Mathematical induction is a mathematical proof technique that is 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.
- 4.1: The Principle of Mathematical Induction
- In this section, we will learn a new proof technique, called mathematical induction, that is often used to prove statements of the form (∀n∈N)(P(n))
- 4.3: Induction and Recursion
- In a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can think of a sequence as an infinite list of numbers that are indexed by the natural numbers. Another way to define a sequence is to give a specific definition of the first term and then state how to determine the next term in terms of previous terms; this process is known as definition by recursion.
Thumbnail: Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes. Image used wtih permission (CC BY-SA 3.0; Pokipsy76).