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Mathematical induction is a mathematical proof technique. It is essentially used to prove that a property P(n) holds for every natural number n, i.e. for n = 0, 1, 2, 3, and so on. Metaphors can be informally used to understand the concept of mathematical induction, such as the metaphor of falling dominoes or climbing a ladder: Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step). — Concrete Mathematics The method of induction requires two cases to be proved. The first case, called the base case (or, sometimes, the basis), proves that the property holds for the number 0. The second case, called the induction step, proves that, if the property holds for one natural number n, then it holds for the next natural number n + 1. These two steps establish the property P(n) for every natural number n = 0, 1, 2, 3, ... The base step need not begin with zero. Often it begins with the number one, and it can begin with any natural number, establishing the truth of the property for all natural numbers greater than or equal to the starting number. The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction, in some form, is the foundation of all correctness proofs for computer programs

Jagat Chaudhary
Qualified IIT-JEE,IIT-JAM. Expert faculty for IIT-JEE Mathematics Courses. M.Sc. Ph.D. (MATHEMATICS) IIT Bhubaneswar.Cofounder at Aspiration

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  1. Joint M.Sc. Ph.D. (MATHEMATICS) IIT-BHUBANESWAR IIT-EE (main+Advaneed) Follow me on unacademy RateReview VRecommend JAGAT CHAUDHARY

  2. Objectives of this course Provide Online education to students preparing for IIT-JEE Exams. Course including Concepts, lllustrations, Objectives and Subjective solved Problems.a roda Solve problems in given time f(x)dx

  3. TARGET AUDIENCE For students of Classes XI and XII. IIT JEE Exams Any competitive exam for Engineering Defence exams VF(x)

  4. Principal of Mathematical Induction Proofs for formulas by PMI Inequality Problems Multiples and Division . Cases where PMI fails

  5. IIT-JEE (main +Advaneed) RINCIPAL OF MATHEMATICAL INDUCTION n= -R n=1 Part 1 Part 2