best way to check variables against long value list
Check variable equality against a list of values
Let $f_n(x) : \mathbb{R} \rightarrow \mathbb{R}$ be defined as $\dfrac{x}{n}$. Is $f_n$ uniformly convergent?   With "$(a_n)$ is limited and $(b_n)$ converges to 0 $\Rightarrow (a_nb_n)$ converges also to 0" i would guess that $x\cdot \dfrac{1}{n}$ converges uniformly but $x$ is not limited in this case. So does ist converge uniformly or not? Formally, is it correct to write:     A number of questions has been asked here.   or:     A number of questions have been asked here.   As a non-native speaker of English, I would prefer the former: the subject seems to be "number", therefore the verb ought to be singular, I'd say. However, the latter seems more common, and therefore I believe that my gut feeling is just plain wrong — but I would really like to have a definite answer.  Moreover, is it the same for "a myriad of", "a plethora of", and so on? My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream - spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.  Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.  How is my explanation incorrect? Windows 8 turns program sound volume down randomly I recently upgraded to Windows 8 from Win 7 64 bit and have started to encounter a strange issue. When I have any program running which plays sound, such as a game or spotify, after a random interval (usually around 5-10 minutes) the program sound will set itself really low.    If I Alt-Tab to the desktop and check the Mixer I can see that the Application volume has automatically set itself really low - the other volume levels (i.e. the Device speakers) stay the same.  I'm able to just set the application volume back to a reasonable level and it stays that way for another 5 - 10 minutes then goes quiet again.  My sound is Realtek High Definition Audio and my machine is an Acer Aspire 5738G if that helps in any way.  Any help much appreciated! While executing an INSERT statement with many rows, I want to skip duplicate entries that would otherwise cause failure. After some research, my options appear to be the use of either:  ON DUPLICATE KEY UPDATE which implies an unnecessary update at some cost, or INSERT IGNORE implies an invitation for other kinds of failure to slip in unannounced.  Am I right in these assumptions? What's the best way to simply skip the rows that might cause duplicates and just continue on to the other rows? Getting my File Manager to link to my Google Drive I have a very small amount of storage on my computer and would like to conserve it, so I would like to know if there is a way to mount my Google Drive in Thunar or Nautilus on Ubuntu 12.04.5 LTS.   Yes, I know, it's weird that I'm saying that I have a small amount of storage when I have 2 file managers installed, but I literally have 5GB out of 16GB left. I am currently thinking about open-sourcing a project of mine and am in the process of preparing the source code and project structure to be released to the public. Now I got one question: how should I handle the signature key for my assemblies? Should I create a new key for the open-source version and publish it along with the other files to the SVN repository? Should I leave the key out and everyone who wants to compile the code should generate his own key?  How do you handle this? I feel a little bit uncomfortable with releasing a signature key to the public. Eclipse error: "The import XXX cannot be resolved" How to test multiple variables against a single value? How do I restore a Places folder I accidentally deleted in Nautilus? Query Which Profiles Have Read Access To Specific Object? Since I couldn't think of how to write this query off the top of my head, I thought it might be worth sharing. How can I query which Profiles have Read permission on a specific object? I knew it would have something to do with ObjectPermissions and PermissionSet, but had to look up the documentation for both to piece it together. How can I transfer large files from Linux to iPad over a cable or wifi? I am looking for a way to transfer large files to the iPad without using iTunes or pushing to and pulling from a remote server.  I run an Ubuntu laptop as my only OS at the moment and want to be able to transfer movies to my iPad.  I currently transfer most of my files by way of the dropbox app which works well for small files but is quite slow for larger files and eats up my bandwidth.  Ideally I'd like to be able to transfer over a cable or through WiFi.  Thanks for any tips. Prove $(1+a+b)(1+b+c)(1+c+a)\ge 9(ab+bc+ca)$ How one can prove the following.  Let $a$, $b$ and $c$ be non-negative real numbers. Then the inequality holds:  $(1+a+b)(1+b+c)(1+c+a)\ge9(ab+bc+ca).$  WLOG one can assume that $0\le a\le b\le c$.  It is not difficult to prove the statement when $0\le a\le b\le c\le 1$ or $1\le a\le b\le c$. Does Hard reboot damage my Ubuntu How do I uninstall the command line tools for Xcode? We have a bunch of Mac at work that no longer require Xcode or command line tools so we'd like to remove them so the compilers aren't hanging around and we don't have to keep updating them when updates arrive. , but now that Xcode is an app store app you are left with the tools if you ever install them. Can we clean this other than wiping the OS for macs running 10.10 and newer? How do I transfer a Gmail account to a different Google account? How do I compare 2 rows from the same table (SQL Server)? I need to create a background job that processes a table looking for rows matching on a particular id with different statuses. It will store the row data in a string to compare the data against a row with a matching id. I know the syntax to get the row data, but I have never tried comparing 2 rows from the same table before. How is it done? Would I need to use variables to store the data from each? Or some other way? (Using SQL Server 2008) Baking with oven without bottom heating element My mom wants to do baking but her oven doesn't have bottom heating element. It only has an element on top, with a fan at the back.  She told me that she can't make me a good pizza or cake without it.  Is there any way around? If $a_k\geq0$ is a decreasing sequence converging to $0$, do we have $\lim_{n\to\infty}\frac{\sum_{k=1}^n a_k}n = 0$? Let $a_k\geq 0$ be a non-increasing sequence satisfying $\lim_{k\to\infty} a_k = 0$. Is it always true that $$\lim_{n\to\infty} \frac{\sum_{k=1}^n a_k}n=0$$ ?  I tried proving with "brute force" but failed: Let $\varepsilon&gt;0$. Then there exists a $K\in\mathbb N$ such that $a_k\le\varepsilon$ for all $k\geq K$. Let $C=\sum_{k=1}^K a_k$. We have $$\frac{\sum_{k=1}^{\left\lceil\frac C\varepsilon\right\rceil}a_k}{\left\lceil\frac C\varepsilon\right\rceil}=\frac{C}{\left\lceil\frac C\varepsilon\right\rceil}+\sum_{k=K+1}^{\left\lceil\frac C\varepsilon\right\rceil} a_k\le \varepsilon +\varepsilon\cdot\left( \left\lceil\frac C\varepsilon\right\rceil-K\right).$$  However, this is not good, as the right-hand side depends on $C$, which can get large for small $\varepsilon$.   Also, numerical computations for example with $a_k=\frac1{\log\log k}$ seem to confirm the statement though...  (Additionally, note that I didn't use the non-increasing fact, but I am not sure if it is needed.) What is the best regular expression to check if a string is a valid URL? How can I check if a given string is a valid URL address?  My knowledge of regular expressions is basic and doesn't allow me to choose from the hundreds of regular expressions I've already seen on the web.