We can consider all numeric operations to be defined by recursions. For more details, read about the Peano axioms that define the essential features of numbers at: http://en.wikipedia.org/wiki/Peano_axioms.
From these axioms, we can see that addition is defined recursively using more primitive notions of the next number, or successor of a number, n, 
.
To simplify the presentation, we'll assume that we can define a predecessor function, 
, such that 
, as long as 
. This formalizes the idea that a number is the successor of the number's predecessor.
Addition between two natural numbers could be defined recursively as follows:
If we use the more common 
and 
instead of 
and 
, we can see that 
.
This translates neatly into Python, as shown in the following command snippet:
def add(a: int...
