In geometry, a two-dimensional point and a vector are not the same, even if they both have an x and y component. In Julia, we can also define them as different types as follows:

   # see the code in Chapter 6\unions.jl
type Point
    x::Float64
    y::Float64
end

type Vector2D
    x::Float64
    y::Float64
end

Here are the two objects:

Suppose we want to define the sum for these types as a point that has coordinates as the sum of the corresponding coordinates:

+(p, v)

This results in an ERROR: `+` has no method matching +(::Point, ::Vector2D) error message.

Even after defining the following, +(p, v) still returns the same error because of multiple dispatch (Julia has no way of knowing that +(p,v) should be the same as +(v,p)):

+(p::Point,    q::Point) = Point(p.x + q.x, p.y + q.y)
+(u::Vector2D, v::Vector2D) = Point(u.x + v.x, u.y + v.y)
+(u::Vector2D, p::Point) = Point(u.x + p.x, u.y...