Reading 5 : Induction

In the last reading we began discussing proofs. We mentioned some proof paradigms that are generally applicable. For implications, we saw how to write a direct proof and an indirect proof. We saw how to prove equivalences by proving two implications and by constructing a chain of equivalences. We also saw two techniques applicable to proofs of any statements, namely proof by contradiction and proof by cases. However, you should not feel limited to using only those methods when you write proofs. Any sequence of logical deductions starting from a set of axioms and ending with the proposition you want to prove is acceptable. In this reading, we focus on a proof paradigm called induction. Induction is an important proof technique in the realm of discrete mathematics and in computer science.