Do we even need the real numbers??

We explore the possibility of a calculus only over the rational numbers. This leads us to the important role of the axiom of completeness in the important theorems from first semester calculus. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathematics/ Randolph College Math and Science on Facebook: https://www.facebook.com/randolph.science/ Research Gate profile: https://www.researchgate.net/profile/Michael_Penn5 Google Scholar profile: https://scholar.google.com/citations?user=W5wkSxcAAAAJ&hl=en If you are going to use an ad-blocker, considering using brave and tipping me BAT! https://brave.com/sdp793 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 Analysis: Abbot: https://amzn.to/3cwYtuF How to think about Analysis: https://amzn.to/2AIhwVm 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