Uploaded October 2024 | Updated September 2026, 1 week ago

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Video on supremum: youtu.be/o0TksrG5OsY

Paper on real induction: arxiv.org/pdf/1208.0973

Proof by induction is often taught as something that only works for integers, natural numbers, or whole numbers. However, there's 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: youtube.com/playlist?list=PLug5ZIRrShJEGnUPxM1KUVOHkW4kN6QU_

0:00 The Theorem
4:36 Proof

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Music: C418 - Smooth Fall