These are excerpts from a Vsauce video explaining the Banach-Tarski paradox. The paradox proves mathematically that, using the concept of infinity, a sphere can be divided into five parts and transformed into two identical spheres by simply rearranging them. However, this cannot be implemented in the concrete world because it requires parts of infinite complexity. The text also deals with topics such as different dimensions of infinity, countable and uncountable infinity, and the effects of this paradox on mathematics, physics and philosophy. Finally, recommended books are listed to better understand the subject.
