The two sentences I encountered when I read grammar book are as follows:   I had no place to live in. A good place to eat is the Sichuan restaurant around the corner.   Regarding the 1st sentence, the grammar book says the infinitive phrase to live in serves as attributive to modify place. The sentence can be changed into: I had no place in which I can live. And there must be a preposition in to form the phrase to live in the place.  Thus, if the rule of the grammar book is right, there should be a preposition at right after eat and the sentence will be A good place to eat at is the Sichuan restaurant around the corner for the 2nd one, which makes up the phrase A good place at which we can eat.  So, what do I want to know now is which one is right or both of them are correct?
New York is a great place to live. New York is a great place to live in.  I've seen the former usage a lot and I've started wondering what the grammar aspects of it are. The main question I'm asking involves the grammar when the preposition in the end of the sentence is deleted. Is it equally formal or correct to omit it? What are the grammar properties of this? Some more examples of similar usage:  This organisation is a great place to work. This is a great place to stay/sit/study/travel/go.  Just to show that 'live' isn't special in this case. Note: I'd posted the same question  before, but the answers were not satisfying enough (the answers there did not seem to provide the precise grammar aspects of this, those that could be in a serious grammar book), so I'm posting this here to get some more views on the question. I hope it is acceptable.
How do electromagnetic waves wave? Electromagnetic waves have a physical crest and trough as observed in microwaves and radio waves. I understand that is electromagnetic field vectors that wave, not the photon. But how do they wave? What does causes them to change direction? Visual Studio Solutions Folder as real Folders I have a Visual Studio Solution. Currently, it is an empty solution (=no projects) and I have added a few solution folders.  Solution Folders only seem to be "virtual folders", because they are not really created in the Filesystem and files inside solution folders are just sitting in the same folder as the .sln file.  Is there a setting that i've overlooked that tells Visual Studio to treat Solution Folders as "real" folders, that is to create them in the file system and move files into it when I move them inside the solution into one of those folders?  Edit: Thanks. Going to make a suggestion for VS2010 then :) Prevent abstract environment to reset pagenumbering $\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups. What is the meaning of equation of a circle or equation of a cube? We have an equation of a Circle $$x^2 + y^2 = 1$$ and equation of a Cube $${||x-y|+|x+y|-2z|+||x-y|+|x+y|+2z|=1}$$  When I substitute x,y in first equation or x,y,z in the second equation then the equations are said to be satisfied when LHS and RHS are equal.  I have a quick question. If the first equation or second equation get satisfied, because LHS becomes equal to RHS, then those values of x and y of first equation are said to be lying on the circumference of the circle and not inside or outside of the circle and x,y,z of the second equation are said to be lying on the surface of the cube and not on the inside and not on the circle of the cube. Correct? ART has better performance and better battery life on paper at least.  Should I consider switching to it on my moto g? What are the results I can expect? What precautions should I take? Is it easy to turn back to dalvik? How to remove top and bottom whitespace of longtable? I am using longtable instead of tabular environment and noticed that it puts some additional whitespace at the top and at the bottom of the table. Is there some way to remove it (something less hacky than \vskip -\baselineskip before the table)?  Small piece of code for illustration:  \documentclass[12pt]{book} \usepackage{longtable}  \begin{document}  Linelineline  \begin{longtable}{l l} cell1 &amp; cell2 \end{longtable}  Linelineline  \begin{tabular}{l l} cell1 &amp; cell2 \end{tabular}  Linelineline  \end{document}   And that's what I am getting:    Common tabular environment does not have any additional margins, but longtable does. finding rational roots of polynomials Say I have two strings,  String s1 = "AbBaCca"; String s2 = "bac";   I want to perform a check returning that s2 is contained within s1. I can do this with:  return s1.contains(s2);   I am pretty sure that contains() is case sensitive, however I can't determine this for sure from reading the documentation. If it is then I suppose my best method would be something like:  return s1.toLowerCase().contains(s2.toLowerCase());   All this aside, is there another (possibly better) way to accomplish this without caring about case-sensitivity? I've been hearing some rumors from friends, mostly anecdotal indicating that skills, when gone past 10 (such as initially having 10 in one skill, then finding a bobblehead or skillbook), actually improve past 10.     I can't find any proof of this yet, and my current character right now is slightly incapable of maxing any stats soon to 10 and testing it out. So I'd like to understand if SPECIAL stats increased past 10 show any benefit?  Can SPECIAL stats be increased past 10? Gauss's mean value theorem problem Suppose that  $f(z)$ is analytic and $f(z)\neq0$  on the disc $|z|&lt;1$ .  Show that for $0&lt;r&lt;1$,  $$ \exp\left[\frac{1}{2\pi}\int_{0}^{2\pi}{\log}|f(re^{i\theta})|\,d\theta\right] = |f(0)| $$  Any other theorems needed to solve this problem? I don't have any idea just with "Gauss's MVT"  Thank you in advanced. Search and replace a line in a file in Python I want to loop over the contents of a text file and do a search and replace on some lines and write the result back to the file. I could first load the whole file in memory and then write it back, but that probably is not the best way to do it.  What is the best way to do this, within the following code?  f = open(file) for line in f:     if line.contains('foo'):         newline = line.replace('foo', 'bar')         # how to write this newline back to the file What are the different ways that a message can be displayed to a bash shell after a user logs in? I have a CentOS 5.7 VPS using bash as its shell that displays a branded greeting immediately after logging in via SSH. I've been trying to modify it, but can't seem to find where it is in the usual places. So far I've looked in the motd file and checked sshd_config for banner file settings. A banner file is not set.  Where else can I look for where the login message might be? How to launch a command on network connection/disconnection? I have a wifi connection that requires to authenticate using a web form once the wireless link is established. I know how to automate the authentication with a script that uses curl/.  But how can I ask Windows to call my script every time I connect to a particular network connection?  I would be also interested in receiving the name of the wireless profile or the ESSID on the command-line of my script. Pass shell variable as a /pattern/ to awk Having the following in one of my shell functions:  function _process () {   awk -v l="$line" '   BEGIN {p=0}   /'"$1"'/ {p=1}   END{ if(p) print l &gt;&gt; "outfile.txt" }   ' }   , so when called as _process $arg, $arg gets passed as $1, and used as a search pattern. It works this way, because shell expands $1 in place of awk pattern! Also l can be used inside awk program, being declared with -v l="$line". All fine.  Is it possible in same manner give pattern to search as a variable?  Following will not work,  awk -v l="$line" -v search="$pattern" '   BEGIN {p=0}   /search/ {p=1}   END{ if(p) print l &gt;&gt; "outfile.txt" }   '   ,as awk will not interpret /search/ as a variable, but instead literally. extract value between two search patterns on same line How is adding these schemes meant? Could someone be able explain how to add prime divisors or their multiplication with the locally finite set $n_{Z} Z$ in $\sum n_{Z} Z$? . Total number of solutions of an equation What is the total number of solutions of an equation of the form $x_1 + x_2 + \cdots + x_r = m$ such that $1 \le x_1 &lt; x_2 &lt; \cdots &lt; x_r &lt; N$ where $N$ is some natural number and $x_1, x_2, \cdots, x_r, m$ are integers?  Also, what would be the solution in the relaxed case where $x_1, x_2, x_3, \dots, x_r$ could be equal? 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Is it something to do with user groups, or is it a seting somewhere?