---
title: "field"
type: concept
related: [Commutivity, Inverses, Group, Field, Associative]
source: https://www.jemoka.com/posts/kbhfield/
confidence: high
status: active
---

A field is a special set.
constituents distinct elements of at least \(0\) and \(1\) operations of addition and multiplication requirements closed commutativity associativity identities (both additive and multiplicative) inverses (both additive and multiplicative) distribution Therefore, \(\mathbb{R}\) is a field, and so is \(\mathbb{C}\) (which we proved in properties of complex arithmetic).
additional information Main difference between group: there is one operation is group, a field has two operations.
