GTA-V, Online PS3 and PS4
Is GTA Online cross-platform?
Sets with no asymptotical density over $\mathbb N$ Let's consider the  defined by:      Take $ A\subset \mathbb N$; define the sequence $x_n= \dfrac{|A\cap[1,n]|}{n}$, and then if $\lim\limits_{n\to\infty} x_n$ exists, call it $d(A)$, the density of $A$ over $\mathbb N$.   My teacher said that the collection of sets that have a natural density is not an algebra, but I don't know why. I can't even find a set that does not have a natural density.  Please help me )= How do I install the latest stable version of Thunderbird? What is the meaning of the term "thread-safe"? Does it mean that two threads can't change the underlying data simultaneously? Or does it mean that the given code segment will run with predictable results when multiple threads are executing that code segment? Reasons not to use a 741 op-amp? Add a binary to my path I have an executable. I want to execute the executable in terminal with name only like other commands.  I can put my executable in /usr/local/bin or I could add its PATH to ~/.bashrc. Both will work.  What is better?  Is there  any difference? Discouraged by simple Bayesian Question My university is testing an intro Machine Learning (ML) course for us undergrads, and having been interested in ML since the beginning to understand what it was, I jumped at the chance to take it. But being someone who has not been back in school for a long time and much busier than I was in my first years long ago, I am finding that I need more info and examples than the class in its current form has.  I am struggling to figure out what the attached question is asking. I am searching online for help with this particular topic, but I am also finding that everyone seems to have their own way of phrasing similar questions in such a way that I am finding it hard to link the info.   My understanding from stats way back when is that $p(x|\omega_1)$ is stating the probability of $x$ given $\omega_1$ for $0\le x \le 2$ and zero other wise. Same obviously if given $\omega_2$. If I understand, the priors are the probability of $\omega_1$ and $\omega_2$ which are somehow obtained. And honestly that is as far as I am really comprehending. I am not sure what (a) and (b) are truly asking for or how to get them. If anyone is able to help me with some pointed info on the topic it would be greatly appreciated. Dependency problem with mysql-server-core-5.5 When I start the Ubuntu software centre, it says I cannot do anything until the package catalog is repaired. However, repairing fails.  I ran sudo apt-get -f install and found the problem to be:  mysql-server-5.5 depends on mysql-server-core-5.5 (= 5.5.24-0ubuntu0.12.04.1); however:   Version of mysql-server-core-5.5 on system is 5.5.28-0ubuntu0.12.04.2.   So, the question is, how do I install that version and resolve the dependency problem? I'd like to typeset documents using the '' of page layout. Good examples are on pages 40-53 of . The  package is helpful for this, but two additional features would be useful:   Automatic flow of text across (arbitrarily placed) columns / textpos blocks. Vertical line spacing enforced to be an integer multiple of a base line spacing, even when interrupted (for example) by an equation of arbitrary height.   Any ideas as to how either or both of these could be accomplished? Why can I feel my seven pound cat walking across floor of my home? The house is only 9 years old. (I am the second owner)   I know they settle but in the last year I can feel all movement across the floor- year ago I could barely feel anything but did notice that when someone walked across I could feel them go by.  But more recently the cat walking across to go to the chair I can feel that.  What is going on?  I know I should not feel the cat who is 7 lbs walking by or across the floor. Split level home 9 years old Minnesota location  Is anyone out there that can explain this? Bind application to a specific network interface I have tried ForceBindIP, but it has a significant downside - it doesn't affect the children of the application I'm trying to bind, it only affects the application itself. It also can't force an application to always run through a specified interface, it has to be run through forcebindip.exe every time. It becomes a problem with applications like League of Legends where the process tree looks like that:    The launcher runs the patcher, the patcher run the client, etc. I can only affect the parent of all these processes in the tree, so the actual game is not bound to the interface I want, making this whole venture pointless.  Is there a more modern alternative to ForceBindIP for Windows 7? There are many questions similar to this one on this site, but they are mostly old. Maybe there is now a better way to solve this problem?  My current idea is to do the following:   Set up local 3proxy server bound to the desired interface. Run the game through Proxifier or similar software configured to run through that local proxy.   I'm not sure if that will work, but even if it will, it seems like a sub-optimal solution. Do you guys have any better ideas?  Edit: My idea didn't work :(  Edit 2: Basically, what I'm trying to achieve is bind a few applications to a regular interface, while VPN is running. The reason is that I need to connect through VPN most of the time, but some applications (such as games) don't work properly this way, because of higher ping and other issues. I have an independent variable called "quality"; this variable has 3 modalities of response (bad quality; medium quality; high quality). I want to introduce this independent variable into my multiple linear regression. When I have a binary independent variable (dummy variable, I can code 0 / 1) it is easy to introduce it into a multiple linear regression model.  But with 3 modalities of response, I have tried to code this variable like this :  Bad quality      Medium quality      High quality       0                1                  0      1                0                  0      0                0                  1      0                1                  0   But there is a problem when I try to do my multiple linear regression: the modality Medium quality gives me NA:    Coefficients: (1 not defined because of singularities)    How can I code this variable "quality" with 3 modalities? Do I have to create a variable as a factor (factor in R) but then can I introduce this factor in a multiple linear regression? Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$ Applying MVT and IVT (?) to show something about f'''? (edit: actually, Taylor's Theorem using Lagrange remainder) I believe that the correct answer to this question will involve applying both the Mean Value Theorem and the Intermediate Value Theorem, perhaps several times.  However, I can't see how to proceed.  I went down what I thought were the typical paths and just reached dead ends.  Does someone maybe have a hint?  I think that with the appropriate nudge I should be able to solve this question.  If not, I'll edit and ask if someone knows how to solve the whole thing.  Here's the question:  Let $f: \mathbf R \to \mathbf R$ be such that $f$, $f'$, $f''$, and $f'''$ exist and are continuous on $\mathbf R$ and satisfying $f(-3)=-1$, $f(0)=0=f'(0)$, and $f(3)=8$.  Prove that there exists $\xi \in (-3, 3)$ such that $f'''(\xi) \ge 1$. It seems Kylo has an obsession of Darth Vader and has an interest in the dark side because of it.   Does he not realize that Darth Vader turned good and helped destroy the Empire (Spoilers?)? I feel like Kylo would've seen how much better the Light Side was as it was able to turn Vader from the Dark Side if he had known this. When Bottom Navigation Isn't Best I'm developing a mobile app and dealing with various UI/UX issues. I'm open to all kinds of ideas at this stage, however some designers I consult with seem to be zealots for bottom-navigation and are hesitant in actually analyzing whether the bottom-nav is actually best for my app; they just want me to use the bottom tabs navigation as if it's some UI law.  One point I try to bring up is that my business model has users who aren't typical one-handed mobile users, are tech savvy, would use my app more of a tool, and would spend only a few minutes in it. The app isn't a typical lazy-content-browsing experience where you want to minimize fingers-over-top-of-screen interference, and where you want to keep the use transfixed and spending time in the app.  Anyways, I'd like to hear about situations where a bottom nav was decided-on, or started-with, and you had good reason to eliminate it and go with another navigation design.  Most articles out there talk about eliminating hamburger menus and diving into bottom nav. Is the converse simply going back to hamburger menu? Why must a field whose a group of units is cyclic be finite? I've got some lenses of brand X, but I've just got a new camera of brand Y. How can I tell if it's possible to use my lenses on my camera? I accept that I may lose a lot of automatic functionality like autofocus, aperture control and metering when using an adapter to connect the two. While working in a Java app, I recently needed to assemble a comma-delimited list of values to pass to another web service without knowing how many elements there would be in advance. The best I could come up with off the top of my head was something like this:  public String appendWithDelimiter( String original, String addition, String delimiter ) {     if ( original.equals( "" ) ) {         return addition;     } else {         return original + delimiter + addition;     } }  String parameterString = ""; if ( condition ) parameterString = appendWithDelimiter( parameterString, "elementName", "," ); if ( anotherCondition ) parameterString = appendWithDelimiter( parameterString, "anotherElementName", "," );   I realize this isn't particularly efficient, since there are strings being created all over the place, but I was going for clarity more than optimization.  In Ruby, I can do something like this instead, which feels much more elegant:  parameterArray = []; parameterArray &lt;&lt; "elementName" if condition; parameterArray &lt;&lt; "anotherElementName" if anotherCondition; parameterString = parameterArray.join(",");   But since Java lacks a join command, I couldn't figure out anything equivalent.  So, what's the best way to do this in Java? Produce an explicit bijection between rationals and naturals? I remember my professor in college challenging me with this question, which I failed to answer satisfactorily: I know there exists a bijection between the rational numbers and the natural numbers, but can anyone produce an explicit formula for such a bijection? How do I show that there exists variational/action principle for a given classical system? We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following:      If I am given a set of generalized positions and velocities, say, $\{q_{i}, \dot{q}_{i}\}$, which describes a classical system with known dynamics (equations of motion), then, how do I rigorously show that there always exists an action functional $A$, where    $$A ~=~ \int L(q_{i}, \dot{q}_{i})dt,$$    such that $\delta A = 0$ gives the correct equations of motion and trajectory of the system?    I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all.