One of the most common examples of broadcasting is the addition of a function and a constant; if 
is a scalar, we often write:
This is an abuse of notation since you should not be able to add functions and constants. Constants are, however, implicitly broadcast to functions. The broadcast version of the constant 
is the function 
defined by:
Now it makes sense to add two functions together:
We are not being pedantic for the sake of it, but because a similar situation may arise for arrays, as in the following code:
vector = arange(4) # array([0.,1.,2.,3.]) vector + 1. # array([1.,2.,3.,4.])
In this example, everything happens as if the scalar 1. had been converted to an array of the same length as vector, that is, array([1.,1.,1.,1.]), and then added to vector.
This example is exceedingly simple, so we'll proceed to show less obvious situations.