Real Analysis | The density of Q and other consequences of the Axiom of Completeness.

We present three results that follow from the completeness of the real numbers. 1. The Nested Interval Theorem 2. The Archimedean Principal 3. The density of the rational numbers in the real numbers. Please Subscribe: https://www.youtube.com/michaelpennma... Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathem... Research Gate profile: https://www.researchgate.net/profile/... Google Scholar profile: https://scholar.google.com/citations?... Books I like: Abstract Algebra: Judson(online): http://abstract.ups.edu/ Judson(print): https://amzn.to/2Xg92wD Dummit and Foote: https://amzn.to/2zYOrok Gallian: https://amzn.to/2zg4YEo Artin: https://amzn.to/2LQ8l7C Differential Forms: Bachman: https://amzn.to/2z9wljH Number Theory: Crisman(online): http://math.gordon.edu/ntic/ Strayer: https://amzn.to/3bXwLah Andrews: https://amzn.to/2zWlOZ0 Calculus: OpenStax(online): https://openstax.org/subjects/math OpenStax Vol 1: https://amzn.to/2zlreN8 OpenStax Vol 2: https://amzn.to/2TtwoxH OpenStax Vol 3: https://amzn.to/3bPJ3Bn