Uploaded January 2020 | Updated September 2026, 1 week ago
To integrate this, we'll need to figure out where we can make our magic substitution to simplify everything!
You can check out more integral videos here: youtube.com/playlist?list=PLug5ZIRrShJGoUgjNdl12Xs6j4YqTb4zS
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To integrate this, we'll need to figure out where we can make our magic substitution to simplify everything!
You can check out more integral videos here: youtube.com/playlist?list=PLug5ZIRrShJGoUgjNdl12Xs6j4YqTb4zS
New math videos every Monday and Friday. Subscribe to make sure you see them!




![Induction on Real Numbers
Video on supremum: https://youtu.be/o0TksrG5OsY
Paper on real induction: https://arxiv.org/pdf/1208.0973
Proof by induction is often taught as something that only works for integers, natural numbers, or whole numbers. However, theres an analogous concept to induction that applies to intervals on the real numbers, even though the real numbers are an uncountable set! This video explains and proves the result for the interval [0,1], which can be generalized to arbitrary closed intervals in the real numbers.
Topology playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJEGnUPxM1KUVOHkW4kN6QU_
0:00 The Theorem
4:36 Proof
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Music: C418 - Smooth Fall Induction on Real Numbers](https://i.ytimg.com/vi/bXTbGJxW_fE/mqdefault.jpg)





