3.1Relations

3.1.1 Introduction and the Cartesian Product

The idea of things being related enters our consciousness a dozen times a day. We talk about people being related in many way, such as gender, race, height, age, and so on. In mathematics, the word relation is used to show the relations between pairs of objects, as when we say

“is less than” “is a subset of”
“is perpendicular to” “divides”
“is greater than” “is congruent to”
“is parallel to” “is equivalent to”
“is homeomorphic to” “is isomorphic to?”

However, before defining a relation, it is necessary that we introduce the Cartesian product of two sets.

You are already familiar with one Cartesian product, namely the Cartesian plane, which is ℝ × ℝ, often denoted by ℝ2.

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