The Well-Ordering Principle
Channel: Andrew Misseldine
Date: 2022-09-22

In this video, we introduce the Well-Ordering Principle of Natural Numbers, which states that all nonempty subsets of natural numbers have a minimum element. We compare this to other subsets of real numbers. We use the Well-Ordering Principles to prove the Division Algorithm for Integers.

This is lecture 19 (part 1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 3120 - Transition to Advanced Mathematics at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:  https://drive.google.com/file/d/18ojqYDZN4nxlYMIr4kdg4_zsF6fDVzdY/view

This lecture is based upon Sections 1.9, 10.1, and 5.3 of Book of Proof (https://www.people.vcu.edu/~rhammack/BookOfProof/) by Richard Hammack, from the corresponding sections of A Transition to Advanced Mathematics (https://math.byu.edu/~doud/Transition/) by Darrin Doud and Pace P. Nielsen, and from Dr. Misseldine's own notes. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.