Construction of the square root
In this video, I rigorously prove that if x is a non-negative real number, then square root of x exists. It's a really exciting problem that tests your knowledge of the sup. This is based on Theorem 1.21 of Rudin
Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh