The Natural Numbers and the Peano Axioms
Channel: Nightwing52
Date: 2020-05-26

This video constructs the natural numbers through the use of the Peano Axioms. The successor function is discussed and addition is defined with it. After this, various properties such as commutativity, associativity, and the cancellation property are proven. 

This is the first video in a series about constructing the real number system. If you wish to skip to a specific part, timestamps are provided below!

Introduction - 0:00
The Natural Numbers and Peano Axioms - 0:20
Addition - 3:50
Lemma 1- 8:05
Lemma 2 - 10:15
Commutativity - 14:10
Associativity -  16:15
The Cancellation Property - 20:15
Conclusion - 24:15