Rational Numbers

Introduction

Models

Notations

Equivalence Classes

$\textup{Consider the rational number }\frac{2}{4}\textup{. You probably know intuitively it is the same as }\frac{1}{2}\textup{, }\frac{3}{6}\textup{, }\frac{4}{8}\textup{, etc.}$ $\textup{Since the parts of }\frac{1}{2}\textup{ can not be further regrouped, we say it is irreducible or in simplest form. }$

Each rational number is a member of an equivalence class. An equivalence class is a set whose members are pairwise related to each other reflexively, symmetrically, and transitively.

Rational Arithmetic

Rational Algebra

Rational Geometry

Rational Trigonometry

Existence and construction of an ordered field with the least upper bound property