We want only the real 3rd root. By calculation, $[\sqrt[3]{\sqrt 5 +2}-\sqrt[3]{\sqrt 5 -2}]^3= 4-3[\sqrt[3]{\sqrt 5 +2}-\sqrt[3]{\sqrt 5 -2}]$  Therefore, the answer is a root of  $t^3=4-3t$ , which obviously has the real solution $t =1$.   But I want another way of showing $\sqrt[3]{\sqrt 5 +2}-\sqrt[3]{\sqrt 5 -2} =1$, maybe by using simple algebraic formulas.
Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
Stop setInterval call in JavaScript I am using setInterval(fname, 10000); to call a function every 10 seconds in JavaScript. Is it possible to stop calling it on some event?   I want the user to be able to stop the repeated refresh of data. underline omitting the descenders I'm very well aware that it is considered best practice not to use underlining other than on typewriters and in handwriting. But sometimes it is needed nonetheless.  In my opinion the typographically least offending way to underline in print is to leave out the descenders. This is also how I learned to do it in handwriting. Very few fonts offer a pre-made underlined variant, but some text-processors (e.g. OS X text-engine) do -- depending on the font used -- an acceptable job at emulating this effect:    How would I tweak any of the existing ways/packages for underlining to do the same?  As a bonus, I'd like to be able to tweak the behaviour (extent of the omitted part, apply to which letters) per font and text style, preferably working with XeLaTeX. I guess the proof of the identity $$ \sum_{n = 0}^{\infty} \frac{1}{n!} \equiv \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x $$ explains the connection between such different calculations. How is it done? How do I convert or upgrade roads? I'm trying to optimize my road system a bit, mostly converting regular small roads into one-way roads. But the only way I can see to do that is to remove the old road entirely and build a new one. I can't seem to just build over the old one.   I can understand that limitation in cases where the new road type is larger, but it should be possible to upgrade to roads with the same size without tearing down the old road manually.   Is there an easier way to convert or upgrade roads, or do I have to manually remove the existing road every time? Is there a standard function in C that would return the length of an array? What are the limits of the Room of Requirement? cd into all directories, execute command on files in that directory, and return to previous current directory I'm attempting to write a script that will be run in a given directory with many single level sub directories. The script will cd into each of the sub directories, execute a command on the files in the directory, and cd out to continue onto the next directory. What is the best way to do this? How do I add .e00 data into my QGIS project? One thing that seems to be missing in the Top&nbsp;Bar is a link to the Stack&nbsp;Exchange portal. It only displays under the "Current&nbsp;Community" section when you are in the community, but it disappears as soon as you go to another one.  Would it be possible to add a link that would always be there no matter which community you are currently on? Should we improve time to first byte or Page Speed Insights score for SEO? Google posted last summer that "page speed" will impact the search result rankings also on mobile devices. But I think there is a little confusion about the term "page speed".  The test tool which Google offers is called "Page Speed Insights". Many people we are talking with, are thinking that the overall score of this tool for a particular site for example Desktop: 46/100 and Mobile: 45/100 is used for the ranking algorithm.  BUT I found a very interesting article in German language which states that only the TTFB (time to first byte) value is used and this should be optimized not all suggestions which "Page Speed Insights", further called PSI offers. Here is the link to the German article:   In short terms it says that a very large site in this case "The New York Times" has a low overall score of Mobile:41 and Desktop:45. As they are used to sell reader memberships they should  offer a great user experience. So, they should optimize their site. But when I call this site it is amazing fast. The overall PSI score does not reflect this behaviour. But when I believe this article the TTFB for this site is perfect. Also when I call it here from Austria it states 0.881sec.  I really like to know on which value we should focus our work for optimization not to fall in the ranking. Because as many of you already said it is not useful to implement all suggestions from the PSI site for one domain.  So, it would be real  if you could clarify things here or post links to official posts from Google. What I found about this, Google always is talking about "page speed" but what exactly is this? When you add an image strip to the Video Sequence Editor, it stretches/shrinks your image to fit the full output frame.  How can I add an image at its original resolution?  For example, if I add a 60x60 pixel image, it should appear very small in the final 1080p render. How to write uncertainties with the \pm symbol "10 ± 1 K" by using siunitx? Using the siunitx package, if I specify an error with the \pm symbol then it automatically converts it to a form using parenthesis. I would like it to not do this and keep the \pm symbol, but still space the elements of the quantity and symbol in a good way.  e.g. \SI{10 \pm 2}{\kelvin} would produce 10(1) K  I would like it to produce: 10\pm1 K or something similar with spacing taken care of. UnboundLocalError: local variable 'url_request' referenced before assignment Is there any way to ensure that a specific USB key always gets the same drive letter? I use OS X Mavericks and have some company storage drives mounted (using smb or cfs). (smb://username@address.path.toserver.com/directory/data). When I work with files on the drive or copy files to the drive, some hidden files are created. Most of these files start with dot-dash ._ and then the filename of the original file, like:  ._test001.png ._test002.png ._test003.png   And most of the times, the famous ._.DS_Store and .DS_Store are also there.  On my Mac, these . dot items are invisible, but my windows colleagues do see these files. How can I prevent OS X from making these strange invisible files?  On  (and other internet sources) you can find a 'defaults write' to disable the creation of .DS_Store files on your network drives. But this does not work in Mavericks:  defaults write com.apple.desktopservices DSDontWriteNetworkStores -bool true   For now I use this oneliner, but doing a rm -rf does feel wrong in this case.  find . -type f -name "._*" -exec rm "{}" \;   Edit: I don't want to delete the files or exclude them from copying. I want them not to be created in the first place.  Edit: I prefer a 'native' OS X solution over third party apps.  Edit: This questions has two answers, one for the ._ files and one for the .DS_Store files. The bounty is rewarded for dot_clean, this native command line app cleans all ._ files. Unfortunately is does not clear the .DS_Store files, this can effectively be done with Asepsis. Asepsis stores .DS_Stores in a fixed location, and not in the folder itself. I want to upgrade my Ubuntu 13.04 to Ubuntu 13.10. I'm unable to do via GUI.   [ The reason why I'm unable to do so:  Via software updater, I proceed ahead and click upgrade (for upgrading my OS). I authenticate by providing my password. Then it proceeds and downloads upgrade tool. That time only (while downloading the tool) error message comes "system program problem detected". It then doesn't proceed ahead and I click to report the problem ]  So, I tried via command line but here also I couldn't succeed upgrading my OS.  For the same I ran   $ sudo apt-get update   Then I ran  $ sudo apt-get dist-upgrade   And then:  ravbholua@ravbholua-Aspire-5315:~$ sudo do-release-upgrade Checking for a new Ubuntu release Get:1 Upgrade tool signature [198 B]                                                                                                  Get:2 Upgrade tool [1,135 kB]                                                                                                         Fetched 1,135 kB in 6s (32.9 kB/s)                                                                                                    authenticate 'saucy.tar.gz' against 'saucy.tar.gz.gpg'  gpg exited 2 Debug information:    gpg: Signature made Friday 01 November 2013 10:34:27 AM IST using DSA key ID 437D05B5 gpg: Can't check signature: public key not found  Authentication failed Authenticating the upgrade failed. There may be a problem with the network or with the server.  ravbholua@ravbholua-Aspire-5315:~$    Please suggest how to go ahead and upgrade my OS. Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$. Relevance of cycle detection in Pollard's rho integer factorization algorithm I've recently learned about Pollard's rho factorization algorithm, and the way I understand it, it works by using a pseudorandom sequence of integers $x_{k}$ ranging from $0$ to $n-1$, where $n$ is the number to be factored, to find repetitions in an unknown sequence $y_{k} = x_{k} \bmod p$, where $p$ is an unknown, non-trivial factor of $n$. Such a repetition $y_{i}=y_{j}$ occurs when $x_{i}\equiv x_{j} \bmod p$, which can be detected by checking whether $\gcd(x_{i}-x_{j}, n)\gt 1$.  From what I could find on the Internet, Floyd's cycle detection algorithm or a variant thereof is used to find such repetitions. And the reason for this is what I don't understand.   First, Floyd's algorithm requires that each element in the sequence depends solely on the element before it, which, even if it is the case for $x_{k}$, is not necessarily the case for $y_{k}=x_{k}\bmod p$. For example, assuming we want to factorize $6$, let's take the sequence $5, 3, 2, 4, 1, 0, 5, 3, 2, 4, 1, 0,\ldots$. The cycle period is $5, 3, 2, 4, 1, 0$, where every element is contained only once. However, if we take this sequence $\bmod 2$, we get $1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0,\ldots$. Floyd's algorithm cannot be applied here to find the cycle period $1, 1, 0, 0, 1, 0$. Besides, we are not even interested in a cycle, only in repetitions. Whether we find the congruence $\bmod 2$ between $5$ and $3$, $5$ and $1$, or $4$ and $2$ in the first sequence is irrelevant.   Please correct me if my understanding of Pollard's rho algorithm as described above is wrong. But if it is not, it seems to me that one could just as well try out some random numbers between $2$ and $n-1$ and see if they share a divisor with $n$ other than $1$. So what is the benefit of using a cycle detection method like Floyd's algorithm?  I also found , but it is not answered, and the comment on the question does not really answer the question either. Using Mosfet with seperate Logic Converter and Arduino Open maps which are not continuous What is an example of an open map $(0,1) \to \mathbb{R}$ which is not continuous? Is it even possible for one to exist? What about in higher dimensions? The simplest example I've been able to think of is the map $e^{1/z}$ from $\mathbb{C}$ to $\mathbb{C}$ (filled in to be $0$ at $0$). There must be a simpler example, using the usual Euclidean topology, right?