Thanks! Yes, I have seen Banach-Tarski before, here and elsewhere. My confusion was mostly due to not thoroughly remembering what an axiom is... I expected ther

Thanks! Yes, I have seen Banach-Tarski before, here and elsewhere. My confusion was mostly due to not thoroughly remembering what an axiom is... I expected there to be some kind of proof, like an example of a series of non-empty sets that have an empty set as their product. Pure math be crazy. And cool. Indeed pretty cool. Thanks for submitting this fascinating link. Not every set contains the empty set as an element, but every set has the empty set as a subset. Yes, I mixed this up quite badly.