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``Possible Counterexample'' by zexy on 2005-05-01 02:33:46
Assume that all of the subsets are degenerate, and lie within the same (m-1)-dim hyperplane.

The only (m-1)-dim hyperplane that would satisfy the theorem is the hyperplane that the subsets lie within. Yet, can we cut them with the hyperplane? Especially into two equal subsets?

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