Main Question or Discussion Point
Hi! Does anyone think Banach-Tarski's paradox needs reworking? I first came across it in a video by Vsauce. I've been told that things might be reworked as to avoid the paradox, just as set theory was fixed so as to avoid Russell's paradox. How to make sense of a smallest unit of space is what it's about for me. If you take the smallest length and make it the two shorter sizes of a right triangle, than half the hypotenuse would be the true "smallest", and the process goes on unto infinity. The ultimate mathematical magic trick would if someone used the Banach-Tarski paradox to mathematically get a bigger object out of one with smaller measure.