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Hausdorff paradox
In mathematics, the Hausdorff paradox, named after Felix Hausdorff, states that if you remove a certain countable subset of the sphere S², the remainder can be divided into three subsets A, B and C such that A, B, C and B ⪠C are all congruent. In particular, it follows that on S² there is no "finitely additive measure" defined on all subsets such that the measure of congruent sets is equal.
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