PROOF Infinite Nested CUBE Root Makes Sense! | Real Analysis for Beginners! скачать в хорошем качестве

PROOF Infinite Nested CUBE Root Makes Sense! | Real Analysis for Beginners!

We prove that the expression expressed in words as "the cube root of 1 plus the cube root of 1 plus the cube root of 1 plus ..." - an infinite nested radical where the radicals are cube roots - makes sense and is actually a well-defined real number. The proof is based on expressing the infinite nested radical as the limit of a bounded increasing sequence of real numbers. We define the number as the limit of a recursively defined sequence, and we prove by mathematical induction that the sequence is bounded and increasing. The completeness of the real numbers implies that the sequence has a limit, which is the well-defined value of the infinite nested cube root. The video is designed for people interested in learning mathematical proofs and proof techniques (such as proof by induction), as well as people interested in learning important beginner ideas from real analysis. If you enjoy this video, I would love if you could please like ✅ , subscribe 🎉, and share ⏩ with students, classmates, friends and family - it means so much to help support me in my goal of creating elite infinite free accessible math education worldwide! 😊 If you would like to support my channel beyond this (which of course would mean so much to me 🤗), please check out my "Patreon" page! The contributions here make a world of difference to helping me free up time to produce as much math content as possible (I currently do everything on my own), and there are also exclusive perks available when you signup (e.g., exclusive access to a private Discord server to chat and discuss math with me and other members, insider knowledge on my future YouTube content creation, priority replies to YouTube comments, public acknowledgements as a valued sponsor, a personalized thank you message etc.)! 😊 Become a Patreon Member 🤩:   / mathmasterywithamitesh   A HUGE thank you SO much to Alex and Stephan for their continued support of the channel as Ruby Members, and Nathan for their continued support of the channel as a Gold Member!! 🎊 My Channel Membership 🥇:    / @mathmasterywithamitesh   A HUGE thank you SO much to Aman, Bernard, Rob, Shabeed, Nicolas and Stephan for their continued support of the channel as Silver Members!! 🎉 You can also follow me on Instagram!   / math_mastery_with_amitesh