Principle of Mathematical Induction
After studying this chapter, the student will be able to understand:
Principle of mathematical induction
Consider the set N of natural numbers. N has two characteristic proper ties.
- N contains the natural number 1.
- N is closed with respect to addition of 1 to each of its numbers.
Therefore to determine whether a set k consisting of natural numbers is the set of all natural numbers, we have to verify the following two conditions on K:
- Does 1 ∈ K?
- For each natural number K ∈ K; is it true that K ∈ K?
When answer to both the questions is “yes” then K is N. It gives several important principles for establishing the truth of certain classes ...