Defining the Natural Numbers; Peano's Axioms
- Number Theory 1.1

in Mathematics on Number Theory · 1 min

Introduction

Historically, mathematics has been built on the foundation of natural numbers. Natural numbers are the abstraction of counting objects, and have always thought to be the most axiomatic and fundamental concept in mathematics.

“God made natural numbers; all else is the work of man“ - Leopold Kronecker

Peano’s Axioms

After Kronecker, Peano tried to describe the natural numbers in a more mathematical and logical way. He proposed a set of axioms to define the set of natural numbers $\mathbb{N}$, and those are called Peano’s Axioms.