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 ...
