The Cantor Set is an uncountably infinite set with a measure or length of 0. It is the simplest example of a fractal and from a topological perspective is considered a perfect set.
In this video, I go over how the Cantor Set is constructed. I also calculate its cardinality and show why it leads to the possibility of uncountable sets having any length whatsoever. I end with explaining what it means for the Cantor Set to be a compact, totally disconnected, perfect set.
Related Videos:
The Connection Between Measure Theory, Set Theory, and Banach-Tarski:
https://youtu.be/SvfATfaL2qc
Banach-Tarski Paradox Explained: https://youtu.be/R--iM5KbDEg
Intro to Measure Theory: https://youtu.be/1BhSQiHTNbg
Animations created using Manim: https://www.manim.community/