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Induction on Real Numbers

Video on supremum:    • Supremum, Infimum: Definition and Exp...   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, 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:    • Topology   0:00 The Theorem 4:36 Proof Subscribe to see more new math videos! Music: C418 - Smooth Fall