Mathematical Induction

A mathematical statement is a declarative

A mathematical statement is a declarative sentence that is either true or false. For example, '1 + 2 + ... + n = n(n+1)/2' is a statement because it c

If a statement p(n) is true

If a statement p(n) is true for n = 1, and if the truth of p(k) implies the truth of p(k+1), then the statement is true for all natural numbers n.

The base case checks if p(1)

The base case checks if p(1) is true. The inductive step assumes p(k) is true (inductive hypothesis) and uses it to prove p(k+1) is also true.

It is the assumption that

It is the assumption that the statement p(k) is true for some arbitrary natural number k. This assumption is used to prove p(k+1).