I think Coulomb's law because forces are more fundamental than fields (are they?) but Coulomb's  law can be derived from Gauss's law.

Which of these laws is more fundamental or forms the basis of electrostatics? I started off with Coulomb's law and then I studied Gauss' law. I was wondering which one is more universal?  My professor derived Gauss' law using Coulomb's law but didn't do it the other way, so is Coulomb's law more fundamental? And can Gauss' law be used to prove the other?


I'm to write my MSc thesis soon, and am a bit worried that I will get stuck in a rut. By that I mean that I will have very little variety in my daily (work) life, and that it will not only be stressful, but also that I will sort of stare myself blind on the same problems every day.  Any advice? Do I even need to worry about this?  EDIT:  I probably didn't explain myself very well, because everyone seems to have misunderstood my question (don't get me wrong, I really appreciate the feedback, it's useful nonetheless).  I'll be working on the same problems for about 6 months. I'll probably get so tired of it. I'm wondering what I can do to avoid that making me crazy. RasterImage mentioned changing the work environment once in a while, that might do some good.

I am a third year (starting fourth year in the fall) PhD student in mathematics. I've passed all qualifying exams and am currently doing research. As far as I can tell, I am not doing poorly. I have the good fortune of having a great advisor, being in a very supportive department, and having friends and family who genuinely care about my success.   The fact is research is hard. It appears to consist primarily of staring at a problem for days and days and days without getting anywhere. Sometimes, rarely, I do figure something out and that feels wonderful, but the overwhelming majority of my time appears to be spent banging my head against a mostly figurative wall. I am not complaining about the material being hard, and I am not averse to putting in hard work, but I get frequently discouraged when I realize the vast volumes of mathematics that I yet know nothing about (and probably never will). It's very hard to quantify progress - in particular, there are too few tangible returns after too many hours worked. I find myself thinking along the lines of "Oh, if only someone actually smart were thinking about this problem they would have solved it in moments" and so on.   I've talked about this to some number of people; here is some advice I have received:   Take a day off. Putting in hours upon hours of trying things doesn't magically lead to a solution, particularly if the brain is tired and just wants to sleep. Have a hobby. Since math research doesn't exactly provide instant gratification, a hobby might provide some instead.  Talk to other graduate students. Realize that many graduate students go through this.   I'm interested to know how other folks have dealt with being discouraged as a graduate student. Does it get better with time and experience? Is this a sign that research is not for me and that I should seriously consider a life outside academia?


Let $F\subset E$ be an algebraic extension of fields and suppose that every polynomial $f(x) \in F[x]$ has a root in $E$. Is it possible that $E$ is not algebraically closed?  Note that such an example must necessarily be of prime characteristic since over char $0$, $E$ is necessarily algebraically closed. Proof:  Let $g(x) \in E[x]$ be a polynomial with a root $\alpha$ (after fixing an algebraic closure of $E$). Let $f(x)$ be the minimal polynomial of $\alpha$ over $F$ and let $L$ be the splitting field of $f$. By the primitive element theorem, $L=F[\beta]$ and if $h(x)$ is the minimal polynomial for $\beta$, it has some root $\gamma \in E$. Since $F[\beta] = F[\gamma]$, this shows that $L\subset E$.  In particular, if we are looking for counterexamples, we would like $L$ to not be a primitive extension.

Suppose $E/F$ is an algebraic extension, where every polynomial over $F$ has a root in $E$. It's not clear to me why $E$ is actually algebraically closed.  I attempted the following, but I don't think it's correct:   I let $f$ be an irreducible polynomial in $E[X]$. I let $\alpha$ be a root in some extension, so $f=m_{\alpha,E}$. Since $\alpha$ is algebraic over $E$, it is also algebraic over $F$, let $m_{\alpha,F}$ be it's minimal polynomial. I now let $K$ be a splitting field of $m_{\alpha,F}$, which is a finite extension since each root has finite degree over $F$.  If $m_{\alpha,F}$ is separable, then $K/F$ is also separable, so as a finite, separable extension, we can write $K=F(\beta)$ for some primitive element $\beta$. By assumption, $m_{\alpha,F}$ has a root in $E$, call it $r$. Then we can embed $F(\beta)$ into $r$ by mapping $\beta$ to $r$. It follows that $m_{\alpha,F}$ splits in $E$. Since $f\mid m_{\alpha,F}$, we must also have the $f$ is split in $E$.  But what happens if $m_{\alpha,F}$ is not separable? In such case, $F$ must have characteristic $p$. I know we can express $m_{\alpha,F}=g(X^{p^k})$ for some irreducible, separable polynomial $g(X)\in F[X]$. But I'm not sure what follows after that.  NB: I say $E$ is algebraically closed if every nonconstant polynomial in $E[X]$ has a root in $E$.


I've heard that Visual Studio doesn't like the .svn directories in a working copy from a subversion repository, and that using '_svn' is a better choice. Apart from not being hidden by the explorer, what is this mysterious advantage, or is this all a dirty rumour?

We were having a problem with our build server not checking out modifications from source control despite recognizing that there had been changes.  It was traced to the control folder (not sure what it's real name is), the existing working builds were using _svn. Clearing the working folder forced a new complete checkout and I noticed that now the control folder is .svn. It looks like originally our integration routines were checking out code using _svn but now it is using .svn.  The svn.exe being used during integration is from VisualSVN Server can I set this up to use _svn again?  How the original working copies were using _svn I don't know! - we only ever ever used VisualSVN Server and haven't changed this.  We had setup TortoiseSVN to use _svn following the recommendation that this works better for Visual Studio and have also installed TortoiseSVN on the build server in case it is ever needed. Could this be the cause?  Also is this really necessary? As MSBuild is Microsoft's is it recommended as it is for Visual Studio?


How to draw rectangle with Shape Digitizing toolbar in QGIS 2.10.1?

I want to draw a perfect rectangle. How can I do that with QGIS v.3+?  .  Is there a similar solution for the latest QGIS version?


I have add some special characters to be accepted by the input text field In model   [RegularExpression(@"^[a-zA-Z./@/- ]+$", ErrorMessage = "The Last Name field should contain letters only.")] public string LastName { get; set; }   This makes to throw error like parsing "^[a-zA-Z./@/- ]+$" - [x-y] range in reverse order But requirement is to accept these " / , - @ " special character also by the field.

I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them?


I wonder why Ubuntu chose to put the login forms at LightDM in the left instead of centering it. I find it totally ugly and a mental effort when I boot up and try to find the login with my eyes wandering from the center to the left.  Are there any reasons for designing it the way it is? (I could not find anything on the Ubuntu wiki.)   Would there be a super simple way to center everything?

I have a quite wide monitor and it's quite annoying to see the login dialog in the login screen on the far left side of my screen. I literally have to turn my head around to look at it!  Is there a way to center the login dialog?


I recently installed Tor browser and in the site below the installation steps it says to move to the downloaded folder via terminal and then type ./ start-tor-browser to start tor, and it works. If I click the start-tor-browser file a text editor with code pops up..  How can I make a desktop shortcut or,if I can't, a shortcut for the commands to just type Tor(for example) in terminal instead of the two or three required commands every time I want to run tor?

I'd like to know if there is a way to run  program/shell script without typing full path:  /opt/idea/bin/idea.sh


Why the apparatus is rotated by 90 degree? If it is not rotated, there is still path difference between two lights. So why it is rotated?

When I (beginner) learnt Michelson Morley experiment, it was expected that there should be a shift in the fringe pattern when the setup was rotated by 90 deg if the presence of ether is true. But why should there be a shift in fringe after the setup was rotated, assuming the presence of ether?


If I wanted to use cycles for a (example) floor and blender render for a (example) humanoid figure, how would I go about doing it? Is there a non complicated way to combine both cycles and blender render in one render output? Thanks!

I have a scene that's 90% Blender Internal (for speed) with 1 object in Cycles (because that one object looks way better in Cycles). My question is is it possible for me to: Set the single blend file rendering Have it output the BI scene and Cycles scene into a single openEXR multilayer file  I was hoping to render everything as quickly as possible and then do a final composite after everything's rendered so I don't waste time compositing frames that might be wrong or broken. So far I've got a 3rd scene that I've been using to composite both scenes at render time so I know how to get that setup going, I'm just hoping someone can tell me how to render both scenes at the same time without having to composite them.  Ideally I'm looking for:  Scene 1 = Internal -> Outputs to sequence BI_render_.exr Scene 2 = Cycles -> Outputs to sequence Cycles_render_.exr  If it comes down to it I might be able to do the Cycles render separately because the single object should be quite quick to do on its own but I was thinking this would be practice for a more complex setups for the future.  I have to admit I have a horrible feeling this can't be done but I just have to ask.  Thanks


Let $f: [0,1] \rightarrow [0,1]$ be continuous. Any idea on how we can prove that it is not possible for $f$ to map $[0,1]$ onto $[0,1]$ exactly two-to-one. That is, there is no continuous $f$ as above such that for each $y \in [0,1]$, there are exactly two values $x_1$ and $x_2$ such that   $$y = f(x_1) = f(x_2)$$

This is from Apostol's Mathematical Analysis.  Let $f$ be a function defined in $[0, 1]$ such that for each real number $y$ either there is no value of $x \in [0, 1]$ such that $f(x) = y$ or there are exactly two such values of $x$. Prove that a) $f$ must be discontinuous on $[0, 1]$. b) $f$ has an infinite number of discontinuities in $[0, 1]$.  Long back I had tried to solve the problem. I reasoned for a) as follows: Suppose that $f$ is continuous and let $m, M$ be its minimum and maximum values on $[0, 1]$. Clearly if $m = M$ then $f$ is constant and clearly for every $x \in [0, 1]$ we have $f(x) = m = M$ which contradicts given property of $f$. So we must have $m < M$. Clearly there are now four distinct points $a, b, c, d$ in $[0, 1]$ such that $f(a) = f(b) = m, f(c) = f(d) = M$. By checking possible linear orderings of $a, b, c, d$ I could find a find a value of $y \in (m, M)$ for which there exist more than 2 values of $x$ such that $f(x) = y$. However this approach looks very clumsy and I suspect much simpler and easier proof is possible. Part b) seemed bit complex and my only guess was that probably $f$ was discontinuous on each subinterval of $[0, 1]$ but I could not prove this claim (may be the claim is wrong!). Perhaps there is a simpler solution to this part of the problem. Apostol's also asks to provide an example of such a function. Any hints on the overall problem will be appreciated.  Update: After looking at Marc's answer, I think I have found a way to show that there are infinitely many discontinuities. Earlier the solution was a part of the question itself but it made the question look quite lengthy hence I moved it to a separate answer.


I've currently got an eclipse project with two main methods and was wondering if it's possible to create a jar file which runs an Apache Ant script when the jar file is executed. I've provided an Ant script below where two main methods are run. Thanks in advance.      <?xml version="1.0"?>       <project name="Test" default="run_external">         <target name="compile">             <delete dir="bin" />             <mkdir dir="bin" />             <javac srcdir="src" destdir="bin" />         </target>         <target name="run_external" depends="compile">             <parallel>                 <exec executable="cmd" dir="bin">                     <arg value="/c start cmd.exe /k java test.Main" />                 </exec>                 <exec executable="cmd" dir="bin">                     <arg value="/c start cmd.exe /k java test.Main2" />                 </exec>             </parallel>         </target>     </project>

I've compiled a java project into a Jar file, and am having issues running it.  When I run:  java -jar myJar.jar   I get the following error  Could not find the main class: myClass   The class file is not in the root directory of the jar so I've tried changing the path of the main class to match the path to the class file and I get the same issue.  Should I be flattening the file structure? if so how do I do this. I'm using Ant to build the Jar file if thats of any use.  UPDATE   Here is the contents of the jar and the relevant Ant sections, I've changed the name of the firm I work for to "org":  META-INF/ META-INF/MANIFEST.MF dataAccessLayer/ dataAccessLayer/databaseTest.class org/ org/eventService/ org/eventService/DatabaseObject.class org/eventService/DatabaseObjectFactory.class org/eventService/DbEventClientImpl$HearBeatMonitor.class org/eventService/DbEventClientImpl.class org/eventService/EmptyQueryListException.class org/eventService/EventHandlerWorkItem.class org/eventService/EventProcessor.class org/eventService/EventTypeEnum.class org/eventService/EventWorkQueue$MonitorThread.class org/eventService/EventWorkQueue$PoolWorker.class org/eventService/EventWorkQueue.class org/eventService/FailedToLoadDriverException.class org/eventService/IConnectionFailureListener.class org/eventService/InvalidEventTypeException.class org/eventService/JdbcInterfaceConnection.class org/eventService/NullArgumentException.class org/eventService/OracleDatabaseObject.class org/eventService/ProactiveClientEventLogger.class org/eventService/ProactiveClientEventLoggerException.class org/eventService/PropertyMap.class org/eventService/SQLServerDatabaseObject.class org/eventService/TestHarness.class org/eventService/Utilities.class   And the ant target:  <target name="compile" depends="init" description="compile the source ">     <javac srcdir="src" destdir="bin" classpathref="project.class.path"/> </target> <target name="buildjar" description="build jar file" depends="compile">     <mkdir dir="dist"/>     <jar destfile="dist/myJar.jar" basedir="bin" includes="**/*.class" >         <manifest>             <attribute name="Main-Class" value="org.eventService.ProactiveClientEventLogger"/>         </manifest>      </jar> </target>


I use extension for VS named "ReSharper". It corrects my code and always says that i need to use "var" instead explicitly type specify. Why?  P.S. sorry for my english and check me please=)

After discussion with colleagues regarding the use of the 'var' keyword in C# 3 I wondered what people's opinions were on the appropriate uses of type inference via var?  For example I rather lazily used var in questionable circumstances, e.g.:-  foreach(var item in someList) { // ... } // Type of 'item' not clear. var something = someObject.SomeProperty; // Type of 'something' not clear. var something = someMethod(); // Type of 'something' not clear.   More legitimate uses of var are as follows:-  var l = new List<string>(); // Obvious what l will be. var s = new SomeClass(); // Obvious what s will be.   Interestingly LINQ seems to be a bit of a grey area, e.g.:-  var results = from r in dataContext.SomeTable               select r; // Not *entirely clear* what results will be here.   It's clear what results will be in that it will be a type which implements IEnumerable, however it isn't entirely obvious in the same way a var declaring a new object is.  It's even worse when it comes to LINQ to objects, e.g.:-  var results = from item in someList               where item != 3               select item;   This is no better than the equivilent foreach(var item in someList) { // ... } equivilent.  There is a real concern about type safety here - for example if we were to place the results of that query into an overloaded method that accepted IEnumerable<int> and IEnumerable<double> the caller might inadvertently pass in the wrong type.  var does maintain strong typing but the question is really whether it's dangerous for the type to not be immediately apparent on definition, something which is magnified when overloads mean compiler errors might not be issued when you unintentionally pass the wrong type to a method.


When you are sculpting in blender sculpt mode you can switch between a number of different materials. one of them is a red clay like material, i would like to recreate this specific material using nodes. i have attempted to get something similar with the principled shader but to no sucess. could anybody instruct me how to do this? (attached picture depicts the material i am refering to).

I'd like to recreate the shading that is going on in the Sculpting view for high-resolution render. It seems to have a very specific light-setup and way of catching light the soft specular, very thick black creases it creates and the almost solarized fill light (light blueish bottom-lighting)     Is there a Material out there that does this?   Thanks


The Nexus is my favourite Minecraft PC multiplayer server. However, when I try to log in, it says "Connection Lost, Failed to login: Bad login".  I tried direct connect too, but that didn't work either, any ideas?

Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved.


I am currently looking through this problem in this video   The video asks: Prove that 4^k-1 is always a multiple of 3 for n = 1,2,3...  Looks like an induction question, the teacher in this video solves it like this 4^k  - 1 = 3P 4^(k+1) - 1 = 3Q Solve for LHS 4^(k+1) - 1 4^k - 1 + 3*(4^k)  HOW did he get this step??   the next steps is  3P + 3*(4^K) 3(P + 4^K) I understand this step though.

I did some mathematical induction problems on divisibility   $9^n$ $-$ $2^n$ is divisible by 7. $4^n$ $-$ $1$ is divisible by 3. $9^n$ $-$ $4^n$ is divisible by 5.   Can these be generalized as $a^n$ $-$ $b^n$$ = (a-b)N$, where N is an integer? But why is $a^n$ $-$ $b^n$$ = (a-b)N$ ?  I also see that $6^n$ $- 5n + 4$ is divisible by $5$ which is $6-5+4$ and $7^n$$+3n + 8$ is divisible by $9$ which is $7+3+8=18=9\cdot2$.  Are they just a coincidence or is there a theory behind?  Is it about modular arithmetic?


Today I asked a question and someone kindly answered it after 2 minutes. It was a good and correct answer. I put it in my code and it did work.  Then I tried to accept it but system wants me to wait 10 minutes. I don't understand this delay for a situation like this, in which you know for sure the given answer is correct.  Maybe this delay should be removed. In this busy world many of us, when we see a correct answer, will just put in in our code and then leave it for good.   I believe the sooner we can reward the person who answered our question the better.

I hate the new popup "you can accept an answer in 10 minutes". Can you please remove it and let me accept an answer immediately?  I can unaccept it later if a better one appears.


I just noticed . Nothing special but he does have a tag in his About Me:    I clicked it, fully expecting to land , same way as  leads to on Stack Overflow. But I landed  instead, the tag page here on Meta, where of course it contains no questions. It also occurs in all other sites. To top this all, consider his : clicking the tag there leads to  which sends me to search for a panda. Can the tag point to the original site where the user has first wrote the About Me, or at least removed in the network profile? (or just put the tag name, unclickable)

The  tag in my Stack Exchange profile links to different sites depending on where it's being viewed:  Profile on StackOverflow:  [tag:CSS] => https://stackoverflow.com/questions/tagged/css   Profile on StackExchange:  [tag:CSS] => https://stackexchange.com/questions/tagged/css   Profile on CodeReview:  [tag:CSS] => http://codereview.stackexchange.com/questions/tagged/css    I'd like to have these all link to https://stackoverflow.com/questions/tagged/css. You can ; why not add the ability to specify the site with tags? <!-- tag: stackoverflow -->[tag:css] <!--tag: meta -->[tag:feature-request]  The current behavior also cause a bug on my :    All tags send me to find a Panda aka 404 Page Not Found.


In the books, it's clearly written that Cho is one year ahead of Harry academically, but in Deathly Hallows we find Cho in the Room of Requirements with the other students. Given the fact that she should have graduated the previous year, what was she doing there? More specifically, how did she manage to get into Hogwarts despite Snape being headmaster?

Cho is suposed to be a year older than Harry, but she’s in the Room of Requirement before the Battle of Hogwarts with the other students. Harry should have been in his final year (if he’d still been at Hogwarts), so shouldn’t Cho have finished the previous year?


I installed most software from the terminal. I saw that with some programs people give commands like this for example:  sudo apt-add-repository ppa:jfi/ppa sudo apt-get update sudo apt-get install psensor   But some just give commands like this:   sudo apt-get install psensor   If that is the case, and I want to add repository (so that program receives updates more quickly, if I understood it right), how do I know what comes after ppa:? How can I find that out?

I keep reading about  ('PPAs') and people answer questions with a link to a PPA. What's the best way to use these?     There are multiple valid answers for this question spanning over several versions of Ubuntu. For your convenience, an index of each is below.


I'm running WSL 18.04 I am trying to use EPOCH particle in cell code but get: Error:  OpenMPI 2.1.1 detected. This contains a serious bug and should not be used.  So i'm trying to update my OpenMPI. Doing sudo apt-get install --only-upgrade libopenmpi-dev      Says I have the latest version despite the website having version 4.0 as the latest version. How do I go about installing the 4.0 version from a downlaoded tar.gz folder? What directory should I install under? /usr/local? What is the proper protocol for installing in ubuntu? Thanks

I was wondering about generic installations of all applications in linux. And what that means? Well, when I was using windows I knew that if I want to install an application I am double-clicking the .exe file and then next,next,next.  In linux, I have understood that maybe there is a common (not generic) way to install any application. Installing from source maybe? Well is there any step by step method that can be used to install  application like in windows or not?  I am asking because I do not want to keep asking the google, how to? So, I have managed to install recently from source freecad from  and I think that it would be a very nice start as common method, right?  But the thing then is where to find the right source and when an application has a very unique method of installation!


My question is what is the best approach to model an object for a realistic cinematic render when using a Subsurf modifier? Because if I may compare Blender to Photoshop, which uses layers, here all we do is not reversible. Even for the "Add Modifier", I need to apply it before moving to the next step. So for example, if I use the Subsurf, what is the best workflow if I want a realistic look? Do I need to push the values to their maximum (view=6+). What is your advice based on your experience?  Here an image to illustrate what I mean:    This sphere is perfect for me but the view (as shown on the image) is at 6. Broadly my question is how do you work? What is your workflow? Do you work with the shading smooth or keep the mesh with polygons to  modeling hard surfaces of your object and only at the end you turn your object into the final rendering with a smooth shading before applying the skin, colors etc.?

I was wondering if I always need to use the maximum value of the options from the elements of "Add Modifier". For example, do I need to use the view 6 in Subdivision surface? I know it depends of what we are trying to achieve, but we all want the same. Make something look the most believable. So do you always use the maximum value Blender offers?


In order to speed up typing of a long command, we can make an alias of a command, e.g.  alias remcopy='scp user@123.45.67.89:/home/file.txt /home/user/'   And we type user this exact command will be run.   However, is it possible only to load the command and then modify it according to the current need, e.g.  scp user@123.45.67.89:/home/file.txt /home/user/addeddir/

I want to know if I can pass an argument with an alias command.  for example:  alias d="dmesg|grep -iw usb|tail -5"    Now d will print the last 5 lines. If I want to use d to print a different number of lines, I have to make change in the alias command declaration of d again.  Is there any way I can modify the declaration of an alias so that I don't have to retype the declaration to change the number of lines. Like incorporating passing the number of lines as an argument while declaring alias for d? Or is there some other method to solve this?


I have a question regarding comparing two strings? and checking if they are identical. Below is the question explenation  // returns true if f.makeMolecular() is is equal to this.makeMolecular      // e.g. terms = {Term('B',3),Term('A',6)} and f = {Term('B',1),Term('A',3),Term('B',1),Term('A',3)}      // would return true      // The makeMolecular() method sorts the Term Strings into Alphabetical order with the number linked to the letter added and following behind the letter.    E.G  Both of the makeMolecular should return a string of "A6B3"  I want to check if  they are identical using and IF statement and taking advatange of the == method in Java.  Below folows one solution to checking if the strings are identical, but as mentioned i would like to do it with an iff statement.    {    this.makeMolecular();     f.makeMolecular();     return identical(f);    }   This is what i have tried so far:  char b = f.makeMolecular();   char b = f.makeMolecular();    if (a==b){       return true;     }     else{         return false;     }   and i get the following error: Incompatible types: void cannot be converted to char. I am quite certain the use of "char" is incorrect here, but i am not sure of what to use instead.  So I am wondering how to convert these strings(?) to a constant and then checking if  they are identical via an IF-statement.  // Edit:  By request; this is the method for  makeMolecular()  public void makeMolecular() {      char element = ' ';     int atoms = 0;     ArrayList<Term> mol = new ArrayList<Term>();      while (terms.size() > 0){         if (mol.size() > 0 && mol.get(mol.size() - 1).getElement() == nextElement().getElement()  ){             atoms = mol.get(mol.size() - 1).getAtoms() + nextElement().getAtoms();             element = nextElement().getElement();             mol.remove(mol.size() - 1);             mol.add(new Term(element,atoms));         }         else {             mol.add(nextElement());         }         terms.remove(nextElement());     }      terms = mol; }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


This question is mainly about building intuition. A lot of the logic rules on First Order Logic make a lot of intuitive sense, like $\lnot\lnot P\equiv P $. Some less, but with an example, everything becomes clear, like $\lnot P \land \left( P \lor Q \right) \Rightarrow Q$. It might seem convoluted first, but with an example, its truth value becomes intuitively clear: "If I say that I have a dog or a cat, and I don't have a dog, then yeah, of course I have a cat". In the case of the quantifiers ($\forall $ and $\exists$), most of the properties fall on the former, and (at least for me) are quite self evident, like $\forall x \left[ P(a) \rightarrow Q(x) \right] \equiv P(a) \rightarrow \forall x \left[ Q(x) \right]$, but two in specific are not very intuitive without an example. Given a universe $U \neq \emptyset$: $$[1]: \forall x \left[P(x) \Rightarrow Q(a) \right] \equiv \exists x \left[ P(x) \right] \Rightarrow Q(a) $$ $$[2]: \exists x \left[P(x) \Rightarrow Q(a) \right] \equiv \forall x \left[ P(x) \right] \Rightarrow Q(a) $$ After an example, formula [1] becomes quite clear: "Saying 'For any person, if they are on Mars then Mars is populated' is the same as 'If there is a person on mars, then mars is populated' ". My problem really comes with [2]. I tried thinking of an example or some logic for it, but the best I could come up with was (in reverse order): "Saying 'If all people are in a hotel, then the hotel is full' is the same as 'there's one person which decides if the hotel is full or not (the last one)' ". I don't think that's right though, because one: That example is a biconditional, not an implication. And second: that example doesn't imply $\exists x \left[P(x) \rightarrow Q(a) \right]$, but actually $\exists ! x \left[P(x) \rightarrow Q(a) \right]$. So my question is: What is an example that can make that concept more intuitively clear? Edit: Though previously marked as a duplicate of , both the question and answer only talk about one side of the equivalence, being: $\exists x \left[P(x) \Rightarrow Q(a) \right] \Rightarrow (\forall x \left[ Q(x) \right] \Rightarrow P(a)) $, but the answer doesn't touch the $ U \neq \emptyset \land (\forall x \left[ Q(x) \right] \Rightarrow P(a) )\Rightarrow \exists x \left[P(x) \Rightarrow Q(a) \right] $ side of things (corrected with $U \neq \emptyset$ and $\Rightarrow$ as pointed out by tkf), so my doubt still remains.

Let $\mathscr{C}$ and $\mathscr{D}$ be wfs.  Suppose $y$ is not free for $\mathscr{D}$, and $\mathscr{C}(x)$ and $\mathscr{C}(y)$ are similar.  Then in any first-order theory, it is a theorem that $$(\exists y)(\mathscr{C}(y)\supset\mathscr{D})\supset((\forall x)\mathscr{C}(x)\supset\mathscr{D})$$ (cf. Mendelson's Introduction to Mathematical Logic, Lemma 2.30).  I am trying to understand, not how to prove this formula, but how to grasp it intuitively -- the formulas I've encountered in mathematical logic have, until now, all been intuitively agreeable.  For example, suppose that $\mathscr{C}(y)$ means "Day $y$ is rainy", and $\mathscr{D}$ means "Bring an umbrella".  Then what is this theorem imply about rainy days and umbrellas?  Better yet, what's another example that would help make intuitive sense of this theorem?


I have a shapefile of a cut-up map of England. I have overlaid points (lat/long) from a CSV as a separate layer.   Is there a way to output what polygon each point is on. So, i'd want to be able to output that point A,B,C are on Polygon 1, D,E,F is polygon 2 etc.    I've counted how many points per polygon but I do not know how to do to swing it back round so it tells me what polygon each point overlays.

I have gridded depth points in CSV format that I'm trying to add other map data to, in additional columns. I've tried joining fields, hoping that I could link the Shapefile data to the csv, but when I try to display the csv by graduated symbols based on the new fields, it goes blank. I used Nathan's tips from , but imported the csv as csv since I want to add map info to that, rather than adding csv info to a map.  See this picture below for the sea bottom temperature & salinity voronois by month, underneath the csv points (a sample subset), with the joins already made. I added columns on the csv for each of the fields i'm intending to append.    I also tried spatial joins as per  however it says the layers aren't the same CRS (I checked, they are), then gets to 15% and hangs.  I also also tried spatial join through  but it hit a python error. I can try this again and look to debug the problem if this is the right way to go.  In short: appending polygon data as fields on a points-grid csv: what's the best way in QGIS 2.0?


When I try,  user@user-OptiPlex-7010:~$ sudo apt-get install gcc    I got response as,  Reading package lists... Done Building dependency tree        Reading state information... Done gcc is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


I have been booting Ubuntu to 3.13.0-93-generic because the newer releases do not support the RS880 [Radeon HD4250] video card that is built-in on my motherboard.    If I were to install the latest release of Ubuntu, would I be able to use the video driver from my Asus CD that came with the motherboard?    Please see question, "" if you need more detailed information about the problem I am experiencing.  I understand that Ubuntu is not supporting my old video card because AMD did not agree to continue supporting it for another five years, but will my old driver work with the newer release of Ubuntu?  If so, how do I go about installing the driver from my CD?  (I know a little, but never enough.)  Thanks!    I really don't want to buy a new computer just because this one is old.  It still works great with the older software on it, but 14.04 LTS keeps wanting to upgrade and I can't because of the driver issue.  Thanks again!

There aren't any drivers for the video card on my computer or for SiS in Ubuntu repositories and I know that it is poorly supported or one of least supported. I also have Windows installed and on Windows the drivers are installed and available.  Can I use wine or PlayOnLinux to install those drivers from Windows so that I have the drivers installed on Ubuntu?  Is that possible?    I have Ubuntu 12.04 beta so far and Ubuntu 11.10 installed  My video card is:   01:00.0 VGA compatible controller: Silicon Integrated Systems [SiS] 771/671 PCIE VGA Display Adapter (rev 10)   From a previous question that I asked


Ok, so I got an error when I tried to print something based on the user's input. Pretty standard stuff, right? So, if the program would have worked correctly, the user would have entered six words or phrases that would be stored in the string named PhrasesAndWords. Then, each part of the array would have been tested, by creating a while-loop, using the counter as the index in the switch statement. Well, apparently, this didn't work, because it wasn't a constant expression, or a constexpr. The variable can't be a constant expression, though, since that would result in an infinite loop. By the way, here is the error:  C:\Users\henry\Desktop\NotTheActualPathForThisProject\main.cpp|34|error: switch quantity not an integer|  Aaand here's the code I wrote (I have gotten rid of irrelevant variables and such, though):  int main() {  string phrasesAndWords[6];  cin >> phrasesAndWords[0] >> phrasesAndWords[1] >> phrasesAndWords[2] >> phrasesAndWords[3] >> phrasesAndWords[4] >> phrasesAndWords[5]; // Recieve input  int counter = 0;      while (counter < 6) {     switch(phrasesAndWords[counter]) {          case "RandomString":             print("That sure was quite random. \n")         default:             print("I don't understaahnd... \n")     };     counter++; };   };

Compiling the following code and got the error of type illegal.  int main() {     // Compilation error - switch expression of type illegal     switch(std::string("raj"))     {     case"sda":     } }   You cannot use string in either switch or case. Why? Is there any solution that works nicely to support logic similar to switch on strings?


I've been reading up on threading and tried implementing it into my code however I'm not sure if the way I'm doing it, is the best practise.   My code simply imports a self scripted package which pulls weather data and runs the package every 60 seconds thereafter.   I plan on running multiple packages which gather data at once, when I have worked out a good code technique.  from package.weather import weatherapi import threading  def update():   weatherapi()   threading.Timer(60, update).start()  update()    Firstly it just seems messy and if I wanted more packages running in a thread, I'd need to create another update function Secondly I'm not able to kill my process   If anyone has any suggestions, it would be greatly appreciated.

I want to repeatedly execute a function in Python every 60 seconds forever (just like an  in Objective C). This code will run as a daemon and is effectively like calling the python script every minute using a cron, but without requiring that to be set up by the user.  In , the solution appears to effectively just  for x seconds. I don't need such advanced functionality so perhaps something like this would work  while True:     # Code executed here     time.sleep(60)   Are there any foreseeable problems with this code?


I'm developing a small script of js to edit a profile in the way facebook used to be (click a button, edit and save without reloading the page). The problem is that when I run it, the ajax function returns sucess but akes no changes on the database. The function os js is this:  $('.savebtn').click(function(){             var editdata    = $(".editbox").val();             var parameter   = $(this).closest("td").find("#parameter").text();              var datastring  = "data="+editdata+"&parameter="+parameter;              var $t = $(this);              console.log(datastring);              $.ajax({                 type: "POST",                 url: BASE_URL + "/API/update_profile.php",                 data: datastring,                 cache: false,                 success: function()                 {                     $t.closest('td').find('.curr_value').html(editdata);                     $t.closest('td').find('.curr_value').hide;                     console.log(editdata);                     $(this).prev(".edit").hide();                     $(this).prev(".curr_value").show();                     $(this).prev('.edit_link').show();                     $(this).hide();                 }             });         });   (Ignore the $t thing, somehow this works like this, but not if I use $(this))  Ajax executes the code for sucess but doesn't update anything on the database.   The PHP code for the database is:  <?php  include_once("../../config/connect_db.php"); include_once("../../database/cliente.php");  $parameter = $_POST['parameter']; $data = $_POST['data']; $id = $_SESSION['id'];  var_dump($_POST);  try {     updateProfile($parameter, $data, $id); } catch (PDOException $e) {     echo 'Caught exception: ',  $e->getMessage(), "\n"; }   ?>    function updateProfile($parameter, $data, $id) {     global $conn;     $stmt = $conn->prepare("UPDATE biofood.users                              SET ? = ?                             WHERE id = ?");     $stmt->execute(array($parameter, $data. $id)); }   EDIT: As pointed out, this could be a problem with trying to pass a column name as a parameter. Changed the code to the following, but with no sucess:  function updateProfile($parameter, $data, $id) {     global $conn;     $query = "UPDATE biofood.users                SET $parameter = $data               WHERE id = $id";     $stmt = $conn->prepare($query);     $stmt->execute(); }

Why can't I pass the table name to a prepared PDO statement?  $stmt = $dbh->prepare('SELECT * FROM :table WHERE 1'); if ($stmt->execute(array(':table' => 'users'))) {     var_dump($stmt->fetchAll()); }   Is there another safe way to insert a table name into a SQL query? With safe, I mean that I don't want to do  $sql = "SELECT * FROM $table WHERE 1"


My goal:   I have a computer in a location A, let's call it host-A. I have a computer in a location B (host-B) running an ssh server, and I can ssh from host-A into host-B. I want to access a website on the web browser of host-A, say  via an ssh tunnel through host-B.  What I did:  In host-A, I type ssh -v -N -L 8080:example.com:80 host-B. I can check using netstat  --inet -lnp that ssh is indeed listening on 127.0.0.1:8080, with foreign address 0.0.0.0:*. In host-B, I can access example.com. Hence in host-A browser (firefox here), when I type the url "", I should access the example.com webpage.  My questions:  When I do this, I actually get a 404 not found. Yet, in the shell in which I issued the "ssh -L", I see some logs, for instance:  debug1: Connection to port 8080 forwarding to example.com port 80 requested.  (1) So what happened here? I did exactly the same (except using example.com) as, e.g., .  When I try with "www.ubuntuforums.org" (so ssh -v -N -L 8080:www.ubuntuforums.org:80 host-B in host-A),  actually takes me to "". (2) Why is that?  When I try with ssh -v -N -L 8080:www.stackoverflow.com:80 host-B, I get:  Fastly error: unknown domain: localhost. Please check that this domain has been added to a service. Details: cache-cdg20728-CDG (3) Again, why? So many mysteries for me here...

When I capture packets using the packet analyser wireshark while visiting  I can see packets that use the HTTP protocol (e.g.a GET request). My Get request uses 4 protocols: Ethernet II, IPv4, TCP and HTTP.  For the IPv4 I can see my own local IPv4 address of my pc as the source, for the destination I see the IPv4 address 91.198.174.225. When I go to this address in my browser I get to some wikipedia related website that says'wiki does not exist'. Why am I not seeing the Hydrogen article when I go to that ip address?


My Password to enter Windows is in Greek, but in the logon Screen the Greek language is not supported.  The same thing happened with another person in the (), but the answers cannot help me... First I don't have a recovery disk. Second, on the end, he solves the issue with a solution is on a  written in Turkish, which I don't speak.  Please, can somebody somehow help me?  This is really a Problem which Microsoft should have not allowed to happen.    Edit #1  Issues occurs even if I have a CD.  Because until the command line I can make it, even without CD, but the language which I have to write is Greek, and the commands which I have to type are in English.   I turn on the Computer; I press F8; I choose "Repair Computer"; System asks for an input language;  4.1. I choose greek. System asks for Username and Password. In Username, there are 2 options:  5.1. My Administrator Account, which has a Password in Greek language;  5.2. The second option is an accound I see first time - HomeGroupUser$ - which I dont know the Password. I choose my account and I put my password (in greek); Now I have some more options, but the language I can write is greek... and that's the Problem.

I got a brand new Windows 7 machine, installed the operating system, created one account and forgot its password. What can I do?  There is no external CD, the operating system is loaded from somewhere inside the machine.  I already tried to remember passwords and tried all candidates with all possible combinations of caps lock, num lock etc.


Single singleVal = 0.9f; int u = (int)(singleVal * 10.0f); # u = 8   I know this is probably a dumb error but I cant figure out why result of the above expression is 8. I thought it would be 9 for obvious reasons. Is their something special going on in c# that I am failing to notice?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


Getting a NullPointerError on line 24 (second for loop) and an arrayoutofindexexception on the main method. I have no idea how to solve this and an explanation would be much appreciated. Please help!  Edit: 'NullPointerError' solved, just needed to initialize the ArrayList for it, but still can't work out the 'ArrayOutOfIndexException' error.  import java.util.*;  public class SnackBar {     private Random randomizer;     private String[] flavours;     private SnackMachine barMachine;     ArrayList<Student> students;      public SnackBar(int numStudents, int packetsBarMachine, int costPacket)     {         randomizer = new Random();         flavours = new String[] {"prawn cocktail", "tango cheese", "natural", "paprika", "salt and vinegar"};         barMachine = new SnackMachine(packetsBarMachine, costPacket);  students = new ArrayList<Student>();          for(int i = 0; i < packetsBarMachine; i++)         {             barMachine.addPack(new PackOfCrisps(randomFlavour()));             i++;         }          for(int j = 0; j < numStudents; j++)         {             students.add(new Student(randomFlavour(), barMachine));                         j++;         }     }      public String randomFlavour()     {         int random = randomizer.nextInt(flavours.length);         return flavours[random];     }      public void describe()     {         System.out.println("The SnackBar has " + students.size() + " hungry students.");         System.out.println("The Snackmachine has:");         System.out.println(barMachine.countPacks("prawn cocktail") + " packets of prawn cocktail crisps,");         System.out.println(barMachine.countPacks("tango cheese") + " packets of tango cheese crisps,");         System.out.println(barMachine.countPacks("natural") + " packets of natural crisps,");         System.out.println(barMachine.countPacks("paprika") + " packets of paprika crisps,");         System.out.println(barMachine.countPacks("salt and vinegar") + " packets of salt and vinegar crisps.");     }      public void runSnackBar(int nSteps)     {         int step = 1;          while(step <= nSteps)         {             System.out.println("Time Step " + step);             describe();             int atRandom = randomizer.nextInt(students.size());             students.get(atRandom).snackTime();             step++;         }     }      public static void main(String[] args)     {         SnackBar bar = new SnackBar (Integer.parseInt(args[4]), Integer.parseInt(args[20]), Integer.parseInt(args[5]));          bar.runSnackBar(Integer.parseInt(args[30]));     } }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I know that that is used for things and who for people, but in some cases, I can't really explain why, but I'm hesitating between:     There are 4 more people that have watched the film #2 than people that have watched the film #3.   or     There are 4 more people who have watched the film #2 than people who have watched the film #3.   or   another way to say it?

I often get confused when trying to use who vs that.  Some examples that often confuse me:  That     The person that went to the store.      The people that went shopping.      The persons that went shopping.      The group that went shopping.   Who     The person who went to the store.      The people who go shopping.   Please explain when to use either for plural subjects and singular subjects.  Animate and inanimate objects as well.


Since I've become active on the Smoke Detector Project, I accumulated over 85 accounts on various stack exchange sites, and all but three are there mainly to flag spam.   I've recently been searching for a way to view a summary of my network-wide flags, with things like helpful/declined and status, like a per-site flag summary.  Does this already exist (if so where can I find it)?  Or could SE maybe provide something like that?  Or maybe could even an userscript provide something like that?

This morning I flagged something on one of the sites where I have fairly low rep. Now I can't remember which site it was. I've checked my flag history on about half of them, even editing the URL for the site where I have no helpful flags, and I can't find this flag. I've been to my network profile and looked at the Activity tab, but it only shows public things like asking, answering, commenting, editing, and reviewing.  Is there a way to see my flagging history across sites? Can we have such a feature, if it's not possible?


In the code snippet below I am calling nodeDepths(root, depth, depthSum) and expecting updated value in depthSum but every time it's returning 0 to me public static int nodeDepths(BinaryTree root) {             Integer depthSum = 0;             Integer depth = 0;             nodeDepths(root, depth, depthSum);             return depthSum;              }              public static void nodeDepths(BinaryTree root, int depth, Integer depthSum) {             depth = depth + 1;             depthSum = depthSum + depth;                  if (root.left == null && root.right == null) {                 return;             }                  nodeDepths(root.left, depth, depthSum);                  nodeDepths(root.right, depth, depthSum);              }  Note: I have not mentioned the problem scenario and logical part as that is not an issue. The issue I am facing is the "depthSum reference variable not getting updated in caller method"

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


In the first comment in the above image, Chris's username is highlighted, because he is the original question asker. Sam's comment however, looks like anyone else's, despite being the answerer. While in the case of this particular comment chain, it doesn't really matter who is replying to Chris, in others, especially longish chains, it can get confusing who is the asker, answerer, and chimer-inners. Perhaps something minor, such as underlining it?

In addition to the highlighting comments made by the question owner (as described ), I think it would be a good idea to highlight comments left by the author of the answer being commented on. This way, the conversation between asker and answerer is more defined/obvious. Edit: This is an edit to bring this to the site owners attention again - It would help people like me with bad eyesight to track down their comments. I originally opposed the questioner highlighting, but experience has shown me that I was wrong, and I think that answerer highlighting of comments would be very useful.


Of course it would be preferable to say, "He put a box on the shelf," but is it incorrect to say "He put on the shelf a box?"   This sentence was an item on a test for people with aphasia. The target sentence is "He put the box on the shelf." Inversions are acceptable if they're correct. An easier example is "She is giving the boy a present" for "She is giving a present to the boy."

As far as I know, adverbs can't be placed between an object and a verb. But I have seen some sentences not following this rule. Could you please explain why adverbs are placed between objects and verbs? Examples:   You can find below the list of accessories.  I saw yesterday that there was a crime.


In the last episode of Code Geass R2, after Lelouch died, Nunally touched his hand and she suddenly knew what he did and what the Zero Requiem was. Was this a power of Geass?

In the end, when Lelouch is about to die, Nunally holds his hands and is able to see his memories. How? The theory that Lelouch is immortal explains this, but that isn't official.   Is there any official explanation for this?


I like StackExchange's tag system.     I want to know how it works. What libraries does it use?

I am a user on Stack Overflow, and I think every page that shows questions, display all tags and the questions. Are the tags saved in a tags table or are they included together with the questions table?


What are the tiers in arena for awards in Hearthstone?  When do you get 3 boxes, 4 boxes etc?  Thanks

What is the list of keys and their corresponding wins?  I have it listing that the highest number of wins I've had in arena is a Champion key, but it doesn't say how many wins it was.


In a Math lecture , we solved the following DE   $$yy'^2+2xy'-y=0$$  in 3 ways : First we solved for y' by taking y' in one side , making a substitution and integrating.  We solved the DE again for x and one more time for y as following :   We solved the DE for y , by taking y in one side and called y' as p , then we differentiated both sides w.r.t x to get finally a separable DE in p and x that can be solved easily.  And we solved the DE for x by taking x in one side and called y' as p , then we differentiated both side w.r.t y to get finally a separable DE in p and y that can be solved easily.  My problem is that I do not understand why can we need to solve a DE for x and y ?? solving the DE for y' gave us the solution we need . What do the solutions gotten from solving for x and y represent ?? and why do we differentiate w.r.t x when solving for y and differentiate w.r.t. y when solving for x ? ..Is this a standard method to solve non linear DE?? If you can provide me a reference name that introduces this method of solution ,I will be grateful!

Solve the differential equation: $yy'^2-2xy'+y=0$ (*)  I have   $(*)\Leftrightarrow (yy')^2-2xyy'+y^2=0\\ \Leftrightarrow z'^2-4xz+4z^2 =0 \ \ (z=y^2)$  I can't know how to continue.  Could you give me some hints. Thanks for helping.


I updated minecraft to 1.8 and the launcher to 1.5.3 and now I can't install my mods

I've recently changed to the new Minecraft launcher, and I have noticed a change in the .minecraft folder layout. I can no longer install mods just by copying it over into the versions/1.6.1 jar file, as this file refreshes every time it is launched.  For those who don't know what I am talking about, here is the new layout:    I am specifically trying to install Optifine, which does work with 1.6.1. Where do I drag in the mod files now? I can't seem to find a jar file that is suited to it, except in the version folder, but as I stated above, this refreshes every time.  After copying a recent version and renaming it in the version folder, I get this error in the development console:   Unexpected exception refreshing version list java.lang.IllegalArgumentException: Version '1.6.1' is already tracked     at net.minecraft.launcher.updater.VersionList.addVersion(VersionList.java:91)     at net.minecraft.launcher.updater.LocalVersionList.refreshVersions(LocalVersionList.java:44)     at net.minecraft.launcher.updater.VersionManager.refreshVersions(VersionManager.java:47)     at net.minecraft.launcher.Launcher$2.run(Launcher.java:164)     at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source)     at java.util.concurrent.FutureTask$Sync.innerRun(Unknown Source)     at java.util.concurrent.FutureTask.run(Unknown Source)     at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)     at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)     at java.lang.Thread.run(Unknown Source)


Let $I$ be an ideal in $\mathbb{C}[x_1 ,x_2 ,x_3 ,x_4 ]$  such that $I$  is generated by $x_1 x_3$, $x_2 x_3$, $x_1 x_4$,  and $x_2 x_4$. How to show that this I cannot be generated by two elements?    It seems intuitively clear but, can't prove it rigorously

Can $(X_1,X_2) \cap (X_3,X_4)$ be generated with two elements in the ring $R=k[X_1,X_2,X_3,X_4]$? Can it be generated with three elements? (Here $k$ is a field.)    Thanks for any help.


I just finished my dissertation results and trying to interpret them and very confused. Basically, X and Y are not correlated but then when I put X in my regression model with a few other variables X significantly predicts Y. I've been explained this statistically and somewhat understand it --- that when you control for other things the relationship changes, but theoretically it makes absolutely no sense. Can someone give me an example using variables showing how they are not related when looking at them in a vacuum but then becomes a significant predictor in another instance? Having a hard time writing discussion because of this. Thanks.

In a multiple linear regression, why is it possible to have a highly significant F statistic (p<.001) but have very high p-values on all the regressor's t tests?  In my model, there are 10 regressors. One has a p-value of 0.1 and the rest are above 0.9    For dealing with this problem see the .


I'm learning for a test and I think there will be some task similar to this one. I'd like to know if I did it correct and if not can you please say how to do it correctly?     Let $\Omega$ be a set, let $I$ be an index-set and let $A \subseteq \Omega$ and $A_{i} \subseteq \Omega$ for all $i \in I$.      Show that $$\left(\bigcup_{i \in I}A_{i}\right )^{c}=\bigcap_{i \in I}{A_{i}}^{c}$$   We defined this in our readings:  Complement: $A^{c} \equiv \bar{A}= \left\{x \in \Omega; (x \notin A)\right\}$  and $$\overline{\bigcup_{i \in I}A_{i}}=\bigcap_{i \in I}\overline{A_{i}}$$  I did it like this:  $$\left(\bigcup_{i \in I}A_{i}\right)^{c}=\overline{\bigcup_{i \in I}A_{i}}=\bigcap_{i \in I}\overline{A_{i}}=\bigcup_{i \in I}{A_{i}}^{c}$$

I'm working through a book on fundamental topology, and I'm stuck at a proof in set theory. The book provides a proof for:   $$\text{Let }\left\{A_\alpha\right\}_{\alpha\in I}\text{ be an indexed family of subsets of a set }S\text{; then:}$$ $$C\left(\bigcup_{\alpha\in I}A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$$  where $I$ is an indexing set for $\alpha$, and $\alpha\in I$, and $C(S)$ denotes the complement set. They do this by proving first that, if $x\in C\left(\bigcup_{\alpha\in I}A_\alpha\right)$, then $C\left(\bigcup_{\alpha\in I}A_\alpha\right)\subset\bigcap_{\alpha\in I}C\left(A_\alpha\right)$. Then, the prove the converse; that if $x\in\bigcap_{\alpha\in I}C\left(A_\alpha\right)$, then $\bigcap_{\alpha\in I}C\left(A_\alpha\right)\subset C\left(\bigcup_{\alpha\in I}A_\alpha\right)$, so the two sides, being subsets of each other, must be equal.  That makes perfect sense, and is very clear and straightforward. However, what I don't understand is their second proof (under the same conditions):  $$C\left(\bigcap_{\alpha\in I}A_\alpha\right)=\bigcup_{\alpha\in I}C\left(A_\alpha\right)$$  While this statement intuitively makes sense to me, I can't seem to prove it mathematically. Here's what I've done so far:  Let $x\in C\left(\bigcap_{\alpha\in I}A_\alpha\right)$. We know that, conversely, $x\notin \bigcap_{\alpha\in I}A_\alpha$. This is where the proofs diverge, though; if it were the first formula, it would be possible to say that $x\notin \bigcup_{\alpha\in I}A_\alpha$, and as a result, that $x\notin \left\{A_\beta\right\}_{\beta\in I}$. However, I can no longer do that, and approaching it from the other direction gives the same result.  Let $x\in\bigcup_{\alpha\in I}C\left(A_\alpha\right)$. We know that $x\notin\bigcup_{\alpha\in\ I}A_\alpha$, but this still doesn't get me anywhere.   How should I approach this proof? Any hints or pointers for someone new to topology?


Prove that $int(A) =  (cl(A^c))^c$   I draw some diagrams to get the intuition for this exercise but couldn't figure out how to formulate this into a proof.  I'd be glad for a guidance.  Thanks

Let $(X,d)$ a metric space and $A\subset X$. Prove that $$\overline{(A^c)}=\overset{\circ}{(A)}^c$$ i.e. the closure of complement, is  the complement of the interior. Proof. If $x\in \overline{(A^c)}$ then $x\in A^c$ or $x\in (A^c)'$. Since $\overset{\circ}{A} \subset A \Rightarrow A^c \subset \overset{\circ}{(A)}^c$ so, if $x\in A^c$ then $x\in \overset{\circ}{(A)}^c$. Now if $x \not\in A^c$ but $x\in (A^c)'$ then $\forall r>0, B(x;r)-\{x\}\cap A^c \not= \emptyset.$ And now I've to deduce that $x\not\in \overset{\circ}{A}$ so $x\in \overset{\circ}{(A)}^c$, but I can't figure out how.


My ubuntu is in trouble,  I changed my graphic card, tryed some manipulations, and now I get some problems with the login-screen.  I have the login-screen, normal, but when I type on password ( I am sure it's the good one, ssh work fine ), after I valid I get a black screen, some rapid text in textmode, but I can't read, and next the login-screen again.  I tryed to find something strange in Xorg logs, but I don't found. I am not sure to look at the good place.  My card is an ATI RS690. I use VGA for now, but I plan to use it on HDMI.  Ubuntu 13.10 / lightdm  Thx

I am running a VMWare Player with a Ubuntu 12.04 LTS Precise Pangolin as Guest on my Windows 7. Sometimes I get the shutdown blue screen error in Windows, this time it happened when I was running the Player. When I restarted everything Ubuntu gave me the "Login Loop" on adminstrator login. I log in and there's this black screen where I can only read:  piix4...smbus:0.0.0.07.3 Host Smbus controller not enabled .    When I go to the prompt in root mode it fails to update and only upgraded, specially some plugins ( I think graphic plugins) which also appear in one an error message after quitting the prompt, but they´are successfully installed. They are not the error message. After that I have been working with the Fail/safe Mode recovery panel. When I try to update via Root I get errors like this: W:failed to fetch http://extras.ubuntu.com/ubuntu/dists/precise/release.gpg could not        resolve 'extras/ubuntu.com  There are 8 more like this referring to areas like: -archive/canonical.com -ppa.Launchpad.net -security.Ubuntu.com -Us.archive.ubuntu.com - release.gpg                         precise-updates/release.gpg                         precise_backport/release.gpg   Final Message: some index files failed to download.....they have been ignored or old files are used. The black screens most of the time pass by too fast for me to pick up any information. But in general I think I have done everything I was able to in the recovery panel including updating network and graphic packages and recovering filesystem packages and the basic stuff ( I am a beginner regarding Linux ) in the root prompt. Now I am stuck in this screen with graphic options: - Run in low-graphics mode just for one session - Reconfigure Graphics - Troubleshoot the error - Exit to console login  I am trying to choose to reconfigure graphics but the mouse disappears in the virtual machine screen and sometimes when options change it´s only the first and last option. But this happens from the blue without messages. This particular option menu is in the regular GUI style against a black screen in Terminal style. Really strange.


Trying to Implement Glide inside recyclerView App is crashing. Logcat saying          W/ResourceType: No package identifier when getting name for resource number 0x00000000 V/studio.deploy: Package broadcast exit hook { cmd=3, time=75125210000000, thread=2 }     Fixing application and activity contexts W/ResourceType: No package identifier when getting name for resource number 0x00000000 E/RecyclerView: No adapter attached; skipping layout D/AndroidRuntime: Shutting down VM E/AndroidRuntime: FATAL EXCEPTION: main     Process: com.example.tc, PID: 26232     java.lang.IllegalArgumentException: You must pass in a non null View         at com.bumptech.glide.GenericRequestBuilder.into(GenericRequestBuilder.java:685)         at com.bumptech.glide.DrawableRequestBuilder.into(DrawableRequestBuilder.java:457)         at com.example.tc.TCAdapter.onBindViewHolder(TCAdapter.java:44)         at com.example.tc.TCAdapter.onBindViewHolder(TCAdapter.java:22)    My Implementation code is  Glide.with( context ).load( tcImages.get( position ).getFullName() ).into( holder.imageView );   My full Adapter code is   public class TCAdapter extends RecyclerView.Adapter<TCAdapter.MyViewHolder> {      List<TCImages> tcImages;     Context context;       ImageView imageView;      public TCAdapter(List<TCImages> tcImages, Context context){         this.tcImages = tcImages;         this.context = context;     }      @NonNull     @Override     public MyViewHolder onCreateViewHolder(@NonNull ViewGroup parent, int viewType) {         LayoutInflater inflater = LayoutInflater.from( context );         View view = inflater.inflate( R.layout.item_tc_recycler, parent, false );         return new MyViewHolder(view);     }      @Override     public void onBindViewHolder(@NonNull MyViewHolder holder, int position) {         holder.textView.setText( tcImages.get( position ).getEmail() );         Glide.with( context ).load( tcImages.get( position ).getFullName() ).into( holder.imageView ); //        Glide.with( context ).load( "https://www.google.com/images/branding/googlelogo/1x/googlelogo_color_272x92dp.png" ).into( holder.imageView ); //        Toast.makeText(context, tcImages.get( position ).getFullName().toString(), Toast.LENGTH_LONG).show();     }      @Override     public int getItemCount() {         return tcImages.size();     }      public class MyViewHolder extends RecyclerView.ViewHolder {         TextView textView;         ImageView imageView;         public MyViewHolder(@NonNull View itemView) {             super( itemView );             textView = (TextView) itemView.findViewById( R.id.txtItem );             imageView = (ImageView) itemView.findViewById( R.id.imageView );         }     } }    Tried pasting direct string of image address even then it's crashing

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I am reading that entangled particles can share information across long distances and the speed is usually faster than the speed of light...so am I right in assuming that future communications in the world will be without satellites and cell phone towers? Two entangled computers can talk instantaneously ...say between New York and Mumbai?  I sit in New York and feed in "A" in my computer, that information shows up in my friend's computer in Mumbai? Only thing is these two computers (processors/monitors) need to be entangled during manufacture?

Quantum entanglement is 2 atoms that are paired together and when you stop one from spinning the other also stops with the same spin. Can you use these pairs to have faster-than-light (FTL) communication between 2 computers?


Following up my previous questions on the usage of the word / phrase ('banzai' and 'ring the cherries') in Thomas Harris' thriller, ”The Silence of Lambs,” I came across the following passage in the scene Stacy Hubca, an office clerk of Franklin Insurance Agency in Belvedere, Ohio answers to Clarice Starling, an FBI agent.     “She died. She went to Florida to retire and she died down there, Fredrica said. I never did know her. - - - You might could talk to   her family or something. I’ll write it down for you." - ibid Chapter 54.   Page 332.   As an only school textbook-based English language learner, it’s my understanding that an auxiliary verb (might) should be followed by a root of verb. What is the grammatical justification of the sentence, “You might could talk to her family or something”?  Though it "might could" be a midwest dialect, but what’s wrong with simply and normally stating “You might talk to her family” or “You could talk to her family”?

I have a friend from the southern U.S. who uses the phrase “might could” quite often. He’ll say, for example:     I might could do that this weekend.    When I first heard him say this, it made me do a double-take. I wasn’t sure whether it’s incorrect, or correct but just not idiomatic outside the southern U.S.


I do this command:  $ locate config.yml | while read i; do sed -i '/(swipe)|(pinch)/s/[0-9].*/1/' $i; done   output:  sed: couldn't open temporary file /home/user/.config/fusuma/sedHhlVCW: Permission denied sed: couldn't open temporary file /home/var/lib/gems/2.5.0/gems/fusuma-0.11.1/lib/fusuma/sed41YvwW: Permission denied sed: couldn't open temporary file /var/lib/gems/2.5.0/gems/fusuma-1.10.0/lib/fusuma/sedFSNXeV: Permission denied   So I did with sudo (run as sudo sudo su -> #, but then not all files were change, and as I see from the error above, the files are temporary and with changed name (postfix of all them consist of command and random chars), does this pipe? If so why? How can I persist filenames over pipe?  $ uname -a Linux user 4.19.0-9-amd64 #1 SMP Debian 4.19.118-2 (2020-04-29) x86_64 GNU/Linux  $ type sed sed is aliased to `sed -E'

having this command:  $ find / -path /home/oldroot -prune -o -name config.yml -exec sed -i'' '/(swipe)|(pinch)/s/[0-9].*/1/' {} \+   won't edit:  couldn't open temporary file /home/shepherd/.config/fusuma/sedSQVSZd: Permission denied   You can say, it does not work because of sudo. But it does not even work with sudo, the point is the -i flag here. find found file /fusuma/config.yml, but -i change it into /fusuma/sedSQVSZd as sideeffect of in-place edditing. So is there a way to persist filenames with sed?


Anyone know whether ubuntu 17.10/18.04 has a preset keyboard shortcut to to settings?

In previous versions of Ubuntu I could create custom keyboard shortcut to run terminal commands, with something like gksudo reboot for example, and then assign that to something like win+r.  I can't find that option in Ubuntu 17.10 or Ubuntu 18.04 daily build.  Am I missing something?


I have an iPad 2 (MC769LL/A) that is running iOS 5.1.1. I need to update the OS. The device is telling me there's an update for 9.3, but I'm getting an error saying unable to verify the update because I'm no longer connected to the internet.  Before you even suggest it, I did all these things mentioned here (and everywhere else): . Is this iPad in un-update-able hell? Is there some way I can manually update it to a lower version than 9 as a stepping stone?

I have read many post about updating an iPad 1 (iOS 5.1.1) to iOS 8 but all I need at the moment is to update my iPad 1 to at least iOS 6. Is there any way I can update it to iOS 6? No jail breaking or anything, just a normal way of updating.


I am wondering what the advantages and disadvantages are for upgrading you town hall before maxing everything else out. I have heard that rushing isn't worth unlocking new things and that going against lower town halls will allow you to take less loot from them. How much less, and where is this confirmed? Yet, upgrading your TH sometimes results in a lower % amount of loot that enemies can take from your storages. Yes the cap increases, but one could stay below a certain amount of gold so that the lower % is more worth it. See  For example, let's say the cap increases from 150k to 300k but the % loot available to be stolen from storages decreases from 20% to 10% when I upgrade my TH. If I had 750k gold with the lower TH, they could steal 150k, but when I upgrade my TH, I can have up to 1.5 million gold by the time they can take 150k, so as long as I have less than 1.5 million gold/elixir before logging off, they can steal less loot with that higher TH. What are all the advantages and disadvantages of rushing in Clash of Clans, and I want sources for statistics.

I have heard that it is best to upgrade everything to the max before upgrading your Town Hall. Is this true, or is it impractical?


Many companies are now using stylized case for their names. When writing formal documents, how should these names be written? Assuming that the case they've chosen should be honored, how should they be treated at the beginning of a sentence?

I'm a moderator at another StackExchange site and a debate has come up about the usage of the trademarked name that site is about, i.e. WordPress. Note as a trademark it is spelled in  and thus we wanted our guidelines to be that you render it in CamelCase or we'll probably edit it so that it will be consistent (we don't expect that people will all notice this nor are we trying to get people to obey, we just want to let them know that we'd prefer they do it this way and if they don't we'll probably edit it for them as we are writing our answers). Of course there is always at least one person who takes issue when a group tries to create order partly in this case because of a dust-up created by the founder of WordPress who recently added a function to WordPress to CamelCase the name in content on people's sites and has dismissed the outcry about it from a group of passionate people as not his concern. Ignoring whether he should or should not have done that (I see these two issues as orthogonal) my view is that for our site if WordPress is cased as WordPress by its founder it makes our site appear more of an authority if we are generally consistent in that usage. But this one individual wants to debate that and part of his argument is as follows:  Spoken professionally, names should be written orthographically correct. Correct me if I'm wrong, but to my best knowledge in English (both BE and AE), this means with an uppercase first letter per each word -the rest lowercase. I'm aware that companies can get very "creative" to break the "burdening" constraints of language for their own and their products names. But to make everything well read- and understandable, authors should first aim for an orthographically correct writing instead of fulfilling the marketing needs of a specific company.  So I'd like to know if it would be considered more proper in written English and why to use casing such as Mcdonalds, Powerpoint, Thinkpad, Jpmorgan, Ebay, L'oreal, Conocophillips, Unitedhealth, Wellpoint, Pepsico, and Fedex OR the casing that follows their trademarks; i.e. McDonalds, PowerPoint, ThinkPad, JPMorgan, eBay, L'Oreal, ConocoPhillips, UnitedHealth, WellPoint, PepsiCo, and FedEx and relatedly would be be easier to read/more understandable?  Note his last statement seems to imply he is really just trying to use this his statement on the "proper" way to do it in English (which is ironic as he's a non-native speaker) in order to justify his apparent desire to be "anti-marketing." So I am coming here hoping for support that CamelCase for trademarks is the correct form in English usage but will be open minded in hearing your opinions and might even change my mind as I often do when presented with better evidence.


WGS84 is a reference ellipsoid that determines coordinates of every point on Earth using latitude, longitude and height about the its surface.  This ellipsoid is often used as a base to make maps. Though, to make a map on a flat paper or a flat digital screen you need a projection too. An example of a popular projection would be UTM.   Mainstream GIS software give plethora of projection alternatives to display your data layers. Among them, they also let you display your data using WGS84 only.  I think they are using a certain projection but what projection is that?

I like to think I'm relatively well-versed in datums, projections, and coordinate reference systems.  OpenStreetMap data is stored in WGS84 Lat/Lon (EPSG:4326). This CRS is geographic and therefore intended to store locations on a 3D globe. When I see  what am I looking at?  Looking at Reykjavik it appears that the longitude lines are tending towards the North Pole at the Greenwhich Meridian (or maybe they planned the city in perspective view??) so I assume 0,90 is top-centre of the map.  Does this class as a projection, and if so which one?   Is there one projection that is commonly used for lat/lon data?  I have data stored in Oracle using EPSG:4326 and when rendered by GeoServer without a specified projection it also displays these characteristics.


I have been messing around with windows forms and I'm pretty new to C#. So you normally declare an instance like the following:Button example = new Button(); however, if the class Button is inside a namespace you must declare the fully qualified path: foo.bar.Button newButton = foo.bar.Button(); That works well as long as you know every fully qualified path you want to implement. However I stumbled with a situation in which you get the full qualified path from a string, therefore I'm not sure how to declare a new instance of the class.  private void treeLoader_Click(object sender, EventArgs e) {         string viewPath = this.tree.SelectedNode.FullPath;         viewPath = viewPath.Replace(" ", "");         viewPath = viewPath.Replace("\\", ".");         // At this point viewPath equals "foo.bar.Button"          Type newButton = Type.GetType(viewPath); // Failed attempt }

Is there a way to create an instance of a class based on the fact I know the name of the class at runtime. Basically I would have the name of the class in a string.


I need to calculate the following integral $$\int_0^1 e^{i \pi x}x^x(1-x)^{(1-x)} dx$$ I tried parts integration, but it became more complicated, using mathematica shows the result looks like a pure imaginary number.  Any help or hint will be Appreciated

I've found  the following integral.  $$I = \int_{0}^{1}\sin{(\pi (1-x))}x^x(1-x)^{1-x}\,dx=\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx=\frac{\pi e}{24}$$  I've never seen it before and I also didn't find the evaluation on math.se. How could we verify it?  If it is a well-known integral, then could you give a reference?


I am trying to grab an entire row if the date value is the same as what's in my script. So far my date comparison never works and nothing is ever returned. In my sheet I have a simple date:  In App Script I am trying to grab any row that has the date of Oct 5th: function getSheetData() {   var selectDate = new Date('05/10/2020');      var activeSheet = SpreadsheetApp.getActiveSheet();   var dataRange = activeSheet.getDataRange().getValues();   for (var i = 0; i < dataRange.length; i++) {     if (dataRange[i][0] == selectDate) {       return dataRange[i];      }   } }  How do you compare the date object to return the row that has Oct 5th specified?

Can someone suggest a way to compare the values of two dates greater than, less than, and not in the past using JavaScript? The values will be coming from text boxes.


I'm new to Ubuntu and not a programmer, although I am definitely learning a few things on these boards... I am running 14.04 and trying to download Google Chrome, but I get this error when I try to download it in the software center:  Dependency is not satisfiable: libappindicator1  Error   Any ideas? I can give you more information if necessary. Thanks!

How do you install Google Chrome on Ubuntu?


My website is running on AWS EC2 on /var/www/html on port 5000. I would like to create a DNS A Zone test.example.com linked to that website. On the domain page I can only add the IP, not the port, so test.example.com:5000 works, but test.example.com doesn't. How can I do it?  This is my VirtualDirectory:  <VirtualHost *:5000> ServerName test.example.com DocumentRoot /var/www/html </VirtualHost>

I have some subdomains I want to redirect to specific ports on the same server. Say I have  dev.mydomain.com    I want dev.mydomain.com to transparently redirect to mydomain.com:8080 and I want to preserve the original sub-domain name the url of the browser.  How do I do this with Apache 2.2? I have Apache 2.2 running on default port 80. I can't figure out the write configuration to get this to happen.  I have already set up dev.mydomain.com to resolve in DNS to mydomain.com.     This is for an intranet development server that has a non-routable ip   address so I am not so concerned about exploits and security that   would compromise a publicly facing server.


I have a Linux user that needs to be able to execute any command with sudo, but it should ask for their password for all apart from one executable. Currently my sudoers files looks like:  # # This file MUST be edited with the 'visudo' command as root. # # Please consider adding local content in /etc/sudoers.d/ instead of # directly modifying this file. # # See the man page for details on how to write a sudoers file. # Defaults        env_reset Defaults        mail_badpass Defaults        secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"  # Host alias specification  # User alias specification  # Cmnd alias specification  # User privilege specification root    ALL=(ALL:ALL) ALL  # Members of the admin group may gain root privileges %admin ALL=(ALL) ALL  # Allow members of group sudo to execute any command %sudo   ALL=(ALL:ALL) NOPASSWD:/bin/switch.sh  # See sudoers(5) for more information on "#include" directives:  #includedir /etc/sudoers.d   So I have added my user to the sudo group, however I think I have the syntax wrong as now I can only execute switch.sh with sudo and no others

I need to run something as sudo without a password, so I used visudo and added this to my sudoers file:  MYUSERNAME ALL = NOPASSWD: /path/to/my/program   Then I tried it out:  $ sudo /path/to/my/program [sudo] password for MYUSERNAME:    Why does it ask for a password? How can I run/use commands as root with a non-root user, without asking for a password?


I have a problem with the HP DeskJet 2632 printer It worked fine until I updated the UBUNTU operating system "Ubuntu 20.04.1 LTS", that no longer finds the connection USB or wireless. I downloaded the compressed file "linux-5.9.1.tar.xz" from the site "https://www.kernel.org/" and extracted it, hoping it will help me. How can I install it now? Thank you and greetings Ugo Dentice

Let's assume that one has some HP printer and/or scanner and checked its support status on the corresponding page of HPLIP site - .  So one have the following information: the device Model name, Min. HPLIP Version and Driver Plug-in need.   What should one install to make Ubuntu fully support the HP printer and/or scanner?


I have an EpochTime for Now and I want to get 30 days, 3 Months, and 1 Year back epoch time How to do that in java code.  long todayEpochTime = System.currentTimeMillis()/1000; System.out.println(todayEpochTime);

Anyone know a simple way using Java calendar to subtract X days from a date?  I have not been able to find any function which allows me to directly subtract X days from a date in Java. Can someone point me to the right direction?


I'm having some issues updating Ubuntu 18.04. Here is the error output  W: GPG error: http://download.opensuse.org/repositories/home:/strycore/xUbuntu_18.04 ./ Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 2F7F0DA5FD5B64B9 E: The repository 'http://download.opensuse.org/repositories/home:/strycore/xUbuntu_18.04 ./ Release' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   Researching similar problems, for example     Doesn't work. Specifically, I get the error   nik@nik:~$ sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 2F7F0DA5FD5B64B9 Executing: /tmp/apt-key-gpghome.uWb8bIzMR8/gpg.1.sh --keyserver keyserver.ubuntu.com --recv-keys 2F7F0DA5FD5B64B9 gpg: keyserver receive failed: No data  nik@nik:~$ gpg --keyserver hkp://keyserver.ubuntu.com:80 --recv 2F7F0DA5FD5B64B9 gpg: keyserver receive failed: No data   I couldn't find a working solution to that problem though. Any advice? Thanks.

W: GPG error: http://download.opensuse.org/repositories/home:/strycore/xUbuntu_16.04 ./ Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 2F7F0DA5FD5B64B9 W: The repository 'http://download.opensuse.org/repositories/home:/strycore/xUbuntu_16.04 ./ Release' is not signed. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details.   I am trying to get rid of the above error message seemingly related to release key and opensuse url.  What would be the proper solution?


I have a JSON object with the following structure:  obj = {     foo: 'bar',     data: {         hello: this.foo     } }   However, this in the 2nd level is always the Window object. How can I reference foo properly?  NOTE  I know I can put the object into a "class" and referencer the property with selfor something. This is not an option for me. The object must be a standalone JSON object.

I just came across an interesting situation in JavaScript.  I have a class with a method that defines several objects using object-literal notation.  Inside those objects, the this pointer is being used.  From the behavior of the program, I have deduced that the this pointer is referring to the class on which the method was invoked, and not the object being created by the literal.    This seems arbitrary, though it is the way I would expect it to work.  Is this defined behavior?  Is it cross-browser safe?  Is there any reasoning underlying why it is the way it is beyond "the spec says so" (for instance, is it a consequence of some broader design decision/philosophy)?  Pared-down code example:  // inside class definition, itself an object literal, we have this function: onRender: function() {      this.menuItems = this.menuItems.concat([         {             text: 'Group by Module',             rptletdiv: this         },         {             text: 'Group by Status',             rptletdiv: this         }]);     // etc }


The introduction of ‘smart’ ID cards, the use of biometrics,   and electronic road pricing represent major developments in   methods of surveillance. Only the malevolent could legitimately   object to these effective methods of crime control. Would that this   comforting view were true.   Would someone please explain this sentence and its structure? I've never seen it before; I hazard that would that = 'if only'. Even were it true, then the bolded sentence is just a subordinate clause (is this the right term?), and not a proper sentence?   Moreover, is this related to any kind of sentence structure in French? Such a connection may help me to learn this better.   Source: P128, Law, Raymond Wacks

There is a place in Bram Stoker’s Dracula where I can’t quite parse the grammar:     8 May. — I began to fear as I wrote in this book that I was getting too   diffuse. But now I am glad that I went into detail from the first, for   there is something so strange about this place and all in it that I cannot   but feel uneasy. I wish I were safe out of it, or that I had never come. It   may be that this strange night existence is telling on me, but would that   that were all!   I understand the meaning of the text in bold (it’s equivalent to if only that was all!), but I don’t understand the grammar being used. What kind of construct is this?


Let $p_n$ be the n-th prime number.  show that $p_{n+1} \le {p_1 \cdot \ldots \cdot p_n +1}$  I´ve used a few primes and obtained the same result, even when this assumption seems trivial I have no idea how to prove this for the n-th prime.  I'd appreciate some help

Let $p_n$ be the $n$th prime number in its natural order. We want to show that  $$p_{n+1} \leq p_1\dotsc p_n + 1 \tag{1}$$  I know $p_1\dotsc p_n + 1 > 1$, so it has at least one prime divisor, but the text says that $p_{n+1}$ cannot exceed the smallest of these divisors, but I cannot understand why, especially when I imagine $p_{n+1}$ being very large. Although some examples confirm that this statement is true, I cannot make a connection as to why the $n+1$ prime number cannot exceed the smallest prime divisor. Once this has been shown to be true, $(1)$ immediately follows.


here is my problem, reported in a way much more simplified  this is the json (look at the json  if you want)  {"resource":[{"id":"1408694994","obj":[{"id":"1","action":[{"name":"ON","id":"301"},{"name":"OFF","id":"302"}]},{"id":"2","action":[{"name":"ON","id":"303"},{"name":"OFF","id":"304"}]}]},{"id":"1408694995","obj":[{"id":"3","action":[{"name":"ON","id":"305"},{"name":"OFF","id":"306"}]},{"id":"4","action":[{"name":"ON","id":"307"},{"name":"OFF","id":"308"}]}]}]}   Given an id (in this case we say id = 3), I must save the item with that ID. And i save in a new object (newobj) the object with that ID, but changing the array ACTION in an OBJ with the only action ON  Example  <script>       var tt = '{"resource":[{"id":"1408694994","obj":[{"id":"1","action":[{"name":"ON","id":"301"},{"name":"OFF","id":"302"}]},{"id":"2","action":[{"name":"ON","id":"303"},{"name":"OFF","id":"304"}]}]},{"id":"1408694995","obj":[{"id":"3","action":[{"name":"ON","id":"305"},{"name":"OFF","id":"306"}]},{"id":"4","action":[{"name":"ON","id":"307"},{"name":"OFF","id":"308"}]}]}]}';      var myjson = JSON.parse(tt);      var search = 3;       console.log(myjson.resource[1].obj[0]);      for(var i = 0 ; i < myjson.resource.length; i++){          for(j = 0 ; j < myjson.resource[i].obj.length; j++){              if(parseInt(myjson.resource[i].obj[j].id) == search){                  var newobj = myjson.resource[i].obj[j];                  var obj_action = newobj.action;                 for(var k = 0 ; k < obj_action.length ; k++){                      if(obj_action[k].name == "ON"){                         newobj.action = obj_action[k];                     }                 }             }            }     }      console.log(myjson.resource[1].obj[0]);  </script>   I can easily save in the variable newobj the object that i want. But why the initial json is changed ???  UPDATE  ok, I understand that it is clearly problem of how I save the obj in newobj variable. i dont' save the object, but only the reference at the object in json . how can I save it in the variable newobj ? (not by reference?)

What is the most efficient way to clone a JavaScript object? I've seen obj = eval(uneval(o)); being used, but . I've done things like obj = JSON.parse(JSON.stringify(o)); but question the efficiency.  I've also seen recursive copying functions with various flaws.  I'm surprised no canonical solution exists.


Say we have two objects: A and B. In A's IRF, B moves with velocity +v. Then, B undergoes time dilation, and from B's perspective, the passage of time for A has sped up. However, in B's IRF, A moves with velocity -v. Then, A undergoes time dilation, and from B's perspective, the passage of time for B has sped up. This is a contradiction, the passage of time in A can't have sped up relative to B. What am I missing?

Suppose we have two twins travelling away from each other, each twin moving at some speed $v$:    Twin $A$ observes twin $B$’s time to be dilated so his clock runs faster than twin $B$’s clock. But twin $B$ observes twin $A$’s time to be dilated so his clock runs faster than twin $A$’s clock. Each twin thinks their clock is running faster. How can this be? Isn’t this a paradox?


i have an error in the numbering of the tables. some of the number are missing and don't know what is the problem. the following picture illustrate the problem. please i need your help!

For reasons both complex and confusing, I would like to caption a longtable without incrementing the table counter in the process.  I want to have two consecutive longtable environments to be captioned with identical table numbers; i.e. one longtable captioned "Table x.y: Data Set (Part A)" and one captioned "Table x.y: Data Set (Part B)", with x.y being identical for both tables.  Apparently however, even \caption*{} command bumps table. I am a bit at a loss here.  Note: I know that the xtab package would enable me to have one long table with switches of headers and captions mid-table. However I got a (different) problem with that package, akin to  but sadly not solved by egreg's answer there; so this question should be considered longtable-only as xtab, supertabular etc. don't float my boat right now. :-(


I just saw the trailer of the movie Logan, where a female kid has the same supernatural power as Wolverine and does some pretty bad things (nasty killing etc.).  I saw that and my hear squeezed, but in the making some sort of computer graphics should produce what we see. So my question is:  Is there any approach followed to help the kid see as less as possible of this nasty pictures? Or is it allowed by the US law to make a kid do this without a problem?    In general a kid with such experiences, generally speaking, may have a very difficult time being okay later...

Some movies feature child characters put in violent situations. This can range from crude language to extreme horror (e.g. torture, gore, etc.). As an example,  and its sequel has plenty of those scenes. It looks like a paradox that children can be actors in movies that are definitely not for children.  Do the directors usually try and avoid exposing the very young actors to the violence of such scenes, e.g. by clever dubbing and editing? Are there laws that require them to do so, just like there are ratings that prevent children from seeing some movies?


How can I highlight the current row and column like a crosshair in Libreoffice as guide for the eye?    There seems to be an open  and a very similar question for   - but nothing I can find on libreoffice and supported at the moment. How can I get LibreOffice to do this?

I need to work with large table. Something like in this illustation image will be helpfull for better orientation:    Is there some settings which makes this possible?


When you tap at the top of the screen, you jump to the very top floor. Is there an equivalent to jump to the ground floor (i.e. not the quick button for the elevator, but something which is there all the time)?

In Tiny Death Star, you can get to the top of your tower by tapping on the top of the screen while avoiding the "Add Level" button. However, the only way I can find to go to the bottom of the tower is to wait for someone to want an elevator ride, and tap on the button to give them that ride. Is there any other hot-spot for getting to the bottom of your Death Star?


I am trying to validate if a string I entered matches the date format 'MM/yyyy'  Below is a sample of the code I am using for the same:  var date='05/2016' var patt= new RegExp('^((0[1-9])|(1[0-2])|[1-9])\/(\d{4})$'); patt.test(date);   However the above code is returning false.  I tried running it with the regex checker:   The pattern seems to be working fine.  Could someone please let me know what is missing.

I try to write a simple Markdown parser in JavaScript. Therefore I want to check for the [link content][link id] syntax. I use the following code:  data = data.replace( /\[(.*?)\][ ]*\[([0-9]+)\]/g, '$1' );   It works well, but now I want to do this with a RegExp object. So I set up the following bit of code:  var r = new RegExp( '\[(.*?)\][ ]*\[([0-9]+)\]', 'g' ); data = data.replace( r, '$1' );   But it doesn't work. It even says that my regular expression (which works since the first example does a good job) is invalid:     unmatched ) in regular expression   I think it must have to do with some RegExp-object peculiarities I am not aware of. What am I doing wrong and how can the problem be solved?


I'm trying to install Ubuntu 12.04 to run in VirtualBox alongside my Win7 64bit OS, without having to dual-boot.  I added the 64-bit Ubuntu iso to my VM, and powered it up so to proceed with the installation, but it prompted me with this error:     This kernel requires an x86-64 CPU, but only detected an i686 CPU.   Unable to boot - please use a kernel appropriate for your CPU.   Why does it give me this error, seeing as I have a 64bit processor? Is there a way that I can run Ubuntu via my VM in the first place?

I was trying to install Ubuntu 12.04 in VirtualBox 4.2.12r84980. I see    this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot   But I am using a 64 bit Windows 8, and trying same .iso for trying Ubuntu. Then what is the problem?


I want to try achieve something like this image:   So far my attempt is that I have a div for the left column (that contains the image), and a div for the right column which contains the heading and the paragraph stuff. Both of them are displayed as blocks, and floated left. The left column has a fixed with of 96px since the image will be that size. The right div is a percentage width which I eyeballed (65% worked okay).  However, I don't think this is the right way to approach this without it messing up later. Am I approaching this correctly? What is the proper way to do this kind of thing?

I want to put two <div>s next to each other. The right <div> is about 200px; and the left <div> must fill up the rest of the screen width? How can I do this?


Fire is a good example of matter that human beings discovered; Fire has been a part of nature even before human beings found it and at some points and we have used it ever since we discovered the existence of fire.  Then, what about numbers?  Is 0 invented or discovered?   I see some postings that argue that 0 was "there" and we found it, and some say that there had been no concept of zero before we invented it.  However, for number pi, area of the circle has not been changed ever since creation of the universe. Then, is pi discovered?   Any opinions?

I am confused as to what numbers are. Numbers are defined to be what they are, so numbers aren't real? But numbers are found in nature, right? So if we invented them, how can they be found in nature? How can everything be based on something that is not real. Sorry if what I am saying don't make sense, it hard to put it into words. I feel like I've been known numbers all my life yet I don't know what they are. Also why don't complex numbers have an order? Real numbers are an invention just as complex numbers are, so how are imaginary numbers any more imaginary than real numbers? I mean an order was given to the real numbers, so why can't complex numbers be given a definite order?  Thanks