+++
date = "2016-04-24"
draft = true
title = """Vectors"""
slug = "vectors"
tags = ['revision', 'mathematical structures']
banner = ""
aliases = ['/vectors/']
+++

# Fields
Scalars are organised as a structured set called a **field**. A field has two operations: addition and multiplication, each of which is associative, commutative, and has an inverse (except 0 in multiplication). The set of reals, rationals, and booleans are fields but integers and naturals aren't. Natural numbers and integers [don't have inverses](https://proofwiki.org/wiki/Integers_do_not_form_Field).