It only seemed that way as India took lead to Australia.  It seemed only that way as India took lead to Australia.  Both mean the same and both are correct?
I have seen the word 'only' placed both before and after a noun. Where should the word 'only' go in this sentence? Is it the writer's choice?   If you have attended every lesson, only the songs need to be rehearsed at home. If you have attended every lesson, the songs only need to be rehearsed at home.
Node.JS Not working on the internet Multivariable Delta Epsilon Proof $\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^4+y^4}$ --- looking for a hint I have the limit $$\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^4+y^4},$$ and would like to show with an $\epsilon-\delta$ proof that it is zero. I know with a situation like $$\left|\frac{x^4y}{x^4+y^4}\right|\leq y$$  or something similar, but I can't find a way to do the same thing here, as no single term in the numerator is of sufficient degree, although I think I could get this with a small hint. As the topic is there exist a homeomorphism between either pair of $(0, 1),(0,1],[0,1]$ What's the fastest connection speed / shortest elapsed time using Migration Assistant? I have installed the developer preview for Yosemite.  Huge mistake. Everything in my workspace is broken.  I don't have any sort of backup image. I was wondering if I could re-download Mavericks and run the installer - would that effectively downgrade me back to Mavericks? I'm trying to write a simple bash function that takes, as its arguments, a number of files and/or directories. It should:   Fully qualify the filenames. Sort them. Remove duplicates. Print all that actually exist. Return the number of non-existent files.   I have a script that almost does what I want, but falls down on the sorting. The return value of the script as it stands is correct, but the output is not (unsorted and duplicates). If I uncomment the | sort -u statement as indicated, the output is correct but the return value is always 0.  N.B. Simpler solutions to solve the problem are welcome but the question is really about why is this occurring in the code I have. That is, why does adding the pipe seemingly stop the script incrementing the variable r?  Here's the script:  function uniqfile {     local r=0       for arg in "$@"     do           readlink -e "$arg" || (( ++r ))      done #| sort -u    ## remove that comment      return $r } WPF ComboBox without drop-down button How do I change the GRUB boot order? 9-speed system to 11-speed drivetrain upgrade? Is a totally ordered set well-ordered, provided that its countable subsets are? Let $(X,⪯$) be totally ordered set, prove that if every non empty countable subset of $X$ is well ordered then X is well ordered.   It does seem obvious that any subset should have a minimum but I am not sure of how to prove it. Any help would be appreciated, and sorry I put up the same problem earlier but forgot to include the 'countable' subset. UnboundLocalError: local variable 'url_request' referenced before assignment I'm starting out in Visual C++ and I'd like to know how to keep the console window.  For instance this would be a typical "hello world" application:   int _tmain(int argc, _TCHAR* argv[]) {     cout &lt;&lt; "Hello World";     return 0; }   What's the line I'm missing? Let us consider The following example   \documentclass{article} \usepackage{enumerate} \begin{document} \begin{enumerate}  \item Which of the following numbers is the largest ?\\ $2^{3^4},2^{4^3},3^{2^4},3^{4^2},4^{2^3},4^{3^2}.$  \begin{enumerate}[(a)] \item  $2^{3^4}$ \item  $3^{4^2}$ \item  $4^{3^2}$  \item $4^{2^3}$ \end{enumerate}  \end{enumerate} \end{document}   This produces :    But I'd like to produce the following using the same package  :   OR     OR   How can I do that? Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$ I have the following functional equation. Find all continuous functions $f:(-1,1) \to \mathbb R$ such that $$ f(x+y)=\frac{f(x) + f(y)}{1 - f(x)f(y)} $$ The first obvious solution is $f(x) \equiv 0$. Another one I guessed, it is $f(x) = \pm \tan x$. I suspect, that there are no more solutions. The problem is that I don't know how to prove that.  Since we have a rational equation, I have no idea how to make any substitutions in order to get expression for $\tan x$ (as it is not a rational expression).  P.S. I can also show that it is true that (a) $f(0) = 0$ (take $x=y=0$), and (b) $f(-x) = -f(x)$ (take $y=-x$).  Update: there is a solution of this problem also here: I tried for a while to classifiy the singularities of $\frac{1}{z}-\frac{1}{\sin z}$ at the origin, but I am stucked. Is there someone who is able to help me at this point? How many different (circular) garlands can be made using $3$ white flowers and $6m$ red flowers? This is my first question here.   I'm given $3$ white flowers and $6m$ red flowers, for some $m \in \mathbb{N}$. I want to make a circular garland using all of the flowers. Two garlands are considered the same if they can be rotated to be the same. My question is: how many different garlands can I make?  I tried an approach in which I divided the question into three parts:   No. of ways in which the white flowers are all together No. of ways in which two white flowers are together No. of ways in which no two white flowers are together   Can you please help?  The answer is $3m^2+3m+1$ in the book that I saw  Thanks Inequality involving sides of a triangle How can one show that for triangles of sides $a,b,c$ that   $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} &lt; 2$$  My proof is long winded, which is why I am posting the problem here.   Step 1: let $a=x+y$, $b=y+z$, $c=x+z$, and let $x+y+z=1$ to get   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}&lt;2$  Step 2: consider the function $f(x)=\frac{1-x}{1+x}$, and note that it is convex on the interval (0,1), so the minimum of   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}$  is reached when the function takes the extreme points. i.e. $x=y=0, z=1$.    But going back to the fact that this is a triangle, we note that $x=y=0 \implies a=0$ which is not possible, so the inequality is strict. In a certain case, the user will be asked to confirm if he/she wishes to leave the page, due to editing a post, even when he/she has stopped editing.  To reproduce:   Start editing a post (I've only experienced this with a question) Another user finishes editing the post before you and the message "This post has been edited" appears Clicking on the message bar will take you out of editing mode and will show you the updated post from the other user's edits Trying to navigate away from the page will then ask for your confirmation What is the relationship between redshift and conformal time ?   For example in a paper i found:   taking $z_e = 3234 $ at the time of radiaton-matter equality yields the conformal time $\frac{\eta_e}{\eta_0} = 0.007$ and taking $z_E=0.39$ at matter-$\Lambda$ equality yields $\frac{\eta_E}{\eta_0}=0.894$ and setting redshift at decoupling $z_d=1089$ yields $\frac{\eta_d}{\eta_0} = 0.0195$  where $\eta_0$ is the present decoupling time.  Further some cosmological parameters are given as :  $\Omega_r = 8.36 \times 10^{-5}, \Omega_m = \Omega_b + \Omega_{dm} = 0.044 +0.226, \Omega_\Lambda = 0.73,  H_0=0.72$  Now how can i calculate all those $\eta_e, \eta_E, \eta_d, \eta_0$ from given redshift values and/or above parameters ? I searched whole of my text books trying to find an explicit relation for conformal time $\eta$ but all i got was $ \mathrm{d}t=a(t)\mathrm{d}\eta$. Any help would be very helpful. Most common C# bitwise operations on enums For the life of me, I can't remember how to set, delete, toggle or test a bit in a bitfield. Either I'm unsure or I mix them up because I rarely need these. So a "bit-cheat-sheet" would be nice to have.  For example:   flags = flags | FlagsEnum.Bit4;  // Set bit 4.   or  if ((flags &amp; FlagsEnum.Bit4)) == FlagsEnum.Bit4) // Is there a less verbose way?   Can you give examples of all the other common operations, preferably in C# syntax using a [Flags] enum?