I was writing this sentence:     Why are there more of them on some nights than on others?   Is is or are correct here? I was told that is is correct, but to me, are sounds better.
There are so many questions on this website. There is so many questions on this website.  The former &quot;sounds right,&quot; but the contracted form of the latter does as well:  There's so many questions on this website.  Which is correct?
What is the difference between "why are you worried" and "why you are worried"? If a drive doesn't know about partitions and files systems why moving a file from one partition to another takes relatively long time, unlike the instantaneous move on the same partition? Is that file system inefficiency? In this case, NTFS. It seems like the file is being copied and then original is erased, instead of removing the entry about that file in one partition and making it in another? When is it appropriate to use a hyphen? jQuery: live() vs delegate() What would you call a person who doesn't want to learn anything new? Sci-fi story where all 'citizens' had shares in a global company Not everyone was a citizen though, there was a significant underclass who had no shares.  One character was a celebrity in some sort of combat game who was followed by camera drones &amp; used drugs to suppress puberty so he waa an eternal 'child', I have the impression that medical science allowed virtual immortality short of accidents.  One character (may have been the same one) had had a 'previous life' &amp; had committed personality suicide by some form of mind wipe bequeathing his worldly possessions to the new personality that would eventually develop in his old body.  I think the motive for this 'suicide' was essentially boredom, he'd lived a long time.  The mind wipe in question was pretty extensive &amp; all encompassing, he had to be cared for &amp; educated from scratch as if a newborn baby in an adult body, nappies &amp; all (but I'm pretty sure this was purely backstory in the book I read).  He also had miniature nano organisms (or bots?) like miniature worms or millipedes that complimented his immune system &amp; aided healing, they were self replicating, pretty sure they were some sort of bioengineered organism tailored to his DNA rather than bots  but not 100% on that.  There was an organism spanning a large area on the planet that absorbed (or consumed) anything that wandered into it but saved the DNA of anything it had previously absorbed &amp; might randomly reproduce any animal plant or individual it had previously absorbed fully formed.  One of the characters fell into this but got pulled out before the full effects took hold, as a result he grew leaves from his head &amp; his immune system was then constantly battling with the 'infection'.  When did I read this? probably some time in the 80's in the UK.  When was it written? I haven't a clue, sorry.  It was a paperback, probably something I had out of a library, because I never get rid of anything I've bought myself so I'd still have it &amp; be able to dig it out if it wasn't a library loan.  I have lots of fragments of world background &amp; 'colour' that seem to have stuck in my mind there, but a complete lack of any story arc to go with them. I'm very familiar with how symbols display differently in inline mode (with $ ... $) vs. how display math shows them (with \[ ... \] or $$ ... $$).  Two examples would be with limits  $\lim_{n\rightarrow \infty}f(x)$   vs.  \[ \lim_{n\rightarrow \infty}f(x) \]   and with sums  $\sum_{n=1}^{x} n^2$   vs.  \[ \sum_{n=1}^{x} n^2 \]   My Question is:     How do you display these things in inline mode (with all the nice inline formatting) as if they were in display mode ?   The inverse -- how to display things in display mode as if they were in inline mode -- is also of interest. I keep going around in circles with this problem:  Given the functions $f:X\to Y$ and $g:Y\to Z$, if $g\circ f:X\to Z$ is bijective, then prove $f$ must be one-to-one and $g$ must be onto. I was able to prove this without difficulty. However the second part of the problem has me stumped:  a) Find functions $f,g$ where $g\circ f$ is bijective but $f$ fails to be onto.  b) Find functions $f,g$ where $g\circ f$ is bijective but $g$ fails to be one-to-one.  My attempt for (a): Let $f:\mathbb{R}\to \mathbb{R}^+$ be defined by $f(x)=e^x$ and $g:\mathbb{R}^+\to \mathbb{R}$ be defined by $g(x)=\ln(x)$. Then $g\circ f(x)=g(f(x))=g(e^x)=\ln(e^x)=x$ which is bijective, $g$ is onto and $f$ fails to be onto... or so I thought. Upon closer inspection $f$ $\underline{is}$ onto for the given codomain $\mathbb{R}^+$.  And now I'm stuck in a rut. Anyone out there have any hints? What are the fundamental differences between the mainstream *NIX shells? What are the fundamental differences between the mainstream *NIX shells and what scenarios might prompt you to use one over the other?  I understand that some of it probably comes down to user preference but I've only ever used Bash and I'm interested to hear where another shell might be useful. Also, is there an impact on user-written shell scripts when running under one shell or another or is it simply a matter of changing the shell at the top of the file?  My instinct says it's not that easy. What prevents photons from getting mass from higher order Feynman diagrams Why doesn't ZIP Compression compress anything? A 398MB directory was only compressed to 393MB using 7Z and Normal ZIP compression. Is this normal? If so, why do people continue to use ZIP on Windows? BAV99 forward voltage Custom date format with jQuery validation plugin How can I specify a custom date formate to be validated with the  for jQuery? How do I programmatically create a new content type? I'm building a module (my_module) in Drupal 7. It has some functionality and also will create a new content type. In my_module.install, I implemented hook_install() (my_module_install()).    Can I use more hook_install() to create a new content type (my_module_install()) in this module? If the answer is yes, how should I do this? Otherwise, should I do this in another module? How can I separate a separable function I have a question about calculating the degree of a finite field extension over $\mathbb{Q}$.  This is problem 18 in chapter 1 of Patrick Morandi's Field and Galois Theory. The problem asked to show that $$ \left[ \mathbb{Q}{ \left( \sqrt[4]{2},\sqrt{3} \right):\mathbb{Q} }\right] =8 $$ Here's my work : First, we have $$  \left[ \mathbb{Q} ( \sqrt[4]{2},\sqrt{3}):\mathbb{Q}\right] = \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] . \left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right]$$ It's easy to show that $\left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right] =4 $ because the minimal polynomial of $\sqrt[4]{2}$ over $\mathbb{Q}$ is $x^4 -2$. Next, I'm going to show that  $$ \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] =2$$ Consider the polynomial $f(x) = x^2 -3$. It's monic and $\sqrt{3}$ is a root of $f$, but I'm stuck in proving $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ (hence $f$ is irreducible over $\mathbb{Q}(\sqrt[4]{2}))$.  My question is: Is there any proof to show that $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ or another way to caculate the degree of this field extension?  Thank you for your help. Difference In Eigenvectors Linear Transformations: Proving 1 dimensional subspace goes to 1 dimensional I am having trouble understanding this whole question, and how to prove it.  Let $F:\mathbb{R}^n\to\mathbb{R}^m$ be a linear transformation. Prove that if $L$ is a $1$-dimensional subspace of $\mathbb{R}^n$, then  $F(L)=\{y\in\mathbb{R}^m: y=F(x)\text{ for some }x\in L\}$  the image of $L$ under $F$ is a subspace of $\mathbb{R}^m$ with dimension $1$ or $0$. Hence prove that if the kernel of $F$ is $\{0\}$, then the image of $L$ is a $1$-dimensional subspace of $\mathbb{R}^m$ (and so, in this case, $F$ takes lines in $\mathbb{R}^n$ to lines in $\mathbb{R}^m$). Compiling with g++ using multiple cores The additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group An algebraic group is not necessarily a topological group, since for an algebraic group, the product map $G \times G \to G$ is continuous when $G \times G$ is given the Zariski topology, which is finer than the product topology.   So does this tell you that the additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group? The underlying variety of $\mathbb{G}_a \times \mathbb{G}_a$ is $\mathbb{A}_k^1 \times_k \mathbb{A}_k^1 = \mathbb{A}_k^2$, whose Zariski topology is the cofinite topology, where every open set is also open in the product topology (since $\mathbb{A}_k^1$ also has the Zariski topology).