Please tell me what "would" means in this sentence.     In AmE, the phrase "go to hospital' would be not correct. One of the articles, a or the, would be necessary.
Do you think that "was going to be" or "would be" could be used as past tense of will?     I thought this book was going to be your choice.        I thought this book would be your choice.   Do these two sentences basically mean the same thing or are they slightly different?
I have a matrix:  $$ A=\begin{bmatrix}1 &amp; a \\ 0 &amp; 1\end{bmatrix} $$  which satisfies: $A\left( e_{1}\right)=e_{1},A\left( e_{2}\right)=ae_{1}+e_{2}, a\neq 0$  I need compute all powers $A^{n}, n\in \mathbb{Z}$ and find their matrices.  $$ A^n= \begin{bmatrix}1 &amp; na \\ 0 &amp; 1\end{bmatrix} $$  Is it true?  Is there a basis of $V$ (if $V$ is a 2-dimensional real vector space with basis $\left\{e_{1},e_{2}\right\}$) so that the matrix of $A$ is diagonal? Why didn't Doc remember Marty's outfit? In Back to the Future 3, Doc (from 1955) sends Marty back in time wearing a cowboy outfit.  But then, Doc (from 1885) doesn't remember that it was him who offered this outfit to Marty.   Does this mean there are two different Docs (from differing timelines) or is it the same Doc but he somehow forgot the outfit. Story is in a medievalish setting and starts with a woman who has been falsely accused of being a witch being taken by 2 men to be sacrificed to a dragon.  She ends up befriending the (male) dragon, who is able to transform into various forms, including human, and can speak only the language of whatever form he is in. e.g. can speak English in human form, but can't in dragon form.  He needs to return to his dragon form every day at sunrise or he dies.  Contact with iron or steel causes him pain and prevents him from transforming.  Near the end of the book, he's been put in handcuffs by one of the two men from the start and the woman has to get the assistance of the other one (village blacksmith?) to remove them before sunrise, which they manage to do just in time.  I think I read it maybe 10 years ago.    I also remember it was a very short book, probably only about 100 pages. What does a Terminator do after its mission is accomplished? A Terminator is essentially given a mission or an objective ("Go back in time and kill Sarah Connor" or something of the like).  What does a Terminator do once its mission is accomplished?  We see in Terminator 2: Judgment Day (the live-action movie) that the  (played by Arnold Terminator Schwarzenegger) completed its mission of protecting the Connors, and then sort-of just melted itself into nothingness (presumably to protect the world from discovering Terminators again).  But what would the  or the  (in Terminator 3) have done?   Are they given multiple directives ("Go kill Sarah Connor, then go kill Robert Baratheon, and then have a nice hot bath; you've earned it")?  This question is related, but not a dupe: How to explain dropout regularization in simple terms? What is the difference between "source x", ". x" and "./x" in Bash? What does a confidence interval with a negative endpoint mean? For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$ Well I attempted to try this but I failed to solve it: So $$\Phi_{p^{n}}(x)= \frac{x^{p^{n}} - 1}{\Phi_{1}(x) \Phi_{p^{2}}(x) \dots \Phi_{p^{n-1}}(x)}$$  Now I'm just stuck here. I saw a result somewhere on the net that said $\Phi_{p^n}(x) = \Phi_p(x^{p^{n-1}})$. I would just use that, but I don't see why that result is true or know how to show that's true.  How do I approach this? How would you prove the following limit?  $$\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$$  I think the best way is using the squeeze theorem but I can't find left expression.  $$0 \le \frac{x^3y}{x^4 + y^2} \le \frac{x^3y}{x^4} \le \frac{x^3y}{x^3} \le y = 0.$$  But I'm not sure I'm right (especially at $\frac{x^3y}{x^4} \le \frac{x^3y}{x^3}).$  If I'm right - I'd glad if you can accept it.  If I'm wrong - can you please correct me?  Thanks in advance! AES and DES - reusing the same round keys No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy Show there is no analytic function in $\{|z|&lt;1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. I guess something went wrong along the way and I would like your assistance.   $f$ does'nt get a maximum in the domain, because if it did, it would be constant in the domain, meaning $|f(z)|=1\ge 1+|z|^2$ which doesn't hold for all z. Since $f$ isn't zero in the domain, ${1\over f}$ is analytic in the domain. but $|{1\over f(z)}|\le {1\over 1+|z|^2}\le 1={1\over f(0)}$, which indicates a local maximum making ${1\over f}$ constant, contradiction the fact the $f$ isn't. What am I really lacking here? How do I set a background image while I am editing? How to enable hibernation? Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$ Let $a,b,c&gt;0$ be real numbers such that $a+b+c=3$, find the maximum and minimum of:   $$\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$$   I've tried using AM-GM-HM, but I can't find the maximum or the minimum.  Using intuition, substituting $a=b=c=1$ should give us one of the optimums, but I cannot prove that it is the optimum. Chrome: Site has updated in the background I keep getting these notifications despite not having an RT tab open. What gives? This question led to a new package:      I wish to typeset some relatively long URLs in a piece of text, and when I use \url{..}, the resulting text does not respect the margin boundaries that govern the main text body, instead going all the way to the edge of the paper before wrapping around.   For reference, my preamble looks like this:  \documentclass[12pt]{article} \usepackage{mathptmx} \usepackage{fullpage} \usepackage[pdftex]{hyperref}   and example of the url I'm including is:  \begin{itemize} \item Some text  \url{very-long-url} ... \end{itemize}   I'm compiling using pdflatex, although I doubt this makes a difference. Need a MP3 ID3 tagger, and cover fetcher I need to tag my MP3 library, and have tried kid3 (which was manual tagging), when I used Kubuntu 9.10 (I now use Ubuntu Meerkat) Here are the features I am hoping for:   A good and clean UI. Tagging should be automatic, like Winamp's autotag feature, which rocks, btw! It should also embed the cover-art in the mp3, not copy a jpeg file in the folder, because now-a-days all players support displaying cover art. But acceptable if not possible. Rename the files as per some regular expression like %TrackNo - %Artist - %Title.  Should be accurate, and more importantly smart. I want to start tagging at night, and hopefully my collection should be done by the morning, w/o it being stuck at a user prompt at 1%.   If one app cant do all, I am willing to use 3, wouldn't mind exposure to a few more apps ;)  I have used picard or someting, and I didnt like it quite a lot. But wouldn't mind using it, if there is no other alternative.   Thanks for your time! Let $q \in \mathbb C$, $|q|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n:  n \in \mathbb N\}$ is dense in $S^1$.  My attempt: As $(q^n)$ is limited, there is subsequence $(q^{n_j})$ convergent. So given $\epsilon &gt; 0, \exists j_0 \in \mathbb N, \quad |q^{n_j} - q^{n_k}| &lt; \epsilon, \quad \forall j,k \geq j_0$. Supose that $n_j &gt; n_k$, then  $|q^{n_j} - q^{n_k}| = |q^{n_k}||q^{n_j - n_k} - 1| = |q^{n_j - n_k} - 1| &lt; \epsilon, \quad \forall j, k \geq j_0$. So, there is a subsequence of $(q^n)$ that converges to $1$.  Using this fact, how can I ensure that for all $w \in S^1$ there is a subsequence of $(q^n)$ that converges to  $w$? I have some commands to in my rc.local. I know that they are failing. How can I get log file with messages produced by executing rc.local? Where is it located?  I have checked the /var/log/boot.log. I know my messages are not there because I know already what is the reason of failure. But I still want to make sure from log file.  Note, I don't want to run script again, I could but I don't want. I would rather analyse wht happened during startup.  Thanks for any help.  Ubuntu 12.04 Desktop (if it matters) Leaflet Customer Marker Changes Position with Scale