Rectangular collision detection

Question

class Rectangle{
public:
   float x, y, width, height;
   // (x,y) is the lower left corner of the rectangle
};

Is this algorithm correct?

bool Rectangle::colidesWith(Rectangle other) {
   if (x+width < other.x) return false; // "other" is on the far right
   if (other.x+other.width < x) return false; //"other" is on the far left
   if (y+height < other.y) return false // "other" is up
   if (other.y+other.height < y) return false // "other" is down
   return true;
}

Answer 1

It is if the rectangles are filled (i.e. you count as collision the case in which one of them is inside the other).

Answer 2

Yep. You can view it as a special case of the hyperplane separation theorem which is the general version of this problem. You are projecting these rectangles onto the X and Y axis and then checking that the resulting line segments have some separation between them.