“Mind-Bending Math: Riddles and Paradoxes” S:1 E:22 When Measurement Is Impossible

S:1 E:22 When Measurement Is Impossible Prove that some sets can’t be measured – a result that is crucial to understanding the Banach-Tarski paradox, the strangest theorem in all of mathematics, which is presented in Lecture 23. Start by asking why mathematicians want to measure sets. Then learn how to construct a non-measurable set.