Uploaded March 2020 | Updated September 2026, 2 weeks ago
A limit of a summation. There are a few different ways to solve this one!
Check out more calculus problems here: youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
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A limit of a summation. There are a few different ways to solve this one!
Check out more calculus problems here: youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
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)


