Uploaded September 2020 | Updated September 2026, 1 week ago
Intro to quadratic residues: youtu.be/M6gDsFhQugM
The Legendre symbol is a useful notation for describing whether a number is a quadratic residue mod p. Here we explain what the Legendre symbol is and do a practice example with quadratic residues mod 5.
Quadratic Residues playlist: youtube.com/playlist?list=PLug5ZIRrShJGJieICD2KnqU9cRioaEBjB
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Music: OcularNebula - The Lopez
Intro to quadratic residues: youtu.be/M6gDsFhQugM
The Legendre symbol is a useful notation for describing whether a number is a quadratic residue mod p. Here we explain what the Legendre symbol is and do a practice example with quadratic residues mod 5.
Quadratic Residues playlist: youtube.com/playlist?list=PLug5ZIRrShJGJieICD2KnqU9cRioaEBjB
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez



![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)






