Comment on Banach–Tarski ParadoxparentComments−afiori2yIIRC correctly first you split the surface into an uncountable partition then you use the axiom of choice to "color" each point of each partition of a color and then define your finite number of subsets as all the points of each given color.
Comments
IIRC correctly first you split the surface into an uncountable partition then you use the axiom of choice to "color" each point of each partition of a color and then define your finite number of subsets as all the points of each given color.