On: Banach–Tarski Paradox

[adroniser]

To be clear, the construction given here violates the finite additivity property of measure. It's got nothing to do with the countable/uncountable additivity property.

[emblaegh → adroniser]

Yeah but this is only possible if the sets in question are uncountably infinite.

[adroniser → emblaegh]

Yes but you are not taking an uncountable union. You are taking a finite union.