Installing Ubuntu alongside pre-installed Windows 8
How do I install Ubuntu alongside a pre-installed Windows with UEFI?
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric. Question: Let $(X, d)$ be a metric space. Let $A$ and $B$ be disjoint subsets of $X$ that are closed in the topology induced by $d$. Prove that there exist disjoint open sets $U$ and $V$ such that $A\subset U$ and $B\subset V$.   Is this proof correct? : By assumption, $A\cap B=\emptyset$, so there is no pair like $(x_A,x_B)$ (i.e., $x_A\in A$ and $x_B\in B$), such that $x_A=x_B$. Because every metric space is Hausdorff, so for every pair $(x_A,x_B)$ there are two disjoint open sets $U_A\ni x_A$ and $V_B\ni x_B$; and thus union of all $U_A$s (which is an open set containing A) are disjoint from union of all $V_B$s (which is an open set containing A).   Thanks a lot for any help.    PS In special case of standard metric topology on $\mathbb{R}$, if $[a,b]$ and $[c,d]$ are disjoint (say $c&gt;b$), intuitively it is apparent that there is a 'space' between $c$ and $b$ so we can have two disjoint open sets, each of them containing $[a,b]$ or $[c,d]$. I am trying to solve an exercise in Shankar's QM book (concretely 4.2.1), and I am asked the probability of each possible value for the operator $L_x$ when the particle is in a certain eigenstate of another operator $L_z$. I understand that I have to "expand" the state vector in the $L_z$ basis, which in this case is just the appropriate eigenvector, and then change the base to that of $L_x$, i.e to write the $L_z$ eigenstate in the $L_x$ base. The problem is that there is just no way of doing it, since the eigenvectors of $L_x$ don't span the whole Hilbert Space.   I thought all quantum operators had a set of eigenvectors that spanned the whole space, am I wrong on that or am I wrong on my algebra? Example to show the distance between two closed sets can be 0 even if the two sets are disjoint Let $A$ and $B$ be two sets of real numbers. Define the distance from $A$ to $B$ by $$\rho (A,B) = \inf \{ |a-b| : a \in A, b \in B\} \;.$$ Give an example to show that the distance between two closed sets can be $0$ even if the two sets are disjoint. How to clear the interpreter console? Like most Python developers, I typically keep a console window open with the Python interpreter running to test commands, dir() stuff, help() stuff, etc.  Like any console, after a while the visible backlog of past commands and prints gets to be cluttered, and sometimes confusing when re-running the same command several times.  I'm wondering if, and how, to clear the Python interpreter console.  I've heard about doing a system call and either calling cls on Windows or clear on Linux, but I was hoping there was something I could command the interpreter itself to do.  Note: I'm running on Windows, so Ctrl+L doesn't work. What is the probability that $x_1+x_2+...+x_n \le n$? Given that $X_1, X_2...$ are mutually independent random variables. For each $i$ with $1\le i \le n$   the variable $X_i$ is equal to either $0$ or $n+1$ $E(X_i)$ = $1$   also.. if $X_i$ is equal to either $0$ or $n+1$, doesn't that mean that all $X_i$ need to be $0$?  Thanks A word to describe someone or something that is not last? I'm looking for a word that describes the state of not being last. A word that would apply to everything in an ordered list that is not the last thing in that list.  From     I wasn't the last person to finish the race.   to (the phrasing is off, but it seems to illustrate my point)     I was .. person to finish the race.   One word that comes to mind is "intermediate", but I don't think that includes the first item in a list. How to install "vanilla" TeXLive on Debian or Ubuntu? Debian and Ubuntu have very good texlive packaging. But I'd like to use tlmgr to have a more fine-grained control about upgrades and which packages I want to be installed.   So how do I install "vanilla" TeXLive on Debian/Ubuntu?   Also how do I make dpkg aware that I have TeXLive installed? I'm fairly excited for Unity, as it looks like a promising new direction for Ubuntu.  However, I do have a concern - will it be possible to use Unity without the global menu?  I have my window manager set to focus-follows-mouse/sloppy focus, and find the productivity gains to be immense. Sloppy focus is incompatible, however, with global menus, as it is possible for the focus to change while you move from window to menu.  Will Unity support an option to use window menus while still using Unity? What is an "index out of range" exception, and how do I fix it? Difference beween wiki page, application page, web part page and publishing page There are lots places in msdn sharepoint forums and blogs where these terms are used and I am confused between them. Can anybody clarify? Are there any differences between Skyrim & Skyrim: Special Edition? I need to create a metadata-table for all files in a File Geodatabase.   Is it possible to automatically be updated with new filenames, and possibly even metadata (as created in the ArcGIS metadata editor)? Split a string by a delimiter in python Connectedness of the Hausdorff distance. Does anyone know a proof of connectedness of the Hausdorff distance?  I mean a proof of the following:  Theorem  If $(X, \rho )$ is a connected metric space, then $(F(X), d_h )$ is also connected.  Remark:  $F(X) = \{ A \subseteq X | A \text{ is nonempty, closed and bounded } \} $, and $d_h$ stands for the Hausdorff distance. Up my street and down the lane Possible Duplicate:          Except where there is obvious difference in elevation e.g. on a sloping road, how do native speakers decide whether to use up or down in phrases like up the road when referring to a location along the same road? How do you access the matched groups in a JavaScript regular expression? I want to match a portion of a string using a  and then access that parenthesized substring:  var myString = "something format_abc"; // I want "abc"  var arr = /(?:^|\s)format_(.*?)(?:\s|$)/.exec(myString);  console.log(arr);     // Prints: [" format_abc", "abc"] .. so far so good. console.log(arr[1]);  // Prints: undefined  (???) console.log(arr[0]);  // Prints: format_undefined (!!!)   What am I doing wrong?    I've discovered that there was nothing wrong with the regular expression code above: the actual string which I was testing against was this:  "date format_%A"   Reporting that "%A" is undefined seems a very strange behaviour, but it is not directly related to this question, so I've opened a new one, .    The issue was that console.log takes its parameters like a printf statement, and since the string I was logging ("%A") had a special value, it was trying to find the value of the next parameter. Is there a way to set an "Adventure Mode Boundary" in Minecraft?  I am trying to create this village where players can spawn in, and then set out to explore the world and build and do normal minecraft stuff. I don't want them to destroy this village, so I want them to be in adventure mode when they are in the village and then switch them to survival when they leave, and vice-versa. When they return to the village, they get switched back to adventure mode.  In other words, I want to set an "Adventure Mode Boundary" to protect buildings. I am working without mods. I am hoping there is an simple way using command blocks. I have some difficulties with a task in algebra. I guess it's trivial and really easy but I can't figure out how to solve it.  I have a set $G$ and a binary operation on it, let it be $\circ$. I have that the operation is associative and that the equations $a\circ x = b$ and $x\circ a = b$ have unique solutions. I have to prove that $(G, \circ)$ is a group.  I already have that the operation is binary and associative, so I have to prove that there is unique identity element and unique inverse element and it will come from the equations, but how exactly? Automatically change é to \'e – most convenient setup for accented letters? I assume this is really basic question, I'm new to LaTeX, I read a first step tutorial to get ready to write some documents but I couldn't answer my own question at this time and I really don't know where to search.  When I try to write é and compile my document, this character is not shown. I know the sequence is \'e to make it happen in the document but that is really disturbing to write.  Is there someway to write a paragraph "normally" and convert all the special chars into the LaTeX syntax? Or is there a way to allow é, à, ... writing so the compilation includes them into the document? How to draw simple table