Mathematical Induction

Mathematical induction, also called simple induction, is a method of mathematical proof usually used to prove that a given statement is true for all nutural positive numbers. This induction seems to me as one that is, by far the most powerful and commonly-used proof technique in computer science and mathematics, and SIMPLE!! as the name tells.

the Principle of Simple Induction

- Establish that the property is true at the starting point(Predicate), simply prove that P(n) is true
- Establish that the property spreads from each natural number to its successor:

explanation:
Let P(n) be a predicate. If:
- P(0) is true, and <- BaseCase
- P(n) implies P(n+1) for all non-negative integers, n. <- Induction Step.

Nothing too complicated about this induction. We've already covered this in the previous course of CSC165. But sure it is definitely important to have a clear understanding of this fundamental and essential one-of-kind induction.