When leaving the US do you have to go through customs?
What immigration and customs checks are performed for passengers leaving the U.S.?
Good-morning Math Exchange (and good evening to some!)  I have a very basic question that is confusing me.   At school I was told that $\sqrt {a^2} = \pm a$  However, does this mean that $\sqrt {a^2} = +2$ *and*$-2$ or does it mean: $\sqrt {a^2} = +2$ *OR*$-2$  Is it wrong to say 'and'? What are the implications of choosing 'and'/'or'  Any help would be greatly appreciated. Thanks in advance and enjoy the rest of your day :) I have a table similar to this:  CREATE TABLE example (   id integer primary key,   name char(200),   parentid integer,   value integer);   I can use the parentid field to arrange data into a tree structure.  Now here's the bit I can't work out. Given a parentid, is it possible to write an SQL statement to add up all the value fields under that parentid and recurse down the branch of the tree ?  UPDATE: I'm using posgreSQL so the fancy MS-SQL features are not available to me. In any case, I'd like this to be treated as a generic SQL question.  BTW, I'm very impressed to have 6 answers within 15 minutes of asking the question! Go stack overflow! Why do Google search results include pages disallowed in robots.txt? I have some pages on my site that I want to keep search engines away from, so I disallowed them in my robots.txt file like this: User-Agent: * Disallow: /email  Yet I recently noticed that Google still sometimes returns links to those pages in their search results.  Why does this happen, and how can I stop it? Background: Several years ago, I made a simple web site for a club a relative of mine was involved in.  They wanted to have e-mail links on their pages, so, to try and keep those e-mail addresses from ending up on too many spam lists, instead of using direct mailto: links I made those links point to a simple redirector /  script running on my own site.  This script would return either a 301 redirect to the actual mailto: URL, or, if it detected a suspicious access pattern, a page containing lots of random fake e-mail addresses and links to more such pages.  To keep legitimate search bots away from the trap, I set up the robots.txt rule shown above, disallowing the entire space of both legit redirector links and trap pages. Just recently, however, one of the people in the club searched Google for their own name and was quite surprised when one of the results on the first page was a link to the redirector script, with a title consisting of their e-mail address followed by my name.  Of course, they immediately e-mailed me and wanted to know how to get their address out of Google's index.  I was quite surprised too, since I had no idea that Google would index such URLs at all, seemingly in violation of my robots.txt rule. I did manage to submit a removal request to Google, and it seems to have worked, but I'd like to know why and how Google is circumventing my robots.txt like that and how to make sure that none of the disallowed pages will show up in their search results. Ps. I actually found out a possible explanation and solution, which I'll post below, while preparing this question, but  in case someone else might have the same problem.  Please do feel free to post your own answers.  I'd also be interested in knowing if other search engines do this too, and whether the same solutions work for them also. Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$ Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$ What ensures big holes in my bread? Since I can't find any alternative to Linux'  elevation command, I have the following question:  How to define a PowerShell function which requires elevation? I mean UAC prompt.  Say, such function follows:  function system-check {     SFC /ScanNow }   System:  Windows 8.1 Pro 64-bit  PowerShell:   Major  Minor  Build  Revision -----  -----  -----  -------- 5      0      10586  117    EDIT1:  To be 100% understandable let me rephrase:   I run PowerShell as user I run the aforementioned function system-check I want the function to elevate in order to be able to execute the command; note, that I want the UAC prompt to appear This might be a bizarre but crucial question, can I fully trust leaving my laptop in repairs (Genius Bar) while they have full access to it ?  I recently went to the genius bar to get my display fixed, and apparently they asked for my laptop's password just in case they need some "testing" after they're done. Can't they do that as a guest account ?  I got sensitive information on my laptop such as passport copies etc, as well as passwords saved in Safari's keychains for my bank account, paypal, amazon etc ..  The service is due later on today, shall I change my password and ask them to contact me directly if they need something specific ?? They're going to fix in 3 hours so I'll be in the mall whilst they finish. I want to find the interval of convergence of $$\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(2x)^n$$ By the root test, $\sqrt[n]{|(\frac{n}{n+1})^{n^2}(2x)^n|}=|(\frac{n}{n+1})^{n}(2x)|$  And $(\frac{n}{n+1})^n=(1-\frac{1}{n+1})^n\to\frac1e$ as $n\to\infty$  So I've got an open interval(of convergence) s.t. $|\frac1e 2x|&lt;1\implies |x|&lt;\frac e2$.  Now I need to figure out whether the series is convergent or not at the end points, $x=\frac e2, -\frac e2$.  So there are two series I need to deal with, namely, $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}e^n$ and $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(-1)^ne^n$.  Suppose $(\frac{n}{n+1})^{n^2}$ is increasing. Then $$(\frac{n}{n+1})^{n^2}&lt;(\frac{n+1}{n+2})^{(n+1)^2}\iff 1&lt;(\frac{n+1}{n+2})^{(n+1)^2}(\frac{n+1}{n})^{n^2}$$ $$\iff 1&lt;(1-\frac{1}{n+2})^{2n+1}(1+\frac{1}{n^2+2n})^{n^2}$$  But $(1-\frac{1}{n+2})^{2n+1}\to\frac{1}{e^2}$ and $(1+\frac{1}{n^2+2n})^{n^2}&lt;(1+\frac{1}{n^2})^{n^2}\to e$  So I have $1&lt;\frac1e&lt;1$, which is a contradiction. Hence $(\frac{n}{n+1})^{n^2}$ is not increasing. But I don't know if it's decreasing. (is it true that $(1+\frac{1}{n^2+2n})^{n^2}\to e$?)  If $(1+\frac{1}{n^2+2n})^{n^2}\to e$ is true, then $(\frac{n}{n+1})^{n^2}e^n$ converges to some positive number, so $\sum(\frac{n}{n+1})^{n^2}e^n$ diverges. But I don't know if it's decreasing: can't apply the alternating series convergence test(Leibniz's criterion).  So, can you help me with the two end points? How to factor numbers that are the product of two primes System of linear equations having a real solution has also a rational solution. I saw this question     Let $A ∈ M_{m\times n}(\mathbb{Q})$ and $b ∈ \mathbb{Q}^m$. Suppose   that the system of linear equations $Ax = b$ has a solution in   $\mathbb{R}^n$. Does it necessarily have a solution in $\mathbb{Q}^n$?   and I thought I'd give an interesting, possibly wrong, approach to solving it. I'm not sure if such things can be done, if not maybe you can help me refine.    I considered the form of the equality as  $$ A^{(1)}x_1+\cdots+A^{(n)}x_n=b, $$  where $A^{(i)}$ is a column vector of $A$. I then noticed that for $x_i\in\mathbb{R\setminus Q}=\mathbb{T}$ then, and this is where I think I'm doing something forbidden, each $x$ has the represenation  $$ x_1  =  k_{11}\tau_1+\cdots+k_{1p}\tau_p \\  x_2= k_{21}\tau_1+\cdots+k_{2p}\tau_p \\ \vdots \hspace{4cm} \vdots \\ x_n=k_{n1}\tau_1+\cdots+k_{np}\tau_p,$$  where $\tau_i$ is a distinct irrational number, $k_{ij}\in\mathbb{R}$, and $p$ is the number of such distinct irrational numbers. I wound this out, but there may be a discrepancy with $p$ and $m$. I feel this method can lead me to the answer, but I'm not sure where to go from here.  EDIT$^1$:  I end up getting something like this, I believe, after substitution:  $$ A(k^{(1)}\tau_1+\cdots+k^{(p)}\tau_p)=b$$  Here, $k^{(i)}$ is the vector  $$\begin{pmatrix} k_{1i} \\ \vdots \\ k_{ni} \end{pmatrix}.$$  EDIT$^2$:  I think there is no discrepancy with $p$ and $m$ because $A\in M_{m\times n}(\mathbb{Q})$, $K\in M_{n\times p}(\mathbb{R})$, and $\tau\in M_{p\times 1}(\mathbb{T})$, so  $$ (m\times n)\cdot (n\times p)\cdot (p\times 1) = m\times 1. $$ Variance of sum of $k$ randomly drawn numbers from $1,...,n$. if command in find -exec I was just trying to list all directories and files under current directory and also write if they are file or directory with the following command:  find -exec echo `echo {} : ;if [ -f {} ]; then echo file; else echo directory;fi` \;   I know it is a silly command, I can use other things like -type f or -type d, but I want to learn why that piece of code did not work as I expected. It just prints directory to all of them. For example while output of find is:  . ./dir ./dir/file   output of my code is :  . : directory ./dir : directory ./dir/file : directory   And output of   echo `echo dir/file : ;if [ -f dir/file ]; then echo file; else echo directory;fi`   is  dir/file : file   I am working on Ubuntu 14.10 and using find (GNU findutils) 4.4.2 Is it correct to use that/which in the relative clause when it is referring to the place as an object pronoun? I was teaching an ESL class and came across this sentence which confused me a lot:  &quot;The Queen Alice is the place that I go to the most&quot; &quot;Isn't that the place which kids under 12 can't enter?&quot;  Are these 2 sentences correct? Shouldn't &quot;where&quot; be used for both sentences when it's referring to the place and replacing the object? How do I cd into a directory in the home folder? How do I change directories to downloads, from the home folder, in the latest version Ubuntu 12.10? I tried cd /downloads, but it gave an error saying that there is no such directory. Z-axis issue with the floating review info panel, permits various elements to flow over it I was having a look at an old question of mine when I browsed the  from the timeline. I scrolled downwards and realized the Review completed panel comes along for the ride. While that might be , tags flowing over top of it as pictured below probably isn't.  Here's a .gif of the Question and Duplicate tabs flowing over it as well. Note that the timeline button also flows over. If vote buttons are present, they will also flow over it.  Reproduced on Chrome and Microsoft Edge. Update Per  by Tiago Martins Peres, this issue also happens in other Review types, namely Late Answers, First Posts and Low Quality Posts. In addition to that, it is causing the action buttons on reviews to become unclickable if you scroll low enough.  As a temporary workaround, you can use 's , which  this issue. I'm on a Sprint Samsung Galaxy S3 with Android 4.3.  I would love to become a power user of the dictation feature to dictate text messages and emails. More often than not, however, I have to hand-edit the dictated text not because of text comprehension issues but because of punctuation, capitalization and spacing problems.  These are the "commands" I've found to work. What is the full list?  "period"     --&gt; .   (works fairly reliably) "comma"      --&gt; ,   (works fairly reliably) "new line"   --&gt; \n  (works about 50% of the time)   I've not gotten capital or anything like that to work, or acronyms. If you know how it works, please share. Show all of my question/answers to me even if they are deleted How to set Ubuntu to synchronize my clock with a time server? Evaluating string "3*(4+2)" yield int 18