Mathematical induction is a
mathematical proof technique, most commonly used to establish a given statement for all
natural numbers, although it can be used to prove statements about any
well-ordered set. It is a form of
direct proof, and it is done in two steps. The first step, known as the
base case, is to prove the given statement for the first natural number. The second step, known as the
inductive step, is to prove that the given statement for any one natural number
implies the given statement for the next natural number. From these two steps, mathematical induction is the
rule from which we infer that the given statement is established for all natural numbers.