PPT-Mathematical Induction I

In general mathematical induction is a method for proving that a property defined for integers n is true for all values of n that are greater than or equal to some initial integer Mathematical Induction I. EECS . 203. : Discrete Mathematics. Lecture . 11 . Spring 2015. 1. Climbing the Ladder. We want to show that ∀. n. ≥1 . P. (. n. ) is true.. Think of the positive integers as a ladder.. 1, 2, 3, 4, 5, 6, . . .. Chapter 5. With Question/Answer Animations. Chapter Summary. Mathematical Induction. Strong Induction. Well-Ordering. Recursive Definitions. Structural Induction. Recursive Algorithms. Program Correctness (. Chapter 5. With Question/Answer Animations. 1. Chapter Summary. Mathematical Induction. Strong Induction. Well-Ordering. Recursive Definitions. Structural Induction. Recursive Algorithms. Program Correctness (. Chapter 5. With Question/Answer Animations. Chapter Summary. Mathematical Induction. Strong Induction. Well-Ordering. Recursive Definitions. Structural Induction. Recursive Algorithms. Program Correctness (. Section 5.1. Climbing an . Infinite Ladder. Suppose we have an infinite ladder:. We can reach the first rung of the ladder.. If we can reach a particular rung of the ladder, then we can reach the next rung.. Discrete Mathematics: A Concept-based Approach. 1. Introduction. The mathematical Induction is a technique for proving results over a set of positive integers. It is a process of inferring the truth from a general statement for particular cases. A statement may be true with reference to more than hundred cases, yet we cannot conclude it to be true in general. It is extremely important to note that mathematical induction is not a tool for discovering formulae or theorems. . Chapter Summary. Mathematical Induction. Strong Induction. Well-Ordering. Recursive Definitions. Structural Induction. Recursive Algorithms. Mathematical Induction. Section 5.1. Section Summary. Mathematical Induction. Section Summary. Mathematical Induction. Examples of Proof by Mathematical Induction. Mistaken Proofs by Mathematical Induction. Guidelines for Proofs by Mathematical Induction. Climbing an . Infinite Ladder. Introduction. Proof by mathematical induction is an extremely powerful tool for proving mathematical statements. As we know, proof is essential in . Maths. as although something may seem to work for a number of cases, we need to be sure it will work in every case. Mathematics. 1. Mathematical . vs. Strong Induction . To prove that . P. (. n. ) is true for all positive . n. .. Mathematical. induction:. Strong. induction:. 2. Climbing the Ladder (Strongly). We want to show that ∀. Strong Induction EECS 203: Discrete Mathematics 1 Mathematical vs Strong Induction To prove that P ( n ) is true for all positive n . Mathematical induction: Strong induction: 2 Climbing the Ladder (Strongly) Induction and recursion Chapter 5 With Question/Answer Animations Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. With Question/Answer Animations. 1. Chapter Summary. Mathematical Induction. Strong Induction. Well-Ordering. Recursive Definitions. Structural Induction. Recursive Algorithms. Program Correctness (. Why is it a legitimate proof method?. How to use it?. Z all integers (whole numbers). Z. +. the positive integers. Z. -. the negative integers. N Natural . numbers: non-negative integers.