making a flat list out of a list of lists where the elements are strings
How to flatten a list to return a new list with all the elements?
Ordered N-Tuples as Cartesian Products of Indexed Families In Introduction to Topology, Mendelson defines the Cartesian Product of an Indexed Family as follows:     DEFINITION  Let $\{X_\alpha\}_{\alpha \in I}$ be an indexed family of sets. The product  of the sets $\{X_\alpha\}_{\alpha \in I}$,    written  $\prod_{x\in I}X_\alpha$ consists of all functions $x$ with domain the indexing set $I$ having the property that for each $\alpha \in I$, $x(\alpha)\in X_\alpha$.    Halmos, in Naive Set Theory, makes the following observation about this sort of product:     Ordered triples, ordered quadruples, etc., may be defined as families whose index sets are unordered triples, quadruples, etc.   However, it is not immediately apparent to me why this is true. It makes sense if we understand the prior assertions in Halmos that $\prod_{i \in I} X_i = X_i$ and that $\prod_{i \in I} X_i = X_a \times X_b$ when $I = \{a, b\}$, but these already pose difficulty for me.  Let $I = \{0, 1\}$, let $X_0 = \{A, B\}$, and let $X_1 = \{C, D\}$. Then by Mendelson's (and Halmos's) definitions, it would seem to me that . . .  $$\prod_{i \in I} X_ i = \{\{(0, A), (1, C)\}, \{(0, A), (1, D)\}, \{(0, B), (1, C)\}, \{(0, B), (1, D)\}\}$$  This would appear to me to be the set of all functions matching the definition given, but it is not equal to $X_0 \times X_1$. Moreover, extending this to a case where the index set $I$ is a triple, we would not end up with ordered triples, but with each subset of the product containing three ordered pairs.  When Halmos posits the equalities he does, the idea seems easy to grasp, but the peculiar wording of Mendelson's definition suggests something different to me. Currently, the only way to link to a revision (clicking "link"), you just get  which shows what the post looked like at that revision:        Personally, I rarely use this and haven't ever found myself in a scenario (as far as I remember) where I would prefer the way it currently works to what I'm suggesting here.  Could we:   Add another link, or Change the current link   Such that it:   Displays the diff on a separate page (I'd prefer this, since the highlight and scroll thing doesn't always work properly - although perhaps it has something to do with loading images, so it might not apply here, or, if it doesn't, we could fix that instead), or          Highlights and scrolls to a diff, like what is done when you link to an answer () Why are trivial edits discouraged? Looking at  privilege, I find this to be a surprising requirement:  Try to make the post substantively better when you edit, not just change a single character. Tiny, trivial edits are discouraged.  What motivated this, or rather, what does this mean exactly? Does that, for example, include removing stuff like &quot;Hi, all&quot;, and &quot;thanks in advance&quot;? [update] I was led to a  talking about this topic, but it has a million Comments, and doesn't really justify the rule (unless it's hidden in those million Comments). However, looking at Jeff's Comments gives me an idea that this was meant as a general guideline, instead of a hard-and-fast rule: If you edit a post, check elsewhere on that post if there are other improvements that can be made. How can I search for a keyword with special characters in Google Search? Re-mounting an un-mounted USB stick Given a string of JSON data, how can I safely turn that string into a JavaScript object?  Obviously I can do this unsafely with something like:  var obj = eval("(" + json + ')');   but that leaves me vulnerable to the JSON string containing other code, which it seems very dangerous to simply eval. I've recently searched how I could get the application's directory in Java. I've finally found the answer but I've needed surprisingly long because searching for such a generic term isn't easy. I think it would be a good idea to compile a list of how to achieve this in multiple languages.  Feel free to up/downvote if you (don't) like the idea and please contribute if you like it.  Clarification:  There's a fine distinction between the directory that contains the executable file and the current working directory (given by pwd under Unix). I was originally interested in the former but feel free to post methods for determining the latter as well (clarifying which one you mean). Find $f(x)$ for $f(f(x))=\sin x$ Find all (if that's possible) functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f(f(x))=\sin x.$$  This is a problem a friend gave me. He said he saw it on a book a long time ago, but he couldn't remember what book. I literally have no idea how to solve this so I can't post my attempt here. Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics? 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? Isomorphism between dual space and bilinear forms Studying from Roman's Advanced Linear Algebra, I want to prove that $$U^* \otimes V^* \cong (U \otimes V)^* \cong \hom(U,V;\mathbb{F})$$ The author proves that $U^* \otimes V^* \cong (U \otimes V)^*$ by showing that there is an unique linear transformation   $$\theta:U^* \otimes V^* \to (U \otimes V)^*$$  defined by $\theta(f \otimes g)=f \odot g$ where $(f \odot g)(u \otimes v)=f(u)g(v)$  I want to prove that $U^* \otimes V^* \cong \hom(U,V;\mathbb{F})$. I tried to use the universal property by fixing $f \in U^*, g\in V^*$ and defining $S: U^*\times V^* \to \hom(U,V;\mathbb{F})$ as $S(f,g)=F_{f,g}$, where $F_{f,g}(u,v)=f(u)g(v)$, but I got stuck. How do I install Ubuntu from an USB drive / create a live USB-stick in Windows? I tried to use the usb-creator.exe from Ubuntu 10.10 desktop i386 ISO image and it does create an USB stick that doesn't boot. When I try to boot from it I get:     Operating System not found.   I try to do this from Windows 7 x64. I'm not looking to create a live Ubuntu media, only an installation USB disk.  I repeated the process several times and I even tried to reformat the USB drive (FAT32), no success yet.  The USB stick is a 8GB one. Template specialization based on inherit class Iterate two Lists or Arrays with one ForEach statement in C# GTA 5 Social club I used to play gta 5 online on my ps3 but it ended up breaking and I can't use it anymore I purchased the game for xbox 360 and started playing the game all over again and some of you know how hard that can be specially online.. So I was wondering if I could somehow transfer my old ps3 social club account to my xbox an use it on xbox from now on? In Java, is there any way to use the JDK libraries to discover the private classes implemented within another class? Or do I need so use something like asm? $a _{1} = \frac{1}{2}, a _{2} = 1, a _{n}= \frac{1}{2} a_{n-1} + \sqrt{a _{n-2} }$  Show by the induction that it's $\le 4$ and also by the induction that $a_{n+1}-a_n \ge 0$  If it comes to first I don't know what to do and if it comes to second I tried many different ways but I couldn't prove it. Invariance of a maximally entangled state under unitary operation $U \otimes U^\dagger$ Copy files from a list to a folder Why does SharePoint always prompt me to download SharePoint Designer when I already have it installed? For example, if I click Edit page -&gt; Edit in SharePoint Designer from within my SharePoint site, I'm always presented with a dialog prompting me to download Designer.  I already have Designer installed.  Seems like it should a.) launch it for me, or b.) at least stop prompting me to  download it.  UPDATE: Turns out this stemmed back to the 64-bit IE compatibility issue that was causing me grief here: I wonder if this is a bug, or if I missed something... When a light hits tangentially convex surfaces with "smooth shading", the shadow on this surface seems to "partially ignore" the smoothness of the surface. Here is an example with a simple cylinder :    On the left, a cylinder with "flat shading". Everything's ok. On the right, the same with "smooth". We can see an edge, bad shadowed.  With or without the "Edge split" modifier, no matters, the edge is still there. The shader is a simple white diffuse shader with no texture nor displace.  I have to add a subsurf modifier with at least 2 levels, which will insanely increase the vertex count... And I can't do that for my project.  I hope someone already saw it, and have a little tip to share. Or if someone already know it's a bug, or a limit of the current Cycles renderer ?