Set of Real Numbers

Section: Axioms of Addition

Introduction

Please note that the four axioms of addition presented here are a special case of a more general definition, which can be found for the four axioms used to define an abstract algebraic structure, called an abelian group. The more general definition uses an abstract binary operation (instead of the concrete addition used here) and a more general set (instead of the concrete set of real numbers used here).

This means that the set of real numbers \(\mathbb R\), together with the addition \( + \) as a binary operation form the abelian group \((\mathbb R,+)\).

Subordinated Structure:

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