Overview

The development of mathematical induction was one of the great forward steps in mathematics. An elegant principle that played a large part in the continuing evolution of mathematical logic, and affected the development of other mathematical disciplines, including algebra and analytic geometry, mathematical induction is related to the nonmathematical process called inductive reasoning. As opposed to deductive reasoning, by which a large general truth is taken as the starting point from which smaller, more specific truths are derived, induction provided a tool for moving from the specific to the general, from small individual truths to larger overall ones. By the process of induction, the truth of an entire mathematical proposition is proved one step at...