(ii) Mathematical Induction
Mathematical induction, is a strategy, of proving a proposition which is deductive in
nature The whole basis of proof of this method depends on the following axiom:
For a given subset S of N, if
(i)
the natural number 1 ∈ S  and
(ii)
the natural number k + 1 ∈ S whenever k ∈ S, then S = N According to the principle of mathematical induction, if a statement “S(n) is true
for n = 1” (or for some starting point j), and if “S(n) is true for n = k” implies that “S(n)
is true for n = k + 1” (whatever integer k ≥  j may be), then the statement is true for any
positive integer n, for all n ≥ j We now consider some examples