Principle of Mathematical Induction

The Principle of Mathematical Induction is a fundamental concept in mathematics that provides a powerful method for proving statements about natural numbers. It is based on the idea that if a given statement holds for the number one (the base case) and if the truth of the statement for an arbitrary number n implies its truth for n + 1 (the inductive step), then the statement is true for all natural numbers. This category covers various topics related to mathematical induction, including its principles, applications, examples, and common pitfalls, making it essential for students and enthusiasts alike.