|Class 11 Maths Mathematical Induction||Principle of Mathematical Induction|
The Principle of Mathematical Induction
Deduction: Generalization of Specific Instance
Induction: Specific Instances à Generalization
For a statement P(n) involving the natural number n , if
Then, P(n) is true for all natural numbers n.
Property (i) is simply a statement of fact.
Property (ii) is a conditional property. It does not assert that the given statement is true for n = k, but only that if it is true for n = k, then it is also true for n = k +1. This is sometimes referred to as inductive step. The assumption that the given statement is true for n = k in this inductive step is called the inductive hypothesis.