In mathematics, a function is written as a map that uniquely assigns an element y from the range R to every element x from the domain D.
This is expressed by f : D → R
Alternatively, when considering particular elements x and y, one writes f : x → y
Here, f is called the name of the function and f(x) is its value when applied to x. Here, x is sometimes called the argument of f. Let's first look at an example before considering functions in Python.
For example, D = ℝ x ℝ and y = f(x1, x2) = x1 - x2 . This function maps two real numbers to their difference.
In mathematics, functions can have numbers, vectors, matrices, and even other functions as arguments. Here is an example of a function with mixed arguments:
.
In this case, a number is returned. When working with functions, we have to distinguish between two different steps:
- The definition of the function
- The evaluation of the function, that is, the computation of f(x) for a given value of x
The first step is done once, while the second...