+1)})$  $\leftrightarrow$ $( \frac{k+2}{(2)(k+1)})$  We need to demonstrate that   $(\frac{1}{2^2})*...*(1- \frac{1}{n^2}) = \frac{n+1}{2n}$  holds true for $n \geq 2$  The question is do I just substitute a number that is greater than two after I did the induction? I wonder a generalization of Jensen's inequality: let $\mathbf{X,Y}$ be two positive definite matrices, can we obtain the following Jensen like inequality $$(1-\lambda)\mathbf{X}^{-1}+\lambda\mathbf{Y}^{-1} \succeq((1-\lambda)\mathbf{X}+\lambda\mathbf{Y})^{-1}$$ for any $\lambda \in (0,1)$, where the notation $\mathbf{A}\succeq \mathbf{B}$ represents matrix $(\mathbf{A-B})$ positive semi-definite. How can I create launcher icon for PhpStorm? There was a book (it actually had a second book as well) where a guy gets paid with a group of others to go to a planet that is enclosed in a metallic sphere.   There are many species in this planet. I don't recall if they actually met the races in the first or the second book but there an incident where an alien in the first book ate fruit from a tree that removed any signs of gender from it. Maximum number of files being uploaded by input type file How do I pipe each command given to the shell? I'd like to edit my .bashrc so that every command executed on the shell is piped to something, for example:   $ sudo apt update   _________________ &lt; sudo apt update &gt;  -----------------     \   ^__^      \  (oo)\_______         (__)\       )\/\             ||----w |             ||     ||   I have managed something rather similar, but not entirely:  $ bash $ exec &gt; &gt;(cowsay) $ echo "Hello AU!" $ exit  _______ &lt; Hello AU! &gt;  -------     \   ^__^      \  (oo)\_______         (__)\       )\/\             ||----w |             ||     ||   It is not the desired result, as it only happens after exiting the current shell.  It's mainly for fun/learning purposes. Georeferencing scanned map using ArcMap? Effective way to find any file's Encoding Is it true that the light from some galaxies will never reach us?   The explanation for that is that the Universe expanding faster than the speed of light. But, if the speed of light is constant in all reference frames, then in the reference frame of a galaxy, light must move at the speed of light and thus it must reach us (?).   Could you also explain  how is it possible that the Universe is expanding faster than the speed of light if an object can never be observed to move faster than light? (without Doppler effects). Loopy integral $\int xe^x\sin(x)$ Blender 2.78 with Windows 10 lags when interacting with the UI Update  This has been confirmed resolved in a later version 376.33 and possibly the update prior.     Okay, I recently did a computer update. I used to run Blender 2.77 on a Dell desktop (5 GB RAM, 2.7 GHZ, Windows 8, build in graphics card). Since that computer wasn't fast enough for my preference, I saved up and got a new gaming laptop - the Asus ROG GL552 (Windows 10, 16 GB DDR4 RAM, Nvidia GeForce GTX 960M with 4 GB DDR5 RAM, 2.6-3.5 Ghz, and quad-core intel processor). That laptop has been known to have outdated drivers, so when I got it, I updated it to up to date Windows 10 drivers.  As soon as I started Blender, I immediately noticed its speed. Even doing simple things, like clicking buttons, or rotating the view with the middle mouse button, took too long to register in the program. I tried changing some User Preference System settings, but that didn't really help much. And the hardware seems to be fine - the render is lightning fast (renders the startup scene in under .1 second; it's just laggy when loading the uv screen), so I don't know why it's like this, or what to do. Also, I ran Blender 2.77 on this computer, and it was also slow (although it was fine on my previous computer).  It could be an issue with drivers perhaps (or maybe OpenGL?), but I ran Unreal Engine 4, and had none of the same issues - the speed was pretty decent on that; so I'm not sure why Blender would be so slow. Any help is appreciated - thanks guys! $f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$? Let $f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?          A. $\{0\}$.          B. $(0,1)$.          C.$[0,1)$.          D.$[0,1]$.      My effort: Continuous image of connected set connected. $(0,1]$ is connected and remove $1$ from the set left the set connected...but removing any point from $(0,1)$ make it disconnected.....I am not sure though I have a question related to modeling short time-series. It is not a question , but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$)? By "best" I mean here the most robust one, that is the least prone to errors due the fact of limited numbers of observations. With short series single observations could influence the forecast, so the method should provide a cautious estimate of errors and possible variability connected to the forecast. I am generally interested in univariate time-series but it would be also interesting to know about other methods. I accidentally changed /var owner/group to my username and then changed it back to root, but not all the /var folders' owners are root, so is there anyway to change back owner/group of files/folders to default state?  Or at least those files/folders that are created by packages? I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, strong nuclear force, and electromagnetism.  Those are my understandings going in. If I'm wrong, please correct me. I've done some googling, and I haven't found anything confirming or denying that dark matter is affected by either of the fundamental nuclear forces.  So since dark matter only interacts with gravity, what causes any dark matter particle to be repelled from another? If they can pass freely through each other, and they are gravitationaly attracted to each other, why don't such particles clump together in a single 'point' in space?   It seems to me that particles occupying a single 'space' are philosophically not distinct particles, but I don't know how actual physics would play into this.  Edit , author's credentials unknown, but implicitly claims to be a physicist or astronomer, says "...[P]hysicists generally take all dark matter to be composed of a single type of particle that essentially interacts only through gravity."  Edit 2 The author is this , "Professor of Science on the physics faculty of Harvard University." I have always had a problem installing and removing compiled software, so I have decided I would like to build software from source into a .deb package for easier installation/removal.  I would like to know of an easy and short way to build source into a .deb package, as an end user.  I have tried:   , which did not work for me This  guide, but I found it too long