# constructing the rationals

## Summary

The rational numbers can be constructed from the integers.

## Context

This concept has the prerequisites:

- equivalence relations (The rational numbers are defined as equivalence relations.)
- order relations (One needs to define an ordering on the rationals.)
- constructing the integers (The rationals are constructed from the integers.)
- fields (One must show the rational satisfy the field axioms.)

## Goals

- Construct the rational numbers from the integers

- Define addition, multiplication, additive and multiplicative inverses, and the comparison operators

- Show that these definitions satisfy the field axioms

## Core resources (read/watch one of the following)

## -Paid-

→ Elements of Set Theory

An introductory textbook on axiomatic set theory.

Location:
Chapter 5, "Construction of the real numbers," subsection "Rational numbers," pages 101-111

## See also

-No Additional Notes-