# constructing the integers

## Summary

The integers can be constructed from the natural numbers.

## Context

This concept has the prerequisites:

- equivalence relations (The integers can be defined using an equivalence relation.)
- order relations (One needs to define an ordering on the integers.)

## Goals

- Construct the integers from the natural numbers

- Define addition and multiplication, negation, and the comparison operators

- Show that all of these have the properties we would expect

## 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 "Integers," pages 90-101

## See also

-No Additional Notes-