Introduction

Overview

Before we dive into functions, we first need to understand a simpler idea called a relation. A relation describes how elements from one set can be connected or "related" to elements of another set. To define these connections properly, we need a tool called the Cartesian product.

The Cartesian product helps us pair every element in one set with every element in another set, creating all possible combinations of pairs. By doing this, we can then choose certain pairs that meet specific conditions, and this selection forms a relation.

This step is important because once we know how to define relations, we can go one step further and define functions. Functions are special types of relations with unique rules, and they play a big role in mathematics.

So, learning about the Cartesian product first will make it easier for us to understand relations, and understanding relations will prepare us for learning about functions. This sequence helps us build up to the idea of functions in a clear and logical way.