Uploaded October 2019 | Updated September 2026, 2 weeks ago
If you aren't familiar with how the determinant relates to linear independence, check out my video on determinants: youtu.be/A9eJdQt5quw
How do we check that solutions are linearly independent? We take the determinant of a matrix, of course!
Full Dissecting Differential Equations playlist: youtube.com/playlist?list=PLug5ZIRrShJF-vOxStdHg1jyntiTKrAYO
New math videos every Monday and Friday. Subscribe to make sure you see them!
If you aren't familiar with how the determinant relates to linear independence, check out my video on determinants: youtu.be/A9eJdQt5quw
How do we check that solutions are linearly independent? We take the determinant of a matrix, of course!
Full Dissecting Differential Equations playlist: youtube.com/playlist?list=PLug5ZIRrShJF-vOxStdHg1jyntiTKrAYO
New math videos every Monday and Friday. Subscribe to make sure you see them!
![I Want to Play a Game: Proving [0,1] is Uncountable](https://i.ytimg.com/vi/Mcfnnp8rxkI/mqdefault.jpg "I Want to Play a Game: Proving [0,1] is Uncountable
The interval [0,1] is uncountable, and there are many ways to prove that. Cantors diagonal argument is a classic example. But theres another way: proof by playing a game. This video is an explanation of a proof by contradiction after assuming that the infinite set [0,1] is countable and playing a game on that interval. All we need is basic calculus for the limits of sequences!
Original based on Grossman & Turett: https://arxiv.org/pdf/math/0606253
Calculus Problems playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
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Music: C418 - Smooth Fall")
