® The principle of mathematical induction is one such tool which can be used to prove a wide variety of mathematical statements. Each such statement is assumed as P( n ) associated with positive integer n , for which the correctness MATHEMATICS for the case n = is examined. Then assuming the truth of P( k ) for some positive integer k , the truth of P ( k+ ) is established. Historical Note Unlike other concepts and methods, proof by mathematical induction is not the invention of a particular individual at a fixed moment.
It is said that the principle of mathematical induction was known by the Pythagoreans. The French mathematician Blaise Pascal is credited with the origin of the principle of mathematical induction. The name induction was used by the English mathematician John Wallis. Later the principle was employed to provide a proof of the binomial theorem.
De Morgan contributed many accomplishments in the field of mathematics on many different subjects. He was the first person to define and name “mathematical induction” and developed De Morgan’s rule to determine the convergence of a mathematical series. G. Peano undertook the task of deducing the properties of natural numbers from a set of explicitly stated assumptions, now known as Peano’s axioms.The principle of mathematical induction is a restatement of one of the Peano’s axioms.