Let *T* be the circle and let *K* be the countable subset. By a counting argument, there is a rotation ρ such that for no member *x* of *K* do we have an *n* such that ρ^{n}(*x*)∈*K*. Let *A*=*K*∪ρ(*K*)∪ρ^{2}(*K*)∪.... Then (*T*−*A*)∪*A*=*T* and (*T*−*A*)∪ρ(*A*)=*T*−*K*.

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