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Curated by: Anna1.618 (104 videos)
Support the production of this course by joining Wrath of Math to access all my real analysis videos plus the lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Get the coolest math clothes in the world! https://mathshion.com/ Real Analysis course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook! https://amzn.to/45kcMjq We introduce perfect sets in the real numbers, which are closed sets with no isolated points. We'll discuss the Cantor set and prove it is perfect, and finish by proving perfect sets are uncountable by using the nested compact interval property. #realanalysis Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 0:54 Definition 1:35 Cantor Set is Perfect 8:23 Uncountability 19:14 Conclusion