Week Program, Semester Week 6

Induction

This week we cover the topic of induction. This is a tool will explore the truth value for all natural numbers \(n\) of propositions where \(n\) is included as a parameter. For example, identities like \(\sum_{i=1}^n i = \frac{n(n+1)}{2}\) can be shown to be true for all \(n \in \mathbb{N}\) using induction.

Key Terms

The induction principle. Proofs using induction.

Preparation and Syllabus

This week covers sections 5.4 and 5.5 from [05 - Recursion and induction].

Exercises

Exercises for Long Day.

Short Day is dedicated to Theme Exercise 2.