From a practical standpoint, the obvious examples are approximation methods that, through repeated application, yield a result as precise as desired.
Of course, a calculation can be repeated, but so can an argument. You'll recognize an allusion to induction, which epitomizes the duality between inductive and deductive reasoning.
By breaking a larger problem down into identical but smaller problems, recursion provides an effective method that is easy to implement.
Today, all these iterative techniques permeate every branch of mathematics and computer science, from the most concrete applications to the most theoretical considerations. They also appear in countless forms in many other fields. Their ubiquity could perhaps even make them a characteristic of mathematical activity.
