Uploaded December 2019 | Updated September 2026, 1 week ago
Main cross product video: youtu.be/RecUff64IX0
The last step to proving that the two cross product definitions are equal is an explanation of why the cross product is distributive. It's time for some geometry!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
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Main cross product video: youtu.be/RecUff64IX0
The last step to proving that the two cross product definitions are equal is an explanation of why the cross product is distributive. It's time for some geometry!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
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)




