Hacker News Reader

I wonder if a square of the same area is too constraining for the axiom of choice?

Perhaps they should try making it into two identical circles or a square of twice the area instead?

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

Would you be able to elaborate a bit what you mean here? There is no version of Banach-Tarski in two dimensions - you can prove that there exists a finitely additive set function which is invariant under isometries.

Reply on news.ycombinator.com