The Continuity Axiom
Channel: Andrew Misseldine
Date: 2022-02-16

In this video, we discuss the notion of continuity and completeness in geometry. We define a Dedekind cut of a line and present the Dedekind Axiom of Continuity. We defined a complete geometry and a neutral geometry, and we present some examples.

This is part 22 (1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 3130 - Modern Geometries 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/1sIsOyVbPg8Je-wnoCL51EnTD0LmC5h3i/view

This lecture is loosely based upon Section 3.4 of Euclidean and Non-Euclidean Geometries by Greenberg. 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.