Finding a injective mapping to prove the countability of $ \mathscr{P}_{\text{fin}}(\mathbb{N}) $.
Neatest proof that set of finite subsets is countable?
What happens with lethargy when Haste is cast again on a creature before first cast runs out? Haste states     When the spell ends, the target can't move or take actions until after its next turn, as a wave of lethargy sweeps over it.   However, let's say Character A cast Haste on Character B. In the 10th round (final round of haste if concentration not broken), Character B casts Haste on himself.  What happens during the next round?    Do they lose a round of the "new" haste while they are lethargic and lose movement and actions? Does the new haste override the lethargy until it ends? Is it some combination? Retain AC/Dex modifications but lose actions/movement? None of the above? How to delineate watersheds in QGIS? I am using qgis 2.14.17 with ubuntu16. Having as input data a DEM of the region and a river network. In the manual of qgis they suggest to use a toll of qgis: Catchment area (Parallel); I dont have this in my toolbox, anybody made the same experience and could tell me the reason for it and how to get it. It seems to offer the best solution for me.  Tools which are available are from GRASS7 and TauDEM, the latter need much more data it seems. And I am not sure if I am able to create these just out of a DEM? The GRASS7 has one tool r.water.outlet: but here one has to put the outlet coordinates, which clearly I could get out of the river network, but the idea is that they are generated by delineating the watersheds.  Somebody has an idea how to solve it?  I managed now to get SAGA run in the toolbox, nevertheless would be great if somebody could help me with the qgis tool, since it should appear?! Pivot in sql server How to enable default file manager(nautilus) to handle desktop icons When I choose the Connection Type in VPN Connections, I have only PPTP and I can't find OpenVPN, but I already installed it via terminal with the command sudo apt-get install openvpn easy-rsa  Why I can't find it? Ball to Ball Collision - Detection and Handling With the help of the Stack Overflow community I've written a pretty basic-but fun physics simulator.    You click and drag the mouse to launch a ball.  It will bounce around and eventually stop on the "floor".  My next big feature I want to add in is ball to ball collision.  The ball's movement is broken up into a x and y speed vector.  I have gravity (small reduction of the y vector each step), I have friction (small reduction of both vectors each collision with a wall). The balls honestly move around in a surprisingly realistic way.  I guess my question has two parts:   What is the best method to detect ball to ball collision? Do I just have an O(n^2) loop that iterates over each ball and checks every other ball to see if it's radius overlaps? What equations do I use to handle the ball to ball collisions? Physics 101 How does it effect the two balls speed x/y vectors?  What is the resulting direction the two balls head off in?  How do I apply this to each ball?     Handling the collision detection of the "walls" and the resulting vector changes were easy but I see more complications with ball-ball collisions.  With walls I simply had to take the negative of the appropriate x or y vector and off it would go in the correct direction.  With balls I don't think it is that way.  Some quick clarifications: for simplicity I'm ok with a perfectly elastic collision for now, also all my balls have the same mass right now, but I might change that in the future.    Edit: Resources I have found useful  2d Ball physics with vectors:  2d Ball collision detection example:     Success!  I have the ball collision detection and response working great!  Relevant code:  Collision Detection:  for (int i = 0; i &lt; ballCount; i++)   {       for (int j = i + 1; j &lt; ballCount; j++)       {           if (balls[i].colliding(balls[j]))           {             balls[i].resolveCollision(balls[j]);         }     } }   This will check for collisions between every ball but skip redundant checks (if you have to check if ball 1 collides with ball 2 then you don't need to check if ball 2 collides with ball 1.  Also, it skips checking for collisions with itself).  Then, in my ball class I have my colliding() and resolveCollision() methods:  public boolean colliding(Ball ball) {     float xd = position.getX() - ball.position.getX();     float yd = position.getY() - ball.position.getY();      float sumRadius = getRadius() + ball.getRadius();     float sqrRadius = sumRadius * sumRadius;      float distSqr = (xd * xd) + (yd * yd);      if (distSqr &lt;= sqrRadius)     {         return true;     }      return false; }  public void resolveCollision(Ball ball) {     // get the mtd     Vector2d delta = (position.subtract(ball.position));     float d = delta.getLength();     // minimum translation distance to push balls apart after intersecting     Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d);        // resolve intersection --     // inverse mass quantities     float im1 = 1 / getMass();      float im2 = 1 / ball.getMass();      // push-pull them apart based off their mass     position = position.add(mtd.multiply(im1 / (im1 + im2)));     ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2)));      // impact speed     Vector2d v = (this.velocity.subtract(ball.velocity));     float vn = v.dot(mtd.normalize());      // sphere intersecting but moving away from each other already     if (vn &gt; 0.0f) return;      // collision impulse     float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2);     Vector2d impulse = mtd.normalize().multiply(i);      // change in momentum     this.velocity = this.velocity.add(impulse.multiply(im1));     ball.velocity = ball.velocity.subtract(impulse.multiply(im2));  }   Source Code:     If anyone has some suggestions for how to improve this basic physics simulator let me know!  One thing I have yet to add is angular momentum so the balls will roll more realistically.  Any other suggestions?  Leave a comment! Java: Detect duplicates in ArrayList? I've just updated to the latest Google Chrome Dev build, and they've changed from the annoying-but-ok new tab page to an ugly and less usable page.  On the old one, nine thumbnails was not enough, and now they've restricted it to eight.  There's an empty "Tips and Suggestions" box which I wouldn't want even if it had stuff in; they've added Recent Downloads - on the rare occasions when I need that, I'll hit Ctrl-J to open the Downloads tab; and the site-specific search box on the right has now gone!  Is there a way to get the old new tab page back, or a plugin to provide a superior one?   Update: I launch Chrome by pressing Win+R and entering "chrome" - I have a shortcut on the Path with a Target of "C:\Documents and Settings\&lt;user&gt;\Local Settings\Application Data\Google\Chrome\Application\chrome.exe" --old-new-tab-page and whilst double-clicking this shortcut brings up the previous new tab page, using the keyboard method results in the old one.  How do I get it working via the Run box? (Without using a batch file, which slows things down too much.)  Update 2: GRRR! Now they've gone and stopped the --old-new-tab-page parameter from working at all! I hate this new version of the page that they're forcing upon us - can anyone provide a method to get rid of it and get the decent page back? JSON+Node.js - Unexpected token o Multiple logistic regression power analysis I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this? How do you set a default value for a MySQL Datetime column? How do you set a default value for a MySQL Datetime column?  In SQL Server it's getdate(). What is the equivalant for MySQL? I'm using MySQL 5.x if that is a factor. What's the shelf life on crushed specialty grains? How to change Blender's default startup settings? How can I change Blender from the default cube/lamp/camera default setup? Also, is it possible to change other features, such as the default view direction (Top, Side, etc) or the Editor type (3D View, Node Editor, Graph Editor, etc)? I'm trying to install CentOS 7 on a HP DL120 gen 9 server with a b140i controller. I have 4 1TB HDD setup in a raid 1+0 and the CentOS installer doesn't seem to recognize the logical drive created from the storage utility.  From my understanding i need some drivers for CentOS 7 to recognize the B140i controller. Also, the driver seems to be closed source by HP.  What is my approach here? Is there any other free linux OS that i can use on this server and that would recognize the raid controller?  Thank you. Is the total energy of the universe zero? How can I recover my external hard drive's free space? I had these partitions on an external hard drive:  /dev/disk2 (external, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *2.0 TB     disk2    1:                        EFI EFI                     209.7 MB   disk2s1    2:                  Apple_HFS Android                 63.9 GB    disk2s2    3:                  Apple_HFS RiptideHUP              968.0 GB   disk2s3    4:       Microsoft Basic Data RiptideF                967.8 GB   disk2s4   My aim was to delete disk2s2 and then resize disk2s3 to occupy the leftover space by deleting disk2s2.  I deleted disk2s2 using this command:  diskutil  erasevolume  "Free Space"  ""  /dev/disk2s2   Now, to resize the volume, I used:  diskutil  resizevolume  /dev/disk2s3  R   However, I got this error:  Started partitioning on disk2s3 RiptideHUP Error: -69743: The new size must be different than the existing size   I did a bit of research and realised the free space was created before disk2s3 RiptideHUP so it cannot resize itself. Is there still a way I can reclaim the Free Space?  NOTE: Using diskutil list now shows:  /dev/disk2 (external, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *2.0 TB     disk2    1:                        EFI EFI                     209.7 MB   disk2s1    2:                  Apple_HFS RiptideHUP              968.0 GB   disk2s3    3:       Microsoft Basic Data RiptideF                967.8 GB   disk2s4 I've been reading about a lot of different types of philosophies, religions, ways of thinking etc. I was wondering what are the most recently created philosophical ways of looking at the universe? Where can one find out about new cutting edge ideas?  Example: Before we had Marxism, Communism, Zen, Christianity etc. Now X,Y, and Z have been created building on and evolving the ideas of A,B,C.   Everything I read about are ideas that were created a long time ago. What is new and updated? Why the following example prints "0" and what must change for it to print "1" as I expected ?  #include &lt;iostream&gt; struct base {    virtual const int value() const {       return 0;    }    base() {       std::cout &lt;&lt; value() &lt;&lt; std::endl;    }    virtual ~base() {} };  struct derived : public base {    virtual const int value() const {       return 1;    } };  int main(void) {    derived example; } How to boot from iso with Grub2/Burg boot loader