Real Analysis | Perfect Sets

We define the notion of a perfect set of real numbers and prove that all perfect sets are uncountable. Please Subscribe: https://www.youtube.com/michaelpennma... Merch: https://teespring.com/stores/michael-... Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathem... Randolph College Math and Science on Facebook:   / randolph.science   Research Gate profile: https://www.researchgate.net/profile/... Google Scholar profile: https://scholar.google.com/citations?... If you are going to use an ad-blocker, considering using brave and tipping me BAT! https://brave.com/sdp793 Buy textbooks here and help me out: https://amzn.to/31Bj9ye Buy an amazon gift card and help me out: https://amzn.to/2PComAf 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 My Filming Equipment: Camera: https://amzn.to/3kx2JzE Lense: https://amzn.to/2PFxPXA Audio Recorder: https://amzn.to/2XLzkaZ Microphones: https://amzn.to/3fJED0T Lights: https://amzn.to/2XHxRT0 White Chalk: https://amzn.to/3ipu3Oh Color Chalk: https://amzn.to/2XL6eIJ